{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","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":"2025-12-14T00:00:00.000Z","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":272,"title":"Generalized N-Cards Problem","description":"Preface: This is a generalized version of the problem I presented \u003chttp://www.mathworks.com/matlabcentral/cody/problems/271-n-cards-problem here\u003e.\r\n\r\nYou have a deck of N cards numbered in order from 1 to N. You are given a pattern to discard a certain number of cards and move a number of cards to the bottom of the deck. Eventually, you will have one card left. What is the number of that card?\r\n\r\nThe sequence of discarding/moving cards will be given in a row vector of 1s and -1s where 1 represents moving a card to the bottom of the deck and -1 represents discarding a card. This sequence should be repeated until there is only one card left (e.g. [-1 1] would return this problem to the non-generalized case).\r\n\r\n*Example*\r\n\r\n    generalNCardsProblem(5,[-1 1])\r\n    deck = [ 1 2 3 4 5 ]\r\n    deck = [ 2 3 4 5 ]\r\n    deck = [ 3 4 5 2 ]\r\n    deck = [ 4 5 2 ]\r\n    deck = [ 5 2 4 ]\r\n    deck = [ 2 4 ]\r\n    deck = [ 4 2 ]\r\n    deck = [ 2 ]\r\n\r\n    generalNCardsProblem(5,[-1 1 1 -1])\r\n    deck = [ 1 2 3 4 5 ]\r\n    deck = [ 2 3 4 5 ]\r\n    deck = [ 3 4 5 2 ]\r\n    deck = [ 4 5 2 3 ]\r\n    deck = [ 5 2 3 ]\r\n    deck = [ 2 3 ]\r\n    deck = [ 3 2 ]\r\n    deck = [ 2 3 ]\r\n    deck = [ 3 ]","description_html":"\u003cp\u003ePreface: This is a generalized version of the problem I presented \u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/271-n-cards-problem\"\u003ehere\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eYou have a deck of N cards numbered in order from 1 to N. You are given a pattern to discard a certain number of cards and move a number of cards to the bottom of the deck. Eventually, you will have one card left. What is the number of that card?\u003c/p\u003e\u003cp\u003eThe sequence of discarding/moving cards will be given in a row vector of 1s and -1s where 1 represents moving a card to the bottom of the deck and -1 represents discarding a card. This sequence should be repeated until there is only one card left (e.g. [-1 1] would return this problem to the non-generalized case).\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample\u003c/b\u003e\u003c/p\u003e\u003cpre\u003e    generalNCardsProblem(5,[-1 1])\r\n    deck = [ 1 2 3 4 5 ]\r\n    deck = [ 2 3 4 5 ]\r\n    deck = [ 3 4 5 2 ]\r\n    deck = [ 4 5 2 ]\r\n    deck = [ 5 2 4 ]\r\n    deck = [ 2 4 ]\r\n    deck = [ 4 2 ]\r\n    deck = [ 2 ]\u003c/pre\u003e\u003cpre\u003e    generalNCardsProblem(5,[-1 1 1 -1])\r\n    deck = [ 1 2 3 4 5 ]\r\n    deck = [ 2 3 4 5 ]\r\n    deck = [ 3 4 5 2 ]\r\n    deck = [ 4 5 2 3 ]\r\n    deck = [ 5 2 3 ]\r\n    deck = [ 2 3 ]\r\n    deck = [ 3 2 ]\r\n    deck = [ 2 3 ]\r\n    deck = [ 3 ]\u003c/pre\u003e","function_template":"function y = generalNCardsProblem(N,S)\r\n  y = N;\r\nend","test_suite":"%%\r\nx = 1;\r\nS = [-1 1];\r\ny_correct = 1;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 5;\r\nS = [-1 1];\r\ny_correct = 2;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 50;\r\nS = [-1 1];\r\ny_correct = 36;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 1000;\r\nS = [-1 1];\r\ny_correct = 976;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 10000;\r\nS = [-1 1];\r\ny_correct = 3616;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 5;\r\nS = [-1 1 1 -1];\r\ny_correct = 3;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 301;\r\nS = [-1 1 1 -1];\r\ny_correct = 91;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 2012;\r\nS = [1 -1 -1 1 -1 1 1 1 1 -1 -1 1 -1];\r\ny_correct = 1832;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 12345;\r\nS = [-1];\r\ny_correct = 12345;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":"2012-02-06T22:32:02.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-06T22:32:02.000Z","updated_at":"2025-11-13T18:00:35.000Z","published_at":"2012-02-06T22:32:02.000Z","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\u003ePreface: This is a generalized version of the problem I presented\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/271-n-cards-problem\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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:r\u003e\u003cw:t\u003eYou have a deck of N cards numbered in order from 1 to N. You are given a pattern to discard a certain number of cards and move a number of cards to the bottom of the deck. Eventually, you will have one card left. What is the number of that card?