{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-07-15T00:25:42.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-07-15T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":42685,"title":"Cody meets Xiangqi: foresee the unseen (Part 2)","description":"This is the second part of the Xiangqi series. The first part in this series is: \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42674-cody-meets-xiangqi-foresee-the-unseen Cody meets Xiangqi: foresee the unseen (Part 1)\u003e\r\n\r\nBeing increasingly interested in \u003chttps://en.wikipedia.org/wiki/Xiangqi Xiangqi\u003e (a.k.a., *Chinese Chess*), Mr. Cody has designed a new Xiangqi match for \u003chttps://en.wikipedia.org/wiki/Xiang_Yu Xiang Yu\u003e and \u003chttps://de.wikipedia.org/wiki/Han_Gaozu Liu Bang\u003e by taking into account the likelihood of tie games. The new rule is described as follows:\r\n\r\nOnce\r\n\r\n   1) Xiang Yu wins Na games consecutively,\r\n   2) Liu Bang wins Nb games consecutively, \r\n   3) No ties occur consecutively, \r\n\r\n*whichever comes first*, Mr. Cody announces the outcome accordingly as follows:\r\n\r\n   1) Xiang Yu is the final winner,\r\n   2) Liu Bang is the final winner, \r\n   3) They end up with a final draw.\r\n\r\nAgain, Cody asks us --- active Cody players --- to foresee the outcome of this unseen match using Monte Carlo simulations. Our task is to write the following function\r\n\r\n                         [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)\r\n\r\nwhere \r\n\r\n* a: the probability that Xiang Yu wins one individual game\r\n* b: the probability that Liu Bang wins one individual game\r\n* Na: # of consecutive wins required for Xiang Yu to become the final winner\r\n* Nb: # of consecutive wins required for Liu Bang to become the final winner\r\n* Nc: # of consecutive ties required to result in a final draw\r\n* Pa: the probability that Xiang Yu wins the match\r\n* Pb: the probability that Liu Bang wins the match\r\n* Pc: the probability of a final draw\r\n\r\nThe main focus of this problem is on *Monte Carlo simulations*, rather than analytical approaches. Your provided solution Xiangqi2.m will be checked by a P-file EvaluateSolution.p, which mainly does 3 things as follows:\r\n\r\n1) Call your function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc) and then Check if the result P = [Pa, Pb, Pc] is within tolerance of its expected value Q. That is, If norm(P - Q) \u003c tol holds, it means that your solution is accurate enough. If this does not hold, your solution will be rejected. \r\n\r\n2) Check if your solution is based on *pure Monte Carlo simulations* or *analytical approaches*. If it is based on analytical approaches (i.e., using analytical expressions to directly compute the probabilities), then your solution will be rejected. EvaluateSolution.p accomplishes this goal by exploiting a combination of distinct features possessed by analytical solutions, but are generally not shared by Monte Carlo simulations. \r\n\r\n3) If your solution passes the above two checks, then the score of your solution will be determined based on the speed of your code. The faster your solution is, the smaller score you get. \r\n\r\nIf you have any concerns or suggestions on this problem, please feel free to leave me a comment. Thanks. \r\n\r\n ","description_html":"\u003cp\u003eThis is the second part of the Xiangqi series. The first part in this series is: \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42674-cody-meets-xiangqi-foresee-the-unseen\"\u003eCody meets Xiangqi: foresee the unseen (Part 1)\u003c/a\u003e\u003c/p\u003e\u003cp\u003eBeing increasingly interested in \u003ca href = \"https://en.wikipedia.org/wiki/Xiangqi\"\u003eXiangqi\u003c/a\u003e (a.k.a., \u003cb\u003eChinese Chess\u003c/b\u003e), Mr. Cody has designed a new Xiangqi match for \u003ca href = \"https://en.wikipedia.org/wiki/Xiang_Yu\"\u003eXiang Yu\u003c/a\u003e and \u003ca href = \"https://de.wikipedia.org/wiki/Han_Gaozu\"\u003eLiu Bang\u003c/a\u003e by taking into account the likelihood of tie games. The new rule is described as follows:\u003c/p\u003e\u003cp\u003eOnce\u003c/p\u003e\u003cpre\u003e   1) Xiang Yu wins Na games consecutively,\r\n   2) Liu Bang wins Nb games consecutively, \r\n   3) No ties occur consecutively, \u003c/pre\u003e\u003cp\u003e\u003cb\u003ewhichever comes first\u003c/b\u003e, Mr. Cody announces the outcome accordingly as follows:\u003c/p\u003e\u003cpre\u003e   1) Xiang Yu is the final winner,\r\n   2) Liu Bang is the final winner, \r\n   3) They end up with a final draw.\u003c/pre\u003e\u003cp\u003eAgain, Cody asks us --- active Cody players --- to foresee the outcome of this unseen match using Monte Carlo simulations. Our task is to write the following function\u003c/p\u003e\u003cpre\u003e                         [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)\u003c/pre\u003e\u003cp\u003ewhere\u003c/p\u003e\u003cul\u003e\u003cli\u003ea: the probability that Xiang Yu wins one individual game\u003c/li\u003e\u003cli\u003eb: the probability that Liu Bang wins one individual game\u003c/li\u003e\u003cli\u003eNa: # of consecutive wins required for Xiang Yu to become the final winner\u003c/li\u003e\u003cli\u003eNb: # of consecutive wins required for Liu Bang to become the final winner\u003c/li\u003e\u003cli\u003eNc: # of consecutive ties required to result in a final draw\u003c/li\u003e\u003cli\u003ePa: the probability that Xiang Yu wins the match\u003c/li\u003e\u003cli\u003ePb: the probability that Liu Bang wins the match\u003c/li\u003e\u003cli\u003ePc: the probability of a final draw\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe main focus of this problem is on \u003cb\u003eMonte Carlo simulations\u003c/b\u003e, rather than analytical approaches. Your provided solution Xiangqi2.m will be checked by a P-file EvaluateSolution.p, which mainly does 3 things as follows:\u003c/p\u003e\u003cp\u003e1) Call your function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc) and then Check if the result P = [Pa, Pb, Pc] is within tolerance of its expected value Q. That is, If norm(P - Q) \u0026lt; tol holds, it means that your solution is accurate enough. If this does not hold, your solution will be rejected.\u003c/p\u003e\u003cp\u003e2) Check if your solution is based on \u003cb\u003epure Monte Carlo simulations\u003c/b\u003e or \u003cb\u003eanalytical approaches\u003c/b\u003e. If it is based on analytical approaches (i.e., using analytical expressions to directly compute the probabilities), then your solution will be rejected. EvaluateSolution.p accomplishes this goal by exploiting a combination of distinct features possessed by analytical solutions, but are generally not shared by Monte Carlo simulations.\u003c/p\u003e\u003cp\u003e3) If your solution passes the above two checks, then the score of your solution will be determined based on the speed of your code. The faster your solution is, the smaller score you get.\u003c/p\u003e\u003cp\u003eIf you have any concerns or suggestions on this problem, please feel free to leave me a comment. Thanks.\u003c/p\u003e","function_template":"function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)\r\n% a: the probability that Xiang Yu wins one individual game\r\n% b: the probability that Liu Bang wins one individual game\r\n% Na: # of consecutive wins required for Xiang Yu to become the final winner\r\n% Nb: # of consecutive wins required for Liu Bang to become the final winner\r\n% Nc: # of consecutive ties required to result in a final draw\r\n% Pa: the probability that Xiang Yu wins the match\r\n% Pb: the probability that Liu Bang wins the match\r\n% Pc: the probability of a final draw\r\n    Pa = ;\r\n    Pb = ;\r\n    Pc = ;\r\nend","test_suite":"%%\r\n% Thanks to Alfonso Nieto-Castanon\r\nurlwrite('https://sites.google.com/a/alfnie.com/alfnie/software/SetSolutionScore.p?attredirects=0\u0026amp;d=1','SetSolutionScore.p');\r\nrehash path;\r\n\r\n%%\r\nfh = fopen('EvaluateSolution.p','wb');\r\nfwrite(fh, hex2dec(reshape('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',2,[]).')); rehash path; fclose(fh);\r\n\r\n%%\r\nfid = fopen('Xiangqi2.m');\r\ndelim = {' ', '\\n', ',', '.', ';', '''', '@', '+', '-', '*', '/', '\\', '^', '\u003e', '\u003c', '=', '\u0026', '|', '~', '{', '}', '[', ']', '(', ')'};\r\nfile = textscan(fid, '%s', 'CommentStyle', '%', 'MultipleDelimsAsOne', 1, 'Delimiter', delim); fclose(fid); \r\nassert(~any(ismember({'rng','RandStream','seed','state','twister','shufle','default'},file{1})));\r\n\r\n%%\r\na = 0; b = 0; Na = 2; Nb = 3; Nc = 2; tol = 1e-6;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol); \r\n\r\n%%\r\na = 0; b = 1; Na = 1; Nb = 2; Nc = 1; tol = 1e-6;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol); \r\n\r\n%%\r\na = 1; b = 0; Na = 3; Nb = 2; Nc = 1; tol = 1e-6;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol); \r\n\r\n%%\r\na = 0.15; b = 0.85; Na = 4; Nb = 2; Nc = 1; tol = 1e-4;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol);\r\n\r\n%%\r\na = 0.9; b = 0; Na = 3; Nb = 1; Nc = 2; tol = 1e-3;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol);\r\n\r\n%%\r\na = 0.65; b = 0.3; Na = 3; Nb = 2; Nc = 2; tol = 1e-3;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol);\r\n\r\n%%\r\nNa = 3; Nb = 2; Nc = 1; tol = 2e-3; \r\np = sort(rand(2,30)); \r\np = sort([p(1,:);diff(p);1-p(2,:)]);\r\nfor k = size(p,2):-1:1\r\n    a = p(3,k); b = p(2,k);\r\n    score(k) = EvaluateSolution(a, b, Na, Nb, Nc, tol);    \r\nend\r\nSetSolutionScore(round(mean(score)));","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2015-11-12T00:41:35.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2015-11-08T20:51:55.000Z","updated_at":"2026-07-16T14:32:19.000Z","published_at":"2015-11-10T00:22:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the second part of the Xiangqi series. The first part in this series is:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42674-cody-meets-xiangqi-foresee-the-unseen\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody meets Xiangqi: foresee the unseen (Part 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBeing increasingly interested in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Xiangqi\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eXiangqi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (a.k.a.,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eChinese Chess\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e), Mr. Cody has designed a new Xiangqi match for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Xiang_Yu\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eXiang Yu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://de.wikipedia.org/wiki/Han_Gaozu\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLiu Bang\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e by taking into account the likelihood of tie games. The new rule is described as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnce\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   1) Xiang Yu wins Na games consecutively,\\n   2) Liu Bang wins Nb games consecutively, \\n   3) No ties occur consecutively,]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhichever comes first\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, Mr. Cody announces the outcome accordingly as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   1) Xiang Yu is the final winner,\\n   2) Liu Bang is the final winner, \\n   3) They end up with a final draw.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAgain, Cody asks us --- active Cody players --- to foresee the outcome of this unseen match using Monte Carlo simulations. Our task is to write the following function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[                         [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea: the probability that Xiang Yu wins one individual game\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb: the probability that Liu Bang wins one individual game\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNa: # of consecutive wins required for Xiang Yu to become the final winner\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNb: # of consecutive wins required for Liu Bang to become the final winner\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNc: # of consecutive ties required to result in a final draw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePa: the probability that Xiang Yu wins the match\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePb: the probability that Liu Bang wins the match\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePc: the probability of a final draw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe main focus of this problem is on\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMonte Carlo simulations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, rather than analytical approaches. Your provided solution Xiangqi2.m will be checked by a P-file EvaluateSolution.p, which mainly does 3 things as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1) Call your function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc) and then Check if the result P = [Pa, Pb, Pc] is within tolerance of its expected value Q. That is, If norm(P - Q) \u0026lt; tol holds, it means that your solution is accurate enough. If this does not hold, your solution will be rejected.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) Check if your solution is based on\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epure Monte Carlo simulations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eanalytical approaches\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. If it is based on analytical approaches (i.e., using analytical expressions to directly compute the probabilities), then your solution will be rejected. EvaluateSolution.p accomplishes this goal by exploiting a combination of distinct features possessed by analytical solutions, but are generally not shared by Monte Carlo simulations.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3) If your solution passes the above two checks, then the score of your solution will be determined based on the speed of your code. The faster your solution is, the smaller score you get.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you have any concerns or suggestions on this problem, please feel free to leave me a comment. Thanks.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61358,"title":"Basic Physics IV","description":"Calculate the Mechanical Energy (ME).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eCalculate the Mechanical Energy (ME).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ME = ME(PE,KE)\r\n  ME = ;\r\nend","test_suite":"%%\r\nPE = 1;\r\nKE = 1;\r\nME = PE+KE;\r\nassert(isequal(ME(PE,KE),ME))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-26T14:58:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2026-05-26T14:58:18.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-26T14:56:53.000Z","updated_at":"2026-07-20T16:53:37.000Z","published_at":"2026-05-26T14:56:53.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCalculate the Mechanical Energy (ME).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61350,"title":"Circle Perimeter","description":"Get the perimeter of the Circle by PI.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGet the perimeter of the Circle by PI.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = circleP(r)\r\n  p = ;\r\nend","test_suite":"%%\r\nr = 1;\r\np = 2*pi*r;\r\nassert(isequal(circleP(r),p))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-24T11:52:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2026-05-24T11:52:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-24T11:50:23.000Z","updated_at":"2026-07-21T16:19:33.000Z","published_at":"2026-05-24T11:52:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGet the perimeter of the Circle by PI.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61362,"title":"Calculate the h-index (revisited)","description":"H-index is a powerful tool for quantifying the scientific contribution of a researcher. The \r\nH-index is defined as follows (from source - wikipedia):\r\n\"a scholar with an index of h has published h papers each of which has been cited in other papers at least h times\".\r\nIn this problem, citations of published works of an author will be provided as a vector. Each element of the vector denotes the number of citations of a specific paper of the author. Calculate the h-index.\r\nExample:\r\nInput = [4 4 4 4]; Output = 4\r\nCalculate the h-index score \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(33, 33, 33); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 315px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 243.5px 157.5px; transform-origin: 243.5px 157.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 21px; text-align: left; transform-origin: 219.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eH-index is a powerful tool for quantifying the scientific contribution of a researcher. The \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eH-index is defined as follows (from source - wikipedia):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 21px; text-align: left; transform-origin: 219.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"a scholar with an index of h has published h papers each of which has been cited in other papers at least h times\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 31.5px; text-align: left; transform-origin: 219.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem, citations of published works of an author will be provided as a vector. Each element of the vector denotes the number of citations of a specific paper of the author. Calculate the h-index.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput = [4 4 4 4]; Output = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the h-index score \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [3 3 2 1];\r\ny_correct = 2;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = [5 2 10 11 2 7 9 10 7];\r\ny_correct = 6;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 4*ones(1,4);\r\ny_correct = 4;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = zeros(1,1000);\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = [3 2 0 0 1];\r\ny_correct = 2;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":584788,"edited_by":584788,"edited_at":"2026-05-27T22:40:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2026-05-27T22:40:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-27T18:21:09.000Z","updated_at":"2026-07-11T19:45:24.000Z","published_at":"2026-05-27T18:21:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eH-index is a powerful tool for quantifying the scientific contribution of a researcher. The \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eH-index is defined as follows (from source - wikipedia):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"a scholar with an index of h has published h papers each of which has been cited in other papers at least h times\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, citations of published works of an author will be provided as a vector. Each element of the vector denotes the number of citations of a specific paper of the author. Calculate the h-index.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput = [4 4 4 4]; Output = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the h-index score \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61384,"title":"varargin","description":"Write a function that can take a diffrent Amount of inputs for every run Which gives you the sum of all Inputs.\r\nExample:\r\nf(a,b) = a+b,    f(1,...,n) = 1+...+n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401.5px 55.5px; transform-origin: 401.5px 55.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that can take a diffrent Amount of inputs for every run Which gives you the sum of all Inputs.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ef(a,b) = a+b,    f(1,...,n) = 1+...+n\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = summ(va )\r\ny = ;\r\nend","test_suite":"%%\r\ny_correct = 6;\r\nassert(isequal(summ(1,2,3),y_correct))\r\n%%\r\ny_correct = sum(1:200:10^10);\r\nassert(isequal(summ(1:200:10^10),y_correct))\r\n%%\r\ny_correct = sum(-5:3.2:200);\r\nassert(isequal(summ(-5:3.2:200),y_correct))\r\n%%\r\nfor k = 1:100\r\n    x = num2cell(randi(100,1,randi(10)));\r\n\r\n    erwartet = sum([x{:}]);\r\n    erhalten = summ(x{:});\r\n\r\n    assert(isequal(erhalten, erwartet))\r\nend\r\n%%\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5124132,"edited_by":5124132,"edited_at":"2026-06-01T17:04:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2026-06-01T17:04:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-01T16:52:16.000Z","updated_at":"2026-07-14T15:55:12.000Z","published_at":"2026-06-01T17:04:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that can take a diffrent Amount of inputs for every run Which gives you the sum of all Inputs.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(a,b) = a+b,    f(1,...,n) = 1+...+n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61342,"title":"Swept Volume and Clearance Volume","description":"The swept volume (V_s) is the volume displaced by the piston as it travels from BDC (Bottom Dead Centre) to TDC (Top Dead Centre). \r\nThe clearance volume (V_c) is the remaining volume above the piston at TDC .It cannot be swept and defines the compression limit.\r\n\r\nGiven total cylinder volume at BDC V_BDC (m³) and clearance volume at TDC V_TDC (m³), compute the swept volume V_s and confirm it matches the bore-stroke formula using bore B (m) and stroke S (m).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 624px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 312px; transform-origin: 468.5px 312px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe swept volume (V_s) is the volume displaced by the piston as it travels from BDC (Bottom Dead Centre) to TDC (Top Dead Centre). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe clearance volume (V_c) is the remaining volume above the piston at TDC .It cannot be swept and defines the compression limit.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 513px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 256.5px; text-align: left; transform-origin: 444.5px 256.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"685\" height=\"507\" style=\"vertical-align: baseline;width: 685px;height: 507px\" src=\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven total cylinder volume at BDC V_BDC (m³) and clearance volume at TDC V_TDC (m³), compute the swept volume V_s and confirm it matches the bore-stroke formula using bore B (m) and stroke S (m).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [Vs, Vc] = sweptClearanceVolume(V_BDC, V_TDC)\r\nVs = 0;\r\nVc = 0;\r\nend","test_suite":"%%Test 1\r\nV_BDC=550e-6; V_TDC=50e-6;\r\n[Vs,Vc] = sweptClearanceVolume(V_BDC,V_TDC);\r\nassert(abs(Vs - 500e-6) \u003c 1e-9)\r\nassert(abs(Vc - 50e-6) \u003c 1e-9)\r\n%%Test 2\r\nV_BDC=750e-6; V_TDC=62.5e-6;\r\n[Vs,Vc] = sweptClearanceVolume(V_BDC,V_TDC);\r\nassert(abs(Vs - 687.5e-6) \u003c 1e-9)\r\nassert(abs(Vc - 62.5e-6) \u003c 1e-9)\r\n%%Test 3\r\nV_BDC=400e-6; V_TDC=36.36e-6;\r\n[Vs,Vc] = sweptClearanceVolume(V_BDC,V_TDC);\r\nassert(abs(Vs - (V_BDC-V_TDC)) \u003c 1e-9)\r\nassert(abs(Vc - V_TDC) \u003c 1e-9)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-28T03:17:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T10:13:10.000Z","updated_at":"2026-07-22T20:13:51.000Z","published_at":"2026-05-21T10:13:10.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe swept volume (V_s) is the volume displaced by the piston as it travels from BDC (Bottom Dead Centre) to TDC (Top Dead Centre). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe clearance volume (V_c) is the remaining volume above the piston at TDC .It cannot be swept and defines the compression limit.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"507\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"685\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven total cylinder volume at BDC V_BDC (m³) and clearance volume at TDC V_TDC (m³), compute the swept volume V_s and confirm it matches the bore-stroke formula using bore B (m) and stroke S (m).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61418,"title":"Play the Disk ","description":"To access the memory address of program on disk, MS-DOS uses sectors,cylinders and heads, on disk in 3D coordinates. Given the head angle position (in deg), cylinders and heads locate the logical sector number to access the program on disk ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 31.5px; transform-origin: 401px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 31.5px; text-align: left; transform-origin: 377px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo access the memory address of program on disk, MS-DOS uses sectors,cylinders and heads, on disk in 3D coordinates. Given the head angle position (in deg), cylinders and heads locate the logical sector number to access the program on disk \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = disk_sector_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nhead_ref = 90;\r\nnum_heads = 6\r\ncylinder = 2\r\nsector = 4;\r\nhead = 5;\r\ny_correct = 71;\r\nassert(isequal(disk_sector_name(head_ref,num_heads,cylinder,sector,head),y_correct))\r\n\r\n%%\r\nhead_ref = 45;\r\nnum_heads = 5\r\ncylinder = 1\r\nsector = 1;\r\nhead = 3;\r\ny_correct = 64;\r\nassert(isequal(disk_sector_name(head_ref,num_heads,cylinder,sector,head),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":584788,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-07-05T07:02:36.000Z","updated_at":"2026-07-23T03:22:40.000Z","published_at":"2026-07-05T07:02:36.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo access the memory address of program on disk, MS-DOS uses sectors,cylinders and heads, on disk in 3D coordinates. Given the head angle position (in deg), cylinders and heads locate the logical sector number to access the program on disk \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61353,"title":"Basic Algebra II","description":"You have the equation X^2 = n you should find the value of X.\r\nGOOD LUCK!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 25.5px; transform-origin: 401px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou have the equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eX^2 = n \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eyou should find the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function X = equation(n)\r\n  X = ;\r\nend","test_suite":"%%\r\nn = 1;\r\nX = sqrt(n);\r\nassert(isequal(equation(n),X))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-24T13:23:14.000Z","deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":"2026-05-24T13:23:14.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-24T13:20:58.000Z","updated_at":"2026-07-23T03:27:30.000Z","published_at":"2026-05-24T13:23:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have the equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX^2 = n \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eyou should find the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eGOOD LUCK!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61346,"title":"Find The Area Of Triangle Using Base \u0026 Height","description":"You should find the area of the Triangle using base and height.\r\nGood Luck!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 25.5px; transform-origin: 401px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eYou should find the area of the Triangle using base and height.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGood Luck!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = triangleArea(base, height)\r\n  area = ;\r\nend","test_suite":"%%\r\nbase = 1;\r\nheight = 1;\r\narea = 0.5;\r\nassert(isequal(triangleArea(base, height),area))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-23T17:34:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":"2026-05-23T16:51:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-23T16:46:19.000Z","updated_at":"2026-07-23T03:31:52.000Z","published_at":"2026-05-23T16:49:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYou should find the area of the Triangle using base and height.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGood Luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61355,"title":"Basic Algebra III","description":"Get the Cube Root of the number n.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGet the Cube Root of the number n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ans = cbRt(n)\r\n  ans = ;\r\nend","test_suite":"%%\r\nn = 8;\r\nans = nthroot(n,3);\r\nassert(isequal(cbRt(n),ans))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-26T12:25:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2026-05-26T12:25:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-26T12:24:06.000Z","updated_at":"2026-07-22T19:58:55.000Z","published_at":"2026-05-26T12:24:06.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGet the Cube Root of the number n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61336,"title":"Brake Mean Effective Pressure (BMEP)","description":"BMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\r\nA higher BMEP indicates a more efficient use of displacement.\r\n\r\nGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 599.719px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 299.859px; transform-origin: 468.5px 299.859px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA higher BMEP indicates a more efficient use of displacement.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 488.719px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 244.359px; text-align: left; transform-origin: 444.5px 244.359px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://static.wixstatic.com/media/1efdb1_5ced4cd83869436cbfd4286a5c83ab9b~mv2.png\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function bmep = calcBMEP(T, Vd, k)\r\nbmep = 0;\r\nend","test_suite":"%%\r\nT = 200; Vd = 0.002; k = 4;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n%%\r\nT = 350; Vd = 0.003; k = 4;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n%%\r\nT = 80; Vd = 0.0005; k = 2;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-26T03:50:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T09:38:18.000Z","updated_at":"2026-07-22T20:10:03.000Z","published_at":"2026-05-21T09:38:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA higher BMEP indicates a more efficient use of displacement.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"802\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"1477\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"https://static.wixstatic.com/media/1efdb1_5ced4cd83869436cbfd4286a5c83ab9b~mv2.png\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61338,"title":"Fuel-Air Equivalence Ratio (Lambda)","description":"Lambda (λ) is the ratio of actual air-fuel ratio to the stoichiometric air-fuel ratio. \r\nλ = 1 is perfect stoichiometry, \r\nλ \u003c 1 is rich, \r\nλ \u003e 1 is lean. \r\nEngine management systems constantly target λ = 1 for optimal catalyst performance.\r\n\r\nGiven actual AFR and stoichiometric AFR (AFR_s), compute lambda.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 572px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 286px; transform-origin: 468.5px 286px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLambda (λ) is the ratio of actual air-fuel ratio to the stoichiometric air-fuel ratio. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eλ = 1 is perfect stoichiometry, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eλ \u0026lt; 1 is rich, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eλ \u0026gt; 1 is lean. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEngine management systems constantly target λ = 1 for optimal catalyst performance.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 392px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 196px; text-align: left; transform-origin: 444.5px 196px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://i.ytimg.com/vi/9uFdrcPkMGE/hq720.jpg?sqp=-oaymwEhCK4FEIIDSFryq4qpAxMIARUAAAAAGAElAADIQj0AgKJD\u0026amp;rs=AOn4CLDLLtOPt4b2zx4L72ztX9tL_4S0vw\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven actual AFR and stoichiometric AFR (AFR_s), compute lambda.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function lam = calcLambda(AFR, AFR_s)\r\nlam = 0;\r\nend","test_suite":"%%Test 1\r\nassert(abs(calcLambda(14.7, 14.7) - 1.0) \u003c 1e-6)\r\n%%Test 2\r\nassert(abs(calcLambda(12.5, 14.7) - 12.5/14.7) \u003c 1e-6)\r\n%%Test 3\r\nassert(abs(calcLambda(16.2, 14.7) - 16.2/14.7) \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-27T03:46:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T09:51:05.000Z","updated_at":"2026-07-22T20:11:24.000Z","published_at":"2026-05-21T09:51:05.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLambda (λ) is the ratio of actual air-fuel ratio to the stoichiometric air-fuel ratio. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eλ = 1 is perfect stoichiometry, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eλ \u0026lt; 1 is rich, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eλ \u0026gt; 1 is lean. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEngine management systems constantly target λ = 1 for optimal catalyst performance.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"386\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"686\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven actual AFR and stoichiometric AFR (AFR_s), compute lambda.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.jpg\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.jpg\",\"contentType\":\"image/jpg\",\"content\":\"https://i.ytimg.com/vi/9uFdrcPkMGE/hq720.jpg?sqp=-oaymwEhCK4FEIIDSFryq4qpAxMIARUAAAAAGAElAADIQj0AgKJD\u0026rs=AOn4CLDLLtOPt4b2zx4L72ztX9tL_4S0vw\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61387,"title":"Multiply the Diagonals of Two Vectors","description":"Find the diagonals of vectors a and b and multiply them.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21.0085px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 400.994px 10.4972px; transform-origin: 400.994px 10.5043px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eFind the diagonals of vectors a and b and multiply them.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = diagonalsProduct(a,b)\r\n  s = \r\nend","test_suite":"%%\r\na = [0 1 2; 3 4 5; 6 7 8]\r\nb = [9 10 11; 12 13 14; 15 16 17]\r\ns = diag(a).*diag(b);\r\nassert(isequal(diagonalsProduct(a,b),s))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-06-05T15:39:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2026-06-05T15:39:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-05T15:37:19.000Z","updated_at":"2026-07-22T20:05:52.000Z","published_at":"2026-06-05T15:37:19.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFind the diagonals of vectors a and b and multiply them.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61337,"title":"Volumetric efficiency","description":"Volumetric efficiency measures how well an engine breathes.\r\nThe ratio of the actual air mass drawn in per cycle to the theoretical maximum based on displacement. \r\nNaturally aspirated engines typically achieve 80–95%.\r\n\r\nGiven actual air mass m_actual (kg), air density ρ (kg/m³), and displacement V_d (m³), compute volumetric efficiency η_v.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 634.383px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 317.18px; transform-origin: 467.496px 317.191px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eVolumetric efficiency measures how well an engine breathes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe ratio of the actual air mass drawn in per cycle to the theoretical maximum based on displacement. