{"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":2479,"title":"Mongean Shuffle","description":"A Mongean shuffle of an n card deck starts with putting the initial deck on the left hand side.\r\n\r\n* The top card of the deck is taken and put on the right hand side. \r\n* The second card from the deck on left is taken and put on top of right deck. \r\n* The third card is taken from the left and and put at the bottom of the right deck.\r\n* The fourth card is put on top of right deck.\r\n* The fifth card is put at the bottom of right deck.\r\n\r\nThis process is continued until all the cards on left are transferred to the right.\r\n\r\nThe initial state of the cards will be given. Return the state after this shuffle.","description_html":"\u003cp\u003eA Mongean shuffle of an n card deck starts with putting the initial deck on the left hand side.\u003c/p\u003e\u003cul\u003e\u003cli\u003eThe top card of the deck is taken and put on the right hand side.\u003c/li\u003e\u003cli\u003eThe second card from the deck on left is taken and put on top of right deck.\u003c/li\u003e\u003cli\u003eThe third card is taken from the left and and put at the bottom of the right deck.\u003c/li\u003e\u003cli\u003eThe fourth card is put on top of right deck.\u003c/li\u003e\u003cli\u003eThe fifth card is put at the bottom of right deck.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThis process is continued until all the cards on left are transferred to the right.\u003c/p\u003e\u003cp\u003eThe initial state of the cards will be given. Return the state after this shuffle.\u003c/p\u003e","function_template":"function y = mshuffle(x)\r\n\r\n\r\nend","test_suite":"%%\r\n% trivial\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(mshuffle(x),y_correct))\r\n\r\n%%\r\nx = 1:5;\r\ny_correct = [4     2     1     3     5];\r\nassert(isequal(mshuffle(x),y_correct))\r\n\r\n\r\n%%\r\na = magic(5);\r\na=a(:)';\r\ny_correct = [3    16     2    20     8    19     7    18     6    24    10    23    17     4    11     5    12     1    13    25    14    21    15    22     9];\r\nassert(isequal(mshuffle(a),y_correct));\r\n\r\n\r\n%%\r\nx = 7:-1:1;\r\ny_correct = [2     4     6     7     5     3     1];\r\nassert(isequal(mshuffle(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":17203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":95,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":15,"created_at":"2014-08-04T10:33:51.000Z","updated_at":"2026-04-02T19:19:20.000Z","published_at":"2014-08-04T10:33:51.000Z","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\":[],\"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\u003eA Mongean shuffle of an n card deck starts with putting the initial deck on the left hand side.\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 top card of the deck is taken and put on the right hand side.\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 second card from the deck on left is taken and put on top of right deck.\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 third card is taken from the left and and put at the bottom of the right deck.\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 fourth card is put on top of right deck.\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 fifth card is put at the bottom of right deck.\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 process is continued until all the cards on left are transferred to the right.\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 initial state of the cards will be given. Return the state after this shuffle.\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":2481,"title":"Mongean Shuffle : 2","description":"Extension to  \u003chttps://www.mathworks.com/matlabcentral/cody/problems/2479-mongean-shuffle problem 2479\u003e:\r\n\r\nDetermine the number of complete set of Mongean shuffles required to get the original status of a deck of cards of length n.","description_html":"\u003cp\u003eExtension to  \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/2479-mongean-shuffle\"\u003eproblem 2479\u003c/a\u003e:\u003c/p\u003e\u003cp\u003eDetermine the number of complete set of Mongean shuffles required to get the original status of a deck of cards of length n.