\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 sequence of discarding/moving cards will be given in a row vector of 1s and -1s where 1 represents moving a card to the bottom of the deck and -1 represents discarding a card. This sequence should be repeated until there is only one card left (e.g. [-1 1] would return this problem to the non-generalized 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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\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=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    generalNCardsProblem(5,[-1 1])\\n    deck = [ 1 2 3 4 5 ]\\n    deck = [ 2 3 4 5 ]\\n    deck = [ 3 4 5 2 ]\\n    deck = [ 4 5 2 ]\\n    deck = [ 5 2 4 ]\\n    deck = [ 2 4 ]\\n    deck = [ 4 2 ]\\n    deck = [ 2 ]\\n\\n    generalNCardsProblem(5,[-1 1 1 -1])\\n    deck = [ 1 2 3 4 5 ]\\n    deck = [ 2 3 4 5 ]\\n    deck = [ 3 4 5 2 ]\\n    deck = [ 4 5 2 3 ]\\n    deck = [ 5 2 3 ]\\n    deck = [ 2 3 ]\\n    deck = [ 3 2 ]\\n    deck = [ 2 3 ]\\n    deck = [ 3 ]]]\u003e\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":2318,"title":"Combine Cards to make 21","description":"Given between two and six cards, e.g.\r\n\r\n A _ 3 _ 7 _ 6 _ 2\r\n\r\nplace one of the mathematical symbols (+,-,*,/) in the space between each\r\npair of cards to make the equation equal 21.\r\n\r\nThe input will be a string, e.g.\r\n\r\n* 'A3762'\r\n\r\nThe output should be a cell array of mathematical symbols in the order that satisfies the puzzle, e.g. for the string given above, the output would be:\r\n\r\n  {'+-*/'}\r\n\r\nWhich means that A + 3 - 7 * 6 / 2 = 21.\r\n\r\n*  A + 3 = 14\r\n* 14 - 7 = 7\r\n*  7 * 6 = 42\r\n* 42 / 2 = 21\r\n\r\nRules:\r\n\r\n* The Ace can represent either 1 or 11.\r\n* All operations should be performed from left to right\r\n* Cards will be represented by the characters: A,2,3,4,5,6,7,8,9,J,Q,K\r\n","description_html":"\u003cp\u003eGiven between two and six cards, e.g.\u003c/p\u003e\u003cpre\u003e A _ 3 _ 7 _ 6 _ 2\u003c/pre\u003e\u003cp\u003eplace one of the mathematical symbols (+,-,*,/) in the space between each\r\npair of cards to make the equation equal 21.\u003c/p\u003e\u003cp\u003eThe input will be a string, e.g.\u003c/p\u003e\u003cul\u003e\u003cli\u003e'A3762'\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe output should be a cell array of mathematical symbols in the order that satisfies the puzzle, e.g. for the string given above, the output would be:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e{'+-*/'}\r\n\u003c/pre\u003e\u003cp\u003eWhich means that A + 3 - 7 * 6 / 2 = 21.\u003c/p\u003e\u003cul\u003e\u003cli\u003eA + 3 = 14\u003c/li\u003e\u003cli\u003e14 - 7 = 7\u003c/li\u003e\u003cli\u003e7 * 6 = 42\u003c/li\u003e\u003cli\u003e42 / 2 = 21\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eRules:\u003c/p\u003e\u003cul\u003e\u003cli\u003eThe Ace can represent either 1 or 11.\u003c/li\u003e\u003cli\u003eAll operations should be performed from left to right\u003c/li\u003e\u003cli\u003eCards will be represented by the characters: A,2,3,4,5,6,7,8,9,J,Q,K\u003c/li\u003e\u003c/ul\u003e","function_template":"function mathSyms = solveBlackjackPuzzle(cards)\r\n  mathSyms  = {'+'};\r\nend","test_suite":"%% Example Case\r\ncards = 'A3762';\r\nmathSymbols = {'+-*/'};\r\nassert(isequal(sort(solveBlackjackPuzzle(cards)), sort(mathSymbols)))\r\n\r\n%%\r\ncards = 'A23QJK';\r\nmathSymbols = {'+-/++'};\r\nassert(isequal(sort(solveBlackjackPuzzle(cards)), sort(mathSymbols)))\r\n\r\n%%\r\ncards = '923';\r\nmathSymbols = {'*+', '-*'};\r\nassert(isequal(sort(solveBlackjackPuzzle(cards)), sort(mathSymbols)))\r\n\r\n%%\r\ncards = 'A23456';\r\nmathSymbols = {'**+++', '*+*-+', '*-+*+', '+++++', '+++-+', '-+/*+', '--+++', '/-*++', '/--+*'};\r\nassert(isequal(sort(solveBlackjackPuzzle(cards)), sort(mathSymbols)))\r\n\r\n%%\r\ncards = 'JQKA';\r\nmathSymbols = {'*/+', '+-+', '-++', '/*+'};\r\nassert(isequal(sort(solveBlackjackPuzzle(cards)), sort(mathSymbols)))\r\n\r\n%%\r\ncards = 'KA';\r\nmathSymbols = {'+'};\r\nassert(isequal(sort(solveBlackjackPuzzle(cards)), sort(mathSymbols)))\r\n\r\n%%\r\ncards = 'AAA';\r\nmathSymbols =  {'+-','-+'};\r\nassert(isequal(sort(solveBlackjackPuzzle(cards)), sort(mathSymbols)))","published":true,"deleted":false,"likes_count":4,"comments_count":4,"created_by":1446,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":40,"test_suite_updated_at":"2014-05-16T13:53:18.000Z","rescore_all_solutions":false,"group_id":15,"created_at":"2014-05-13T15:52:33.000Z","updated_at":"2026-02-15T04:01:31.000Z","published_at":"2014-05-13T15:53:27.000Z","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 between two and six cards, e.g.\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[ A _ 3 _ 7 _ 6 _ 2]]\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\u003eplace one of the mathematical symbols (+,-,*,/) in the space between each pair of cards to make the equation equal 21.\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 input will be a string, e.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\u003e'A3762'\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 output should be a cell array of mathematical symbols in the order that satisfies the puzzle, e.g. for the string given above, the output would be:\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[{'+-*/'}]]\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\u003eWhich means that A + 3 - 7 * 6 / 2 = 21.\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 + 3 = 14\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\u003e14 - 7 = 7\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\u003e7 * 6 = 42\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\u003e42 / 2 = 21\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\u003eRules:\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\u003eThe Ace can represent either 1 or 11.\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\u003eAll operations should be performed from left to right\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\u003eCards will be represented by the characters: A,2,3,4,5,6,7,8,9,J,Q,K\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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":272,"title":"Generalized N-Cards Problem","description":"Preface: This is a generalized version of the problem I presented \u003chttp://www.mathworks.com/matlabcentral/cody/problems/271-n-cards-problem here\u003e.\r\n\r\nYou have a deck of N cards numbered in order from 1 to N. You are given a pattern to discard a certain number of cards and move a number of cards to the bottom of the deck. Eventually, you will have one card left. What is the number of that card?\r\n\r\nThe sequence of discarding/moving cards will be given in a row vector of 1s and -1s where 1 represents moving a card to the bottom of the deck and -1 represents discarding a card. This sequence should be repeated until there is only one card left (e.g. [-1 1] would return this problem to the non-generalized case).\r\n\r\n*Example*\r\n\r\n    generalNCardsProblem(5,[-1 1])\r\n    deck = [ 1 2 3 4 5 ]\r\n    deck = [ 2 3 4 5 ]\r\n    deck = [ 3 4 5 2 ]\r\n    deck = [ 4 5 2 ]\r\n    deck = [ 5 2 4 ]\r\n    deck = [ 2 4 ]\r\n    deck = [ 4 2 ]\r\n    deck = [ 2 ]\r\n\r\n    generalNCardsProblem(5,[-1 1 1 -1])\r\n    deck = [ 1 2 3 4 5 ]\r\n    deck = [ 2 3 4 5 ]\r\n    deck = [ 3 4 5 2 ]\r\n    deck = [ 4 5 2 3 ]\r\n    deck = [ 5 2 3 ]\r\n    deck = [ 2 3 ]\r\n    deck = [ 3 2 ]\r\n    deck = [ 2 3 ]\r\n    deck = [ 3 ]","description_html":"\u003cp\u003ePreface: This is a generalized version of the problem I presented \u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/271-n-cards-problem\"\u003ehere\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eYou have a deck of N cards numbered in order from 1 to N. You are given a pattern to discard a certain number of cards and move a number of cards to the bottom of the deck. Eventually, you will have one card left. What is the number of that card?\u003c/p\u003e\u003cp\u003eThe sequence of discarding/moving cards will be given in a row vector of 1s and -1s where 1 represents moving a card to the bottom of the deck and -1 represents discarding a card. This sequence should be repeated until there is only one card left (e.g. [-1 1] would return this problem to the non-generalized case).