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNaturally aspirated engines typically achieve 80–95%.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 514.477px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 257.227px; text-align: left; transform-origin: 443.508px 257.238px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven actual air mass m_actual (kg), air density ρ (kg/m³), and displacement V_d (m³), compute volumetric efficiency η_v.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function eta_v = volEfficiency(m_actual, rho, Vd)\r\neta_v = 0;\r\nend","test_suite":"%%Test 1\r\nm = 0.00180; rho = 1.2; Vd = 0.002;\r\nassert(abs(volEfficiency(m,rho,Vd) - m/(rho*Vd)) \u003c 1e-6)\r\n%%Test 2\r\nm = 0.00252; rho = 1.2; Vd = 0.003;\r\nassert(abs(volEfficiency(m,rho,Vd) - m/(rho*Vd)) \u003c 1e-6)\r\n%%Test 3\r\nm = 0.00096; rho = 1.15; Vd = 0.0012;\r\nassert(abs(volEfficiency(m,rho,Vd) - m/(rho*Vd)) \u003c 1e-6)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-21T09:48:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T09:45:01.000Z","updated_at":"2026-07-22T20:10:43.000Z","published_at":"2026-05-21T09:48:02.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVolumetric efficiency measures how well an engine breathes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe ratio of the actual air mass drawn in per cycle to the theoretical maximum based on displacement. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNaturally aspirated engines typically achieve 80–95%.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven actual air mass m_actual (kg), air density ρ (kg/m³), and displacement V_d (m³), compute volumetric efficiency η_v.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":811,"title":"Genome Sequence 004: Long 3rd Generation Segment Correction","description":"The Melopsittacus undulates genome, Parrot Budgerigar, was successfully sequenced in July 2012 using long 3rd Gen sequences provided by \u003chttp://www.pacificbiosciences.com/ PacBio\u003e. The \u003chttp://assemblathon.org/a-parrot-a-fish-and-a-snake-walk-into-a-bar Assemblathon Genome Contest\u003e led the team of Phillippy, Koren and Jarvis to successfully \u003chttp://www.sciencedaily.com/releases/2012/07/120702210229.htm Sequence Parrot DNA\u003e using the PacBio 3rd Generation data and Illumina 2nd Gen data.\r\n\r\nThe 3rd gen PacBio data is very long, 1K-20K, but has 15% error rate. The Illumina data is 100-500 long with \u003c1% error rate. Jarvis and his team combined this data to achieve \u003c 0.1% error rate.\r\n\r\nGenome Challenge 004 is the correction of simplified PacBio simulated reads with high error rate.\r\n\r\n*Input:* \r\n\r\nCall 1: empty array, segment Width, Flag=0\r\n\r\nCall 2: N PacBio DNA vectors (N x width), Segment Width, Flag=1\r\n\r\n*Output:* \r\n\r\nCall 1: empty vector, Number of Requested Vectors\r\n\r\nCall 2: Corrected DNA vector, Number of Requested Vectors\r\n\r\n*Score:* Number of N vectors used to produce correct vector for w=1024 case\r\n\r\nThe first call to the PacBio_fix routine returns the number of vectors requested to produce a final product. This may be a function of w.\r\n\r\nThe second call to PacBio_fix will have a DNA matix (N x width) and flag=1.\r\n\r\nThe response to the second call is the fixed DNA sequence, vector of width w.\r\n\r\n*example:*\r\nFirst call return : N=3\r\n\r\n  01230123111122223333 Truth\r\n  Input example\r\n  01232123112122221332 Injected errors\r\n  01130123111122123323\r\n  11230133121122223333\r\n\r\n  Output: \r\n  01230123111122223333 Truth, hopefully\r\n\r\n\r\nThis data is simplified by only having simple substitutions and the data sets are provided pre-aligned. \r\n\r\nThe real PacBio data is quite a bit more complicated. Values may be added, deleted, substituted, and are of varying lengths. This causes alignment issues.\r\n\r\nFollow-Up Challenges: Sample Data from the PacBio site for \u003chttp://www.cbcb.umd.edu/software/PBcR/ Lambda Phage\u003e will be molded into various Challenges. Possible challenges are correcting individual long segments and assembling multiple long segments into the full Lambda Phage genome. The Parrot genome is too big for Cody to solve in 50 seconds.\r\n","description_html":"\u003cp\u003eThe Melopsittacus undulates genome, Parrot Budgerigar, was successfully sequenced in July 2012 using long 3rd Gen sequences provided by \u003ca href=\"http://www.pacificbiosciences.com/\"\u003ePacBio\u003c/a\u003e. The \u003ca href=\"http://assemblathon.org/a-parrot-a-fish-and-a-snake-walk-into-a-bar\"\u003eAssemblathon Genome Contest\u003c/a\u003e led the team of Phillippy, Koren and Jarvis to successfully \u003ca href=\"http://www.sciencedaily.com/releases/2012/07/120702210229.htm\"\u003eSequence Parrot DNA\u003c/a\u003e using the PacBio 3rd Generation data and Illumina 2nd Gen data.\u003c/p\u003e\u003cp\u003eThe 3rd gen PacBio data is very long, 1K-20K, but has 15% error rate. The Illumina data is 100-500 long with \u0026lt;1% error rate. Jarvis and his team combined this data to achieve \u0026lt; 0.1% error rate.\u003c/p\u003e\u003cp\u003eGenome Challenge 004 is the correction of simplified PacBio simulated reads with high error rate.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eCall 1: empty array, segment Width, Flag=0\u003c/p\u003e\u003cp\u003eCall 2: N PacBio DNA vectors (N x width), Segment Width, Flag=1\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eCall 1: empty vector, Number of Requested Vectors\u003c/p\u003e\u003cp\u003eCall 2: Corrected DNA vector, Number of Requested Vectors\u003c/p\u003e\u003cp\u003e\u003cb\u003eScore:\u003c/b\u003e Number of N vectors used to produce correct vector for w=1024 case\u003c/p\u003e\u003cp\u003eThe first call to the PacBio_fix routine returns the number of vectors requested to produce a final product. This may be a function of w.\u003c/p\u003e\u003cp\u003eThe second call to PacBio_fix will have a DNA matix (N x width) and flag=1.\u003c/p\u003e\u003cp\u003eThe response to the second call is the fixed DNA sequence, vector of width w.\u003c/p\u003e\u003cp\u003e\u003cb\u003eexample:\u003c/b\u003e\r\nFirst call return : N=3\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e01230123111122223333 Truth\r\nInput example\r\n01232123112122221332 Injected errors\r\n01130123111122123323\r\n11230133121122223333\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eOutput: \r\n01230123111122223333 Truth, hopefully\r\n\u003c/pre\u003e\u003cp\u003eThis data is simplified by only having simple substitutions and the data sets are provided pre-aligned.\u003c/p\u003e\u003cp\u003eThe real PacBio data is quite a bit more complicated. Values may be added, deleted, substituted, and are of varying lengths. This causes alignment issues.\u003c/p\u003e\u003cp\u003eFollow-Up Challenges: Sample Data from the PacBio site for \u003ca href=\"http://www.cbcb.umd.edu/software/PBcR/\"\u003eLambda Phage\u003c/a\u003e will be molded into various Challenges. Possible challenges are correcting individual long segments and assembling multiple long segments into the full Lambda Phage genome. The Parrot genome is too big for Cody to solve in 50 seconds.\u003c/p\u003e","function_template":"function [M_fix,N]=PacBio_fix(M,w,flag)\r\n% 1st Call\r\n% M is empty\r\n% w is width of segment\r\n% flag is 0\r\n% Ouput is N, the number of segments requested to fix the segment\r\n% 2nd Call\r\n% M is an Nxw array of values [0:3]\r\n\r\n M_fix=[];\r\n N=1; % needed for 2nd call with flag==1\r\n if flag==0 % Requested number of Segments\r\n  N=1;\r\n  return;\r\n end\r\n\r\nM_fix=M(1,:);\r\n\r\n\r\nend","test_suite":"%%\r\nfeval(@assignin,'caller','score',0);\r\n%%\r\nM=[];\r\nflag=0;\r\nw=100;\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\n\r\nM_truth=randi(4,1,w,'uint8')-1;\r\nM=repmat(M_truth,N,1);\r\n\r\n% Apply 15% substitution error\r\nqerr=floor(.15*N*w);\r\nerrvec=randi(N*w,qerr,1);\r\nerrval=randi(4,qerr,1)-1;\r\n\r\nM(errvec)=errval;\r\n\r\nflag=1;\r\ntic\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\ntoc\r\n\r\nassert(isequal(M_fix,M_truth),sprintf('Error Count=%i',sum(M_fix~=M_truth)))\r\n%%\r\nM=[];\r\nflag=0;\r\nw=6144;\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\n\r\nM_truth=randi(4,1,w,'uint8')-1;\r\nM=repmat(M_truth,N,1);\r\n\r\n% Apply 15% substitution error\r\nqerr=floor(.15*N*w);\r\nerrvec=randi(N*w,qerr,1);\r\nerrval=randi(4,qerr,1)-1;\r\n\r\nM(errvec)=errval;\r\n\r\nflag=1;\r\ntic\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\ntoc\r\n\r\nassert(isequal(M_fix,M_truth),sprintf('Error Count=%i',sum(M_fix~=M_truth)))\r\n\r\n%%\r\n% Size Performance is based on w=1024 case\r\nM=[];\r\nflag=0;\r\nw=1024;\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\n\r\nM_truth=randi(4,1,w,'uint8')-1;\r\nM=repmat(M_truth,N,1);\r\n\r\n% Apply 15% substitution error\r\nqerr=floor(.15*N*w);\r\nerrvec=randi(N*w,qerr,1);\r\nerrval=randi(4,qerr,1)-1;\r\n\r\nM(errvec)=errval;\r\n\r\nflag=1;\r\ntic\r\n[M_fix,not_N]=PacBio_fix(M,w,flag);\r\ntoc\r\n\r\nassert(isequal(M_fix,M_truth),sprintf('Error Count=%i',sum(M_fix~=M_truth)))\r\n\r\nfeval(@assignin,'caller','score',min(20,N));\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2012-10-08T02:30:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-01T05:26:57.000Z","updated_at":"2026-07-22T16:47:43.000Z","published_at":"2012-10-08T02:29:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Melopsittacus undulates genome, Parrot Budgerigar, was successfully sequenced in July 2012 using long 3rd Gen sequences provided by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.pacificbiosciences.com/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePacBio\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://assemblathon.org/a-parrot-a-fish-and-a-snake-walk-into-a-bar\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAssemblathon Genome Contest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e led the team of Phillippy, Koren and Jarvis to successfully\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.sciencedaily.com/releases/2012/07/120702210229.htm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSequence Parrot DNA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e using the PacBio 3rd Generation data and Illumina 2nd Gen data.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe 3rd gen PacBio data is very long, 1K-20K, but has 15% error rate. The Illumina data is 100-500 long with \u0026lt;1% error rate. Jarvis and his team combined this data to achieve \u0026lt; 0.1% error rate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenome Challenge 004 is the correction of simplified PacBio simulated reads with high error rate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 1: empty array, segment Width, Flag=0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 2: N PacBio DNA vectors (N x width), Segment Width, Flag=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 1: empty vector, Number of Requested Vectors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 2: Corrected DNA vector, Number of Requested Vectors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScore:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Number of N vectors used to produce correct vector for w=1024 case\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first call to the PacBio_fix routine returns the number of vectors requested to produce a final product. This may be a function of w.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe second call to PacBio_fix will have a DNA matix (N x width) and flag=1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe response to the second call is the fixed DNA sequence, vector of width w.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexample:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e First call return : N=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[01230123111122223333 Truth\\nInput example\\n01232123112122221332 Injected errors\\n01130123111122123323\\n11230133121122223333\\n\\nOutput: \\n01230123111122223333 Truth, hopefully]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis data is simplified by only having simple substitutions and the data sets are provided pre-aligned.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe real PacBio data is quite a bit more complicated. Values may be added, deleted, substituted, and are of varying lengths. This causes alignment issues.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollow-Up Challenges: Sample Data from the PacBio site for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.cbcb.umd.edu/software/PBcR/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLambda Phage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e will be molded into various Challenges. Possible challenges are correcting individual long segments and assembling multiple long segments into the full Lambda Phage genome. The Parrot genome is too big for Cody to solve in 50 seconds.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61419,"title":"Caesar Cipher: shift a lowercase string","description":"A Caesar cipher shifts every letter forward through the alphabet by a fixed amount, wrapping around from z back to a.\r\n\r\nGiven a lowercase string s and a whole number n, return the encoded string where each letter is shifted forward by n positions. The shift may be larger than 26, and wrapping must work correctly (shifting z by 1 gives a).\r\n\r\nExamples:\r\n  s = 'abc',   n = 1    -\u003e  'bcd'\r\n  s = 'xyz',   n = 3    -\u003e  'abc'\r\n  s = 'hello', n = 13   -\u003e  'uryyb'","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 315px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 244px 157.5px; transform-origin: 244px 157.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 21px; text-align: left; transform-origin: 220px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA Caesar cipher shifts every letter forward through the alphabet by a fixed amount, wrapping around from z back to a.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 10.5px; text-align: left; transform-origin: 220px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 42px; text-align: left; transform-origin: 220px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a lowercase string s and a whole number n, return the encoded string where each letter is shifted forward by n positions. The shift may be larger than 26, and wrapping must work correctly (shifting z by 1 gives a).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 10.5px; text-align: left; transform-origin: 220px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 10.5px; text-align: left; transform-origin: 220px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 10.5px; text-align: left; transform-origin: 220px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  s = 'abc',   n = 1    -\u0026gt;  'bcd'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 10.5px; text-align: left; transform-origin: 220px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  s = 'xyz',   n = 3    -\u0026gt;  'abc'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 10.5px; text-align: left; transform-origin: 220px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  s = 'hello', n = 13   -\u0026gt;  'uryyb'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function out = caesar(s, n)\r\n    out = s;\r\nend","test_suite":"%%\r\nassert(isequal(caesar('abc', 1), 'bcd'))\r\n%%\r\nassert(isequal(caesar('xyz', 3), 'abc'))\r\n%%\r\nassert(isequal(caesar('hello', 13), 'uryyb'))\r\n%%\r\nassert(isequal(caesar('zebra', 27), 'afcsb'))\r\n%%\r\nassert(isequal(caesar('abc', 0), 'abc'))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5142412,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-07-08T13:56:36.000Z","updated_at":"2026-07-22T17:28:56.000Z","published_at":"2026-07-08T13:56:36.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Caesar cipher shifts every letter forward through the alphabet by a fixed amount, wrapping around from z back to a.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a lowercase string s and a whole number n, return the encoded string where each letter is shifted forward by n positions. The shift may be larger than 26, and wrapping must work correctly (shifting z by 1 gives a).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e  s = 'abc',   n = 1    -\u0026gt;  'bcd'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e  s = 'xyz',   n = 3    -\u0026gt;  'abc'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e  s = 'hello', n = 13   -\u0026gt;  'uryyb'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61399,"title":"MATLAB 101: Conditional Product or Sum Calculator","description":"Write a MATLAB function that accepts two integer numbers. If the product of the two numbers is less than or equal to 1000, return their product; otherwise, return their sum.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that accepts two integer numbers. If the product of the two numbers is less than or equal to 1000, return their product; otherwise, return their sum.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = product_or_sum(number1, number2)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: First Provided Test Case (Product \u003c= 1000)\r\n% 20 * 30 = 600 (\u003c= 1000), should return product\r\nassert(product_or_sum(20, 30) == 600);\r\n\r\n%% Test 2: Second Provided Test Case (Product \u003e 1000)\r\n% 40 * 30 = 1200 (\u003e 1000), should return sum (40 + 30)\r\nassert(product_or_sum(40, 30) == 70);\r\n\r\n%% Test 3: Boundary Condition Exactly 1000\r\n% 10 * 100 = 1000 (\u003c= 1000), should return product\r\nassert(product_or_sum(10, 100) == 1000);\r\n\r\n%% Test 4: Boundary Condition Just Above 1000\r\n% 20 * 51 = 1020 (\u003e 1000), should return sum (20 + 51)\r\nassert(product_or_sum(20, 51) == 71);\r\n\r\n%% Test 5: Handling Negative Numbers\r\n% -5 * 10 = -50 (\u003c= 1000), should return product\r\nassert(product_or_sum(-5, 10) == -50);","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-13T17:39:41.000Z","updated_at":"2026-07-22T19:34:41.000Z","published_at":"2026-06-13T17:39:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that accepts two integer numbers. If the product of the two numbers is less than or equal to 1000, return their product; otherwise, return their sum.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61333,"title":"Given the ratio of the two legs (longer / shorter), and the hypotenuse length, find the shorter leg.","description":"Further to the problem 43236, find the length of shorter leg\r\nP.S No built-in functions allowed","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(33, 33, 33); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 243.5px 25.5px; transform-origin: 243.5px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFurther to the problem 43236, find the length of shorter leg\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eP.S No built-in functions allowed\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = FindShortLeg(x,ratio)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 40;\r\nratio = 16/9;\r\ny_correct = 19.6104;\r\nassert(abs(FindShortLeg(x,ratio)-y_correct)\u003c0.01)\r\n\r\n%%\r\nx = 25;\r\nratio = 16/9;\r\ny_correct = 12.2565;\r\nassert(abs(FindShortLeg(x,ratio)-y_correct)\u003c0.01)\r\n\r\n%%\r\nx = 10;\r\nratio = 16/9;\r\ny_correct =  4.9026;\r\nassert(abs(FindShortLeg(x,ratio)-y_correct)\u003c0.01)\r\n\r\n%%\r\nx = 5;\r\nratio = 4/3;\r\ny_correct = 3;\r\nassert(abs(FindShortLeg(x,ratio)-y_correct)\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":584788,"edited_by":584788,"edited_at":"2026-05-21T11:24:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2026-05-21T05:44:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T05:28:33.000Z","updated_at":"2026-07-23T05:09:08.000Z","published_at":"2026-05-21T05:28:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFurther to the problem 43236, find the length of shorter leg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP.S No built-in functions allowed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61425,"title":"Reverse the Sign","description":"Write a function that returns the input with the sign of every element reversed.\r\nThe input may be a scalar, vector, or matrix.\r\nSome built-in functions and signs are forbidden.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"baseline-shift: 0px; block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 55.5px; transform-origin: 468.5px 55.5px; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 240.242px 8px; transform-origin: 240.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the input with the sign of every element reversed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 135.725px 8px; transform-origin: 135.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe input may be a scalar, vector, or matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 147.825px 8px; transform-origin: 147.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSome built-in functions and signs are forbidden.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = \r\nend","test_suite":"%%\r\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'sum')))\r\nassert(isempty(strfind(filetext, '-')))\r\nassert(isempty(strfind(filetext, '+')))\r\nassert(isempty(strfind(filetext, 'exp')))\r\nassert(isempty(strfind(filetext, 'uminus')))\r\nassert(isempty(strfind(filetext, 'abs')))\r\nassert(isempty(strfind(filetext, 'regexp')))\r\nassert(isempty(strfind(filetext, 'echo')))\r\nassert(isempty(strfind(filetext, 'assignin')))\r\nassert(isempty(strfind(filetext, 'ans')))\r\nassert(isempty(strfind(filetext, 'conv')))\r\nassert(isempty(strfind(filetext, 'inv')))\r\nassert(isempty(strfind(filetext, 'persistent')))\r\nassert(isempty(strfind(filetext, 'global')))\r\nassert(isempty(strfind(filetext, 'sign')))\r\n%%\r\nassert(isequal(your_fcn_name(4),-4))\r\n%%\r\nassert(isequal(your_fcn_name(-9),9))\r\n%%\r\nassert(isequal(your_fcn_name(0),0))\r\n%%\r\nassert(isequal(your_fcn_name([1 2 -3]),[-1 -2 3]))\r\n%%\r\nassert(isequal(your_fcn_name([1 -2;3 -4]),[-1 2;-3 4]))\r\n%%\r\nx = [Inf 0 12 -3];\r\ny_corrected = [-Inf 0 -12 3]\r\nassert(isequal(your_fcn_name(x),y_corrected))\r\n%%\r\nassert(isequal(your_fcn_name(55),-55))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5046205,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-07-23T11:24:51.000Z","updated_at":"2026-07-23T13:12:41.000Z","published_at":"2026-07-23T11:24:51.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the input with the sign of every element reversed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe input may be a scalar, vector, or matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSome built-in functions and signs are forbidden.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61312,"title":"Electric Power Steering (EPS) Motor Torque with Efficiency","description":"In EPS systems, the motor must generate additional torque to compensate for system losses.\r\nGiven Required assist torque at rack Ta and Mechanical efficiency η (0 \u003c η ≤ 1)\r\nCompute required motor torque Tm.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn EPS systems, the motor must generate additional torque to compensate for system losses.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Required assist torque at rack \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTa \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMechanical efficiency \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eη (0 \u0026lt; η ≤ 1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute required motor torque \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTm\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Tm = epsMotorTorque(Ta,eta)\r\nTm = 0;\r\nend","test_suite":"%%\r\nTa = 10; eta = 0.9;\r\nTm_expected = Ta / eta;\r\nassert(abs(epsMotorTorque(Ta,eta) - Tm_expected) \u003c 1e-6)\r\n\r\n%%\r\nTa = 15; eta = 0.85;\r\nTm_expected = Ta / eta;\r\nassert(abs(epsMotorTorque(Ta,eta) - Tm_expected) \u003c 1e-6)\r\n\r\n%%\r\nTa = 8; eta = 0.8;\r\nTm_expected = Ta / eta;\r\nassert(abs(epsMotorTorque(Ta,eta) - Tm_expected) \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:46:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:46:15.000Z","updated_at":"2026-07-23T09:55:42.000Z","published_at":"2026-04-28T09:46:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn EPS systems, the motor must generate additional torque to compensate for system losses.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Required assist torque at rack \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTa \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eMechanical efficiency \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eη (0 \u0026lt; η ≤ 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute required motor torque \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTm\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":843,"title":"Hyperspectral Processing: Determine Material Components given a Hyperspectral vector","description":"Given a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages. \r\n\r\n\u003chttp://aviris.jpl.nasa.gov/aviris/index.html NASA AVIRIS\u003e\r\n\r\nA Ground Square is imaged by hundreds of pixels, each at a different wavelength.\r\nThe signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance.\r\nPixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\r\n\r\nLet S(i,j) be the response of Material i for band j\r\n\r\ng( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\r\n\r\nA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\r\n\r\n*g=S*f*  where f is the percentage of the imaged pixel covered by the\r\nmaterial.\r\n\r\n*Input:* \r\ng spectral sum [301,1]; \r\nS spectral material response [301,9]  Nine materials\r\n\r\n*Output:*\r\nSolve for f  ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\r\n\r\n( f should sum to 1, max(f) is 1 and min(f) is 0 )\r\n\r\nThe test Suite will round to 2 decimal places.\r\nCases of \"other materials\" which will induce negative values are not\r\ntested.\r\n\r\nThis is introductory and ignores atmospheric absorption.\r\n\r\nThere is a matrix operation hint in the test suite for a method to solve for f.\r\n\r\n\r\n\u003chttp://aviris.jpl.nasa.gov/data/free_data.html AVARIS Free Data\u003e\r\nThese data files are large with 224 bands x 750 channels x 2000 samples\r\n\r\nTo expand these files may require a tar converter\r\n\u003chttp://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme NASA readme\u003e\r\n...and... \r\n\u003chttp://aviris.jpl.nasa.gov/alt_gulf/ NASA Tools bottom Left\u003e\r\nThere are some possible issues with the NASA tar tool. Two non-standard files can be found at \u003chttp://dll-files.org/7968/index.html libiconv-2.dll\u003e and \u003chttp://dll-files.org/7975/libintl-2.dll.html libintl-2.dll\u003e\r\n\r\nSee the Test Suite for details on opening the AVIRIS Moffett Field file.","description_html":"\u003cp\u003eGiven a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://aviris.jpl.nasa.gov/aviris/index.html\"\u003eNASA AVIRIS\u003c/a\u003e\u003c/p\u003e\u003cp\u003eA Ground Square is imaged by hundreds of pixels, each at a different wavelength.\r\nThe signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance.\r\nPixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\u003c/p\u003e\u003cp\u003eLet S(i,j) be the response of Material i for band j\u003c/p\u003e\u003cp\u003eg( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\u003c/p\u003e\u003cp\u003eA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\u003c/p\u003e\u003cp\u003e\u003cb\u003eg=S*f\u003c/b\u003e  where f is the percentage of the imaged pixel covered by the\r\nmaterial.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e \r\ng spectral sum [301,1]; \r\nS spectral material response [301,9]  Nine materials\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\r\nSolve for f  ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\u003c/p\u003e\u003cp\u003e( f should sum to 1, max(f) is 1 and min(f) is 0 )\u003c/p\u003e\u003cp\u003eThe test Suite will round to 2 decimal places.\r\nCases of \"other materials\" which will induce negative values are not\r\ntested.\u003c/p\u003e\u003cp\u003eThis is introductory and ignores atmospheric absorption.\u003c/p\u003e\u003cp\u003eThere is a matrix operation hint in the test suite for a method to solve for f.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://aviris.jpl.nasa.gov/data/free_data.html\"\u003eAVARIS Free Data\u003c/a\u003e\r\nThese data files are large with 224 bands x 750 channels x 2000 samples\u003c/p\u003e\u003cp\u003eTo expand these files may require a tar converter \u003ca href=\"http://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme\"\u003eNASA readme\u003c/a\u003e\r\n...and...  \u003ca href=\"http://aviris.jpl.nasa.gov/alt_gulf/\"\u003eNASA Tools bottom Left\u003c/a\u003e\r\nThere are some possible issues with the NASA tar tool. Two non-standard files can be found at \u003ca href=\"http://dll-files.org/7968/index.html\"\u003elibiconv-2.dll\u003c/a\u003e and \u003ca href=\"http://dll-files.org/7975/libintl-2.dll.html\"\u003elibintl-2.dll\u003c/a\u003e\u003c/p\u003e\u003cp\u003eSee the Test Suite for details on opening the AVIRIS Moffett Field file.\u003c/p\u003e","function_template":"function f = hyperspectral(g,S)\r\n% g is [301,1]\r\n% S is [301,9]\r\n  f = zeros(size(S,2),1);\r\nend","test_suite":"%%\r\n% The AVIRIS fileread info is at the bottom\r\n% Solution Hint:\r\n% The Matrix hint is inv(S'S)(S'S)=I\r\n% With g=Sf multiply both sides by h'\r\n% S'g=S'Sf, now multiply both sides by inv(S'S)\r\n% inv(S'S)(S'g)=inv(S'S)(S'S)f which is I*f\r\n% Now simplify the right side and there is a solution\r\n% Solution Bigger/Better Hint: Search on mldivide\r\n%%\r\nglobal S\r\n%http://tinyurl.com/matlab-hyper-spectra\r\n%http://rmatlabtest.appspot.com/Spectra.mat\r\nurlwrite('http://rmatlabtest.appspot.com/Spectra.mat','Spectra.mat') ;\r\nload('Spectra.mat'); % S is the variable in Spectra.mat\r\nf_exp=[.5 .5 0 0 0 0 0 0 0 ]';\r\ng=S*f_exp;\r\n\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\nglobal S\r\nf_exp=[0 .5 0.25 0 0 0 0.25 0 0 ]';\r\ng=S*f_exp;\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\nglobal S\r\nf_exp=[0 .25 0.6 0 0 0 0 0.15 0 ]';\r\ng=S*f_exp;\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\n%\r\n%Reading of the full Moffett Field file: (8GB RAM recommended)\r\n% The file is 600MB\r\n%cd 'C:\\Users\\???' % Your file location\r\n%fn='f080611t01p00r07rdn_c_sc01_ort_img'\r\n%fid = fopen (fn,'r');\r\n%A = int16(fread(fid, 'int16', 'ieee-be'));\r\n%A2 = reshape (A, 224,753,1924); % Specifics found in text files\r\n%A3 = permute (A2,[3 2 1]); % X Y Band\r\n%figure;imagesc(squeeze(A3(:,:,1))); % To view top layer\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":8,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2013-02-02T19:05:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-19T02:49:02.000Z","updated_at":"2026-07-23T10:07:49.000Z","published_at":"2012-07-19T03:34:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/aviris/index.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA AVIRIS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Ground Square is imaged by hundreds of pixels, each at a different wavelength. The signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance. Pixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet S(i,j) be the response of Material i for band j\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eg( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eg=S*f\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e where f is the percentage of the imaged pixel covered by the material.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e g spectral sum [301,1]; S spectral material response [301,9] Nine materials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Solve for f ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e( f should sum to 1, max(f) is 1 and min(f) is 0 )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test Suite will round to 2 decimal places. Cases of \\\"other materials\\\" which will induce negative values are not tested.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is introductory and ignores atmospheric absorption.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere is a matrix operation hint in the test suite for a method to solve for f.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/data/free_data.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAVARIS Free Data\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e These data files are large with 224 bands x 750 channels x 2000 samples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo expand these files may require a tar converter\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA readme\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ...and... \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/alt_gulf/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA Tools bottom Left\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e There are some possible issues with the NASA tar tool. Two non-standard files can be found at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://dll-files.org/7968/index.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003elibiconv-2.dll\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://dll-files.org/7975/libintl-2.dll.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003elibintl-2.dll\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee the Test Suite for details on opening the AVIRIS Moffett Field file.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61269,"title":"Precise Almost Pythagorean Triples ","description":"This  is essentially the same as:  Problem 52834. Easy Sequences 32: Almost Pythagorean Triples; it even presents the same set of test problems.  The difference is that the \"correct\" solutions for larger cases of 52834 were the result of roundoff errors due to values being larger than flintmax('double').  This problem requires care to avoid such roundoff.\r\nRepeating the original problem description:\t\t\t\t\r\nAn Almost Pythagorean Triple (abbreviated as \"APT'), is a set of 3 integers in which square of the largest element, which we will call as its 'hypotenuse', is 1 less than the sum of square of the smaller elements (shorter sides). This means that if c is the hypotenuse and a and b are the shorter sides, , satisfies the following equation: \r\n        \r\n        where:  \r\nThe smallest  is the triple , with  and perimeter (the sum of the 3 elements)  of . Some researchers consider  as the smallest , but here, we will only look at 's where the hypotenuse is \"strictly\" greater than the other shorter sides. Other examples of 's are , and . \r\nUnfortunately, unlike Pythagorean Triples, a 'closed formula' for generating all possible 's, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with 's with a known ratio between the hypotenuse and the shortest side: . \r\nGiven the value of r, find the perimeter of the  with the r-th smallest perimeter. For example for , that is , the smallest perimeter is  for  , while the second (r-th) smallest perimeter is , for the  with dimensions . For , the third smallest perimeter is  for  . \r\nThe output can be very large, so please present only the last 12 digits if the number of digits of the perimeter exceeds 12.\r\nFinally, as with the original, the use of java, BigInteger, persistent, and global are not allowed.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 669.833px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 334px 334.917px; transform-origin: 334px 334.917px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 42px; text-align: left; transform-origin: 310px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.675px 7.91667px; transform-origin: 102.675px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis  is essentially the same as:  \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52834\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem 52834. Easy Sequences 32: Almost Pythagorean Triples\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; it even presents the same set of test problems.  