\u003c/p\u003e","function_template":"function y = Mnum(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 52;\r\ny_correct = 12;\r\nassert(isequal(Mnum(x),y_correct))\r\n\r\n%%\r\nx = 10;\r\ny_correct = 6;\r\nassert(isequal(Mnum(x),y_correct))\r\n\r\n%%\r\nx = 9;\r\ny_correct = 4;\r\nassert(isequal(Mnum(x),y_correct))\r\n\r\n%%\r\nx = 1000;\r\ny_correct = 308;\r\nassert(isequal(Mnum(x),y_correct))\r\n\r\n%%\r\nx = 100;\r\ny_correct = 33;\r\nassert(isequal(Mnum(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 2;\r\nassert(isequal(Mnum(x),y_correct))\r\n\r\n%%\r\nx = 17;\r\ny_correct = 5;\r\nassert(isequal(Mnum(x),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":17203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":65,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":15,"created_at":"2014-08-04T14:19:45.000Z","updated_at":"2026-04-02T19:25:52.000Z","published_at":"2014-08-04T14:19:45.000Z","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\u003eExtension to \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://www.mathworks.com/matlabcentral/cody/problems/2479-mongean-shuffle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eproblem 2479\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\u003eDetermine the number of complete set of Mongean shuffles required to get the original status of a deck of cards of length n.\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":2479,"title":"Mongean Shuffle","description":"A Mongean shuffle of an n card deck starts with putting the initial deck on the left hand side.\r\n\r\n* The top card of the deck is taken and put on the right hand side. \r\n* The second card from the deck on left is taken and put on top of right deck. \r\n* The third card is taken from the left and and put at the bottom of the right deck.\r\n* The fourth card is put on top of right deck.\r\n* The fifth card is put at the bottom of right deck.\r\n\r\nThis process is continued until all the cards on left are transferred to the right.\r\n\r\nThe initial state of the cards will be given. Return the state after this shuffle.","description_html":"\u003cp\u003eA Mongean shuffle of an n card deck starts with putting the initial deck on the left hand side.\u003c/p\u003e\u003cul\u003e\u003cli\u003eThe top card of the deck is taken and put on the right hand side.\u003c/li\u003e\u003cli\u003eThe second card from the deck on left is taken and put on top of right deck.\u003c/li\u003e\u003cli\u003eThe third card is taken from the left and and put at the bottom of the right deck.\u003c/li\u003e\u003cli\u003eThe fourth card is put on top of right deck.\u003c/li\u003e\u003cli\u003eThe fifth card is put at the bottom of right deck.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThis process is continued until all the cards on left are transferred to the right.\u003c/p\u003e\u003cp\u003eThe initial state of the cards will be given. Return the state after this shuffle.\u003c/p\u003e","function_template":"function y = mshuffle(x)\r\n\r\n\r\nend","test_suite":"%%\r\n% trivial\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(mshuffle(x),y_correct))\r\n\r\n%%\r\nx = 1:5;\r\ny_correct = [4     2     1     3     5];\r\nassert(isequal(mshuffle(x),y_correct))\r\n\r\n\r\n%%\r\na = magic(5);\r\na=a(:)';\r\ny_correct = [3    16     2    20     8    19     7    18     6    24    10    23    17     4    11     5    12     1    13    25    14    21    15    22     9];\r\nassert(isequal(mshuffle(a),y_correct));\r\n\r\n\r\n%%\r\nx = 7:-1:1;\r\ny_correct = [2     4     6     7     5     3     1];\r\nassert(isequal(mshuffle(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":17203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":95,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":15,"created_at":"2014-08-04T10:33:51.000Z","updated_at":"2026-04-02T19:19:20.000Z","published_at":"2014-08-04T10:33:51.000Z","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\":[],\"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\u003eA Mongean shuffle of an n card deck starts with putting the initial deck on the left hand side.\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 top card of the deck is taken and put on the right hand side.\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 second card from the deck on left is taken and put on top of right deck.\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 third card is taken from the left and and put at the bottom of the right deck.\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 fourth card is put on top of right deck.\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 fifth card is put at the bottom of right deck.\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 process is continued until all the cards on left are transferred to the right.\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 initial state of the cards will be given. Return the state after this shuffle.\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":2481,"title":"Mongean Shuffle : 2","description":"Extension to  \u003chttps://www.mathworks.com/matlabcentral/cody/problems/2479-mongean-shuffle problem 2479\u003e:\r\n\r\nDetermine the number of complete set of Mongean shuffles required to get the original status of a deck of cards of length n.","description_html":"\u003cp\u003eExtension to  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