\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample\u003c/b\u003e\u003c/p\u003e\u003cpre\u003e    generalNCardsProblem(5,[-1 1])\r\n    deck = [ 1 2 3 4 5 ]\r\n    deck = [ 2 3 4 5 ]\r\n    deck = [ 3 4 5 2 ]\r\n    deck = [ 4 5 2 ]\r\n    deck = [ 5 2 4 ]\r\n    deck = [ 2 4 ]\r\n    deck = [ 4 2 ]\r\n    deck = [ 2 ]\u003c/pre\u003e\u003cpre\u003e    generalNCardsProblem(5,[-1 1 1 -1])\r\n    deck = [ 1 2 3 4 5 ]\r\n    deck = [ 2 3 4 5 ]\r\n    deck = [ 3 4 5 2 ]\r\n    deck = [ 4 5 2 3 ]\r\n    deck = [ 5 2 3 ]\r\n    deck = [ 2 3 ]\r\n    deck = [ 3 2 ]\r\n    deck = [ 2 3 ]\r\n    deck = [ 3 ]\u003c/pre\u003e","function_template":"function y = generalNCardsProblem(N,S)\r\n  y = N;\r\nend","test_suite":"%%\r\nx = 1;\r\nS = [-1 1];\r\ny_correct = 1;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 5;\r\nS = [-1 1];\r\ny_correct = 2;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 50;\r\nS = [-1 1];\r\ny_correct = 36;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 1000;\r\nS = [-1 1];\r\ny_correct = 976;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 10000;\r\nS = [-1 1];\r\ny_correct = 3616;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 5;\r\nS = [-1 1 1 -1];\r\ny_correct = 3;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 301;\r\nS = [-1 1 1 -1];\r\ny_correct = 91;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 2012;\r\nS = [1 -1 -1 1 -1 1 1 1 1 -1 -1 1 -1];\r\ny_correct = 1832;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))\r\n\r\n%%\r\nx = 12345;\r\nS = [-1];\r\ny_correct = 12345;\r\nassert(isequal(generalNCardsProblem(x,S),y_correct))","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":"2012-02-06T22:32:02.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-06T22:32:02.000Z","updated_at":"2025-11-13T18:00:35.000Z","published_at":"2012-02-06T22:32:02.000Z","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\u003ePreface: This is a generalized version of the problem I presented\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/271-n-cards-problem\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehere\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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:r\u003e\u003cw:t\u003eYou have a deck of N cards numbered in order from 1 to N. You are given a pattern to discard a certain number of cards and move a number of cards to the bottom of the deck. Eventually, you will have one card left. What is the number of that card?\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 sequence of discarding/moving cards will be given in a row vector of 1s and -1s where 1 represents moving a card to the bottom of the deck and -1 represents discarding a card. This sequence should be repeated until there is only one card left (e.g. [-1 1] would return this problem to the non-generalized 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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\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=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    generalNCardsProblem(5,[-1 1])\\n    deck = [ 1 2 3 4 5 ]\\n    deck = [ 2 3 4 5 ]\\n    deck = [ 3 4 5 2 ]\\n    deck = [ 4 5 2 ]\\n    deck = [ 5 2 4 ]\\n    deck = [ 2 4 ]\\n    deck = [ 4 2 ]\\n    deck = [ 2 ]\\n\\n    generalNCardsProblem(5,[-1 1 1 -1])\\n    deck = [ 1 2 3 4 5 ]\\n    deck = [ 2 3 4 5 ]\\n    deck = [ 3 4 5 2 ]\\n    deck = [ 4 5 2 3 ]\\n    deck = [ 5 2 3 ]\\n    deck = [ 2 3 ]\\n    deck = [ 3 2 ]\\n    deck = [ 2 3 ]\\n    deck = [ 3 ]]]\u003e\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":2318,"title":"Combine Cards to make 21","description":"Given between two and six cards, e.g.\r\n\r\n A _ 3 _ 7 _ 6 _ 2\r\n\r\nplace one of the mathematical symbols (+,-,*,/) in the space between each\r\npair of cards to make the equation equal 21.\r\n\r\nThe input will be a string, e.g.\r\n\r\n* 'A3762'\r\n\r\nThe output should be a cell array of mathematical symbols in the order that satisfies the puzzle, e.g. for the string given above, the output would be:\r\n\r\n  {'+-*/'}\r\n\r\nWhich means that A + 3 - 7 * 6 / 2 = 21.\r\n\r\n*  A + 3 = 14\r\n* 14 - 7 = 7\r\n*  7 * 6 = 42\r\n* 42 / 2 = 21\r\n\r\nRules:\r\n\r\n* The Ace can represent either 1 or 11.