The difference is that the \"correct\" solutions for larger cases of 52834 were the result of roundoff errors due to values being larger than flintmax('double').  This problem requires care to avoid such roundoff.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 10.5px; text-align: left; transform-origin: 310px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201.933px 7.91667px; transform-origin: 201.933px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRepeating the original problem description:\t\t\t\t\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 86.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 43.4583px; text-align: left; transform-origin: 310px 43.4583px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 303.05px 7.91667px; transform-origin: 303.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn Almost Pythagorean Triple (abbreviated as \"APT'), is a set of 3 integers in which square of the largest element, which we will call as its 'hypotenuse', is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.91667px; transform-origin: 3.89167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.45px 7.91667px; transform-origin: 12.45px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eless\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.8917px 7.91667px; transform-origin: 94.8917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e than the sum of square of the smaller elements (shorter sides). This means that if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.5px 7.91667px; transform-origin: 3.5px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.35px 7.91667px; transform-origin: 72.35px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hypotenuse and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.91667px; transform-origin: 3.89167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.91667px; transform-origin: 3.89167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 7.91667px; transform-origin: 49.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are the shorter sides, \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.692px 7.91667px; transform-origin: 102.692px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, satisfies the following equation: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 24.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 12.4583px; text-align: left; transform-origin: 310px 12.4583px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5333px 7.91667px; transform-origin: 15.5333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"99\" height=\"19\" style=\"vertical-align: baseline;width: 99px;height: 19px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 23.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 11.9583px; text-align: left; transform-origin: 310px 11.9583px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.425px 7.91667px; transform-origin: 40.425px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        where:  \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"62\" height=\"18\" style=\"vertical-align: baseline;width: 62px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 96.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 48.3333px; text-align: left; transform-origin: 310px 48.3333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.6167px 7.91667px; transform-origin: 41.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe smallest \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.725px 7.91667px; transform-origin: 37.725px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the triple \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"48\" height=\"18\" style=\"vertical-align: baseline;width: 48px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.275px 7.91667px; transform-origin: 18.275px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, with \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"100\" height=\"19\" style=\"vertical-align: baseline;width: 100px;height: 19px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.508px 7.91667px; transform-origin: 101.508px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and perimeter (the sum of the 3 elements)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 7.91667px; transform-origin: 7.775px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eof \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"18\" height=\"18\" style=\"vertical-align: baseline;width: 18px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6UlEQVRYhe2WQQ3DMAxFP4cwCIESGIIiKIMxKINSKIZBKIdRKIZR6A6ztWiHxkm+qkjzl6xenOQpL5UMeDyevhIBhEzPAOBmrKEFZAVwGDbZpc9SSylISEC0zoDGApgDn1syZwQwy/dpBNqk4klPkH32EpjfzAagKIfk3tiESl01QBYFD1ToqgGyRHW9kL/JS4BU19oCwwRSXWMPQDRdLCCaLhYQTRcDiKqLAUTVxQDaQNTVChRB1tUKdAdZVyuQTgpTD0CprrORpCg6VijQXLBWdW0skAXfoSutVQ7LRdfT/i6Px+P5u7wB3c96XQFb71kAAAAASUVORK5CYII=\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91.4083px 7.91667px; transform-origin: 91.4083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Some researchers consider \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"48\" height=\"18\" style=\"vertical-align: baseline;width: 48px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGEAAAAlCAYAAABSz4fZAAACcklEQVRoge2aXZWDMBBGrwcc1AAGUFAFOKgDHNRCNSABD1hYDbWw+zCdQ0qbPxpSFvKdM08tnXRuMhkmgaKioqLNq7NY881B/QM12GMXrV9gBIaZtSlGumO1vMZsROIZrV/KrE+lhi9BqD94NlTNw3L4Ohn+qshns0NogR+gX+I0QBVwQ8Zn2h24rODvjPyfub8BAROibBDmg10DwgkJ9jwgpl0T+rt6fN0JA5EFwhWZhRfWhTAgoM3ioOZ1ZZwT+NLA3ZgCXTGtdPU1RvxWtJamo7UgnJGZZ8v/XWLfIwLgnSqeV6RvT9oNhB53zq94ThOfqEZmu2sDNlOVby/aDQQzLdg0kAbCmfDAHgpCiBTCkMGXCcEXp0NB0A1zjVJ1rvbhy5e24EAQTkxBCa3fP5FWZCE9ocNA0OooxyrQ6ihkFcBBIGhQcuwFMAEPjc8hIPRIXR/b01miGvl/Md3k3UO4IGkhRxOveviKbY3sGoK2EHIBGFnWm9othP8CAHYKQTu2LgA16UrVEACupuFmIVRIPu+Im801Ugm5xqYz14SgZ78tcRv4DX/V1WJv9qnvTUKYt59DQCiAEftheoesEjNw+iIXu0p1jFeHL/2OK1ZZIZjtZN+ba89zYFwzCSYArkMW25lC/eZzX6p6d3pnM9+ZQhYILRLU+S2DAXu6qY1n7vgh2H7/nfW8ppyO55sPLgjnCF8hN1C+dtAfo5xXaRpklebU5iGEHKCklO9waA1tGkKNpIcctT5Iykt5ESBUH0G4MN21UUtVe1dIQHK0nUHSXY6UZ95PUtMLENGyVQKL7lQeSGaFOLeioqKioqKiresPwN5Zrqu1TD0AAAAASUVORK5CYII=\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5583px 7.91667px; transform-origin: 50.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as the smallest \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.7917px 7.91667px; transform-origin: 70.7917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, but here, we will only look at \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 243.942px 7.91667px; transform-origin: 243.942px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's where the hypotenuse is \"strictly\" greater than the other shorter sides. Other examples of \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.8333px 7.91667px; transform-origin: 18.8333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's are \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"56\" height=\"18\" style=\"vertical-align: baseline;width: 56px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 7.91667px; transform-origin: 17.5px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"71\" height=\"18\" style=\"vertical-align: baseline;width: 71px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 71.75px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 35.875px; text-align: left; transform-origin: 310px 35.875px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 269.142px 7.91667px; transform-origin: 269.142px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUnfortunately, unlike Pythagorean Triples, a 'closed formula' for generating all possible \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.9417px 7.91667px; transform-origin: 21.9417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.775px 7.91667px; transform-origin: 6.775px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's with a known ratio between the hypotenuse and the shortest side: \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"50\" height=\"18\" style=\"vertical-align: baseline;width: 50px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 95.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 47.8333px; text-align: left; transform-origin: 310px 47.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.2083px 7.91667px; transform-origin: 62.2083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 7.91667px; transform-origin: 2.33333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.925px 7.91667px; transform-origin: 85.925px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the perimeter of the \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.3167px 7.91667px; transform-origin: 30.3167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e with the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.6167px 7.91667px; transform-origin: 41.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003er-th smallest\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3417px 7.91667px; transform-origin: 37.3417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e perimeter. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.4417px 7.91667px; transform-origin: 12.4417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"35\" height=\"18\" style=\"vertical-align: baseline;width: 35px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.4917px 7.91667px; transform-origin: 24.4917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"43\" height=\"18\" style=\"vertical-align: baseline;width: 43px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.675px 7.91667px; transform-origin: 81.675px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the smallest perimeter is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"18\" height=\"18\" style=\"vertical-align: baseline;width: 18px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABLUlEQVRYhe2WUbHDIBBFjwccYKAGoiAK4qAOcBAL0RAJeKiFaoiFvg+WmX2dPEIC5fWDO7Nfu1lOLiwJdHV1fZcsYE4+M0jcaoMswCuzsQFm4Ak4iafEvQTEKJAYR0AWeMji726u0sPv5A41Et5slAVygWKt28kZYEvks+UygaaMOu34aZfOAsUt2RI1GvqyS7lAcTtSQIPqtX4aKNakgGxmXVWgo/PRDMiruvEbgO4cn4+mW2YIF2LKJT32j08DIXkN5eX5meDIqnJLCyAITk2yoBcIR9iumbxzVhUoBRrvqr1vXXMg3Wcq6FMF6MbxBDYD0tN36dejJpCeurUGjOX3GJ/5QjvCId4o/FOMIDPB4vdY/ljAEEY53jle6opduSorAMN/QnR1dXWV6Ae9sZqCc2SAGwAAAABJRU5ErkJggg==\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 7.91667px; transform-origin: 12.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"48\" height=\"18\" style=\"vertical-align: baseline;width: 48px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.9583px 7.91667px; transform-origin: 57.9583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, while the second (r-th) smallest perimeter is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"18\" height=\"18\" style=\"vertical-align: baseline;width: 18px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2WUQ2DMBCGfw91UAMYmIIqwMEc4AAL1TAJ9TALaJgF9sBd0i2DXQ9u4+G+5MIDBT74QgBwHOc/dAAuwumE54wAglZoAjALZxSIZForlX8hNcjMWJ7SJ0IlwqMSKjRxY02gC0wr+xOAgbb3PUKRLvKtdQ9ZLpDYLqG1BDU3bOc6TEgC53pA9taYC3GuLFxvLsS50hmEWnOZC7XmMhdqzWUqpMllKqTJZSpU0J7LTChCl8tM6ApdLjMh/mL3ZxCqc239kvxMiHMVxbH8O8NCwxFCI8m0vF2xOu59MpabdBzHcSQ8AUZlel3qgGXQAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6583px 7.91667px; transform-origin: 25.6583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, for the \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.6833px 7.91667px; transform-origin: 53.6833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with dimensions \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"71\" height=\"18\" style=\"vertical-align: baseline;width: 71px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.325px 7.91667px; transform-origin: 16.325px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"35\" height=\"18\" style=\"vertical-align: baseline;width: 35px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1083px 7.91667px; transform-origin: 31.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the third smallest perimeter is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"33\" height=\"18\" style=\"vertical-align: baseline;width: 33px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 7.91667px; transform-origin: 12.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"101\" height=\"18\" style=\"vertical-align: baseline;width: 101px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 21px; text-align: left; transform-origin: 310px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 305.717px 7.91667px; transform-origin: 305.717px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe output can be very large, so please present only the last 12 digits if the number of digits of the perimeter exceeds 12.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 21px; text-align: left; transform-origin: 310px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 282.908px 7.91667px; transform-origin: 282.908px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFinally, as with the original, the use of java, BigInteger, persistent, and global are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function function perimeter = rthPerAPTdbl(r)\r\n  perimeter = r^2;\r\nend","test_suite":"%% Test Case 1\r\nr = 2;\r\np_correct = 71;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 2\r\nr = 3;\r\np_correct = 1393;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 3\r\nr = 5;\r\np_correct = 1046629;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 4\r\nr = 10;\r\np_correct = 737287485879;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 5\r\nr = 100;\r\np_correct = 16183149010201;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 6\r\nrs = 101:150;\r\nps = arrayfun(@(r) rthPerAPTdbl(r),rs);\r\nps = mod([sum(ps) ps(5:5:end) floor(std(double(ps)))],1e6);\r\nps_correct = [12636 824229 203679 227761 926641 15749 664839 210241 515881 139269 477199 789840];\r\nassert(isequal(ps,ps_correct))\r\n%% Test Case 7\r\nr = 1000;\r\np_correct = 499499001002001;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 8\r\nr = 10000;\r\np_correct = 100020001;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 9\r\nr = 123456;\r\np_correct = uint64(76696064606196865);\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 10: Forbid java and BigInteger\r\nfiletext = fileread('rthPerAPTdbl.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":2404920,"edited_by":2404920,"edited_at":"2026-03-04T15:24:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-04T14:14:29.000Z","updated_at":"2026-07-23T10:14:17.000Z","published_at":"2026-03-04T15:24:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis  is essentially the same as:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52834\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 52834. Easy Sequences 32: Almost Pythagorean Triples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e; it even presents the same set of test problems.  The difference is that the \\\"correct\\\" solutions for larger cases of 52834 were the result of roundoff errors due to values being larger than flintmax('double').  This problem requires care to avoid such roundoff.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRepeating the original problem description:\\t\\t\\t\\t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn Almost Pythagorean Triple (abbreviated as \\\"APT'), is a set of 3 integers in which square of the largest element, which we will call as its 'hypotenuse', is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eless\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e than the sum of square of the smaller elements (shorter sides). This means that if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the hypotenuse and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are the shorter sides, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, satisfies the following equation: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"19\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"99\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        where:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"62\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe smallest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the triple \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"48\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"19\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"100\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and perimeter (the sum of the 3 elements)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eof \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Some researchers consider \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"48\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId7\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the smallest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, but here, we will only look at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's where the hypotenuse is \\\"strictly\\\" greater than the other shorter sides. Other examples of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"56\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId8\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"71\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId9\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUnfortunately, unlike Pythagorean Triples, a 'closed formula' for generating all possible \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's with a known ratio between the hypotenuse and the shortest side: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"50\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId10\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the perimeter of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e with the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er-th smallest\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e perimeter. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"35\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId11\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, that is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"43\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId12\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the smallest perimeter is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId13\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"48\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId14\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, while the second (r-th) smallest perimeter is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId15\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, for the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"71\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId16\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"35\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId17\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the third smallest perimeter is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"33\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId18\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"101\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId19\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe output can be very large, so please present only the last 12 digits if the number of digits of the perimeter exceeds 12.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFinally, as with the original, the use of java, BigInteger, persistent, and global are not 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version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven length of matrix initialize a matrix consisting of natural numbers from 1 to n:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10; x = [ 1 2 3 4 5 6 7 8 9 10];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 5; x = [1 2 3 4 5];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":58758,"title":"Hemisphere Volume on Top of a Cylinder","description":"This MATLAB function has to calculate the volume of a hemisphere placed on top of a cylinder, given valid inputs. It takes the radius of the cylinder and the height of the cylinder as input, and returns the total volume of the hemisphere and the cylinder combined.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 332px 46.5px; transform-origin: 332px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 31.5px; text-align: left; transform-origin: 309px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis MATLAB function has to calculate the volume of a hemisphere placed on top of a cylinder, given valid inputs. It takes the radius of the cylinder and the height of the cylinder as input, and returns the total volume of the hemisphere and the cylinder combined.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function volume = computeHemisphereVolume(radius, height)\r\n\r\n    volume = 0;\r\nend","test_suite":"%%\r\nradius = 3;\r\nheight = 8;\r\nexpectedOutput = 282.743338823081;\r\nvolume = computeHemisphereVolume(radius, height);\r\nassert(abs(expectedOutput - volume) \u003c 1e-4)\r\n%%\r\nradius = 2.5;\r\nheight = 5;\r\nexpectedOutput = 130.899693899575;\r\nvolume = computeHemisphereVolume(radius, height);\r\nassert(abs(expectedOutput - volume) \u003c 1e-4)\r\n%%\r\nradius = 10;\r\nheight = 15;\r\nexpectedOutput = 6806.78408277789;\r\nvolume = computeHemisphereVolume(radius, height);\r\nassert(abs(expectedOutput - volume) \u003c 1e-4)\r\n%%\r\nradius = 0;\r\nheight = 12;\r\nexpectedOutput = 0;\r\nvolume = computeHemisphereVolume(radius, height);\r\nassert(abs(expectedOutput - volume) \u003c 1e-4)\r\n%%\r\nradius = 7.2;\r\nheight = 3.5;\r\nexpectedOutput = 1351.73935424539;\r\nvolume = computeHemisphereVolume(radius, height);\r\nassert(abs(expectedOutput - volume) \u003c 1e-4)\r\n","published":true,"deleted":false,"likes_count":13,"comments_count":4,"created_by":3429354,"edited_by":26769,"edited_at":"2023-12-02T00:24:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":75,"test_suite_updated_at":"2023-12-02T00:24:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-07-18T21:20:09.000Z","updated_at":"2026-06-04T17:19:01.000Z","published_at":"2023-07-18T21:20:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis MATLAB function has to calculate the volume of a hemisphere placed on top of a cylinder, given valid inputs. It takes the radius of the cylinder and the height of the cylinder as input, and returns the total volume of the hemisphere and the cylinder combined.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2014,"title":"\"Find out the best cricket\"","description":"This is how I originally read Problem 2013, so let's just go with it.  Give me the first and last name of the best cricket, regardless of your input.","description_html":"\u003cp\u003eThis is how I originally read Problem 2013, so let's just go with it.  Give me the first and last name of the best cricket, regardless of your input.\u003c/p\u003e","function_template":"function y = BestCricket(x)\r\n  y = x;\r\nend","test_suite":"x = 1;\r\nassert(isequal(BestCricket(x),'Jiminy Cricket'))\r\n%%\r\nx = magic(7);\r\nassert(isequal(BestCricket(x),'Jiminy Cricket'))\r\n%%\r\nx='Who is the best cricket?';\r\nassert(isequal(BestCricket(x),'Jiminy Cricket'))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":132,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-11-26T16:35:20.000Z","updated_at":"2026-07-19T16:23:27.000Z","published_at":"2013-11-26T16:35:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is how I originally read Problem 2013, so let's just go with it. Give me the first and last name of the best cricket, regardless of your input.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44688,"title":"World Cup 2018 Prediction!","description":"Which team will be the winner?\r\n","description_html":"\u003cp\u003eWhich team will be the winner?\u003c/p\u003e","function_template":"function y = Worldcup2018winner()\r\n  y = \"????\"\r\nend","test_suite":"%%\r\nteams={'Russia','Saudi Arabia', 'Egypt', 'Uruguay', 'Portugal', 'Spain','Morocco','Iran',...\r\n    'France','Australia', 'Peru','Denmark', 'Brazil', 'Switzerland', 'Costa Rica', 'Serbia', ...\r\n    'Germany', 'Mexico', 'Sweden', 'STH Korea', 'Belgium', 'Panama', 'Tunisia', 'England' , ...\r\n    'Argentina','Iceland', 'Croatia', 'Nigeria', 'Poland', 'Senegal', 'Colombia', 'Japan'};\r\nd=false;\r\nfor i=1:numel(teams)\r\n    if strcmp(Worldcup2018winner(),teams{i})\r\n        d=true;\r\n        break;\r\n    end\r\nend\r\nassert(d)","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":218677,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":144,"test_suite_updated_at":"2018-06-15T17:39:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-06-15T17:38:14.000Z","updated_at":"2026-07-19T11:31:00.000Z","published_at":"2018-06-15T17:38:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhich team will be the winner?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":56230,"title":"compter le nombre de zéros dans une matrice","description":"écrire une fonction count_zeros qui prend en entrée une matrice M et détermine le nombre de zéros dans une matrice","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eécrire une fonction count_zeros qui prend en entrée une matrice M et détermine le nombre de zéros dans une matrice\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function N = count_zeros(M)\r\n  %a vous de jouer\r\nend","test_suite":"%%\r\nx = 0;\r\ny_correct = 1;\r\nassert(isequal(count_zeros(x),y_correct))\r\n%%\r\nx = [0 0 1 1 0 0.5];\r\ny_correct = 3;\r\nassert(isequal(count_zeros(x),y_correct))\r\n%%\r\nx = [0 0 1; 1 2 0.5; 0 0 3];\r\ny_correct = 4;\r\nassert(isequal(count_zeros(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":63915,"edited_by":26769,"edited_at":"2022-11-23T21:23:15.000Z","deleted_by":null,"deleted_at":null,"solvers_count":59,"test_suite_updated_at":"2022-11-23T21:23:15.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-06T10:19:12.000Z","updated_at":"2026-06-03T00:17:04.000Z","published_at":"2022-10-06T10:19:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eécrire une fonction count_zeros qui prend en entrée une matrice M et détermine le nombre de zéros dans une matrice\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44264,"title":"Calculate feeling temperature before climbing a mountain","description":"I sometimes climb a mountain.\r\nAs is well known, when the altitude becomes 100 (m) higher, the temperature lowers by 0.6 degrees Celsius.\r\nIn addition there is wind.\r\nAt wind velocity 1(m/s), the feeling temperature falls  1 degree Celsius.\r\n\r\ne.g.\r\n\r\n* temperature of the level ground(gT) : 25 degrees Celsius\r\n* wind velocity(v) : 10 m/s\r\n* at altitude(h) : 3000 m\r\n\r\nIn this case, feeling temperature(fT) is calculated as -3 degrees Celsius.\r\n","description_html":"\u003cp\u003eI sometimes climb a mountain.\r\nAs is well known, when the altitude becomes 100 (m) higher, the temperature lowers by 0.6 degrees Celsius.\r\nIn addition there is wind.\r\nAt wind velocity 1(m/s), the feeling temperature falls  1 degree Celsius.\u003c/p\u003e\u003cp\u003ee.g.\u003c/p\u003e\u003cul\u003e\u003cli\u003etemperature of the level ground(gT) : 25 degrees Celsius\u003c/li\u003e\u003cli\u003ewind velocity(v) : 10 m/s\u003c/li\u003e\u003cli\u003eat altitude(h) : 3000 m\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eIn this case, feeling temperature(fT) is calculated as -3 degrees Celsius.\u003c/p\u003e","function_template":"function fT =  feeling_temperature(gT,h,v)\r\n  fT = gT;\r\nend","test_suite":"%%\r\ngT=25;\r\nh=3000;\r\nv=10;\r\n\r\nfT_correct = -3;\r\nassert(isequal(feeling_temperature(gT,h,v),fT_correct))\r\n\r\n%%\r\ngT=30;\r\nh=500;\r\nv=0;\r\n\r\nfT_correct=27;\r\nassert(isequal(feeling_temperature(gT,h,v),fT_correct))\r\n\r\n%%\r\ngT=28;\r\nh=2500;\r\nv=3;\r\n\r\nfT_correct=10;\r\nassert(isequal(feeling_temperature(gT,h,v),fT_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":102298,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":74,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-16T14:13:00.000Z","updated_at":"2026-05-22T11:48:16.000Z","published_at":"2017-07-16T14:28:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI sometimes climb a mountain. As is well known, when the altitude becomes 100 (m) higher, the temperature lowers by 0.6 degrees Celsius. In addition there is wind. At wind velocity 1(m/s), the feeling temperature falls 1 degree Celsius.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ee.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003etemperature of the level ground(gT) : 25 degrees Celsius\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewind velocity(v) : 10 m/s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eat altitude(h) : 3000 m\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this case, feeling temperature(fT) is calculated as -3 degrees Celsius.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":54595,"title":"String Logic 18","description":"Examples:\r\n'DIG' --\u003e 'DG'\r\n'IMPORTANT' --\u003e 'IPRAT'\r\n'DEAL' --\u003e 'DA'\r\n'LIMB' --\u003e 'LM'\r\n'MOSTLY' --\u003e 'MSL'","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 171px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 85.5px; transform-origin: 407px 85.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e'DIG' --\u0026gt; 'DG'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e'IMPORTANT' --\u0026gt; 'IPRAT'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e'DEAL' --\u0026gt; 'DA'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e'LIMB' --\u0026gt; 'LM'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e'MOSTLY' --\u0026gt; 'MSL'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = StringLogic(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 'DIG';\r\ny_correct = 'DG';\r\nassert(isequal(StringLogic(x),y_correct))\r\n\r\n%%\r\nx = 'IMPORTANT';\r\ny_correct = 'IPRAT';\r\nassert(isequal(StringLogic(x),y_correct))\r\n\r\n%%\r\nx = 'DEAL';\r\ny_correct = 'DA';\r\nassert(isequal(StringLogic(x),y_correct))\r\n\r\n%%\r\nx = 'LIMB';\r\ny_correct = 'LM';\r\nassert(isequal(StringLogic(x),y_correct))\r\n\r\n%%\r\nx = 'MOSTLY';\r\ny_correct = 'MSL';\r\nassert(isequal(StringLogic(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":232412,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":102,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-05-05T07:12:14.000Z","updated_at":"2026-07-21T08:14:41.000Z","published_at":"2022-05-05T07:12:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'DIG' --\u0026gt; 'DG'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'IMPORTANT' --\u0026gt; 'IPRAT'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'DEAL' --\u0026gt; 'DA'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'LIMB' --\u0026gt; 'LM'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'MOSTLY' --\u0026gt; 'MSL'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42678,"title":"For a given linear index as input for n sized square matrix, find corresponding row and column.","description":"If input is 1, the row and column will be 1 and 1 respectively.","description_html":"\u003cp\u003eIf input is 1, the row and column will be 1 and 1 respectively.\u003c/p\u003e","function_template":"function rc = your_fcn_name(i,n)\r\n  % i is index and n is length of matrix \r\nend","test_suite":"%%\r\ni = 1;n = 1;\r\ny_correct = [1,1];\r\nassert(isequal(your_fcn_name(i,n),y_correct))\r\n%%\r\ni = 7;n = 3;\r\ny_correct = [1,3];\r\nassert(isequal([your_fcn_name(i,n)],y_correct))\r\n%%\r\ni = 16;n = 7;\r\ny_correct = [2,3];\r\nassert(isequal([your_fcn_name(i,n)],y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":28123,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":78,"test_suite_updated_at":"2015-10-31T18:52:14.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2015-10-31T16:23:03.000Z","updated_at":"2026-05-28T14:42:21.000Z","published_at":"2015-10-31T16:38:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf input is 1, the row and column will be 1 and 1 respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45537,"title":"Get the area of ​​the square.","description":"Four circles are inscribed in the square ABCD. The perimeter of each circle is *aπ*.\r\n\r\n\u003c\u003chttp://imgfz.com/i/UzgCJut.png\u003e\u003e\r\n\r\nGiven *a*, obtain the area of ​​the square.\r\n","description_html":"\u003cp\u003eFour circles are inscribed in the square ABCD. The perimeter of each circle is \u003cb\u003eaπ\u003c/b\u003e.\u003c/p\u003e\u003cimg src = \"http://imgfz.com/i/UzgCJut.png\"\u003e\u003cp\u003eGiven \u003cb\u003ea\u003c/b\u003e, obtain the area of ​​the square.\u003c/p\u003e","function_template":"function y = squartArea(a)\r\n     y = a;\r\nend","test_suite":"%%\r\na = 0;\r\ny = 0;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 8;\r\ny = 256;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 1;\r\ny = 4;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 10;\r\ny = 400;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 50;\r\ny = 10000;\r\nassert(isequal(squartArea(a),y))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":446926,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":106,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-18T03:09:51.000Z","updated_at":"2026-07-12T15:43:27.000Z","published_at":"2020-05-18T03:09:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFour circles are inscribed in the square ABCD. The perimeter of each circle is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eaπ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, obtain the area of the square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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the n-th rand number with given seed","description":"Given seed s, return the n-th rand number using rand(). Round the answer with 4 digits.\r\nn is a postive integer.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 276px 8px; transform-origin: 276px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven seed s, return the n-th rand number using rand(). Round the answer with 4 digits.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67px 8px; transform-origin: 67px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en is a postive integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ans = getNthRand(s,n)\r\n","test_suite":"%%\r\ns = 1; n = 3;\r\ny_correct = .0001;\r\nassert(isequal(getNthRand(s,n),y_correct))\r\n%%\r\ns = 2; n = 100;\r\ny_correct = .8817;\r\nassert(isequal(getNthRand(s,n),y_correct))\r\n%%\r\ns = 1.2; n = 7;\r\ny_correct = .1863;\r\nassert(isequal(getNthRand(s,n),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":2044730,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":43,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-03-04T18:35:12.000Z","updated_at":"2026-07-18T12:53:42.000Z","published_at":"2022-03-04T18:35:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven seed s, return the n-th rand number using rand(). Round the answer with 4 digits.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en is a postive integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55915,"title":"Juros Compostos","description":"Faça uma função que receba um capital inicial (C), uma taxa de juros a ser aplicada (i) e um tempo (t) para qual será aplicado o investimento. Retorne o montante final.\r\nTodos os calculos faram baseados em meses. E o valor final deve ser expresso em 2 casas decimais.\r\n\r\nJurosCompostos(2000, 0.03, 4) = 2251.02 ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132.438px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 66.2188px; transform-origin: 407px 66.2188px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFaça uma função que receba um capital inicial (C), uma taxa de juros a ser aplicada (i) e um tempo (t) para qual será aplicado o investimento. Retorne o montante final.