{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":1393,"title":"A (wrong) place for everything, and everything in its (wrong) place","description":"You have an equal number of cups and balls, each labelled from one to N.  You randomly place one ball in each cup.  Determine the number of possible combinations such that no balls are in the cup with a matching number.  For example, if you have three balls and three cups, there are two valid solutions:\r\n\r\n* 2, 3, 1\r\n* 3, 1, 2\r\n\r\nThe following permutations do not meet the criteria for the reasons listed:\r\n\r\n* 1, 2, 3  (all three balls are in the correct cups)\r\n* 1, 3, 2  (ball 1 is in cup 1)\r\n* 3, 2, 1  (ball 2 is in cup 2)\r\n* 2, 1, 3  (ball 3 is in cup 3)\r\n\r\nGood luck!","description_html":"\u003cp\u003eYou have an equal number of cups and balls, each labelled from one to N.  You randomly place one ball in each cup.  Determine the number of possible combinations such that no balls are in the cup with a matching number.  For example, if you have three balls and three cups, there are two valid solutions:\u003c/p\u003e\u003cul\u003e\u003cli\u003e2, 3, 1\u003c/li\u003e\u003cli\u003e3, 1, 2\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe following permutations do not meet the criteria for the reasons listed:\u003c/p\u003e\u003cul\u003e\u003cli\u003e1, 2, 3  (all three balls are in the correct cups)\u003c/li\u003e\u003cli\u003e1, 3, 2  (ball 1 is in cup 1)\u003c/li\u003e\u003cli\u003e3, 2, 1  (ball 2 is in cup 2)\u003c/li\u003e\u003cli\u003e2, 1, 3  (ball 3 is in cup 3)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eGood luck!\u003c/p\u003e","function_template":"function y = disorganized(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nassert(isequal(disorganized(2),1))\r\n%%\r\nassert(isequal(disorganized(3),2))\r\n%%\r\nassert(isequal(disorganized(5),44))\r\n%%\r\nassert(isequal(disorganized(7),1854))\r\n%%\r\nassert(isequal(disorganized(10),1334961))\r\n%%\r\nassert(isequal(disorganized(15),481066515734))\r\n%%\r\nassert(isequal(disorganized(18),2355301661033953))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":57,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-03-26T17:39:08.000Z","updated_at":"2026-02-08T20:35:16.000Z","published_at":"2013-03-26T17:39:07.000Z","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\u003eYou have an equal number of cups and balls, each labelled from one to N. You randomly place one ball in each cup. Determine the number of possible combinations such that no balls are in the cup with a matching number. For example, if you have three balls and three cups, there are two valid solutions:\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\u003e2, 3, 1\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\u003e3, 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe following permutations do not meet the criteria for the reasons listed:\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\u003e1, 2, 3 (all three balls are in the correct cups)\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\u003e1, 3, 2 (ball 1 is in cup 1)\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\u003e3, 2, 1 (ball 2 is in cup 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2, 1, 3 (ball 3 is in cup 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\u003c/w:pPr\u003e\u003cw:r\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\"},{\"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":1393,"title":"A (wrong) place for everything, and everything in its (wrong) place","description":"You have an equal number of cups and balls, each labelled from one to N.  You randomly place one ball in each cup.  Determine the number of possible combinations such that no balls are in the cup with a matching number.  For example, if you have three balls and three cups, there are two valid solutions:\r\n\r\n* 2, 3, 1\r\n* 3, 1, 2\r\n\r\nThe following permutations do not meet the criteria for the reasons listed:\r\n\r\n* 1, 2, 3  (all three balls are in the correct cups)\r\n* 1, 3, 2  (ball 1 is in cup 1)\r\n* 3, 2, 1  (ball 2 is in cup 2)\r\n* 2, 1, 3  (ball 3 is in cup 3)\r\n\r\nGood luck!","description_html":"\u003cp\u003eYou have an equal number of cups and balls, each labelled from one to N.  You randomly place one ball in each cup.  Determine the number of possible combinations such that no balls are in the cup with a matching number.  For example, if you have three balls and three cups, there are two valid solutions:\u003c/p\u003e\u003cul\u003e\u003cli\u003e2, 3, 1\u003c/li\u003e\u003cli\u003e3, 1, 2\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe following permutations do not meet the criteria for the reasons listed:\u003c/p\u003e\u003cul\u003e\u003cli\u003e1, 2, 3  (all three balls are in the correct cups)\u003c/li\u003e\u003cli\u003e1, 3, 2  (ball 1 is in cup 1)\u003c/li\u003e\u003cli\u003e3, 2, 1  (ball 2 is in cup 2)\u003c/li\u003e\u003cli\u003e2, 1, 3  (ball 3 is in cup 3)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eGood luck!\u003c/p\u003e","function_template":"function y = disorganized(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nassert(isequal(disorganized(2),1))\r\n%%\r\nassert(isequal(disorganized(3),2))\r\n%%\r\nassert(isequal(disorganized(5),44))\r\n%%\r\nassert(isequal(disorganized(7),1854))\r\n%%\r\nassert(isequal(disorganized(10),1334961))\r\n%%\r\nassert(isequal(disorganized(15),481066515734))\r\n%%\r\nassert(isequal(disorganized(18),2355301661033953))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":57,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-03-26T17:39:08.000Z","updated_at":"2026-02-08T20:35:16.000Z","published_at":"2013-03-26T17:39:07.000Z","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\u003eYou have an equal number of cups and balls, each labelled from one to N. You randomly place one ball in each cup. Determine the number of possible combinations such that no balls are in the cup with a matching number. For example, if you have three balls and three cups, there are two valid solutions:\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\u003e2, 3, 1\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\u003e3, 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe following permutations do not meet the criteria for the reasons listed:\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\u003e1, 2, 3 (all three balls are in the correct cups)\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\u003e1, 3, 2 (ball 1 is in cup 1)\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\u003e3, 2, 1 (ball 2 is in cup 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2, 1, 3 (ball 3 is in cup 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\u003c/w:pPr\u003e\u003cw:r\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\"},{\"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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