\r\n* All operations should be performed from left to right\r\n* Cards will be represented by the characters: A,2,3,4,5,6,7,8,9,J,Q,K\r\n","description_html":"\u003cp\u003eGiven between two and six cards, e.g.\u003c/p\u003e\u003cpre\u003e A _ 3 _ 7 _ 6 _ 2\u003c/pre\u003e\u003cp\u003eplace one of the mathematical symbols (+,-,*,/) in the space between each\r\npair of cards to make the equation equal 21.\u003c/p\u003e\u003cp\u003eThe input will be a string, e.g.\u003c/p\u003e\u003cul\u003e\u003cli\u003e'A3762'\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe output should be a cell array of mathematical symbols in the order that satisfies the puzzle, e.g. for the string given above, the output would be:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e{'+-*/'}\r\n\u003c/pre\u003e\u003cp\u003eWhich means that A + 3 - 7 * 6 / 2 = 21.\u003c/p\u003e\u003cul\u003e\u003cli\u003eA + 3 = 14\u003c/li\u003e\u003cli\u003e14 - 7 = 7\u003c/li\u003e\u003cli\u003e7 * 6 = 42\u003c/li\u003e\u003cli\u003e42 / 2 = 21\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eRules:\u003c/p\u003e\u003cul\u003e\u003cli\u003eThe Ace can represent either 1 or 11.\u003c/li\u003e\u003cli\u003eAll operations should be performed from left to right\u003c/li\u003e\u003cli\u003eCards will be represented by the characters: A,2,3,4,5,6,7,8,9,J,Q,K\u003c/li\u003e\u003c/ul\u003e","function_template":"function mathSyms = solveBlackjackPuzzle(cards)\r\n  mathSyms  = {'+'};\r\nend","test_suite":"%% Example Case\r\ncards = 'A3762';\r\nmathSymbols = {'+-*/'};\r\nassert(isequal(sort(solveBlackjackPuzzle(cards)), sort(mathSymbols)))\r\n\r\n%%\r\ncards = 'A23QJK';\r\nmathSymbols = {'+-/++'};\r\nassert(isequal(sort(solveBlackjackPuzzle(cards)), sort(mathSymbols)))\r\n\r\n%%\r\ncards = '923';\r\nmathSymbols = {'*+', '-*'};\r\nassert(isequal(sort(solveBlackjackPuzzle(cards)), sort(mathSymbols)))\r\n\r\n%%\r\ncards = 'A23456';\r\nmathSymbols = {'**+++', '*+*-+', '*-+*+', '+++++', '+++-+', '-+/*+', '--+++', '/-*++', '/--+*'};\r\nassert(isequal(sort(solveBlackjackPuzzle(cards)), sort(mathSymbols)))\r\n\r\n%%\r\ncards = 'JQKA';\r\nmathSymbols = {'*/+', '+-+', '-++', '/*+'};\r\nassert(isequal(sort(solveBlackjackPuzzle(cards)), sort(mathSymbols)))\r\n\r\n%%\r\ncards = 'KA';\r\nmathSymbols = {'+'};\r\nassert(isequal(sort(solveBlackjackPuzzle(cards)), sort(mathSymbols)))\r\n\r\n%%\r\ncards = 'AAA';\r\nmathSymbols =  {'+-','-+'};\r\nassert(isequal(sort(solveBlackjackPuzzle(cards)), sort(mathSymbols)))","published":true,"deleted":false,"likes_count":4,"comments_count":4,"created_by":1446,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":40,"test_suite_updated_at":"2014-05-16T13:53:18.000Z","rescore_all_solutions":false,"group_id":15,"created_at":"2014-05-13T15:52:33.000Z","updated_at":"2026-02-15T04:01:31.000Z","published_at":"2014-05-13T15:53:27.000Z","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 between two and six cards, e.g.\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[ A _ 3 _ 7 _ 6 _ 2]]\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\u003eplace one of the mathematical symbols (+,-,*,/) in the space between each pair of cards to make the equation equal 21.\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 input will be a string, e.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\u003e'A3762'\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 output should be a cell array of mathematical symbols in the order that satisfies the puzzle, e.g. for the string given above, the output would be:\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[{'+-*/'}]]\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\u003eWhich means that A + 3 - 7 * 6 / 2 = 21.\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 + 3 = 14\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\u003e14 - 7 = 7\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\u003e7 * 6 = 42\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\u003e42 / 2 = 21\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\u003eRules:\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\u003eThe Ace can represent either 1 or 11.\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\u003eAll operations should be performed from left to right\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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