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTodos os calculos faram baseados em meses. E o valor final deve ser expresso em 2 casas decimais.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4375px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eJurosCompostos(2000, 0.03, 4) = 2251.02 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function m = JurosCompostos(c, i, t)\r\n  % faça a sua função\r\nend","test_suite":"%%\r\nc = 2000;\r\ni = 0.03;\r\nt = 4;\r\ny_correct = 2251.02 ;\r\nassert(isequal(JurosCompostos(c, i, t) ,y_correct))\r\n\r\n\r\n%%\r\nc = 8000;\r\ni = 0.012;\r\nt = 6;\r\ny_correct = 8593.56 ;\r\nassert(isequal(JurosCompostos(c, i, t) ,y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":2564100,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-17T19:11:27.000Z","updated_at":"2026-06-02T03:53:41.000Z","published_at":"2022-09-17T19:11:27.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFaça uma função que receba um capital inicial (C), uma taxa de juros a ser aplicada (i) e um tempo (t) para qual será aplicado o investimento. Retorne o montante final.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTodos os calculos faram baseados em meses. E o valor final deve ser expresso em 2 casas decimais.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[JurosCompostos(2000, 0.03, 4) = 2251.02 ]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1382,"title":"Schwarzschild radius","description":"Compute the Schwarzschild radius for objects of mass m (kg). Use c = 299,792.458 km/s and G = 6.6738*10^-11 N*(m/kg)^2. Your function should give the result in m.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSchwarzschild radius\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 246px 8px; transform-origin: 246px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for objects of mass m (kg). Use c = 299,792.458 km/s and G = 6.6738*10^-11 N*(m/kg)^2. Your function should give the result in m.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Schwarzschild_radius(m)\r\n  y = m;\r\nend","test_suite":"%%\r\nm = 5.98e24/81; % Moon\r\ny_correct = 1e-4; % m\r\nassert(isequal(Schwarzschild_radius(m),y_correct))\r\n\r\n%%\r\nm = 5.98e24; % Earth\r\ny_correct = 0.0089; % m\r\nassert(isequal(Schwarzschild_radius(m),y_correct))\r\n\r\n%%\r\nm = 1.89813e27; % Jupiter\r\ny_correct =  2.819; % m\r\nassert(isequal(Schwarzschild_radius(m),y_correct))\r\n\r\n%%\r\nm = 2e30; % Sun\r\ny_correct =  2970.2416; % m\r\nassert(isequal(Schwarzschild_radius(m),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":810,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":"2013-03-27T16:02:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-03-24T00:27:37.000Z","updated_at":"2026-06-25T07:37:23.000Z","published_at":"2013-03-24T00:30:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSchwarzschild radius\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for objects of mass m (kg). Use c = 299,792.458 km/s and G = 6.6738*10^-11 N*(m/kg)^2. Your function should give the result in m.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51163,"title":"Total price with tax calculation for (m) items and price (p)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 40.8889px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 20.4444px; transform-origin: 406.5px 20.4444px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 20.4444px; text-align: left; transform-origin: 383.5px 20.4444px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a code that will calculate the total price with tax (T) of (m) items that carry price (p). Consider the tax rate as (r). Round the total price to two decimal places. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = Total_price(m,n,r)\r\n\r\nend","test_suite":"%%\r\np = 1;\r\nm=2;\r\nr=0.05;\r\nT_correct = 2.1;\r\nassert(isequal(Total_price(p,m,r),T_correct))\r\n\r\n%%\r\np = 4;\r\nm=5;\r\nr=0.1;\r\nT_correct = 22;\r\nassert(isequal(Total_price(p,m,r),T_correct))\r\n\r\n%%\r\np = 4.85;\r\nm=5;\r\nr=0.1;\r\nT_correct = 26.68;\r\nassert(isequal(Total_price(p,m,r),T_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":995198,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-24T06:47:24.000Z","updated_at":"2026-06-30T14:43:15.000Z","published_at":"2021-03-24T06:47:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a code that will calculate the total price with tax (T) of (m) items that carry price (p). Consider the tax rate as (r). Round the total price to two decimal places. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56408,"title":"Zero or hero","description":"A number will be given as an input. You can be hero if it's not zero.\r\n(Just for fun)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 25.5px; transform-origin: 343px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA number will be given as an input. You can be hero if it's not zero.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(Just for fun)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 'Hero';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 0;\r\ny_correct = 'Zero';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 'Hero';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 10;\r\ny_correct = 'Hero';\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":589324,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-23T03:54:31.000Z","updated_at":"2026-07-19T16:34:37.000Z","published_at":"2022-10-23T03:54:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA number will be given as an input. You can be hero if it's not zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(Just for fun)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44473,"title":"Let's make puddings !","description":"We will make puddings with eggs, milk and sugar.\r\nTo make one pudding, we need one egg, 140(cc) of milk, 15 (g) of sugar.\r\nNow We have x eggs,  y (cc) of milk, z (g) of sugar.\r\nHow many puddings can we make?\r\n\r\neg. When we have 3 eggs, 300cc milk, 300g sugar...\r\n\r\ninput :  x = 3, y = 300, z = 300\r\n\r\noutput :  Puddings= 2","description_html":"\u003cp\u003eWe will make puddings with eggs, milk and sugar.\r\nTo make one pudding, we need one egg, 140(cc) of milk, 15 (g) of sugar.\r\nNow We have x eggs,  y (cc) of milk, z (g) of sugar.\r\nHow many puddings can we make?\u003c/p\u003e\u003cp\u003eeg. When we have 3 eggs, 300cc milk, 300g sugar...\u003c/p\u003e\u003cp\u003einput :  x = 3, y = 300, z = 300\u003c/p\u003e\u003cp\u003eoutput :  Puddings= 2\u003c/p\u003e","function_template":"function Puddings = Egg_Milk_Sugar(x,y,z)\r\n  Puddings = 100;\r\nend","test_suite":"%% 1\r\nx = 3;\r\ny = 300;\r\nz = 300;\r\nC = 2;\r\nassert(isequal(Egg_Milk_Sugar(x,y,z),C))\r\n%% 2 \r\nx = 0;\r\ny = 999;\r\nz = 999;\r\nC = 0;\r\nassert(isequal(Egg_Milk_Sugar(x,y,z),C))\r\n%% 3\r\nx = 12;\r\ny = 1000;\r\nz = 100;\r\nC = 6;\r\nassert(isequal(Egg_Milk_Sugar(x,y,z),C))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":137687,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-12-27T02:51:08.000Z","updated_at":"2026-07-09T12:41:05.000Z","published_at":"2017-12-27T03:32:17.000Z","restored_at":"2018-02-06T15:11:49.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe will make puddings with eggs, milk and sugar. To make one pudding, we need one egg, 140(cc) of milk, 15 (g) of sugar. Now We have x eggs, y (cc) of milk, z (g) of sugar. How many puddings can we make?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eeg. When we have 3 eggs, 300cc milk, 300g sugar...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einput : x = 3, y = 300, z = 300\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutput : Puddings= 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42976,"title":"iteration of N blank spot","description":"we have N spot which can be blank o filled calculate the number of iteration for these spots. e.g. N=2 1- blank blank 2- blank full 3- full blank 4- full full iteration is 4 e.g. N=3 1- blank blank blank 2- blank blank full 3- blank full blank 4- blank full full 5- full blank blank 6- full blank full 7- full full blank 8- full full full iteration is 8","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 372.5px 8px; transform-origin: 372.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewe have N spot which can be blank o filled calculate the number of iteration for these spots. e.g. N=2 1- blank blank 2- blank full 3- full blank 4- full full iteration is 4 e.g. N=3 1- blank blank blank 2- blank blank full 3- blank full blank 4- blank full full 5- full blank blank 6- full blank full 7- full full blank 8- full full full iteration is 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 2;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 32;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 256;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 11;\r\ny_correct = 2048;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 16;\r\ny_correct = 65536;\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":86389,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":61,"test_suite_updated_at":"2021-06-17T14:24:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-09-02T16:46:32.000Z","updated_at":"2026-04-22T05:15:27.000Z","published_at":"2016-09-02T16:46:32.000Z","restored_at":"2022-02-16T22:15:33.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewe have N spot which can be blank o filled calculate the number of iteration for these spots. e.g. N=2 1- blank blank 2- blank full 3- full blank 4- full full iteration is 4 e.g. N=3 1- blank blank blank 2- blank blank full 3- blank full blank 4- blank full full 5- full blank blank 6- full blank full 7- full full blank 8- full full full iteration is 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55935,"title":"Loja de tintas","description":"Faça um programa para uma loja de tintas. O programa deverá receber o tamanho em metros quadrados da área a ser pintada. Considere que a cobertura da tinta é de 1 litro para cada 3 metros quadrados e que a tinta é vendida em latas de 18 litros, que custam R$ 80,00. Informe ao usuário a quantidades de latas de tinta a serem compradas e o preço total.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFaça um programa para uma loja de tintas. O programa deverá receber o tamanho em metros quadrados da área a ser pintada. Considere que a cobertura da tinta é de 1 litro para cada 3 metros quadrados e que a tinta é vendida em latas de 18 litros, que custam R$ 80,00. Informe ao usuário a quantidades de latas de tinta a serem compradas e o preço total.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = QuantidadeTinta(m)\r\n  % Escreva a sua solução\r\nend","test_suite":"%%\r\nx = 9;\r\ny_correct = 3;\r\nassert(isequal(QuantidadeTinta(x),y_correct));\r\n\r\n%%\r\nx = 10;\r\ny_correct = 4;\r\nassert(isequal(QuantidadeTinta(x),y_correct));\r\n\r\n%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(QuantidadeTinta(x),y_correct));","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":2564100,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-17T20:20:44.000Z","updated_at":"2026-06-02T13:22:12.000Z","published_at":"2022-09-17T20:20:44.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFaça um programa para uma loja de tintas. O programa deverá receber o tamanho em metros quadrados da área a ser pintada. Considere que a cobertura da tinta é de 1 litro para cada 3 metros quadrados e que a tinta é vendida em latas de 18 litros, que custam R$ 80,00. Informe ao usuário a quantidades de latas de tinta a serem compradas e o preço total.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51630,"title":"Highest building","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 377.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 334px 188.7px; transform-origin: 334px 188.7px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 311px 10.4px; text-align: left; transform-origin: 311px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSketch of the outline of the buildings in a matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 311px 20.8px; text-align: left; transform-origin: 311px 20.8px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe column number of the highest building and height of it. In two or more building are the  highest, you need to choose the first one.  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 311px 10.4px; text-align: left; transform-origin: 311px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 311px 10.4px; text-align: left; transform-origin: 311px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eLet us consider buildings described by the matrix\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 80px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 331px 40px; transform-origin: 331px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 331px 10px; transform-origin: 331px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eM=[0 0 1 0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 331px 10px; transform-origin: 331px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   1 0 1 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 331px 10px; transform-origin: 331px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   1 1 1 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 331px 10px; transform-origin: 331px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   1 1 1 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cul style=\"block-size: 83.2px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 318px 41.6px; transform-origin: 318px 41.6px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.8px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 290px 10.4px; text-align: left; transform-origin: 290px 10.4px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eThe height of the first building (1st column) is 3, \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.8px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 290px 10.4px; text-align: left; transform-origin: 290px 10.4px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ethe height of the second building (2nd column) is 2,\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.8px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 290px 10.4px; text-align: left; transform-origin: 290px 10.4px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ethe height of the third building is 4,\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.8px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 290px 10.4px; text-align: left; transform-origin: 290px 10.4px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ethe height of the last building is 3.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 43.2px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 311px 21.6px; text-align: left; transform-origin: 311px 21.6px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eThe correct answer to highest_building(M) is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e3\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e4\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e] (t\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ehe\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e building n°3 is the highest with height = 4).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = highest_building(M)\r\n\r\nend","test_suite":"%%\r\nM=[0 0 1 0;\r\n   1 0 1 1;\r\n   1 1 1 1;\r\n   1 1 1 1];\r\ny_correct = [3,4];\r\nsol=highest_building(M)\r\nassert(isequal(sol,y_correct))\r\n%%\r\nM=[0 0 0 0;\r\n   0 0 0 0;\r\n   0 0 0 0;\r\n   0 0 0 1];\r\ny_correct = [4,1];\r\nsol=highest_building(M)\r\nassert(isequal(sol,y_correct))\r\n%%\r\nM=[1 0 0 0 0;\r\n   1 1 0 0 0;\r\n   1 1 1 1 0;\r\n   1 1 1 1 1];\r\ny_correct = [1,4];\r\nsol=highest_building(M)\r\nassert(isequal(sol,y_correct))\r\n%%\r\nM=[0 0 0 0 0 0 0;\r\n   0 0 1 1 0 0 0;\r\n   1 1 1 1 1 1 0;\r\n   1 1 1 1 1 1 1];\r\ny_correct = [3,3];\r\nsol=highest_building(M)\r\nassert(isequal(sol,y_correct))\r\n%%\r\nM=zeros(randi([10,15]),randi([10,15]));\r\ny_correct = [0,0];\r\nfor j=1:size(M,2)\r\n    v=ones(randi([1,size(M,1)]),1);\r\n    M(1:numel(v),j)=v;\r\n    if sum(v)\u003ey_correct(2)\r\n        y_correct = [j,sum(v)];\r\n    end\r\nend\r\nM=M(end:-1:1,:);\r\nsol=highest_building(M);\r\nassert(isequal(sol,y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-01T14:35:42.000Z","updated_at":"2026-06-05T09:28:16.000Z","published_at":"2021-05-01T15:11:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eSketch of the outline of the buildings in a matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe column number of the highest building and height of it. In two or more building are the  highest, you need to choose the first one.  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet us consider buildings described by the matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[M=[0 0 1 0;\\n   1 0 1 1;\\n   1 1 1 1;\\n   1 1 1 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe height of the first building (1st column) is 3, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe height of the second building (2nd column) is 2,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe height of the third building is 4,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe height of the last building is 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe correct answer to highest_building(M) is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e] (t\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ehe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e building n°3 is the highest with height = 4).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":49657,"title":"Determine the area of square if length of the diagonal is given","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe have to find the area of square if the length of the diagonal of a square is given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 4;\r\ny_correct = 8;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":822117,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":76,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-29T15:05:52.000Z","updated_at":"2026-07-17T11:17:58.000Z","published_at":"2020-12-29T15:05:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe have to find the area of square if the length of the diagonal of a square is given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55160,"title":"Find distance travelled by an object starting from rest in time 't' and linear acceleration 'a' = 3t","description":"Find distance travelled by an object starting from rest in time 't' with linear acceleration a = 3t. You are given time t as an input to the function.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind distance travelled by an object starting from rest in time 't' with linear acceleration a = 3t. You are given time t as an input to the function.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = your_fcn_name(t)\r\n  s = a;\r\nend","test_suite":"%%\r\nt = 2;\r\ny_correct = 4;\r\nassert(isequal(your_fcn_name(t),y_correct))\r\n\r\n%%\r\nt = 0;\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(t),y_correct))\r\n\r\n%%\r\nt = 1;\r\ny_correct = 0.5;\r\nassert(isequal(your_fcn_name(t),y_correct))\r\n\r\n%%\r\nt = 12;\r\ny_correct = 864;\r\nassert(isequal(your_fcn_name(t),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":2439180,"edited_by":2439180,"edited_at":"2022-07-13T19:07:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-13T19:07:08.000Z","updated_at":"2026-07-20T16:58:04.000Z","published_at":"2022-07-13T19:07:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind distance travelled by an object starting from rest in time 't' with linear acceleration a = 3t. You are given time t as an input to the function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44634,"title":"Basic matrix operations using standard MATLAB commands","description":"Create the matrix:\r\n\r\n 1.0e+15 *\r\n\r\n    0.0000    0.0000    0.0000    0.0000    0.0000\r\n    0.0000    0.0000    0.0000    0.0000    0.0000\r\n    0.0001    0.0010    0.0100    0.1000    1.0000\r\n\r\nFind the row vector of all column means\r\n\r\nHint: Use _logspace_ to create the matrix. Avoid looking at the test suite before writing a solution","description_html":"\u003cp\u003eCreate the matrix:\u003c/p\u003e\u003cpre\u003e 1.0e+15 *\u003c/pre\u003e\u003cpre\u003e    0.0000    0.0000    0.0000    0.0000    0.0000\r\n    0.0000    0.0000    0.0000    0.0000    0.0000\r\n    0.0001    0.0010    0.0100    0.1000    1.0000\u003c/pre\u003e\u003cp\u003eFind the row vector of all column means\u003c/p\u003e\u003cp\u003eHint: Use \u003ci\u003elogspace\u003c/i\u003e to create the matrix. Avoid looking at the test suite before writing a solution\u003c/p\u003e","function_template":"function y = matrix_ls_means()\r\n  y = x;\r\nend","test_suite":"%%\r\ny_correct = mean([logspace(1,5,5);logspace(6,10,5);logspace(11,15,5)]);\r\nassert(isequal(matrix_ls_means(),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":171559,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":"2018-05-09T05:37:01.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-05-09T05:32:41.000Z","updated_at":"2026-07-14T15:34:29.000Z","published_at":"2018-05-09T05:35:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate the matrix:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 1.0e+15 *\\n\\n    0.0000    0.0000    0.0000    0.0000    0.0000\\n    0.0000    0.0000    0.0000    0.0000    0.0000\\n    0.0001    0.0010    0.0100    0.1000    1.0000]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the row vector of all column means\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Use\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elogspace\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to create the matrix. Avoid looking at the test suite before writing a solution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47493,"title":"reverse the order and combine a matrix","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ea cool way to shape a Matrix \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)  \r\ny=x;\r\nend","test_suite":"%%\r\nx = 1:6\r\ny_correct = [6,5,4,3,2,1; 1,2,3,4,5,6]';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":541988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":70,"test_suite_updated_at":"2020-11-13T19:51:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-13T02:37:10.000Z","updated_at":"2026-07-19T16:35:55.000Z","published_at":"2020-11-13T19:51:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea cool way to shape a Matrix \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54094,"title":"Check if a matrix Diagonal is equal to its secondary diagonal ","description":"Your function should return True if the secondary diagonal is equal to diagonal, and False otherwise.\r\nEg: M = [1 2 1 \r\n               3 4 4\r\n               7 5 7]\r\nThe output is True\r\nM=[1 2\r\n       1 2]\r\nThe output is False. Always check the diagonal top to bottom. Return True if the matrix is empty.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 231px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 115.5px; transform-origin: 407px 115.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYour function should return True if the secondary diagonal is equal to diagonal, and False otherwise.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEg: M = [1 2 1 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e               3 4 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e               7 5 7]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe output is True\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eM=[1 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e       1 2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe output is False. Always check the diagonal top to bottom. Return True if the matrix is empty.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = check_Diagonals(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [1 2 1; 3 4 4 ; 7 5 7];\r\ny_correct = 1;\r\nassert(isequal(check_Diagonals(x),y_correct))\r\n\r\n%%\r\nx = [1 2 ; 1 2];\r\ny_correct = 0;\r\nassert(isequal(check_Diagonals(x),y_correct))\r\n\r\n%%\r\nx = [1 2 ; 1 2];\r\ny_correct = 0;\r\nassert(isequal(check_Diagonals(x),y_correct))\r\n\r\n%%\r\nx = [7];\r\ny_correct = 1;\r\nassert(isequal(check_Diagonals(x),y_correct))\r\n\r\n%%\r\nx = [];\r\ny_correct = 1;\r\nassert(isequal(check_Diagonals(x),y_correct))\r\n\r\n%%\r\nx = [17 21 13 4 17; -4 21 -1 21 56 ; 4 99 26 156 -352; 43 5 0 5 6; 9 1 49 101 9];\r\ny_correct=1;\r\nassert(isequal(check_Diagonals(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":1985630,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":40,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-03-04T17:27:28.000Z","updated_at":"2026-06-01T01:20:53.000Z","published_at":"2022-03-04T17:27:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function should return True if the secondary diagonal is equal to diagonal, and False otherwise.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEg: M = [1 2 1 \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e               3 4 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e               7 5 7]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe output is True\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eM=[1 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e       1 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe output is False. Always check the diagonal top to bottom. Return True if the matrix is empty.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55195,"title":"Sequence","description":"Let S be a sequence of numbers \r\n\r\nLet \r\n\r\nFind  for some , where  and .\r\n\r\nUpdate - test suite cleaned up on 2-9-22","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 204px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 102px; transform-origin: 407px 102px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105px 8px; transform-origin: 105px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet S be a sequence of numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 52px; height: 20px;\" width=\"52\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 102px; height: 20px;\" width=\"102\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 15px; height: 20px;\" width=\"15\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.5px 8px; transform-origin: 31.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for some \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25px 8px; transform-origin: 25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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0px; margin-top: 0px; perspective-origin: 127.5px 8px; transform-origin: 127.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUpdate - test suite cleaned up on 2-9-22\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = summation(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nassert(isequal(summation(1),1))\r\n%%\r\nassert(isequal(summation(2),2))\r\n%%\r\nassert(isequal(summation(3),1))\r\n%%\r\nassert(isequal(summation(4),-1))\r\n%%\r\nassert(isequal(summation(5),-2))\r\n%%\r\nassert(isequal(summation(6),-1))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":2457030,"edited_by":223089,"edited_at":"2022-09-02T13:52:45.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":"2022-09-02T13:49:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-13T21:23:39.000Z","updated_at":"2026-06-02T00:29:40.000Z","published_at":"2022-07-13T21:23:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" 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radius represents the radius of the circular path followed by a vehicle.\r\nGiven Wheelbase L and Steering angle δ, Compute the turning radius R.\r\nEquation:\r\nR = L / tan(delta)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe turning radius represents the radius of the circular path followed by a vehicle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Wheelbase \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eL and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSteering angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eδ, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the turning radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eR = L / tan(delta)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function R = turningRadius(L,delta)\r\nR = 0;\r\nend","test_suite":"%%\r\nL = 2.5; delta = 30*pi/180;\r\nR_expected = 4.3301;\r\nassert(abs(turningRadius(L,delta) - R_expected) \u003c 1e-3)\r\n\r\n%%\r\nL = 3.0; delta = 20*pi/180;\r\nR_expected = 8.2426;\r\nassert(abs(turningRadius(L,delta) - R_expected) \u003c 1e-3)\r\n\r\n%%\r\nL = 2.8; delta = 10*pi/180;\r\nR_expected = 15.866;\r\nassert(abs(turningRadius(L,delta) - R_expected) \u003c 1e-1)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:16:45.000Z","deleted_by":null,"deleted_at":null,"solvers_count":47,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:13:54.000Z","updated_at":"2026-07-01T17:26:00.000Z","published_at":"2026-04-28T09:16:45.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe turning radius represents the radius of the circular path followed by a vehicle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Wheelbase \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eSteering angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eδ, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the turning radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = L / tan(delta)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2121,"title":"Find offset of given matrix element from first matrix element","description":"Given matrix m and an element of that matrix, return the offset from its first element.\r\ne.g. m=[11 2 34; 40 51 6; 87 8 109]\r\nelement = 51\r\nThen, offset = 5\r\n\r\nReturn 0, if that element if not a matrix element","description_html":"\u003cp\u003eGiven matrix m and an element of that matrix, return the offset from its first element.\r\ne.g. m=[11 2 34; 40 51 6; 87 8 109]\r\nelement = 51\r\nThen, offset = 5\u003c/p\u003e\u003cp\u003eReturn 0, if that element if not a matrix element\u003c/p\u003e","function_template":"function offset= FindOffset(m, element)\r\n  y = x;\r\nend","test_suite":"%%\r\nm=[11 2 34; 40 51 6; 87 8 109]\r\nelement = 51;\r\noffset = 5;\r\nassert(isequal(FindOffset(m,element),offset));\r\n\r\n%%\r\nm=reshape([1:10],5,2);\r\nelement = 9;\r\noffset = 9;\r\nassert(isequal(FindOffset(m,element),offset));\r\n\r\n%%\r\nm=eye(7);\r\nelement = 0;\r\noffset = 2;\r\nassert(isequal(FindOffset(m,element),offset));\r\n\r\n%%\r\nm=[10 20 30 40; 50 60 70 80;];\r\nelement = 56;\r\noffset = 0;\r\nassert(isequal(FindOffset(m,element),offset));\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":16381,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":85,"test_suite_updated_at":"2014-01-15T19:28:24.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-01-15T19:21:32.000Z","updated_at":"2026-02-28T08:07:23.000Z","published_at":"2014-01-15T19:21:46.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven matrix m and an element of that matrix, return the offset from its first element. e.g. m=[11 2 34; 40 51 6; 87 8 109] element = 51 Then, offset = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn 0, if that element if not a matrix element\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47380,"title":"Intercambiar columnas - UC3M","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 220.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 110.2px; transform-origin: 407px 110.2px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 41.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.8px; text-align: left; transform-origin: 384px 20.8px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ex es una matriz cuadrada nxn. Necesitamos intercambiar los valores de la primera columna por los de la última, las demás se quedan igual.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePor ejemplo, si\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ex=[ 1 2 3 4;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e      5 6 7 8]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003equeremos conseguir \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ey=[ 4 2 3 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e      8 6 7 5]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function x = intercambiarCols(x)\r\n% La nueva matriz tambien se guarda en la variable x\r\n\r\nend","test_suite":"%%\r\nx = [1 2 3;4 5 6];\r\ny_correct = [3 2 1;6 5 4];\r\nassert(isequal(intercambiarCols(x),y_correct))\r\n%%\r\nx = [1 2 3 4;5 6 7 8];\r\ny_correct = [4 2 3 1;8 6 7 5];\r\nassert(isequal(intercambiarCols(x),y_correct))\r\n%%\r\nx = [1 2 3 4 5; 6 7 8 9 10];\r\ny_correct = [5 2 3 4 1;10 7 8 9 6];\r\nassert(isequal(intercambiarCols(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":583531,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T14:40:40.000Z","updated_at":"2026-05-30T19:12:31.000Z","published_at":"2020-11-06T14:40:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex es una matriz cuadrada nxn. Necesitamos intercambiar los valores de la primera columna por los de la última, las demás se quedan igual.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePor ejemplo, si\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=[ 1 2 3 4;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e      5 6 7 8]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003equeremos conseguir \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ey=[ 4 2 3 1;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e      8 6 7 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"problems":[{"id":42685,"title":"Cody meets Xiangqi: foresee the unseen (Part 2)","description":"This is the second part of the Xiangqi series. The first part in this series is: \u003chttp://www.mathworks.com/matlabcentral/cody/problems/42674-cody-meets-xiangqi-foresee-the-unseen Cody meets Xiangqi: foresee the unseen (Part 1)\u003e\r\n\r\nBeing increasingly interested in \u003chttps://en.wikipedia.org/wiki/Xiangqi Xiangqi\u003e (a.k.a., *Chinese Chess*), Mr. Cody has designed a new Xiangqi match for \u003chttps://en.wikipedia.org/wiki/Xiang_Yu Xiang Yu\u003e and \u003chttps://de.wikipedia.org/wiki/Han_Gaozu Liu Bang\u003e by taking into account the likelihood of tie games. The new rule is described as follows:\r\n\r\nOnce\r\n\r\n   1) Xiang Yu wins Na games consecutively,\r\n   2) Liu Bang wins Nb games consecutively, \r\n   3) No ties occur consecutively, \r\n\r\n*whichever comes first*, Mr. Cody announces the outcome accordingly as follows:\r\n\r\n   1) Xiang Yu is the final winner,\r\n   2) Liu Bang is the final winner, \r\n   3) They end up with a final draw.\r\n\r\nAgain, Cody asks us --- active Cody players --- to foresee the outcome of this unseen match using Monte Carlo simulations. Our task is to write the following function\r\n\r\n                         [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)\r\n\r\nwhere \r\n\r\n* a: the probability that Xiang Yu wins one individual game\r\n* b: the probability that Liu Bang wins one individual game\r\n* Na: # of consecutive wins required for Xiang Yu to become the final winner\r\n* Nb: # of consecutive wins required for Liu Bang to become the final winner\r\n* Nc: # of consecutive ties required to result in a final draw\r\n* Pa: the probability that Xiang Yu wins the match\r\n* Pb: the probability that Liu Bang wins the match\r\n* Pc: the probability of a final draw\r\n\r\nThe main focus of this problem is on *Monte Carlo simulations*, rather than analytical approaches. Your provided solution Xiangqi2.m will be checked by a P-file EvaluateSolution.p, which mainly does 3 things as follows:\r\n\r\n1) Call your function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc) and then Check if the result P = [Pa, Pb, Pc] is within tolerance of its expected value Q. That is, If norm(P - Q) \u003c tol holds, it means that your solution is accurate enough. If this does not hold, your solution will be rejected. \r\n\r\n2) Check if your solution is based on *pure Monte Carlo simulations* or *analytical approaches*. If it is based on analytical approaches (i.e., using analytical expressions to directly compute the probabilities), then your solution will be rejected. EvaluateSolution.p accomplishes this goal by exploiting a combination of distinct features possessed by analytical solutions, but are generally not shared by Monte Carlo simulations. \r\n\r\n3) If your solution passes the above two checks, then the score of your solution will be determined based on the speed of your code. The faster your solution is, the smaller score you get. \r\n\r\nIf you have any concerns or suggestions on this problem, please feel free to leave me a comment. Thanks. \r\n\r\n ","description_html":"\u003cp\u003eThis is the second part of the Xiangqi series. The first part in this series is: \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/42674-cody-meets-xiangqi-foresee-the-unseen\"\u003eCody meets Xiangqi: foresee the unseen (Part 1)\u003c/a\u003e\u003c/p\u003e\u003cp\u003eBeing increasingly interested in \u003ca href = \"https://en.wikipedia.org/wiki/Xiangqi\"\u003eXiangqi\u003c/a\u003e (a.k.a., \u003cb\u003eChinese Chess\u003c/b\u003e), Mr. Cody has designed a new Xiangqi match for \u003ca href = \"https://en.wikipedia.org/wiki/Xiang_Yu\"\u003eXiang Yu\u003c/a\u003e and \u003ca href = \"https://de.wikipedia.org/wiki/Han_Gaozu\"\u003eLiu Bang\u003c/a\u003e by taking into account the likelihood of tie games. The new rule is described as follows:\u003c/p\u003e\u003cp\u003eOnce\u003c/p\u003e\u003cpre\u003e   1) Xiang Yu wins Na games consecutively,\r\n   2) Liu Bang wins Nb games consecutively, \r\n   3) No ties occur consecutively, \u003c/pre\u003e\u003cp\u003e\u003cb\u003ewhichever comes first\u003c/b\u003e, Mr. Cody announces the outcome accordingly as follows:\u003c/p\u003e\u003cpre\u003e   1) Xiang Yu is the final winner,\r\n   2) Liu Bang is the final winner, \r\n   3) They end up with a final draw.\u003c/pre\u003e\u003cp\u003eAgain, Cody asks us --- active Cody players --- to foresee the outcome of this unseen match using Monte Carlo simulations. Our task is to write the following function\u003c/p\u003e\u003cpre\u003e                         [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)\u003c/pre\u003e\u003cp\u003ewhere\u003c/p\u003e\u003cul\u003e\u003cli\u003ea: the probability that Xiang Yu wins one individual game\u003c/li\u003e\u003cli\u003eb: the probability that Liu Bang wins one individual game\u003c/li\u003e\u003cli\u003eNa: # of consecutive wins required for Xiang Yu to become the final winner\u003c/li\u003e\u003cli\u003eNb: # of consecutive wins required for Liu Bang to become the final winner\u003c/li\u003e\u003cli\u003eNc: # of consecutive ties required to result in a final draw\u003c/li\u003e\u003cli\u003ePa: the probability that Xiang Yu wins the match\u003c/li\u003e\u003cli\u003ePb: the probability that Liu Bang wins the match\u003c/li\u003e\u003cli\u003ePc: the probability of a final draw\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe main focus of this problem is on \u003cb\u003eMonte Carlo simulations\u003c/b\u003e, rather than analytical approaches. Your provided solution Xiangqi2.m will be checked by a P-file EvaluateSolution.p, which mainly does 3 things as follows:\u003c/p\u003e\u003cp\u003e1) Call your function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc) and then Check if the result P = [Pa, Pb, Pc] is within tolerance of its expected value Q. That is, If norm(P - Q) \u0026lt; tol holds, it means that your solution is accurate enough. If this does not hold, your solution will be rejected.\u003c/p\u003e\u003cp\u003e2) Check if your solution is based on \u003cb\u003epure Monte Carlo simulations\u003c/b\u003e or \u003cb\u003eanalytical approaches\u003c/b\u003e. If it is based on analytical approaches (i.e., using analytical expressions to directly compute the probabilities), then your solution will be rejected. EvaluateSolution.p accomplishes this goal by exploiting a combination of distinct features possessed by analytical solutions, but are generally not shared by Monte Carlo simulations.\u003c/p\u003e\u003cp\u003e3) If your solution passes the above two checks, then the score of your solution will be determined based on the speed of your code. The faster your solution is, the smaller score you get.\u003c/p\u003e\u003cp\u003eIf you have any concerns or suggestions on this problem, please feel free to leave me a comment. Thanks.\u003c/p\u003e","function_template":"function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)\r\n% a: the probability that Xiang Yu wins one individual game\r\n% b: the probability that Liu Bang wins one individual game\r\n% Na: # of consecutive wins required for Xiang Yu to become the final winner\r\n% Nb: # of consecutive wins required for Liu Bang to become the final winner\r\n% Nc: # of consecutive ties required to result in a final draw\r\n% Pa: the probability that Xiang Yu wins the match\r\n% Pb: the probability that Liu Bang wins the match\r\n% Pc: the probability of a final draw\r\n    Pa = ;\r\n    Pb = ;\r\n    Pc = ;\r\nend","test_suite":"%%\r\n% Thanks to Alfonso Nieto-Castanon\r\nurlwrite('https://sites.google.com/a/alfnie.com/alfnie/software/SetSolutionScore.p?attredirects=0\u0026amp;d=1','SetSolutionScore.p');\r\nrehash path;\r\n\r\n%%\r\nfh = fopen('EvaluateSolution.p','wb');\r\nfwrite(fh, hex2dec(reshape('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',2,[]).')); rehash path; fclose(fh);\r\n\r\n%%\r\nfid = fopen('Xiangqi2.m');\r\ndelim = {' ', '\\n', ',', '.', ';', '''', '@', '+', '-', '*', '/', '\\', '^', '\u003e', '\u003c', '=', '\u0026', '|', '~', '{', '}', '[', ']', '(', ')'};\r\nfile = textscan(fid, '%s', 'CommentStyle', '%', 'MultipleDelimsAsOne', 1, 'Delimiter', delim); fclose(fid); \r\nassert(~any(ismember({'rng','RandStream','seed','state','twister','shufle','default'},file{1})));\r\n\r\n%%\r\na = 0; b = 0; Na = 2; Nb = 3; Nc = 2; tol = 1e-6;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol); \r\n\r\n%%\r\na = 0; b = 1; Na = 1; Nb = 2; Nc = 1; tol = 1e-6;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol); \r\n\r\n%%\r\na = 1; b = 0; Na = 3; Nb = 2; Nc = 1; tol = 1e-6;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol); \r\n\r\n%%\r\na = 0.15; b = 0.85; Na = 4; Nb = 2; Nc = 1; tol = 1e-4;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol);\r\n\r\n%%\r\na = 0.9; b = 0; Na = 3; Nb = 1; Nc = 2; tol = 1e-3;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol);\r\n\r\n%%\r\na = 0.65; b = 0.3; Na = 3; Nb = 2; Nc = 2; tol = 1e-3;\r\nEvaluateSolution(a, b, Na, Nb, Nc, tol);\r\n\r\n%%\r\nNa = 3; Nb = 2; Nc = 1; tol = 2e-3; \r\np = sort(rand(2,30)); \r\np = sort([p(1,:);diff(p);1-p(2,:)]);\r\nfor k = size(p,2):-1:1\r\n    a = p(3,k); b = p(2,k);\r\n    score(k) = EvaluateSolution(a, b, Na, Nb, Nc, tol);    \r\nend\r\nSetSolutionScore(round(mean(score)));","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2015-11-12T00:41:35.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2015-11-08T20:51:55.000Z","updated_at":"2026-07-16T14:32:19.000Z","published_at":"2015-11-10T00:22:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the second part of the Xiangqi series. The first part in this series is:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/42674-cody-meets-xiangqi-foresee-the-unseen\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody meets Xiangqi: foresee the unseen (Part 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBeing increasingly interested in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Xiangqi\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eXiangqi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (a.k.a.,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eChinese Chess\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e), Mr. Cody has designed a new Xiangqi match for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Xiang_Yu\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eXiang Yu\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://de.wikipedia.org/wiki/Han_Gaozu\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLiu Bang\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e by taking into account the likelihood of tie games. The new rule is described as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOnce\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   1) Xiang Yu wins Na games consecutively,\\n   2) Liu Bang wins Nb games consecutively, \\n   3) No ties occur consecutively,]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewhichever comes first\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, Mr. Cody announces the outcome accordingly as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   1) Xiang Yu is the final winner,\\n   2) Liu Bang is the final winner, \\n   3) They end up with a final draw.]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAgain, Cody asks us --- active Cody players --- to foresee the outcome of this unseen match using Monte Carlo simulations. Our task is to write the following function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[                         [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea: the probability that Xiang Yu wins one individual game\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb: the probability that Liu Bang wins one individual game\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNa: # of consecutive wins required for Xiang Yu to become the final winner\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNb: # of consecutive wins required for Liu Bang to become the final winner\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNc: # of consecutive ties required to result in a final draw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePa: the probability that Xiang Yu wins the match\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePb: the probability that Liu Bang wins the match\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePc: the probability of a final draw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe main focus of this problem is on\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMonte Carlo simulations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, rather than analytical approaches. Your provided solution Xiangqi2.m will be checked by a P-file EvaluateSolution.p, which mainly does 3 things as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1) Call your function [Pa, Pb, Pc] = Xiangqi2(a, b, Na, Nb, Nc) and then Check if the result P = [Pa, Pb, Pc] is within tolerance of its expected value Q. That is, If norm(P - Q) \u0026lt; tol holds, it means that your solution is accurate enough. If this does not hold, your solution will be rejected.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) Check if your solution is based on\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epure Monte Carlo simulations\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eanalytical approaches\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. If it is based on analytical approaches (i.e., using analytical expressions to directly compute the probabilities), then your solution will be rejected. EvaluateSolution.p accomplishes this goal by exploiting a combination of distinct features possessed by analytical solutions, but are generally not shared by Monte Carlo simulations.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3) If your solution passes the above two checks, then the score of your solution will be determined based on the speed of your code. The faster your solution is, the smaller score you get.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you have any concerns or suggestions on this problem, please feel free to leave me a comment. Thanks.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61358,"title":"Basic Physics IV","description":"Calculate the Mechanical Energy (ME).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eCalculate the Mechanical Energy (ME).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ME = ME(PE,KE)\r\n  ME = ;\r\nend","test_suite":"%%\r\nPE = 1;\r\nKE = 1;\r\nME = PE+KE;\r\nassert(isequal(ME(PE,KE),ME))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-26T14:58:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2026-05-26T14:58:18.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-26T14:56:53.000Z","updated_at":"2026-07-20T16:53:37.000Z","published_at":"2026-05-26T14:56:53.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCalculate the Mechanical Energy (ME).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61350,"title":"Circle Perimeter","description":"Get the perimeter of the Circle by PI.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGet the perimeter of the Circle by PI.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = circleP(r)\r\n  p = ;\r\nend","test_suite":"%%\r\nr = 1;\r\np = 2*pi*r;\r\nassert(isequal(circleP(r),p))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-24T11:52:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2026-05-24T11:52:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-24T11:50:23.000Z","updated_at":"2026-07-21T16:19:33.000Z","published_at":"2026-05-24T11:52:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGet the perimeter of the Circle by PI.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61362,"title":"Calculate the h-index (revisited)","description":"H-index is a powerful tool for quantifying the scientific contribution of a researcher. The \r\nH-index is defined as follows (from source - wikipedia):\r\n\"a scholar with an index of h has published h papers each of which has been cited in other papers at least h times\".\r\nIn this problem, citations of published works of an author will be provided as a vector. Each element of the vector denotes the number of citations of a specific paper of the author. Calculate the h-index.\r\nExample:\r\nInput = [4 4 4 4]; Output = 4\r\nCalculate the h-index score \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(33, 33, 33); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 315px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 243.5px 157.5px; transform-origin: 243.5px 157.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 21px; text-align: left; transform-origin: 219.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eH-index is a powerful tool for quantifying the scientific contribution of a researcher. The \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eH-index is defined as follows (from source - wikipedia):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 21px; text-align: left; transform-origin: 219.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"a scholar with an index of h has published h papers each of which has been cited in other papers at least h times\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 31.5px; text-align: left; transform-origin: 219.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem, citations of published works of an author will be provided as a vector. Each element of the vector denotes the number of citations of a specific paper of the author. Calculate the h-index.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInput = [4 4 4 4]; Output = 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the h-index score \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [3 3 2 1];\r\ny_correct = 2;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = [5 2 10 11 2 7 9 10 7];\r\ny_correct = 6;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 4*ones(1,4);\r\ny_correct = 4;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = zeros(1,1000);\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = [3 2 0 0 1];\r\ny_correct = 2;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":584788,"edited_by":584788,"edited_at":"2026-05-27T22:40:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2026-05-27T22:40:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-27T18:21:09.000Z","updated_at":"2026-07-11T19:45:24.000Z","published_at":"2026-05-27T18:21:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eH-index is a powerful tool for quantifying the scientific contribution of a researcher. The \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eH-index is defined as follows (from source - wikipedia):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"a scholar with an index of h has published h papers each of which has been cited in other papers at least h times\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, citations of published works of an author will be provided as a vector. Each element of the vector denotes the number of citations of a specific paper of the author. Calculate the h-index.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput = [4 4 4 4]; Output = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the h-index score \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61384,"title":"varargin","description":"Write a function that can take a diffrent Amount of inputs for every run Which gives you the sum of all Inputs.\r\nExample:\r\nf(a,b) = a+b,    f(1,...,n) = 1+...+n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401.5px 55.5px; transform-origin: 401.5px 55.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that can take a diffrent Amount of inputs for every run Which gives you the sum of all Inputs.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ef(a,b) = a+b,    f(1,...,n) = 1+...+n\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.5px 10.5px; text-align: left; transform-origin: 377.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = summ(va )\r\ny = ;\r\nend","test_suite":"%%\r\ny_correct = 6;\r\nassert(isequal(summ(1,2,3),y_correct))\r\n%%\r\ny_correct = sum(1:200:10^10);\r\nassert(isequal(summ(1:200:10^10),y_correct))\r\n%%\r\ny_correct = sum(-5:3.2:200);\r\nassert(isequal(summ(-5:3.2:200),y_correct))\r\n%%\r\nfor k = 1:100\r\n    x = num2cell(randi(100,1,randi(10)));\r\n\r\n    erwartet = sum([x{:}]);\r\n    erhalten = summ(x{:});\r\n\r\n    assert(isequal(erhalten, erwartet))\r\nend\r\n%%\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5124132,"edited_by":5124132,"edited_at":"2026-06-01T17:04:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2026-06-01T17:04:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-01T16:52:16.000Z","updated_at":"2026-07-14T15:55:12.000Z","published_at":"2026-06-01T17:04:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that can take a diffrent Amount of inputs for every run Which gives you the sum of all Inputs.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(a,b) = a+b,    f(1,...,n) = 1+...+n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61342,"title":"Swept Volume and Clearance Volume","description":"The swept volume (V_s) is the volume displaced by the piston as it travels from BDC (Bottom Dead Centre) to TDC (Top Dead Centre). \r\nThe clearance volume (V_c) is the remaining volume above the piston at TDC .It cannot be swept and defines the compression limit.\r\n\r\nGiven total cylinder volume at BDC V_BDC (m³) and clearance volume at TDC V_TDC (m³), compute the swept volume V_s and confirm it matches the bore-stroke formula using bore B (m) and stroke S (m).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 624px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 312px; transform-origin: 468.5px 312px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe swept volume (V_s) is the volume displaced by the piston as it travels from BDC (Bottom Dead Centre) to TDC (Top Dead Centre). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe clearance volume (V_c) is the remaining volume above the piston at TDC .It cannot be swept and defines the compression limit.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 513px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 256.5px; text-align: left; transform-origin: 444.5px 256.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"685\" height=\"507\" style=\"vertical-align: baseline;width: 685px;height: 507px\" src=\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven total cylinder volume at BDC V_BDC (m³) and clearance volume at TDC V_TDC (m³), compute the swept volume V_s and confirm it matches the bore-stroke formula using bore B (m) and stroke S (m).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [Vs, Vc] = sweptClearanceVolume(V_BDC, V_TDC)\r\nVs = 0;\r\nVc = 0;\r\nend","test_suite":"%%Test 1\r\nV_BDC=550e-6; V_TDC=50e-6;\r\n[Vs,Vc] = sweptClearanceVolume(V_BDC,V_TDC);\r\nassert(abs(Vs - 500e-6) \u003c 1e-9)\r\nassert(abs(Vc - 50e-6) \u003c 1e-9)\r\n%%Test 2\r\nV_BDC=750e-6; V_TDC=62.5e-6;\r\n[Vs,Vc] = sweptClearanceVolume(V_BDC,V_TDC);\r\nassert(abs(Vs - 687.5e-6) \u003c 1e-9)\r\nassert(abs(Vc - 62.5e-6) \u003c 1e-9)\r\n%%Test 3\r\nV_BDC=400e-6; V_TDC=36.36e-6;\r\n[Vs,Vc] = sweptClearanceVolume(V_BDC,V_TDC);\r\nassert(abs(Vs - (V_BDC-V_TDC)) \u003c 1e-9)\r\nassert(abs(Vc - V_TDC) \u003c 1e-9)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-28T03:17:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T10:13:10.000Z","updated_at":"2026-07-22T20:13:51.000Z","published_at":"2026-05-21T10:13:10.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe swept volume (V_s) is the volume displaced by the piston as it travels from BDC (Bottom Dead Centre) to TDC (Top Dead Centre). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe clearance volume (V_c) is the remaining volume above the piston at TDC .It cannot be swept and defines the compression limit.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"507\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"685\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven total cylinder volume at BDC V_BDC (m³) and clearance volume at TDC V_TDC (m³), compute the swept volume V_s and confirm it matches the bore-stroke formula using bore B (m) and stroke S (m).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61418,"title":"Play the Disk ","description":"To access the memory address of program on disk, MS-DOS uses sectors,cylinders and heads, on disk in 3D coordinates. Given the head angle position (in deg), cylinders and heads locate the logical sector number to access the program on disk ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 31.5px; transform-origin: 401px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 31.5px; text-align: left; transform-origin: 377px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTo access the memory address of program on disk, MS-DOS uses sectors,cylinders and heads, on disk in 3D coordinates. Given the head angle position (in deg), cylinders and heads locate the logical sector number to access the program on disk \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = disk_sector_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nhead_ref = 90;\r\nnum_heads = 6\r\ncylinder = 2\r\nsector = 4;\r\nhead = 5;\r\ny_correct = 71;\r\nassert(isequal(disk_sector_name(head_ref,num_heads,cylinder,sector,head),y_correct))\r\n\r\n%%\r\nhead_ref = 45;\r\nnum_heads = 5\r\ncylinder = 1\r\nsector = 1;\r\nhead = 3;\r\ny_correct = 64;\r\nassert(isequal(disk_sector_name(head_ref,num_heads,cylinder,sector,head),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":584788,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-07-05T07:02:36.000Z","updated_at":"2026-07-23T03:22:40.000Z","published_at":"2026-07-05T07:02:36.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo access the memory address of program on disk, MS-DOS uses sectors,cylinders and heads, on disk in 3D coordinates. Given the head angle position (in deg), cylinders and heads locate the logical sector number to access the program on disk \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61353,"title":"Basic Algebra II","description":"You have the equation X^2 = n you should find the value of X.\r\nGOOD LUCK!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 25.5px; transform-origin: 401px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou have the equation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eX^2 = n \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eyou should find the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function X = equation(n)\r\n  X = ;\r\nend","test_suite":"%%\r\nn = 1;\r\nX = sqrt(n);\r\nassert(isequal(equation(n),X))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-24T13:23:14.000Z","deleted_by":null,"deleted_at":null,"solvers_count":24,"test_suite_updated_at":"2026-05-24T13:23:14.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-24T13:20:58.000Z","updated_at":"2026-07-23T03:27:30.000Z","published_at":"2026-05-24T13:23:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have the equation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX^2 = n \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eyou should find the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eGOOD LUCK!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61346,"title":"Find The Area Of Triangle Using Base \u0026 Height","description":"You should find the area of the Triangle using base and height.\r\nGood Luck!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 25.5px; transform-origin: 401px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eYou should find the area of the Triangle using base and height.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGood Luck!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = triangleArea(base, height)\r\n  area = ;\r\nend","test_suite":"%%\r\nbase = 1;\r\nheight = 1;\r\narea = 0.5;\r\nassert(isequal(triangleArea(base, height),area))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-23T17:34:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":"2026-05-23T16:51:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-23T16:46:19.000Z","updated_at":"2026-07-23T03:31:52.000Z","published_at":"2026-05-23T16:49:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eYou should find the area of the Triangle using base and height.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGood Luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61355,"title":"Basic Algebra III","description":"Get the Cube Root of the number n.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 401px 10.5px; transform-origin: 401px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377px 10.5px; text-align: left; transform-origin: 377px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eGet the Cube Root of the number n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ans = cbRt(n)\r\n  ans = ;\r\nend","test_suite":"%%\r\nn = 8;\r\nans = nthroot(n,3);\r\nassert(isequal(cbRt(n),ans))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-05-26T12:25:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2026-05-26T12:25:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-26T12:24:06.000Z","updated_at":"2026-07-22T19:58:55.000Z","published_at":"2026-05-26T12:24:06.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGet the Cube Root of the number n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61336,"title":"Brake Mean Effective Pressure (BMEP)","description":"BMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\r\nA higher BMEP indicates a more efficient use of displacement.\r\n\r\nGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 599.719px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 299.859px; transform-origin: 468.5px 299.859px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA higher BMEP indicates a more efficient use of displacement.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 488.719px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 244.359px; text-align: left; transform-origin: 444.5px 244.359px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://static.wixstatic.com/media/1efdb1_5ced4cd83869436cbfd4286a5c83ab9b~mv2.png\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function bmep = calcBMEP(T, Vd, k)\r\nbmep = 0;\r\nend","test_suite":"%%\r\nT = 200; Vd = 0.002; k = 4;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n%%\r\nT = 350; Vd = 0.003; k = 4;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n%%\r\nT = 80; Vd = 0.0005; k = 2;\r\nbmep_expected = (T * 2 * pi * k) / Vd;\r\nassert(abs(calcBMEP(T,Vd,k) - bmep_expected) \u003c 1e-3)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-26T03:50:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T09:38:18.000Z","updated_at":"2026-07-22T20:10:03.000Z","published_at":"2026-05-21T09:38:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBMEP is a normalised measure of engine work output per cycle per unit displacement. It lets you compare engines of different sizes on equal footing.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA higher BMEP indicates a more efficient use of displacement.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"802\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"1477\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven torque T (N·m), displacement V_d (m³), and number of strokes k (2 or 4), compute BMEP.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"https://static.wixstatic.com/media/1efdb1_5ced4cd83869436cbfd4286a5c83ab9b~mv2.png\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61338,"title":"Fuel-Air Equivalence Ratio (Lambda)","description":"Lambda (λ) is the ratio of actual air-fuel ratio to the stoichiometric air-fuel ratio. \r\nλ = 1 is perfect stoichiometry, \r\nλ \u003c 1 is rich, \r\nλ \u003e 1 is lean. \r\nEngine management systems constantly target λ = 1 for optimal catalyst performance.\r\n\r\nGiven actual AFR and stoichiometric AFR (AFR_s), compute lambda.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 572px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 286px; transform-origin: 468.5px 286px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLambda (λ) is the ratio of actual air-fuel ratio to the stoichiometric air-fuel ratio. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eλ = 1 is perfect stoichiometry, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eλ \u0026lt; 1 is rich, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eλ \u0026gt; 1 is lean. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEngine management systems constantly target λ = 1 for optimal catalyst performance.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 392px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 196px; text-align: left; transform-origin: 444.5px 196px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://i.ytimg.com/vi/9uFdrcPkMGE/hq720.jpg?sqp=-oaymwEhCK4FEIIDSFryq4qpAxMIARUAAAAAGAElAADIQj0AgKJD\u0026amp;rs=AOn4CLDLLtOPt4b2zx4L72ztX9tL_4S0vw\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven actual AFR and stoichiometric AFR (AFR_s), compute lambda.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function lam = calcLambda(AFR, AFR_s)\r\nlam = 0;\r\nend","test_suite":"%%Test 1\r\nassert(abs(calcLambda(14.7, 14.7) - 1.0) \u003c 1e-6)\r\n%%Test 2\r\nassert(abs(calcLambda(12.5, 14.7) - 12.5/14.7) \u003c 1e-6)\r\n%%Test 3\r\nassert(abs(calcLambda(16.2, 14.7) - 16.2/14.7) \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-27T03:46:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T09:51:05.000Z","updated_at":"2026-07-22T20:11:24.000Z","published_at":"2026-05-21T09:51:05.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLambda (λ) is the ratio of actual air-fuel ratio to the stoichiometric air-fuel ratio. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eλ = 1 is perfect stoichiometry, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eλ \u0026lt; 1 is rich, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eλ \u0026gt; 1 is lean. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEngine management systems constantly target λ = 1 for optimal catalyst performance.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"386\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"686\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven actual AFR and stoichiometric AFR (AFR_s), compute lambda.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.jpg\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.jpg\",\"contentType\":\"image/jpg\",\"content\":\"https://i.ytimg.com/vi/9uFdrcPkMGE/hq720.jpg?sqp=-oaymwEhCK4FEIIDSFryq4qpAxMIARUAAAAAGAElAADIQj0AgKJD\u0026rs=AOn4CLDLLtOPt4b2zx4L72ztX9tL_4S0vw\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61387,"title":"Multiply the Diagonals of Two Vectors","description":"Find the diagonals of vectors a and b and multiply them.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21.0085px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 400.994px 10.4972px; transform-origin: 400.994px 10.5043px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 377.003px 10.4972px; text-align: left; transform-origin: 377.01px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eFind the diagonals of vectors a and b and multiply them.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = diagonalsProduct(a,b)\r\n  s = \r\nend","test_suite":"%%\r\na = [0 1 2; 3 4 5; 6 7 8]\r\nb = [9 10 11; 12 13 14; 15 16 17]\r\ns = diag(a).*diag(b);\r\nassert(isequal(diagonalsProduct(a,b),s))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5122697,"edited_by":5122697,"edited_at":"2026-06-05T15:39:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":"2026-06-05T15:39:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-05T15:37:19.000Z","updated_at":"2026-07-22T20:05:52.000Z","published_at":"2026-06-05T15:37:19.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFind the diagonals of vectors a and b and multiply them.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61337,"title":"Volumetric efficiency","description":"Volumetric efficiency measures how well an engine breathes.\r\nThe ratio of the actual air mass drawn in per cycle to the theoretical maximum based on displacement. \r\nNaturally aspirated engines typically achieve 80–95%.\r\n\r\nGiven actual air mass m_actual (kg), air density ρ (kg/m³), and displacement V_d (m³), compute volumetric efficiency η_v.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 634.383px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 317.18px; transform-origin: 467.496px 317.191px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eVolumetric efficiency measures how well an engine breathes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe ratio of the actual air mass drawn in per cycle to the theoretical maximum based on displacement. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNaturally aspirated engines typically achieve 80–95%.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 514.477px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 257.227px; text-align: left; transform-origin: 443.508px 257.238px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven actual air mass m_actual (kg), air density ρ (kg/m³), and displacement V_d (m³), compute volumetric efficiency η_v.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function eta_v = volEfficiency(m_actual, rho, Vd)\r\neta_v = 0;\r\nend","test_suite":"%%Test 1\r\nm = 0.00180; rho = 1.2; Vd = 0.002;\r\nassert(abs(volEfficiency(m,rho,Vd) - m/(rho*Vd)) \u003c 1e-6)\r\n%%Test 2\r\nm = 0.00252; rho = 1.2; Vd = 0.003;\r\nassert(abs(volEfficiency(m,rho,Vd) - m/(rho*Vd)) \u003c 1e-6)\r\n%%Test 3\r\nm = 0.00096; rho = 1.15; Vd = 0.0012;\r\nassert(abs(volEfficiency(m,rho,Vd) - m/(rho*Vd)) \u003c 1e-6)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-05-21T09:48:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T09:45:01.000Z","updated_at":"2026-07-22T20:10:43.000Z","published_at":"2026-05-21T09:48:02.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVolumetric efficiency measures how well an engine breathes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe ratio of the actual air mass drawn in per cycle to the theoretical maximum based on displacement. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNaturally aspirated engines typically achieve 80–95%.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven actual air mass m_actual (kg), air density ρ (kg/m³), and displacement V_d (m³), compute volumetric efficiency η_v.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"https://media.springernature.com/lw685/springer-static/image/chp%3A10.1007%2F978-3-030-89216-6_3/MediaObjects/521933_1_En_3_Fig3_HTML.png\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":811,"title":"Genome Sequence 004: Long 3rd Generation Segment Correction","description":"The Melopsittacus undulates genome, Parrot Budgerigar, was successfully sequenced in July 2012 using long 3rd Gen sequences provided by \u003chttp://www.pacificbiosciences.com/ PacBio\u003e. The \u003chttp://assemblathon.org/a-parrot-a-fish-and-a-snake-walk-into-a-bar Assemblathon Genome Contest\u003e led the team of Phillippy, Koren and Jarvis to successfully \u003chttp://www.sciencedaily.com/releases/2012/07/120702210229.htm Sequence Parrot DNA\u003e using the PacBio 3rd Generation data and Illumina 2nd Gen data.\r\n\r\nThe 3rd gen PacBio data is very long, 1K-20K, but has 15% error rate. The Illumina data is 100-500 long with \u003c1% error rate. Jarvis and his team combined this data to achieve \u003c 0.1% error rate.\r\n\r\nGenome Challenge 004 is the correction of simplified PacBio simulated reads with high error rate.\r\n\r\n*Input:* \r\n\r\nCall 1: empty array, segment Width, Flag=0\r\n\r\nCall 2: N PacBio DNA vectors (N x width), Segment Width, Flag=1\r\n\r\n*Output:* \r\n\r\nCall 1: empty vector, Number of Requested Vectors\r\n\r\nCall 2: Corrected DNA vector, Number of Requested Vectors\r\n\r\n*Score:* Number of N vectors used to produce correct vector for w=1024 case\r\n\r\nThe first call to the PacBio_fix routine returns the number of vectors requested to produce a final product. This may be a function of w.\r\n\r\nThe second call to PacBio_fix will have a DNA matix (N x width) and flag=1.\r\n\r\nThe response to the second call is the fixed DNA sequence, vector of width w.\r\n\r\n*example:*\r\nFirst call return : N=3\r\n\r\n  01230123111122223333 Truth\r\n  Input example\r\n  01232123112122221332 Injected errors\r\n  01130123111122123323\r\n  11230133121122223333\r\n\r\n  Output: \r\n  01230123111122223333 Truth, hopefully\r\n\r\n\r\nThis data is simplified by only having simple substitutions and the data sets are provided pre-aligned. \r\n\r\nThe real PacBio data is quite a bit more complicated. Values may be added, deleted, substituted, and are of varying lengths. This causes alignment issues.\r\n\r\nFollow-Up Challenges: Sample Data from the PacBio site for \u003chttp://www.cbcb.umd.edu/software/PBcR/ Lambda Phage\u003e will be molded into various Challenges. Possible challenges are correcting individual long segments and assembling multiple long segments into the full Lambda Phage genome. The Parrot genome is too big for Cody to solve in 50 seconds.\r\n","description_html":"\u003cp\u003eThe Melopsittacus undulates genome, Parrot Budgerigar, was successfully sequenced in July 2012 using long 3rd Gen sequences provided by \u003ca href=\"http://www.pacificbiosciences.com/\"\u003ePacBio\u003c/a\u003e. The \u003ca href=\"http://assemblathon.org/a-parrot-a-fish-and-a-snake-walk-into-a-bar\"\u003eAssemblathon Genome Contest\u003c/a\u003e led the team of Phillippy, Koren and Jarvis to successfully \u003ca href=\"http://www.sciencedaily.com/releases/2012/07/120702210229.htm\"\u003eSequence Parrot DNA\u003c/a\u003e using the PacBio 3rd Generation data and Illumina 2nd Gen data.\u003c/p\u003e\u003cp\u003eThe 3rd gen PacBio data is very long, 1K-20K, but has 15% error rate. The Illumina data is 100-500 long with \u0026lt;1% error rate. Jarvis and his team combined this data to achieve \u0026lt; 0.1% error rate.\u003c/p\u003e\u003cp\u003eGenome Challenge 004 is the correction of simplified PacBio simulated reads with high error rate.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eCall 1: empty array, segment Width, Flag=0\u003c/p\u003e\u003cp\u003eCall 2: N PacBio DNA vectors (N x width), Segment Width, Flag=1\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eCall 1: empty vector, Number of Requested Vectors\u003c/p\u003e\u003cp\u003eCall 2: Corrected DNA vector, Number of Requested Vectors\u003c/p\u003e\u003cp\u003e\u003cb\u003eScore:\u003c/b\u003e Number of N vectors used to produce correct vector for w=1024 case\u003c/p\u003e\u003cp\u003eThe first call to the PacBio_fix routine returns the number of vectors requested to produce a final product. This may be a function of w.\u003c/p\u003e\u003cp\u003eThe second call to PacBio_fix will have a DNA matix (N x width) and flag=1.\u003c/p\u003e\u003cp\u003eThe response to the second call is the fixed DNA sequence, vector of width w.\u003c/p\u003e\u003cp\u003e\u003cb\u003eexample:\u003c/b\u003e\r\nFirst call return : N=3\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e01230123111122223333 Truth\r\nInput example\r\n01232123112122221332 Injected errors\r\n01130123111122123323\r\n11230133121122223333\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eOutput: \r\n01230123111122223333 Truth, hopefully\r\n\u003c/pre\u003e\u003cp\u003eThis data is simplified by only having simple substitutions and the data sets are provided pre-aligned.\u003c/p\u003e\u003cp\u003eThe real PacBio data is quite a bit more complicated. Values may be added, deleted, substituted, and are of varying lengths. This causes alignment issues.\u003c/p\u003e\u003cp\u003eFollow-Up Challenges: Sample Data from the PacBio site for \u003ca href=\"http://www.cbcb.umd.edu/software/PBcR/\"\u003eLambda Phage\u003c/a\u003e will be molded into various Challenges. Possible challenges are correcting individual long segments and assembling multiple long segments into the full Lambda Phage genome. The Parrot genome is too big for Cody to solve in 50 seconds.\u003c/p\u003e","function_template":"function [M_fix,N]=PacBio_fix(M,w,flag)\r\n% 1st Call\r\n% M is empty\r\n% w is width of segment\r\n% flag is 0\r\n% Ouput is N, the number of segments requested to fix the segment\r\n% 2nd Call\r\n% M is an Nxw array of values [0:3]\r\n\r\n M_fix=[];\r\n N=1; % needed for 2nd call with flag==1\r\n if flag==0 % Requested number of Segments\r\n  N=1;\r\n  return;\r\n end\r\n\r\nM_fix=M(1,:);\r\n\r\n\r\nend","test_suite":"%%\r\nfeval(@assignin,'caller','score',0);\r\n%%\r\nM=[];\r\nflag=0;\r\nw=100;\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\n\r\nM_truth=randi(4,1,w,'uint8')-1;\r\nM=repmat(M_truth,N,1);\r\n\r\n% Apply 15% substitution error\r\nqerr=floor(.15*N*w);\r\nerrvec=randi(N*w,qerr,1);\r\nerrval=randi(4,qerr,1)-1;\r\n\r\nM(errvec)=errval;\r\n\r\nflag=1;\r\ntic\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\ntoc\r\n\r\nassert(isequal(M_fix,M_truth),sprintf('Error Count=%i',sum(M_fix~=M_truth)))\r\n%%\r\nM=[];\r\nflag=0;\r\nw=6144;\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\n\r\nM_truth=randi(4,1,w,'uint8')-1;\r\nM=repmat(M_truth,N,1);\r\n\r\n% Apply 15% substitution error\r\nqerr=floor(.15*N*w);\r\nerrvec=randi(N*w,qerr,1);\r\nerrval=randi(4,qerr,1)-1;\r\n\r\nM(errvec)=errval;\r\n\r\nflag=1;\r\ntic\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\ntoc\r\n\r\nassert(isequal(M_fix,M_truth),sprintf('Error Count=%i',sum(M_fix~=M_truth)))\r\n\r\n%%\r\n% Size Performance is based on w=1024 case\r\nM=[];\r\nflag=0;\r\nw=1024;\r\n[M_fix,N]=PacBio_fix(M,w,flag);\r\n\r\nM_truth=randi(4,1,w,'uint8')-1;\r\nM=repmat(M_truth,N,1);\r\n\r\n% Apply 15% substitution error\r\nqerr=floor(.15*N*w);\r\nerrvec=randi(N*w,qerr,1);\r\nerrval=randi(4,qerr,1)-1;\r\n\r\nM(errvec)=errval;\r\n\r\nflag=1;\r\ntic\r\n[M_fix,not_N]=PacBio_fix(M,w,flag);\r\ntoc\r\n\r\nassert(isequal(M_fix,M_truth),sprintf('Error Count=%i',sum(M_fix~=M_truth)))\r\n\r\nfeval(@assignin,'caller','score',min(20,N));\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2012-10-08T02:30:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-01T05:26:57.000Z","updated_at":"2026-07-22T16:47:43.000Z","published_at":"2012-10-08T02:29:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Melopsittacus undulates genome, Parrot Budgerigar, was successfully sequenced in July 2012 using long 3rd Gen sequences provided by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.pacificbiosciences.com/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePacBio\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://assemblathon.org/a-parrot-a-fish-and-a-snake-walk-into-a-bar\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAssemblathon Genome Contest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e led the team of Phillippy, Koren and Jarvis to successfully\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.sciencedaily.com/releases/2012/07/120702210229.htm\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSequence Parrot DNA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e using the PacBio 3rd Generation data and Illumina 2nd Gen data.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe 3rd gen PacBio data is very long, 1K-20K, but has 15% error rate. The Illumina data is 100-500 long with \u0026lt;1% error rate. Jarvis and his team combined this data to achieve \u0026lt; 0.1% error rate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenome Challenge 004 is the correction of simplified PacBio simulated reads with high error rate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 1: empty array, segment Width, Flag=0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 2: N PacBio DNA vectors (N x width), Segment Width, Flag=1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 1: empty vector, Number of Requested Vectors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCall 2: Corrected DNA vector, Number of Requested Vectors\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScore:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Number of N vectors used to produce correct vector for w=1024 case\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first call to the PacBio_fix routine returns the number of vectors requested to produce a final product. This may be a function of w.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe second call to PacBio_fix will have a DNA matix (N x width) and flag=1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe response to the second call is the fixed DNA sequence, vector of width w.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eexample:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e First call return : N=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[01230123111122223333 Truth\\nInput example\\n01232123112122221332 Injected errors\\n01130123111122123323\\n11230133121122223333\\n\\nOutput: \\n01230123111122223333 Truth, hopefully]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis data is simplified by only having simple substitutions and the data sets are provided pre-aligned.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe real PacBio data is quite a bit more complicated. Values may be added, deleted, substituted, and are of varying lengths. This causes alignment issues.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollow-Up Challenges: Sample Data from the PacBio site for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.cbcb.umd.edu/software/PBcR/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLambda Phage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e will be molded into various Challenges. Possible challenges are correcting individual long segments and assembling multiple long segments into the full Lambda Phage genome. The Parrot genome is too big for Cody to solve in 50 seconds.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61419,"title":"Caesar Cipher: shift a lowercase string","description":"A Caesar cipher shifts every letter forward through the alphabet by a fixed amount, wrapping around from z back to a.\r\n\r\nGiven a lowercase string s and a whole number n, return the encoded string where each letter is shifted forward by n positions. The shift may be larger than 26, and wrapping must work correctly (shifting z by 1 gives a).\r\n\r\nExamples:\r\n  s = 'abc',   n = 1    -\u003e  'bcd'\r\n  s = 'xyz',   n = 3    -\u003e  'abc'\r\n  s = 'hello', n = 13   -\u003e  'uryyb'","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 315px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 244px 157.5px; transform-origin: 244px 157.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 21px; text-align: left; transform-origin: 220px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA Caesar cipher shifts every letter forward through the alphabet by a fixed amount, wrapping around from z back to a.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 10.5px; text-align: left; transform-origin: 220px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 42px; text-align: left; transform-origin: 220px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a lowercase string s and a whole number n, return the encoded string where each letter is shifted forward by n positions. The shift may be larger than 26, and wrapping must work correctly (shifting z by 1 gives a).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 10.5px; text-align: left; transform-origin: 220px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 10.5px; text-align: left; transform-origin: 220px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 10.5px; text-align: left; transform-origin: 220px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  s = 'abc',   n = 1    -\u0026gt;  'bcd'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 10.5px; text-align: left; transform-origin: 220px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  s = 'xyz',   n = 3    -\u0026gt;  'abc'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 220px 10.5px; text-align: left; transform-origin: 220px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  s = 'hello', n = 13   -\u0026gt;  'uryyb'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function out = caesar(s, n)\r\n    out = s;\r\nend","test_suite":"%%\r\nassert(isequal(caesar('abc', 1), 'bcd'))\r\n%%\r\nassert(isequal(caesar('xyz', 3), 'abc'))\r\n%%\r\nassert(isequal(caesar('hello', 13), 'uryyb'))\r\n%%\r\nassert(isequal(caesar('zebra', 27), 'afcsb'))\r\n%%\r\nassert(isequal(caesar('abc', 0), 'abc'))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5142412,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-07-08T13:56:36.000Z","updated_at":"2026-07-22T17:28:56.000Z","published_at":"2026-07-08T13:56:36.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Caesar cipher shifts every letter forward through the alphabet by a fixed amount, wrapping around from z back to a.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a lowercase string s and a whole number n, return the encoded string where each letter is shifted forward by n positions. The shift may be larger than 26, and wrapping must work correctly (shifting z by 1 gives a).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e  s = 'abc',   n = 1    -\u0026gt;  'bcd'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e  s = 'xyz',   n = 3    -\u0026gt;  'abc'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e  s = 'hello', n = 13   -\u0026gt;  'uryyb'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61399,"title":"MATLAB 101: Conditional Product or Sum Calculator","description":"Write a MATLAB function that accepts two integer numbers. If the product of the two numbers is less than or equal to 1000, return their product; otherwise, return their sum.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a MATLAB function that accepts two integer numbers. If the product of the two numbers is less than or equal to 1000, return their product; otherwise, return their sum.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = product_or_sum(number1, number2)\r\n    % Write your code here\r\nend","test_suite":"%% Test 1: First Provided Test Case (Product \u003c= 1000)\r\n% 20 * 30 = 600 (\u003c= 1000), should return product\r\nassert(product_or_sum(20, 30) == 600);\r\n\r\n%% Test 2: Second Provided Test Case (Product \u003e 1000)\r\n% 40 * 30 = 1200 (\u003e 1000), should return sum (40 + 30)\r\nassert(product_or_sum(40, 30) == 70);\r\n\r\n%% Test 3: Boundary Condition Exactly 1000\r\n% 10 * 100 = 1000 (\u003c= 1000), should return product\r\nassert(product_or_sum(10, 100) == 1000);\r\n\r\n%% Test 4: Boundary Condition Just Above 1000\r\n% 20 * 51 = 1020 (\u003e 1000), should return sum (20 + 51)\r\nassert(product_or_sum(20, 51) == 71);\r\n\r\n%% Test 5: Handling Negative Numbers\r\n% -5 * 10 = -50 (\u003c= 1000), should return product\r\nassert(product_or_sum(-5, 10) == -50);","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2294940,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-06-13T17:39:41.000Z","updated_at":"2026-07-22T19:34:41.000Z","published_at":"2026-06-13T17:39:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a MATLAB function that accepts two integer numbers. If the product of the two numbers is less than or equal to 1000, return their product; otherwise, return their sum.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61333,"title":"Given the ratio of the two legs (longer / shorter), and the hypotenuse length, find the shorter leg.","description":"Further to the problem 43236, find the length of shorter leg\r\nP.S No built-in functions allowed","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(33, 33, 33); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 243.5px 25.5px; transform-origin: 243.5px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFurther to the problem 43236, find the length of shorter leg\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 219.5px 10.5px; text-align: left; transform-origin: 219.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eP.S No built-in functions allowed\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = FindShortLeg(x,ratio)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 40;\r\nratio = 16/9;\r\ny_correct = 19.6104;\r\nassert(abs(FindShortLeg(x,ratio)-y_correct)\u003c0.01)\r\n\r\n%%\r\nx = 25;\r\nratio = 16/9;\r\ny_correct = 12.2565;\r\nassert(abs(FindShortLeg(x,ratio)-y_correct)\u003c0.01)\r\n\r\n%%\r\nx = 10;\r\nratio = 16/9;\r\ny_correct =  4.9026;\r\nassert(abs(FindShortLeg(x,ratio)-y_correct)\u003c0.01)\r\n\r\n%%\r\nx = 5;\r\nratio = 4/3;\r\ny_correct = 3;\r\nassert(abs(FindShortLeg(x,ratio)-y_correct)\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":584788,"edited_by":584788,"edited_at":"2026-05-21T11:24:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2026-05-21T05:44:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-05-21T05:28:33.000Z","updated_at":"2026-07-23T05:09:08.000Z","published_at":"2026-05-21T05:28:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFurther to the problem 43236, find the length of shorter leg\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP.S No built-in functions allowed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61425,"title":"Reverse the Sign","description":"Write a function that returns the input with the sign of every element reversed.\r\nThe input may be a scalar, vector, or matrix.\r\nSome built-in functions and signs are forbidden.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"baseline-shift: 0px; block-size: 111px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 55.5px; transform-origin: 468.5px 55.5px; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 240.242px 8px; transform-origin: 240.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the input with the sign of every element reversed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 135.725px 8px; transform-origin: 135.725px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe input may be a scalar, vector, or matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 147.825px 8px; transform-origin: 147.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSome built-in functions and signs are forbidden.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = \r\nend","test_suite":"%%\r\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'sum')))\r\nassert(isempty(strfind(filetext, '-')))\r\nassert(isempty(strfind(filetext, '+')))\r\nassert(isempty(strfind(filetext, 'exp')))\r\nassert(isempty(strfind(filetext, 'uminus')))\r\nassert(isempty(strfind(filetext, 'abs')))\r\nassert(isempty(strfind(filetext, 'regexp')))\r\nassert(isempty(strfind(filetext, 'echo')))\r\nassert(isempty(strfind(filetext, 'assignin')))\r\nassert(isempty(strfind(filetext, 'ans')))\r\nassert(isempty(strfind(filetext, 'conv')))\r\nassert(isempty(strfind(filetext, 'inv')))\r\nassert(isempty(strfind(filetext, 'persistent')))\r\nassert(isempty(strfind(filetext, 'global')))\r\nassert(isempty(strfind(filetext, 'sign')))\r\n%%\r\nassert(isequal(your_fcn_name(4),-4))\r\n%%\r\nassert(isequal(your_fcn_name(-9),9))\r\n%%\r\nassert(isequal(your_fcn_name(0),0))\r\n%%\r\nassert(isequal(your_fcn_name([1 2 -3]),[-1 -2 3]))\r\n%%\r\nassert(isequal(your_fcn_name([1 -2;3 -4]),[-1 2;-3 4]))\r\n%%\r\nx = [Inf 0 12 -3];\r\ny_corrected = [-Inf 0 -12 3]\r\nassert(isequal(your_fcn_name(x),y_corrected))\r\n%%\r\nassert(isequal(your_fcn_name(55),-55))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5046205,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-07-23T11:24:51.000Z","updated_at":"2026-07-23T13:12:41.000Z","published_at":"2026-07-23T11:24:51.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the input with the sign of every element reversed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe input may be a scalar, vector, or matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSome built-in functions and signs are forbidden.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61312,"title":"Electric Power Steering (EPS) Motor Torque with Efficiency","description":"In EPS systems, the motor must generate additional torque to compensate for system losses.\r\nGiven Required assist torque at rack Ta and Mechanical efficiency η (0 \u003c η ≤ 1)\r\nCompute required motor torque Tm.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn EPS systems, the motor must generate additional torque to compensate for system losses.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Required assist torque at rack \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTa \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMechanical efficiency \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eη (0 \u0026lt; η ≤ 1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute required motor torque \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTm\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Tm = epsMotorTorque(Ta,eta)\r\nTm = 0;\r\nend","test_suite":"%%\r\nTa = 10; eta = 0.9;\r\nTm_expected = Ta / eta;\r\nassert(abs(epsMotorTorque(Ta,eta) - Tm_expected) \u003c 1e-6)\r\n\r\n%%\r\nTa = 15; eta = 0.85;\r\nTm_expected = Ta / eta;\r\nassert(abs(epsMotorTorque(Ta,eta) - Tm_expected) \u003c 1e-6)\r\n\r\n%%\r\nTa = 8; eta = 0.8;\r\nTm_expected = Ta / eta;\r\nassert(abs(epsMotorTorque(Ta,eta) - Tm_expected) \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:46:20.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:46:15.000Z","updated_at":"2026-07-23T09:55:42.000Z","published_at":"2026-04-28T09:46:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn EPS systems, the motor must generate additional torque to compensate for system losses.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Required assist torque at rack \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTa \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eMechanical efficiency \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eη (0 \u0026lt; η ≤ 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute required motor torque \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTm\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":843,"title":"Hyperspectral Processing: Determine Material Components given a Hyperspectral vector","description":"Given a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages. \r\n\r\n\u003chttp://aviris.jpl.nasa.gov/aviris/index.html NASA AVIRIS\u003e\r\n\r\nA Ground Square is imaged by hundreds of pixels, each at a different wavelength.\r\nThe signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance.\r\nPixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\r\n\r\nLet S(i,j) be the response of Material i for band j\r\n\r\ng( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\r\n\r\nA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\r\n\r\n*g=S*f*  where f is the percentage of the imaged pixel covered by the\r\nmaterial.\r\n\r\n*Input:* \r\ng spectral sum [301,1]; \r\nS spectral material response [301,9]  Nine materials\r\n\r\n*Output:*\r\nSolve for f  ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\r\n\r\n( f should sum to 1, max(f) is 1 and min(f) is 0 )\r\n\r\nThe test Suite will round to 2 decimal places.\r\nCases of \"other materials\" which will induce negative values are not\r\ntested.\r\n\r\nThis is introductory and ignores atmospheric absorption.\r\n\r\nThere is a matrix operation hint in the test suite for a method to solve for f.\r\n\r\n\r\n\u003chttp://aviris.jpl.nasa.gov/data/free_data.html AVARIS Free Data\u003e\r\nThese data files are large with 224 bands x 750 channels x 2000 samples\r\n\r\nTo expand these files may require a tar converter\r\n\u003chttp://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme NASA readme\u003e\r\n...and... \r\n\u003chttp://aviris.jpl.nasa.gov/alt_gulf/ NASA Tools bottom Left\u003e\r\nThere are some possible issues with the NASA tar tool. Two non-standard files can be found at \u003chttp://dll-files.org/7968/index.html libiconv-2.dll\u003e and \u003chttp://dll-files.org/7975/libintl-2.dll.html libintl-2.dll\u003e\r\n\r\nSee the Test Suite for details on opening the AVIRIS Moffett Field file.","description_html":"\u003cp\u003eGiven a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://aviris.jpl.nasa.gov/aviris/index.html\"\u003eNASA AVIRIS\u003c/a\u003e\u003c/p\u003e\u003cp\u003eA Ground Square is imaged by hundreds of pixels, each at a different wavelength.\r\nThe signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance.\r\nPixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\u003c/p\u003e\u003cp\u003eLet S(i,j) be the response of Material i for band j\u003c/p\u003e\u003cp\u003eg( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\u003c/p\u003e\u003cp\u003eA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\u003c/p\u003e\u003cp\u003e\u003cb\u003eg=S*f\u003c/b\u003e  where f is the percentage of the imaged pixel covered by the\r\nmaterial.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e \r\ng spectral sum [301,1]; \r\nS spectral material response [301,9]  Nine materials\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e\r\nSolve for f  ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\u003c/p\u003e\u003cp\u003e( f should sum to 1, max(f) is 1 and min(f) is 0 )\u003c/p\u003e\u003cp\u003eThe test Suite will round to 2 decimal places.\r\nCases of \"other materials\" which will induce negative values are not\r\ntested.\u003c/p\u003e\u003cp\u003eThis is introductory and ignores atmospheric absorption.\u003c/p\u003e\u003cp\u003eThere is a matrix operation hint in the test suite for a method to solve for f.\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://aviris.jpl.nasa.gov/data/free_data.html\"\u003eAVARIS Free Data\u003c/a\u003e\r\nThese data files are large with 224 bands x 750 channels x 2000 samples\u003c/p\u003e\u003cp\u003eTo expand these files may require a tar converter \u003ca href=\"http://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme\"\u003eNASA readme\u003c/a\u003e\r\n...and...  \u003ca href=\"http://aviris.jpl.nasa.gov/alt_gulf/\"\u003eNASA Tools bottom Left\u003c/a\u003e\r\nThere are some possible issues with the NASA tar tool. Two non-standard files can be found at \u003ca href=\"http://dll-files.org/7968/index.html\"\u003elibiconv-2.dll\u003c/a\u003e and \u003ca href=\"http://dll-files.org/7975/libintl-2.dll.html\"\u003elibintl-2.dll\u003c/a\u003e\u003c/p\u003e\u003cp\u003eSee the Test Suite for details on opening the AVIRIS Moffett Field file.\u003c/p\u003e","function_template":"function f = hyperspectral(g,S)\r\n% g is [301,1]\r\n% S is [301,9]\r\n  f = zeros(size(S,2),1);\r\nend","test_suite":"%%\r\n% The AVIRIS fileread info is at the bottom\r\n% Solution Hint:\r\n% The Matrix hint is inv(S'S)(S'S)=I\r\n% With g=Sf multiply both sides by h'\r\n% S'g=S'Sf, now multiply both sides by inv(S'S)\r\n% inv(S'S)(S'g)=inv(S'S)(S'S)f which is I*f\r\n% Now simplify the right side and there is a solution\r\n% Solution Bigger/Better Hint: Search on mldivide\r\n%%\r\nglobal S\r\n%http://tinyurl.com/matlab-hyper-spectra\r\n%http://rmatlabtest.appspot.com/Spectra.mat\r\nurlwrite('http://rmatlabtest.appspot.com/Spectra.mat','Spectra.mat') ;\r\nload('Spectra.mat'); % S is the variable in Spectra.mat\r\nf_exp=[.5 .5 0 0 0 0 0 0 0 ]';\r\ng=S*f_exp;\r\n\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\nglobal S\r\nf_exp=[0 .5 0.25 0 0 0 0.25 0 0 ]';\r\ng=S*f_exp;\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\nglobal S\r\nf_exp=[0 .25 0.6 0 0 0 0 0.15 0 ]';\r\ng=S*f_exp;\r\nf = hyperspectral(g,S);\r\nassert(isequal(round(100*f)/100,f_exp),sprintf('%f\\n',f))\r\n%%\r\n%\r\n%Reading of the full Moffett Field file: (8GB RAM recommended)\r\n% The file is 600MB\r\n%cd 'C:\\Users\\???' % Your file location\r\n%fn='f080611t01p00r07rdn_c_sc01_ort_img'\r\n%fid = fopen (fn,'r');\r\n%A = int16(fread(fid, 'int16', 'ieee-be'));\r\n%A2 = reshape (A, 224,753,1924); % Specifics found in text files\r\n%A3 = permute (A2,[3 2 1]); % X Y Band\r\n%figure;imagesc(squeeze(A3(:,:,1))); % To view top layer\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":8,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2013-02-02T19:05:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-07-19T02:49:02.000Z","updated_at":"2026-07-23T10:07:49.000Z","published_at":"2012-07-19T03:34:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a hyperspectral data set and Reflectance Spectral Signature Library determine a pixel's component percentages.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/aviris/index.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA AVIRIS\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Ground Square is imaged by hundreds of pixels, each at a different wavelength. The signal on pixel 1(500nm to 505nm) is a sum of the components (Concrete/Tree/Grass...) by percentage of area covered times the material reflectance. Pixel 2 (510-515nm) is different by the Reflectance deltas between Concrete and a Tree.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet S(i,j) be the response of Material i for band j\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eg( j )= %(Concrete)*S(1,j)+%(Tree)*S(2,j)+...%(Grass)*S(end,j);\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA 300-Band 9-Material Spectral file is loaded. Comparison between foliage and rocks is quite significant. The materials are Bush, Calcite, Concrete, Conifer, Grass (not that type), Fir tree, Gypsum, Maple, Sage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eg=S*f\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e where f is the percentage of the imaged pixel covered by the material.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e g spectral sum [301,1]; S spectral material response [301,9] Nine materials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Solve for f ....( eg f=[0 .5 0 .25 .25 0 0 0 0]' )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e( f should sum to 1, max(f) is 1 and min(f) is 0 )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test Suite will round to 2 decimal places. Cases of \\\"other materials\\\" which will induce negative values are not tested.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is introductory and ignores atmospheric absorption.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere is a matrix operation hint in the test suite for a method to solve for f.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/data/free_data.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAVARIS Free Data\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e These data files are large with 224 bands x 750 channels x 2000 samples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo expand these files may require a tar converter\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/alt_locator/111013_AV_Download.readme\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA readme\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ...and... \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://aviris.jpl.nasa.gov/alt_gulf/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNASA Tools bottom Left\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e There are some possible issues with the NASA tar tool. Two non-standard files can be found at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://dll-files.org/7968/index.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003elibiconv-2.dll\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://dll-files.org/7975/libintl-2.dll.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003elibintl-2.dll\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee the Test Suite for details on opening the AVIRIS Moffett Field file.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61269,"title":"Precise Almost Pythagorean Triples ","description":"This  is essentially the same as:  Problem 52834. Easy Sequences 32: Almost Pythagorean Triples; it even presents the same set of test problems.  The difference is that the \"correct\" solutions for larger cases of 52834 were the result of roundoff errors due to values being larger than flintmax('double').  This problem requires care to avoid such roundoff.\r\nRepeating the original problem description:\t\t\t\t\r\nAn Almost Pythagorean Triple (abbreviated as \"APT'), is a set of 3 integers in which square of the largest element, which we will call as its 'hypotenuse', is 1 less than the sum of square of the smaller elements (shorter sides). This means that if c is the hypotenuse and a and b are the shorter sides, , satisfies the following equation: \r\n        \r\n        where:  \r\nThe smallest  is the triple , with  and perimeter (the sum of the 3 elements)  of . Some researchers consider  as the smallest , but here, we will only look at 's where the hypotenuse is \"strictly\" greater than the other shorter sides. Other examples of 's are , and . \r\nUnfortunately, unlike Pythagorean Triples, a 'closed formula' for generating all possible 's, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with 's with a known ratio between the hypotenuse and the shortest side: . \r\nGiven the value of r, find the perimeter of the  with the r-th smallest perimeter. For example for , that is , the smallest perimeter is  for  , while the second (r-th) smallest perimeter is , for the  with dimensions . For , the third smallest perimeter is  for  . \r\nThe output can be very large, so please present only the last 12 digits if the number of digits of the perimeter exceeds 12.\r\nFinally, as with the original, the use of java, BigInteger, persistent, and global are not allowed.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 669.833px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 334px 334.917px; transform-origin: 334px 334.917px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 42px; text-align: left; transform-origin: 310px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.675px 7.91667px; transform-origin: 102.675px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis  is essentially the same as:  \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52834\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eProblem 52834. Easy Sequences 32: Almost Pythagorean Triples\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e; it even presents the same set of test problems.  The difference is that the \"correct\" solutions for larger cases of 52834 were the result of roundoff errors due to values being larger than flintmax('double').  This problem requires care to avoid such roundoff.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 10.5px; text-align: left; transform-origin: 310px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201.933px 7.91667px; transform-origin: 201.933px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRepeating the original problem description:\t\t\t\t\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 86.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 43.4583px; text-align: left; transform-origin: 310px 43.4583px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 303.05px 7.91667px; transform-origin: 303.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn Almost Pythagorean Triple (abbreviated as \"APT'), is a set of 3 integers in which square of the largest element, which we will call as its 'hypotenuse', is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.91667px; transform-origin: 3.89167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.45px 7.91667px; transform-origin: 12.45px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eless\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.8917px 7.91667px; transform-origin: 94.8917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e than the sum of square of the smaller elements (shorter sides). This means that if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.5px 7.91667px; transform-origin: 3.5px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.35px 7.91667px; transform-origin: 72.35px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hypotenuse and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.91667px; transform-origin: 3.89167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 7.91667px; transform-origin: 3.89167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 7.91667px; transform-origin: 49.3917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are the shorter sides, \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102.692px 7.91667px; transform-origin: 102.692px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, satisfies the following equation: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 24.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 12.4583px; text-align: left; transform-origin: 310px 12.4583px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5333px 7.91667px; transform-origin: 15.5333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"99\" height=\"19\" style=\"vertical-align: baseline;width: 99px;height: 19px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 23.9167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 11.9583px; text-align: left; transform-origin: 310px 11.9583px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.425px 7.91667px; transform-origin: 40.425px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e        where:  \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"62\" height=\"18\" style=\"vertical-align: baseline;width: 62px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 96.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 48.3333px; text-align: left; transform-origin: 310px 48.3333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.6167px 7.91667px; transform-origin: 41.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe smallest \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.725px 7.91667px; transform-origin: 37.725px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the triple \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"48\" height=\"18\" style=\"vertical-align: baseline;width: 48px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.275px 7.91667px; transform-origin: 18.275px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, with \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"100\" height=\"19\" style=\"vertical-align: baseline;width: 100px;height: 19px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.508px 7.91667px; transform-origin: 101.508px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and perimeter (the sum of the 3 elements)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.775px 7.91667px; transform-origin: 7.775px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eof \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"18\" height=\"18\" style=\"vertical-align: baseline;width: 18px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6UlEQVRYhe2WQQ3DMAxFP4cwCIESGIIiKIMxKINSKIZBKIdRKIZR6A6ztWiHxkm+qkjzl6xenOQpL5UMeDyevhIBhEzPAOBmrKEFZAVwGDbZpc9SSylISEC0zoDGApgDn1syZwQwy/dpBNqk4klPkH32EpjfzAagKIfk3tiESl01QBYFD1ToqgGyRHW9kL/JS4BU19oCwwRSXWMPQDRdLCCaLhYQTRcDiKqLAUTVxQDaQNTVChRB1tUKdAdZVyuQTgpTD0CprrORpCg6VijQXLBWdW0skAXfoSutVQ7LRdfT/i6Px+P5u7wB3c96XQFb71kAAAAASUVORK5CYII=\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91.4083px 7.91667px; transform-origin: 91.4083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Some researchers consider \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"48\" height=\"18\" style=\"vertical-align: baseline;width: 48px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5583px 7.91667px; transform-origin: 50.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e as the smallest \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.7917px 7.91667px; transform-origin: 70.7917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, but here, we will only look at \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 243.942px 7.91667px; transform-origin: 243.942px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's where the hypotenuse is \"strictly\" greater than the other shorter sides. Other examples of \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.8333px 7.91667px; transform-origin: 18.8333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's are \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"56\" height=\"18\" style=\"vertical-align: baseline;width: 56px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAAAlCAYAAACao20PAAADbklEQVR4nO2a3bGDIBCFTw92kAZswAqswA7SQTpIC9ZgCfaQFlKDLXgfcIcNEViE1cwdvhke7o3KyuHnLAhUKpVKRYGHp3RXBvXP6eBv92RWAC8As1OGEpFWdhnw3d4vGC2SWVFH2y/Q4UQBb9s9HYDmSKWJtCfXx+tNIaddThGwgxnqE8x8PW73TzDBl+S2PX+BXR/o71mhPs4A4A3zXhL67frVKSlxqgt43669O/9vYQPujwSwQwsrlNuT6bcF5UV0hZAI+MS3cLxI41QVsGfB7E0Nj8jvqVAj+joEdaaxQF3Ec3suPVsiIDX6CCtSAzuC6TkvQf2qAlIwvhe6wQb7PBIEg49o3xpEL7tk1uVDKuAL/k7UwMQXexdCTUDeoO70ySGRc0chvUhoBNI174x6QkgEbLf6Q+/Kp9dQ2wGKAvIpJRTEDHlvC9Hgc+rZayBqmNzR7kMiYA+5KJcKSOtbLIhReJ0E/izXyJCJeUPPiaaYmBBcwNgydYqAoR4vFVpCA7szQdNyB9PrFxiBNfPBUgIOsFN9LF41AXkvCrmpkgIC3yKSkKVSlRClBKSZRLLHqepCJW6q5BRK+ETMWWMllBCQXKhk9AHKAnIjE0quSyf0NKqfzvNL1rFHCQEp9pRdLtWdGG6Jl+3vB+xOOk9cS5gLGtEk1A2fTjelcVLJFZBSr5QTnVP2QltY0WYYEQd8W/9cqPfuNSCfqq/MA300MHGlpjinnka4lDYwNF36pskJuqPwqIC0Zh/JTy8TkG8Z+RLvFLjr9ZkV6e7QUY4ImCMecKGAfDSUcIcSAYHfE1AiXsh4XSIgd6e+4JrtugfkAtOI9pkAvua6hom+N6G1+QipAo4wniDEgPDpyekCkiuNJdfcdEhHKa2pvimZOo7bwPxUJMdFptxP70eufK/QNZINk0PBpgjYwtr5CXFB+BS7Qn6GRx3k5dRxh+k0E/bz0dUpqSkNN2Sx/Va3c4ZKzJ2rCtjCNNwMmwOmpB4TuzflEPaGz7RlRvyTR56bpgg4sDjdsjf9955rfSWWE6oKOGwB55qUMz9X7KCXJ2pwaR4oQXIAWpIJOg5Vi58WsMX3WqbJCL3DXi2yBLzDfs9IpdRhaQPTmJqfAXIG/P5X5fz7USrkrJPxuaZD3+lXRHCn65ZKpVKpVCqV/8Mf0OnMkPT9w/AAAAAASUVORK5CYII=\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 7.91667px; transform-origin: 17.5px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"71\" height=\"18\" style=\"vertical-align: baseline;width: 71px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 71.75px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 35.875px; text-align: left; transform-origin: 310px 35.875px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 269.142px 7.91667px; transform-origin: 269.142px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUnfortunately, unlike Pythagorean Triples, a 'closed formula' for generating all possible \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.9417px 7.91667px; transform-origin: 21.9417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.775px 7.91667px; transform-origin: 6.775px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e's with a known ratio between the hypotenuse and the shortest side: \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"50\" height=\"18\" style=\"vertical-align: baseline;width: 50px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 95.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 47.8333px; text-align: left; transform-origin: 310px 47.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.2083px 7.91667px; transform-origin: 62.2083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven the value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 7.91667px; transform-origin: 2.33333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85.925px 7.91667px; transform-origin: 85.925px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the perimeter of the \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.3167px 7.91667px; transform-origin: 30.3167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e with the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41.6167px 7.91667px; transform-origin: 41.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003er-th smallest\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.3417px 7.91667px; transform-origin: 37.3417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e perimeter. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.4417px 7.91667px; transform-origin: 12.4417px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"35\" height=\"18\" style=\"vertical-align: baseline;width: 35px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.4917px 7.91667px; transform-origin: 24.4917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"43\" height=\"18\" style=\"vertical-align: baseline;width: 43px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 81.675px 7.91667px; transform-origin: 81.675px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the smallest perimeter is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"18\" height=\"18\" style=\"vertical-align: baseline;width: 18px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABLUlEQVRYhe2WUbHDIBBFjwccYKAGoiAK4qAOcBAL0RAJeKiFaoiFvg+WmX2dPEIC5fWDO7Nfu1lOLiwJdHV1fZcsYE4+M0jcaoMswCuzsQFm4Ak4iafEvQTEKJAYR0AWeMji726u0sPv5A41Et5slAVygWKt28kZYEvks+UygaaMOu34aZfOAsUt2RI1GvqyS7lAcTtSQIPqtX4aKNakgGxmXVWgo/PRDMiruvEbgO4cn4+mW2YIF2LKJT32j08DIXkN5eX5meDIqnJLCyAITk2yoBcIR9iumbxzVhUoBRrvqr1vXXMg3Wcq6FMF6MbxBDYD0tN36dejJpCeurUGjOX3GJ/5QjvCId4o/FOMIDPB4vdY/ljAEEY53jle6opduSorAMN/QnR1dXWV6Ae9sZqCc2SAGwAAAABJRU5ErkJggg==\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 7.91667px; transform-origin: 12.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"48\" height=\"18\" style=\"vertical-align: baseline;width: 48px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.9583px 7.91667px; transform-origin: 57.9583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, while the second (r-th) smallest perimeter is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"18\" height=\"18\" style=\"vertical-align: baseline;width: 18px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2WUQ2DMBCGfw91UAMYmIIqwMEc4AAL1TAJ9TALaJgF9sBd0i2DXQ9u4+G+5MIDBT74QgBwHOc/dAAuwumE54wAglZoAjALZxSIZForlX8hNcjMWJ7SJ0IlwqMSKjRxY02gC0wr+xOAgbb3PUKRLvKtdQ9ZLpDYLqG1BDU3bOc6TEgC53pA9taYC3GuLFxvLsS50hmEWnOZC7XmMhdqzWUqpMllKqTJZSpU0J7LTChCl8tM6ApdLjMh/mL3ZxCqc239kvxMiHMVxbH8O8NCwxFCI8m0vF2xOu59MpabdBzHcSQ8AUZlel3qgGXQAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25.6583px 7.91667px; transform-origin: 25.6583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, for the \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEEAAAAkCAYAAADWzlesAAACIklEQVRoge2YS5XDMAxFH4cwCIESCIJBEAZlEAalEAyFEA6hUAyh0FlUmr4o/sj5rMb3nCzq2LItS09OgUqlUqlUrqID0Dj7NtI/96TseW3stV9MD+Athj00MmaWcfxM8ujvWfraBd/NuBeNXah9ibS/ineZ2dBLDPeFYzusN8JObLF20oi1I57SPmDrILb5Y96N0v4oXGuSgSYsNfyD9YlZWsQ3tMjcKZtvbB3UBGwdwi5yLhz/oLHPSB+OBnVyl5iLbU6RPiHn7GbCNxU0z0qM8wbviTmso1TYcjZDkQKcmAqazzYaSioEj7tF+rETcou3Nr1CvZsXLYq97801rSg5pWZFzwlvTmNOZZBJ9NRVqVNhbVGVVuUPwWXQU9I8GnMKDT4O4M3uqRC5E+5Mn1i6MKxP3sPYxYitMnMYeirEDevc7fEVux7rKJnhc4DVJs+YXagY2rznTXkqBIf5gk/oTvSM0qdkI16NOcyEz8mE7uElFaJE8b14NOYw6ukp8nD+5irEFWWM9aD0+u5CxTB1at4KYa+1Z2A15tSvQ0XVP2XcWyGuKGOsMaVXdxequrncZWFKLeSKMsZRGLsqnzJBLsRYHGMV4qoyxnp0+lVZN+ZRW5uXbaDPFWUs9+l8iBu+HvY4wS7GhiX/+aJOCDmqhAbbf6eO2vyjw7YEDpEJOnkXKps6psf2QjRJ255y1ibmfMq7y78gK5VKpVKpVP4Nv14fLJbptxZTAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.6833px 7.91667px; transform-origin: 53.6833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with dimensions \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"71\" height=\"18\" style=\"vertical-align: baseline;width: 71px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.325px 7.91667px; transform-origin: 16.325px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"35\" height=\"18\" style=\"vertical-align: baseline;width: 35px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.1083px 7.91667px; transform-origin: 31.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the third smallest perimeter is \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"33\" height=\"18\" style=\"vertical-align: baseline;width: 33px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 7.91667px; transform-origin: 12.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"32\" height=\"18\" style=\"vertical-align: baseline;width: 32px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"101\" height=\"18\" style=\"vertical-align: baseline;width: 101px;height: 18px\" src=\"data:image/png;base64,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\" data-image-state=\"image-loaded\"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 21px; text-align: left; transform-origin: 310px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 305.717px 7.91667px; transform-origin: 305.717px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe output can be very large, so please present only the last 12 digits if the number of digits of the perimeter exceeds 12.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 310px 21px; text-align: left; transform-origin: 310px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 282.908px 7.91667px; transform-origin: 282.908px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFinally, as with the original, the use of java, BigInteger, persistent, and global are not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function function perimeter = rthPerAPTdbl(r)\r\n  perimeter = r^2;\r\nend","test_suite":"%% Test Case 1\r\nr = 2;\r\np_correct = 71;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 2\r\nr = 3;\r\np_correct = 1393;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 3\r\nr = 5;\r\np_correct = 1046629;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 4\r\nr = 10;\r\np_correct = 737287485879;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 5\r\nr = 100;\r\np_correct = 16183149010201;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 6\r\nrs = 101:150;\r\nps = arrayfun(@(r) rthPerAPTdbl(r),rs);\r\nps = mod([sum(ps) ps(5:5:end) floor(std(double(ps)))],1e6);\r\nps_correct = [12636 824229 203679 227761 926641 15749 664839 210241 515881 139269 477199 789840];\r\nassert(isequal(ps,ps_correct))\r\n%% Test Case 7\r\nr = 1000;\r\np_correct = 499499001002001;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 8\r\nr = 10000;\r\np_correct = 100020001;\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 9\r\nr = 123456;\r\np_correct = uint64(76696064606196865);\r\nassert(isequal(rthPerAPTdbl(r),p_correct))\r\n%% Test Case 10: Forbid java and BigInteger\r\nfiletext = fileread('rthPerAPTdbl.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":2404920,"edited_by":2404920,"edited_at":"2026-03-04T15:24:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-04T14:14:29.000Z","updated_at":"2026-07-23T10:14:17.000Z","published_at":"2026-03-04T15:24:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis  is essentially the same as:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52834\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 52834. Easy Sequences 32: Almost Pythagorean Triples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e; it even presents the same set of test problems.  The difference is that the \\\"correct\\\" solutions for larger cases of 52834 were the result of roundoff errors due to values being larger than flintmax('double').  This problem requires care to avoid such roundoff.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRepeating the original problem description:\\t\\t\\t\\t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn Almost Pythagorean Triple (abbreviated as \\\"APT'), is a set of 3 integers in which square of the largest element, which we will call as its 'hypotenuse', is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eless\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e than the sum of square of the smaller elements (shorter sides). This means that if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the hypotenuse and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are the shorter sides, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, satisfies the following equation: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"19\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"99\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        where:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"62\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe smallest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the triple \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"48\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"19\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"100\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and perimeter (the sum of the 3 elements)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eof \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId6\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Some researchers consider \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"48\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId7\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the smallest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, but here, we will only look at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's where the hypotenuse is \\\"strictly\\\" greater than the other shorter sides. Other examples of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"56\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId8\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"71\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId9\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUnfortunately, unlike Pythagorean Triples, a 'closed formula' for generating all possible \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e's with a known ratio between the hypotenuse and the shortest side: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"50\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId10\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the perimeter of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e with the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er-th smallest\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e perimeter. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"35\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId11\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, that is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"43\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId12\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the smallest perimeter is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId13\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"48\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId14\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, while the second (r-th) smallest perimeter is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId15\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, for the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"71\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId16\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"35\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId17\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the third smallest perimeter is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"33\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId18\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"32\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"18\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"101\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId19\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe output can be very large, so please present only the last 12 digits if the number of digits of the perimeter exceeds 12.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFinally, as with the original, the use of java, BigInteger, persistent, and global are not 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version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven length of matrix initialize a matrix consisting of natural numbers from 1 to n:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10; x = [ 1 2 3 4 5 6 7 8 9 10];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 5; x = [1 2 3 4 5];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":58758,"title":"Hemisphere Volume on Top of a Cylinder","description":"This MATLAB function has to calculate the volume of a hemisphere placed on top of a cylinder, given valid inputs. It takes the radius of the cylinder and the height of the cylinder as input, and returns the total volume of the hemisphere and the cylinder combined.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 332px 46.5px; transform-origin: 332px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 31.5px; text-align: left; transform-origin: 309px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis MATLAB function has to calculate the volume of a hemisphere placed on top of a cylinder, given valid inputs. It takes the radius of the cylinder and the height of the cylinder as input, and returns the total volume of the hemisphere and the cylinder combined.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 309px 10.5px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function volume = computeHemisphereVolume(radius, height)\r\n\r\n    volume = 0;\r\nend","test_suite":"%%\r\nradius = 3;\r\nheight = 8;\r\nexpectedOutput = 282.743338823081;\r\nvolume = computeHemisphereVolume(radius, height);\r\nassert(abs(expectedOutput - volume) \u003c 1e-4)\r\n%%\r\nradius = 2.5;\r\nheight = 5;\r\nexpectedOutput = 130.899693899575;\r\nvolume = computeHemisphereVolume(radius, height);\r\nassert(abs(expectedOutput - volume) \u003c 1e-4)\r\n%%\r\nradius = 10;\r\nheight = 15;\r\nexpectedOutput = 6806.78408277789;\r\nvolume = computeHemisphereVolume(radius, height);\r\nassert(abs(expectedOutput - volume) \u003c 1e-4)\r\n%%\r\nradius = 0;\r\nheight = 12;\r\nexpectedOutput = 0;\r\nvolume = computeHemisphereVolume(radius, height);\r\nassert(abs(expectedOutput - volume) \u003c 1e-4)\r\n%%\r\nradius = 7.2;\r\nheight = 3.5;\r\nexpectedOutput = 1351.73935424539;\r\nvolume = computeHemisphereVolume(radius, height);\r\nassert(abs(expectedOutput - volume) \u003c 1e-4)\r\n","published":true,"deleted":false,"likes_count":13,"comments_count":4,"created_by":3429354,"edited_by":26769,"edited_at":"2023-12-02T00:24:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":75,"test_suite_updated_at":"2023-12-02T00:24:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-07-18T21:20:09.000Z","updated_at":"2026-06-04T17:19:01.000Z","published_at":"2023-07-18T21:20:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis MATLAB function has to calculate the volume of a hemisphere placed on top of a cylinder, given valid inputs. It takes the radius of the cylinder and the height of the cylinder as input, and returns the total volume of the hemisphere and the cylinder combined.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2014,"title":"\"Find out the best cricket\"","description":"This is how I originally read Problem 2013, so let's just go with it.  Give me the first and last name of the best cricket, regardless of your input.","description_html":"\u003cp\u003eThis is how I originally read Problem 2013, so let's just go with it.  Give me the first and last name of the best cricket, regardless of your input.\u003c/p\u003e","function_template":"function y = BestCricket(x)\r\n  y = x;\r\nend","test_suite":"x = 1;\r\nassert(isequal(BestCricket(x),'Jiminy Cricket'))\r\n%%\r\nx = magic(7);\r\nassert(isequal(BestCricket(x),'Jiminy Cricket'))\r\n%%\r\nx='Who is the best cricket?';\r\nassert(isequal(BestCricket(x),'Jiminy Cricket'))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":132,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-11-26T16:35:20.000Z","updated_at":"2026-07-19T16:23:27.000Z","published_at":"2013-11-26T16:35:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is how I originally read Problem 2013, so let's just go with it. Give me the first and last name of the best cricket, regardless of your input.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44688,"title":"World Cup 2018 Prediction!","description":"Which team will be the winner?\r\n","description_html":"\u003cp\u003eWhich team will be the winner?\u003c/p\u003e","function_template":"function y = Worldcup2018winner()\r\n  y = \"????\"\r\nend","test_suite":"%%\r\nteams={'Russia','Saudi Arabia', 'Egypt', 'Uruguay', 'Portugal', 'Spain','Morocco','Iran',...\r\n    'France','Australia', 'Peru','Denmark', 'Brazil', 'Switzerland', 'Costa Rica', 'Serbia', ...\r\n    'Germany', 'Mexico', 'Sweden', 'STH Korea', 'Belgium', 'Panama', 'Tunisia', 'England' , ...\r\n    'Argentina','Iceland', 'Croatia', 'Nigeria', 'Poland', 'Senegal', 'Colombia', 'Japan'};\r\nd=false;\r\nfor i=1:numel(teams)\r\n    if strcmp(Worldcup2018winner(),teams{i})\r\n        d=true;\r\n        break;\r\n    end\r\nend\r\nassert(d)","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":218677,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":144,"test_suite_updated_at":"2018-06-15T17:39:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-06-15T17:38:14.000Z","updated_at":"2026-07-19T11:31:00.000Z","published_at":"2018-06-15T17:38:14.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhich team will be the winner?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":56230,"title":"compter le nombre de zéros dans une matrice","description":"écrire une fonction count_zeros qui prend en entrée une matrice M et détermine le nombre de zéros dans une matrice","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eécrire une fonction count_zeros qui prend en entrée une matrice M et détermine le nombre de zéros dans une matrice\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function N = count_zeros(M)\r\n  %a vous de jouer\r\nend","test_suite":"%%\r\nx = 0;\r\ny_correct = 1;\r\nassert(isequal(count_zeros(x),y_correct))\r\n%%\r\nx = [0 0 1 1 0 0.5];\r\ny_correct = 3;\r\nassert(isequal(count_zeros(x),y_correct))\r\n%%\r\nx = [0 0 1; 1 2 0.5; 0 0 3];\r\ny_correct = 4;\r\nassert(isequal(count_zeros(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":63915,"edited_by":26769,"edited_at":"2022-11-23T21:23:15.000Z","deleted_by":null,"deleted_at":null,"solvers_count":59,"test_suite_updated_at":"2022-11-23T21:23:15.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-06T10:19:12.000Z","updated_at":"2026-06-03T00:17:04.000Z","published_at":"2022-10-06T10:19:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eécrire une fonction count_zeros qui prend en entrée une matrice M et détermine le nombre de zéros dans une matrice\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44264,"title":"Calculate feeling temperature before climbing a mountain","description":"I sometimes climb a mountain.\r\nAs is well known, when the altitude becomes 100 (m) higher, the temperature lowers by 0.6 degrees Celsius.\r\nIn addition there is wind.\r\nAt wind velocity 1(m/s), the feeling temperature falls  1 degree Celsius.\r\n\r\ne.g.\r\n\r\n* temperature of the level ground(gT) : 25 degrees Celsius\r\n* wind velocity(v) : 10 m/s\r\n* at altitude(h) : 3000 m\r\n\r\nIn this case, feeling temperature(fT) is calculated as -3 degrees Celsius.\r\n","description_html":"\u003cp\u003eI sometimes climb a mountain.\r\nAs is well known, when the altitude becomes 100 (m) higher, the temperature lowers by 0.6 degrees Celsius.\r\nIn addition there is wind.\r\nAt wind velocity 1(m/s), the feeling temperature falls  1 degree Celsius.\u003c/p\u003e\u003cp\u003ee.g.\u003c/p\u003e\u003cul\u003e\u003cli\u003etemperature of the level ground(gT) : 25 degrees Celsius\u003c/li\u003e\u003cli\u003ewind velocity(v) : 10 m/s\u003c/li\u003e\u003cli\u003eat altitude(h) : 3000 m\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eIn this case, feeling temperature(fT) is calculated as -3 degrees Celsius.\u003c/p\u003e","function_template":"function fT =  feeling_temperature(gT,h,v)\r\n  fT = gT;\r\nend","test_suite":"%%\r\ngT=25;\r\nh=3000;\r\nv=10;\r\n\r\nfT_correct = -3;\r\nassert(isequal(feeling_temperature(gT,h,v),fT_correct))\r\n\r\n%%\r\ngT=30;\r\nh=500;\r\nv=0;\r\n\r\nfT_correct=27;\r\nassert(isequal(feeling_temperature(gT,h,v),fT_correct))\r\n\r\n%%\r\ngT=28;\r\nh=2500;\r\nv=3;\r\n\r\nfT_correct=10;\r\nassert(isequal(feeling_temperature(gT,h,v),fT_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":102298,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":74,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-07-16T14:13:00.000Z","updated_at":"2026-05-22T11:48:16.000Z","published_at":"2017-07-16T14:28:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI sometimes climb a mountain. As is well known, when the altitude becomes 100 (m) higher, the temperature lowers by 0.6 degrees Celsius. In addition there is wind. At wind velocity 1(m/s), the feeling temperature falls 1 degree Celsius.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ee.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003etemperature of the level ground(gT) : 25 degrees Celsius\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewind velocity(v) : 10 m/s\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eat altitude(h) : 3000 m\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this case, feeling temperature(fT) is calculated as -3 degrees Celsius.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":54595,"title":"String Logic 18","description":"Examples:\r\n'DIG' --\u003e 'DG'\r\n'IMPORTANT' --\u003e 'IPRAT'\r\n'DEAL' --\u003e 'DA'\r\n'LIMB' --\u003e 'LM'\r\n'MOSTLY' --\u003e 'MSL'","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 171px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 85.5px; transform-origin: 407px 85.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e'DIG' --\u0026gt; 'DG'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e'IMPORTANT' --\u0026gt; 'IPRAT'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e'DEAL' --\u0026gt; 'DA'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e'LIMB' --\u0026gt; 'LM'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e'MOSTLY' --\u0026gt; 'MSL'\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = StringLogic(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 'DIG';\r\ny_correct = 'DG';\r\nassert(isequal(StringLogic(x),y_correct))\r\n\r\n%%\r\nx = 'IMPORTANT';\r\ny_correct = 'IPRAT';\r\nassert(isequal(StringLogic(x),y_correct))\r\n\r\n%%\r\nx = 'DEAL';\r\ny_correct = 'DA';\r\nassert(isequal(StringLogic(x),y_correct))\r\n\r\n%%\r\nx = 'LIMB';\r\ny_correct = 'LM';\r\nassert(isequal(StringLogic(x),y_correct))\r\n\r\n%%\r\nx = 'MOSTLY';\r\ny_correct = 'MSL';\r\nassert(isequal(StringLogic(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":232412,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":102,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-05-05T07:12:14.000Z","updated_at":"2026-07-21T08:14:41.000Z","published_at":"2022-05-05T07:12:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'DIG' --\u0026gt; 'DG'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'IMPORTANT' --\u0026gt; 'IPRAT'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'DEAL' --\u0026gt; 'DA'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'LIMB' --\u0026gt; 'LM'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'MOSTLY' --\u0026gt; 'MSL'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42678,"title":"For a given linear index as input for n sized square matrix, find corresponding row and column.","description":"If input is 1, the row and column will be 1 and 1 respectively.","description_html":"\u003cp\u003eIf input is 1, the row and column will be 1 and 1 respectively.\u003c/p\u003e","function_template":"function rc = your_fcn_name(i,n)\r\n  % i is index and n is length of matrix \r\nend","test_suite":"%%\r\ni = 1;n = 1;\r\ny_correct = [1,1];\r\nassert(isequal(your_fcn_name(i,n),y_correct))\r\n%%\r\ni = 7;n = 3;\r\ny_correct = [1,3];\r\nassert(isequal([your_fcn_name(i,n)],y_correct))\r\n%%\r\ni = 16;n = 7;\r\ny_correct = [2,3];\r\nassert(isequal([your_fcn_name(i,n)],y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":28123,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":78,"test_suite_updated_at":"2015-10-31T18:52:14.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2015-10-31T16:23:03.000Z","updated_at":"2026-05-28T14:42:21.000Z","published_at":"2015-10-31T16:38:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf input is 1, the row and column will be 1 and 1 respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45537,"title":"Get the area of ​​the square.","description":"Four circles are inscribed in the square ABCD. The perimeter of each circle is *aπ*.\r\n\r\n\u003c\u003chttp://imgfz.com/i/UzgCJut.png\u003e\u003e\r\n\r\nGiven *a*, obtain the area of ​​the square.\r\n","description_html":"\u003cp\u003eFour circles are inscribed in the square ABCD. The perimeter of each circle is \u003cb\u003eaπ\u003c/b\u003e.\u003c/p\u003e\u003cimg src = \"http://imgfz.com/i/UzgCJut.png\"\u003e\u003cp\u003eGiven \u003cb\u003ea\u003c/b\u003e, obtain the area of ​​the square.\u003c/p\u003e","function_template":"function y = squartArea(a)\r\n     y = a;\r\nend","test_suite":"%%\r\na = 0;\r\ny = 0;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 8;\r\ny = 256;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 1;\r\ny = 4;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 10;\r\ny = 400;\r\nassert(isequal(squartArea(a),y))\r\n%%\r\na = 50;\r\ny = 10000;\r\nassert(isequal(squartArea(a),y))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":446926,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":106,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-18T03:09:51.000Z","updated_at":"2026-07-12T15:43:27.000Z","published_at":"2020-05-18T03:09:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFour circles are inscribed in the square ABCD. The perimeter of each circle is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eaπ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, obtain the area of the square.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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the n-th rand number with given seed","description":"Given seed s, return the n-th rand number using rand(). Round the answer with 4 digits.\r\nn is a postive integer.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 276px 8px; transform-origin: 276px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven seed s, return the n-th rand number using rand(). Round the answer with 4 digits.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67px 8px; transform-origin: 67px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en is a postive integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ans = getNthRand(s,n)\r\n","test_suite":"%%\r\ns = 1; n = 3;\r\ny_correct = .0001;\r\nassert(isequal(getNthRand(s,n),y_correct))\r\n%%\r\ns = 2; n = 100;\r\ny_correct = .8817;\r\nassert(isequal(getNthRand(s,n),y_correct))\r\n%%\r\ns = 1.2; n = 7;\r\ny_correct = .1863;\r\nassert(isequal(getNthRand(s,n),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":2044730,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":43,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-03-04T18:35:12.000Z","updated_at":"2026-07-18T12:53:42.000Z","published_at":"2022-03-04T18:35:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven seed s, return the n-th rand number using rand(). Round the answer with 4 digits.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en is a postive integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55915,"title":"Juros Compostos","description":"Faça uma função que receba um capital inicial (C), uma taxa de juros a ser aplicada (i) e um tempo (t) para qual será aplicado o investimento. Retorne o montante final.\r\nTodos os calculos faram baseados em meses. E o valor final deve ser expresso em 2 casas decimais.\r\n\r\nJurosCompostos(2000, 0.03, 4) = 2251.02 ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132.438px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 66.2188px; transform-origin: 407px 66.2188px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFaça uma função que receba um capital inicial (C), uma taxa de juros a ser aplicada (i) e um tempo (t) para qual será aplicado o investimento. Retorne o montante final.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTodos os calculos faram baseados em meses. E o valor final deve ser expresso em 2 casas decimais.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4375px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eJurosCompostos(2000, 0.03, 4) = 2251.02 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function m = JurosCompostos(c, i, t)\r\n  % faça a sua função\r\nend","test_suite":"%%\r\nc = 2000;\r\ni = 0.03;\r\nt = 4;\r\ny_correct = 2251.02 ;\r\nassert(isequal(JurosCompostos(c, i, t) ,y_correct))\r\n\r\n\r\n%%\r\nc = 8000;\r\ni = 0.012;\r\nt = 6;\r\ny_correct = 8593.56 ;\r\nassert(isequal(JurosCompostos(c, i, t) ,y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":2564100,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-17T19:11:27.000Z","updated_at":"2026-06-02T03:53:41.000Z","published_at":"2022-09-17T19:11:27.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFaça uma função que receba um capital inicial (C), uma taxa de juros a ser aplicada (i) e um tempo (t) para qual será aplicado o investimento. Retorne o montante final.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTodos os calculos faram baseados em meses. E o valor final deve ser expresso em 2 casas decimais.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[JurosCompostos(2000, 0.03, 4) = 2251.02 ]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1382,"title":"Schwarzschild radius","description":"Compute the Schwarzschild radius for objects of mass m (kg). Use c = 299,792.458 km/s and G = 6.6738*10^-11 N*(m/kg)^2. Your function should give the result in m.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.5px 8px; transform-origin: 40.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSchwarzschild radius\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 246px 8px; transform-origin: 246px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for objects of mass m (kg). Use c = 299,792.458 km/s and G = 6.6738*10^-11 N*(m/kg)^2. Your function should give the result in m.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Schwarzschild_radius(m)\r\n  y = m;\r\nend","test_suite":"%%\r\nm = 5.98e24/81; % Moon\r\ny_correct = 1e-4; % m\r\nassert(isequal(Schwarzschild_radius(m),y_correct))\r\n\r\n%%\r\nm = 5.98e24; % Earth\r\ny_correct = 0.0089; % m\r\nassert(isequal(Schwarzschild_radius(m),y_correct))\r\n\r\n%%\r\nm = 1.89813e27; % Jupiter\r\ny_correct =  2.819; % m\r\nassert(isequal(Schwarzschild_radius(m),y_correct))\r\n\r\n%%\r\nm = 2e30; % Sun\r\ny_correct =  2970.2416; % m\r\nassert(isequal(Schwarzschild_radius(m),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":810,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":"2013-03-27T16:02:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-03-24T00:27:37.000Z","updated_at":"2026-06-25T07:37:23.000Z","published_at":"2013-03-24T00:30:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSchwarzschild radius\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for objects of mass m (kg). Use c = 299,792.458 km/s and G = 6.6738*10^-11 N*(m/kg)^2. Your function should give the result in m.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51163,"title":"Total price with tax calculation for (m) items and price (p)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 40.8889px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 20.4444px; transform-origin: 406.5px 20.4444px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 20.4444px; text-align: left; transform-origin: 383.5px 20.4444px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a code that will calculate the total price with tax (T) of (m) items that carry price (p). Consider the tax rate as (r). Round the total price to two decimal places. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = Total_price(m,n,r)\r\n\r\nend","test_suite":"%%\r\np = 1;\r\nm=2;\r\nr=0.05;\r\nT_correct = 2.1;\r\nassert(isequal(Total_price(p,m,r),T_correct))\r\n\r\n%%\r\np = 4;\r\nm=5;\r\nr=0.1;\r\nT_correct = 22;\r\nassert(isequal(Total_price(p,m,r),T_correct))\r\n\r\n%%\r\np = 4.85;\r\nm=5;\r\nr=0.1;\r\nT_correct = 26.68;\r\nassert(isequal(Total_price(p,m,r),T_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":995198,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-24T06:47:24.000Z","updated_at":"2026-06-30T14:43:15.000Z","published_at":"2021-03-24T06:47:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a code that will calculate the total price with tax (T) of (m) items that carry price (p). Consider the tax rate as (r). Round the total price to two decimal places. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56408,"title":"Zero or hero","description":"A number will be given as an input. You can be hero if it's not zero.\r\n(Just for fun)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 25.5px; transform-origin: 343px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA number will be given as an input. You can be hero if it's not zero.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(Just for fun)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 'Hero';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 0;\r\ny_correct = 'Zero';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 'Hero';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 10;\r\ny_correct = 'Hero';\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":589324,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-23T03:54:31.000Z","updated_at":"2026-07-19T16:34:37.000Z","published_at":"2022-10-23T03:54:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA number will be given as an input. You can be hero if it's not zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(Just for fun)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44473,"title":"Let's make puddings !","description":"We will make puddings with eggs, milk and sugar.\r\nTo make one pudding, we need one egg, 140(cc) of milk, 15 (g) of sugar.\r\nNow We have x eggs,  y (cc) of milk, z (g) of sugar.\r\nHow many puddings can we make?\r\n\r\neg. When we have 3 eggs, 300cc milk, 300g sugar...\r\n\r\ninput :  x = 3, y = 300, z = 300\r\n\r\noutput :  Puddings= 2","description_html":"\u003cp\u003eWe will make puddings with eggs, milk and sugar.\r\nTo make one pudding, we need one egg, 140(cc) of milk, 15 (g) of sugar.\r\nNow We have x eggs,  y (cc) of milk, z (g) of sugar.\r\nHow many puddings can we make?\u003c/p\u003e\u003cp\u003eeg. When we have 3 eggs, 300cc milk, 300g sugar...\u003c/p\u003e\u003cp\u003einput :  x = 3, y = 300, z = 300\u003c/p\u003e\u003cp\u003eoutput :  Puddings= 2\u003c/p\u003e","function_template":"function Puddings = Egg_Milk_Sugar(x,y,z)\r\n  Puddings = 100;\r\nend","test_suite":"%% 1\r\nx = 3;\r\ny = 300;\r\nz = 300;\r\nC = 2;\r\nassert(isequal(Egg_Milk_Sugar(x,y,z),C))\r\n%% 2 \r\nx = 0;\r\ny = 999;\r\nz = 999;\r\nC = 0;\r\nassert(isequal(Egg_Milk_Sugar(x,y,z),C))\r\n%% 3\r\nx = 12;\r\ny = 1000;\r\nz = 100;\r\nC = 6;\r\nassert(isequal(Egg_Milk_Sugar(x,y,z),C))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":137687,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-12-27T02:51:08.000Z","updated_at":"2026-07-09T12:41:05.000Z","published_at":"2017-12-27T03:32:17.000Z","restored_at":"2018-02-06T15:11:49.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe will make puddings with eggs, milk and sugar. To make one pudding, we need one egg, 140(cc) of milk, 15 (g) of sugar. Now We have x eggs, y (cc) of milk, z (g) of sugar. How many puddings can we make?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eeg. When we have 3 eggs, 300cc milk, 300g sugar...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einput : x = 3, y = 300, z = 300\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eoutput : Puddings= 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42976,"title":"iteration of N blank spot","description":"we have N spot which can be blank o filled calculate the number of iteration for these spots. e.g. N=2 1- blank blank 2- blank full 3- full blank 4- full full iteration is 4 e.g. N=3 1- blank blank blank 2- blank blank full 3- blank full blank 4- blank full full 5- full blank blank 6- full blank full 7- full full blank 8- full full full iteration is 8","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 372.5px 8px; transform-origin: 372.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewe have N spot which can be blank o filled calculate the number of iteration for these spots. e.g. N=2 1- blank blank 2- blank full 3- full blank 4- full full iteration is 4 e.g. N=3 1- blank blank blank 2- blank blank full 3- blank full blank 4- blank full full 5- full blank blank 6- full blank full 7- full full blank 8- full full full iteration is 8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 2;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 32;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 8;\r\ny_correct = 256;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 11;\r\ny_correct = 2048;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 16;\r\ny_correct = 65536;\r\nassert(isequal(your_fcn_name(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":86389,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":61,"test_suite_updated_at":"2021-06-17T14:24:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-09-02T16:46:32.000Z","updated_at":"2026-04-22T05:15:27.000Z","published_at":"2016-09-02T16:46:32.000Z","restored_at":"2022-02-16T22:15:33.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewe have N spot which can be blank o filled calculate the number of iteration for these spots. e.g. N=2 1- blank blank 2- blank full 3- full blank 4- full full iteration is 4 e.g. N=3 1- blank blank blank 2- blank blank full 3- blank full blank 4- blank full full 5- full blank blank 6- full blank full 7- full full blank 8- full full full iteration is 8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55935,"title":"Loja de tintas","description":"Faça um programa para uma loja de tintas. O programa deverá receber o tamanho em metros quadrados da área a ser pintada. Considere que a cobertura da tinta é de 1 litro para cada 3 metros quadrados e que a tinta é vendida em latas de 18 litros, que custam R$ 80,00. Informe ao usuário a quantidades de latas de tinta a serem compradas e o preço total.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFaça um programa para uma loja de tintas. O programa deverá receber o tamanho em metros quadrados da área a ser pintada. Considere que a cobertura da tinta é de 1 litro para cada 3 metros quadrados e que a tinta é vendida em latas de 18 litros, que custam R$ 80,00. Informe ao usuário a quantidades de latas de tinta a serem compradas e o preço total.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = QuantidadeTinta(m)\r\n  % Escreva a sua solução\r\nend","test_suite":"%%\r\nx = 9;\r\ny_correct = 3;\r\nassert(isequal(QuantidadeTinta(x),y_correct));\r\n\r\n%%\r\nx = 10;\r\ny_correct = 4;\r\nassert(isequal(QuantidadeTinta(x),y_correct));\r\n\r\n%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(QuantidadeTinta(x),y_correct));","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":2564100,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-17T20:20:44.000Z","updated_at":"2026-06-02T13:22:12.000Z","published_at":"2022-09-17T20:20:44.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFaça um programa para uma loja de tintas. O programa deverá receber o tamanho em metros quadrados da área a ser pintada. Considere que a cobertura da tinta é de 1 litro para cada 3 metros quadrados e que a tinta é vendida em latas de 18 litros, que custam R$ 80,00. Informe ao usuário a quantidades de latas de tinta a serem compradas e o preço total.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51630,"title":"Highest building","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 377.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 334px 188.7px; transform-origin: 334px 188.7px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 311px 10.4px; text-align: left; transform-origin: 311px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSketch of the outline of the buildings in a matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 311px 20.8px; text-align: left; transform-origin: 311px 20.8px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe column number of the highest building and height of it. In two or more building are the  highest, you need to choose the first one.  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 311px 10.4px; text-align: left; transform-origin: 311px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 311px 10.4px; text-align: left; transform-origin: 311px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eLet us consider buildings described by the matrix\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 80px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 331px 40px; transform-origin: 331px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 331px 10px; transform-origin: 331px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eM=[0 0 1 0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 331px 10px; transform-origin: 331px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   1 0 1 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 331px 10px; transform-origin: 331px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   1 1 1 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 331px 10px; transform-origin: 331px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   1 1 1 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cul style=\"block-size: 83.2px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 318px 41.6px; transform-origin: 318px 41.6px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.8px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 290px 10.4px; text-align: left; transform-origin: 290px 10.4px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eThe height of the first building (1st column) is 3, \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.8px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 290px 10.4px; text-align: left; transform-origin: 290px 10.4px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ethe height of the second building (2nd column) is 2,\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.8px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 290px 10.4px; text-align: left; transform-origin: 290px 10.4px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ethe height of the third building is 4,\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.8px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 290px 10.4px; text-align: left; transform-origin: 290px 10.4px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ethe height of the last building is 3.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 43.2px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 311px 21.6px; text-align: left; transform-origin: 311px 21.6px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eThe correct answer to highest_building(M) is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e3\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e4\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e] (t\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ehe\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e building n°3 is the highest with height = 4).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = highest_building(M)\r\n\r\nend","test_suite":"%%\r\nM=[0 0 1 0;\r\n   1 0 1 1;\r\n   1 1 1 1;\r\n   1 1 1 1];\r\ny_correct = [3,4];\r\nsol=highest_building(M)\r\nassert(isequal(sol,y_correct))\r\n%%\r\nM=[0 0 0 0;\r\n   0 0 0 0;\r\n   0 0 0 0;\r\n   0 0 0 1];\r\ny_correct = [4,1];\r\nsol=highest_building(M)\r\nassert(isequal(sol,y_correct))\r\n%%\r\nM=[1 0 0 0 0;\r\n   1 1 0 0 0;\r\n   1 1 1 1 0;\r\n   1 1 1 1 1];\r\ny_correct = [1,4];\r\nsol=highest_building(M)\r\nassert(isequal(sol,y_correct))\r\n%%\r\nM=[0 0 0 0 0 0 0;\r\n   0 0 1 1 0 0 0;\r\n   1 1 1 1 1 1 0;\r\n   1 1 1 1 1 1 1];\r\ny_correct = [3,3];\r\nsol=highest_building(M)\r\nassert(isequal(sol,y_correct))\r\n%%\r\nM=zeros(randi([10,15]),randi([10,15]));\r\ny_correct = [0,0];\r\nfor j=1:size(M,2)\r\n    v=ones(randi([1,size(M,1)]),1);\r\n    M(1:numel(v),j)=v;\r\n    if sum(v)\u003ey_correct(2)\r\n        y_correct = [j,sum(v)];\r\n    end\r\nend\r\nM=M(end:-1:1,:);\r\nsol=highest_building(M);\r\nassert(isequal(sol,y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-05-01T14:35:42.000Z","updated_at":"2026-06-05T09:28:16.000Z","published_at":"2021-05-01T15:11:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eSketch of the outline of the buildings in a matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe column number of the highest building and height of it. In two or more building are the  highest, you need to choose the first one.  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet us consider buildings described by the matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[M=[0 0 1 0;\\n   1 0 1 1;\\n   1 1 1 1;\\n   1 1 1 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe height of the first building (1st column) is 3, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe height of the second building (2nd column) is 2,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe height of the third building is 4,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe height of the last building is 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThe correct answer to highest_building(M) is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e] (t\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ehe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e building n°3 is the highest with height = 4).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":49657,"title":"Determine the area of square if length of the diagonal is given","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe have to find the area of square if the length of the diagonal of a square is given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 4;\r\ny_correct = 8;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":822117,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":76,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-29T15:05:52.000Z","updated_at":"2026-07-17T11:17:58.000Z","published_at":"2020-12-29T15:05:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe have to find the area of square if the length of the diagonal of a square is given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55160,"title":"Find distance travelled by an object starting from rest in time 't' and linear acceleration 'a' = 3t","description":"Find distance travelled by an object starting from rest in time 't' with linear acceleration a = 3t. You are given time t as an input to the function.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind distance travelled by an object starting from rest in time 't' with linear acceleration a = 3t. You are given time t as an input to the function.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = your_fcn_name(t)\r\n  s = a;\r\nend","test_suite":"%%\r\nt = 2;\r\ny_correct = 4;\r\nassert(isequal(your_fcn_name(t),y_correct))\r\n\r\n%%\r\nt = 0;\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(t),y_correct))\r\n\r\n%%\r\nt = 1;\r\ny_correct = 0.5;\r\nassert(isequal(your_fcn_name(t),y_correct))\r\n\r\n%%\r\nt = 12;\r\ny_correct = 864;\r\nassert(isequal(your_fcn_name(t),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":2439180,"edited_by":2439180,"edited_at":"2022-07-13T19:07:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":41,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-13T19:07:08.000Z","updated_at":"2026-07-20T16:58:04.000Z","published_at":"2022-07-13T19:07:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind distance travelled by an object starting from rest in time 't' with linear acceleration a = 3t. You are given time t as an input to the function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44634,"title":"Basic matrix operations using standard MATLAB commands","description":"Create the matrix:\r\n\r\n 1.0e+15 *\r\n\r\n    0.0000    0.0000    0.0000    0.0000    0.0000\r\n    0.0000    0.0000    0.0000    0.0000    0.0000\r\n    0.0001    0.0010    0.0100    0.1000    1.0000\r\n\r\nFind the row vector of all column means\r\n\r\nHint: Use _logspace_ to create the matrix. Avoid looking at the test suite before writing a solution","description_html":"\u003cp\u003eCreate the matrix:\u003c/p\u003e\u003cpre\u003e 1.0e+15 *\u003c/pre\u003e\u003cpre\u003e    0.0000    0.0000    0.0000    0.0000    0.0000\r\n    0.0000    0.0000    0.0000    0.0000    0.0000\r\n    0.0001    0.0010    0.0100    0.1000    1.0000\u003c/pre\u003e\u003cp\u003eFind the row vector of all column means\u003c/p\u003e\u003cp\u003eHint: Use \u003ci\u003elogspace\u003c/i\u003e to create the matrix. Avoid looking at the test suite before writing a solution\u003c/p\u003e","function_template":"function y = matrix_ls_means()\r\n  y = x;\r\nend","test_suite":"%%\r\ny_correct = mean([logspace(1,5,5);logspace(6,10,5);logspace(11,15,5)]);\r\nassert(isequal(matrix_ls_means(),y_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":171559,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":58,"test_suite_updated_at":"2018-05-09T05:37:01.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-05-09T05:32:41.000Z","updated_at":"2026-07-14T15:34:29.000Z","published_at":"2018-05-09T05:35:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate the matrix:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 1.0e+15 *\\n\\n    0.0000    0.0000    0.0000    0.0000    0.0000\\n    0.0000    0.0000    0.0000    0.0000    0.0000\\n    0.0001    0.0010    0.0100    0.1000    1.0000]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the row vector of all column means\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Use\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elogspace\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to create the matrix. Avoid looking at the test suite before writing a solution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47493,"title":"reverse the order and combine a matrix","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ea cool way to shape a Matrix \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(x)  \r\ny=x;\r\nend","test_suite":"%%\r\nx = 1:6\r\ny_correct = [6,5,4,3,2,1; 1,2,3,4,5,6]';\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":3,"created_by":541988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":70,"test_suite_updated_at":"2020-11-13T19:51:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-13T02:37:10.000Z","updated_at":"2026-07-19T16:35:55.000Z","published_at":"2020-11-13T19:51:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea cool way to shape a Matrix \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54094,"title":"Check if a matrix Diagonal is equal to its secondary diagonal ","description":"Your function should return True if the secondary diagonal is equal to diagonal, and False otherwise.\r\nEg: M = [1 2 1 \r\n               3 4 4\r\n               7 5 7]\r\nThe output is True\r\nM=[1 2\r\n       1 2]\r\nThe output is False. Always check the diagonal top to bottom. Return True if the matrix is empty.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 231px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 115.5px; transform-origin: 407px 115.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYour function should return True if the secondary diagonal is equal to diagonal, and False otherwise.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEg: M = [1 2 1 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e               3 4 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e               7 5 7]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe output is True\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eM=[1 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e       1 2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe output is False. Always check the diagonal top to bottom. Return True if the matrix is empty.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = check_Diagonals(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = [1 2 1; 3 4 4 ; 7 5 7];\r\ny_correct = 1;\r\nassert(isequal(check_Diagonals(x),y_correct))\r\n\r\n%%\r\nx = [1 2 ; 1 2];\r\ny_correct = 0;\r\nassert(isequal(check_Diagonals(x),y_correct))\r\n\r\n%%\r\nx = [1 2 ; 1 2];\r\ny_correct = 0;\r\nassert(isequal(check_Diagonals(x),y_correct))\r\n\r\n%%\r\nx = [7];\r\ny_correct = 1;\r\nassert(isequal(check_Diagonals(x),y_correct))\r\n\r\n%%\r\nx = [];\r\ny_correct = 1;\r\nassert(isequal(check_Diagonals(x),y_correct))\r\n\r\n%%\r\nx = [17 21 13 4 17; -4 21 -1 21 56 ; 4 99 26 156 -352; 43 5 0 5 6; 9 1 49 101 9];\r\ny_correct=1;\r\nassert(isequal(check_Diagonals(x),y_correct))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":1985630,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":40,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-03-04T17:27:28.000Z","updated_at":"2026-06-01T01:20:53.000Z","published_at":"2022-03-04T17:27:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function should return True if the secondary diagonal is equal to diagonal, and False otherwise.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEg: M = [1 2 1 \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e               3 4 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e               7 5 7]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe output is True\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eM=[1 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e       1 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe output is False. Always check the diagonal top to bottom. Return True if the matrix is empty.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55195,"title":"Sequence","description":"Let S be a sequence of numbers \r\n\r\nLet \r\n\r\nFind  for some , where  and .\r\n\r\nUpdate - test suite cleaned up on 2-9-22","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 204px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 102px; transform-origin: 407px 102px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 105px 8px; transform-origin: 105px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet S be a sequence of numbers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 52px; height: 20px;\" width=\"52\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 102px; height: 20px;\" width=\"102\" height=\"20\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 15px; height: 20px;\" width=\"15\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 31.5px 8px; transform-origin: 31.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for some \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 25px 8px; transform-origin: 25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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0px; margin-top: 0px; perspective-origin: 127.5px 8px; transform-origin: 127.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUpdate - test suite cleaned up on 2-9-22\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = summation(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nassert(isequal(summation(1),1))\r\n%%\r\nassert(isequal(summation(2),2))\r\n%%\r\nassert(isequal(summation(3),1))\r\n%%\r\nassert(isequal(summation(4),-1))\r\n%%\r\nassert(isequal(summation(5),-2))\r\n%%\r\nassert(isequal(summation(6),-1))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":2457030,"edited_by":223089,"edited_at":"2022-09-02T13:52:45.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":"2022-09-02T13:49:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-07-13T21:23:39.000Z","updated_at":"2026-06-02T00:29:40.000Z","published_at":"2022-07-13T21:23:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" 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radius represents the radius of the circular path followed by a vehicle.\r\nGiven Wheelbase L and Steering angle δ, Compute the turning radius R.\r\nEquation:\r\nR = L / tan(delta)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 110.906px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 467.484px 55.4531px; transform-origin: 467.496px 55.4531px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe turning radius represents the radius of the circular path followed by a vehicle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven Wheelbase \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eL and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSteering angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eδ, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the turning radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eR\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEquation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.9766px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 443.508px 10.4766px; text-align: left; transform-origin: 443.508px 10.4883px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eR = L / tan(delta)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function R = turningRadius(L,delta)\r\nR = 0;\r\nend","test_suite":"%%\r\nL = 2.5; delta = 30*pi/180;\r\nR_expected = 4.3301;\r\nassert(abs(turningRadius(L,delta) - R_expected) \u003c 1e-3)\r\n\r\n%%\r\nL = 3.0; delta = 20*pi/180;\r\nR_expected = 8.2426;\r\nassert(abs(turningRadius(L,delta) - R_expected) \u003c 1e-3)\r\n\r\n%%\r\nL = 2.8; delta = 10*pi/180;\r\nR_expected = 15.866;\r\nassert(abs(turningRadius(L,delta) - R_expected) \u003c 1e-1)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-04-28T09:16:45.000Z","deleted_by":null,"deleted_at":null,"solvers_count":47,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-04-28T09:13:54.000Z","updated_at":"2026-07-01T17:26:00.000Z","published_at":"2026-04-28T09:16:45.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe turning radius represents the radius of the circular path followed by a vehicle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven Wheelbase \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eSteering angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eδ, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the turning radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEquation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = L / tan(delta)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2121,"title":"Find offset of given matrix element from first matrix element","description":"Given matrix m and an element of that matrix, return the offset from its first element.\r\ne.g. m=[11 2 34; 40 51 6; 87 8 109]\r\nelement = 51\r\nThen, offset = 5\r\n\r\nReturn 0, if that element if not a matrix element","description_html":"\u003cp\u003eGiven matrix m and an element of that matrix, return the offset from its first element.\r\ne.g. m=[11 2 34; 40 51 6; 87 8 109]\r\nelement = 51\r\nThen, offset = 5\u003c/p\u003e\u003cp\u003eReturn 0, if that element if not a matrix element\u003c/p\u003e","function_template":"function offset= FindOffset(m, element)\r\n  y = x;\r\nend","test_suite":"%%\r\nm=[11 2 34; 40 51 6; 87 8 109]\r\nelement = 51;\r\noffset = 5;\r\nassert(isequal(FindOffset(m,element),offset));\r\n\r\n%%\r\nm=reshape([1:10],5,2);\r\nelement = 9;\r\noffset = 9;\r\nassert(isequal(FindOffset(m,element),offset));\r\n\r\n%%\r\nm=eye(7);\r\nelement = 0;\r\noffset = 2;\r\nassert(isequal(FindOffset(m,element),offset));\r\n\r\n%%\r\nm=[10 20 30 40; 50 60 70 80;];\r\nelement = 56;\r\noffset = 0;\r\nassert(isequal(FindOffset(m,element),offset));\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":16381,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":85,"test_suite_updated_at":"2014-01-15T19:28:24.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-01-15T19:21:32.000Z","updated_at":"2026-02-28T08:07:23.000Z","published_at":"2014-01-15T19:21:46.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven matrix m and an element of that matrix, return the offset from its first element. e.g. m=[11 2 34; 40 51 6; 87 8 109] element = 51 Then, offset = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn 0, if that element if not a matrix element\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47380,"title":"Intercambiar columnas - UC3M","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 220.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 110.2px; transform-origin: 407px 110.2px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 41.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.8px; text-align: left; transform-origin: 384px 20.8px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ex es una matriz cuadrada nxn. Necesitamos intercambiar los valores de la primera columna por los de la última, las demás se quedan igual.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePor ejemplo, si\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ex=[ 1 2 3 4;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e      5 6 7 8]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003equeremos conseguir \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ey=[ 4 2 3 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.4px; text-align: left; transform-origin: 384px 10.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e      8 6 7 5]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function x = intercambiarCols(x)\r\n% La nueva matriz tambien se guarda en la variable x\r\n\r\nend","test_suite":"%%\r\nx = [1 2 3;4 5 6];\r\ny_correct = [3 2 1;6 5 4];\r\nassert(isequal(intercambiarCols(x),y_correct))\r\n%%\r\nx = [1 2 3 4;5 6 7 8];\r\ny_correct = [4 2 3 1;8 6 7 5];\r\nassert(isequal(intercambiarCols(x),y_correct))\r\n%%\r\nx = [1 2 3 4 5; 6 7 8 9 10];\r\ny_correct = [5 2 3 4 1;10 7 8 9 6];\r\nassert(isequal(intercambiarCols(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":583531,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":37,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-11-06T14:40:40.000Z","updated_at":"2026-05-30T19:12:31.000Z","published_at":"2020-11-06T14:40:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex es una matriz cuadrada nxn. 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