{"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":46813,"title":"Card games","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: 20.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.4px; transform-origin: 407px 10.4px; 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 10.4px; 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=\"\"\u003ehow many outputs will a shuffled deck of 52 cards have?\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 =8.0658e+67;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":430136,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2020-10-16T20:35:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-16T20:34:00.000Z","updated_at":"2026-02-18T21:54:27.000Z","published_at":"2020-10-16T20:35:35.000Z","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\u003ehow many outputs will a shuffled deck of 52 cards have?\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":60216,"title":"Perfect shuffle","description":"We call \"perfect shuffle\" the process of cutting a deck of cards into two equal halves, and then perfectly interleaving them: one card from the left stack, one card from the right stack, one card from the left stack, and so on.\r\nLet \"deck\" be an array with an even number of elements. Write a function \"perfect_shuffle(deck)\" that returns a new array constructed according to this shuffle.\r\nFor example, perfect_shuffle([1, 2, 3, 4, 5, 6]) should return [1, 4, 2, 5, 3, 6].\r\nRemark: For an array of 1024 elements, after 10 shuffles, we get back to the initial arrangement.","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: 153.026px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 441.989px 76.5057px; transform-origin: 441.996px 76.5128px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.017px; 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: 418.991px 21.0085px; text-align: left; transform-origin: 418.999px 21.0085px; white-space-collapse: preserve; 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe call \"perfect shuffle\" the process of cutting a deck of cards into two equal halves, and then perfectly interleaving them: one card from the left stack, one card from the right stack, one card from the left stack, and so on.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.017px; 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: 418.991px 21.0085px; text-align: left; transform-origin: 418.999px 21.0085px; white-space-collapse: preserve; 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \"deck\" be an array with an even number of elements. Write a function \"perfect_shuffle(deck)\" that returns a new array constructed according to this shuffle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; 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: 418.991px 10.4972px; text-align: left; transform-origin: 418.999px 10.5043px; white-space-collapse: preserve; 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, perfect_shuffle([1, 2, 3, 4, 5, 6]) should return [1, 4, 2, 5, 3, 6].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; 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: 418.991px 10.4972px; text-align: left; transform-origin: 418.999px 10.5043px; white-space-collapse: preserve; 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRemark: For an array of 1024 elements, after 10 shuffles, we get back to the initial arrangement.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = perfect_shuffle(x)\r\n  \r\nend","test_suite":"%%  \r\nx = [1, 2, 3, 4, 5, 6];\r\ny_correct = [1, 4, 2, 5, 3, 6];\r\ny = perfect_shuffle(x);\r\nassert(isequal(y, y_correct));\r\n\r\n%%  \r\nx = [1, 4, 2, 5, 3, 6];\r\ny_correct = [1, 5, 4, 3, 2, 6];\r\ny = perfect_shuffle(x);\r\nassert(isequal(y, y_correct));\r\n\r\n%%  \r\nx = [10, 20, 30, 40, 50, 60, 70, 80];\r\ny_correct = [10, 50, 20, 60, 30, 70, 40, 80];\r\ny = perfect_shuffle(x);\r\nassert(isequal(y, y_correct));\r\n\r\n%% \r\nx = randperm(6);\r\ny_correct = x;\r\nfor i = 1:4\r\n    y_correct = perfect_shuffle(y_correct);\r\nend\r\nassert(isequal(y_correct, x));\r\n\r\n%% \r\nx = randperm(1024);\r\ny_correct = x;\r\nfor i = 1:10\r\n    y_correct = perfect_shuffle(y_correct);\r\nend\r\nassert(isequal(y_correct, x));\r\n\r\n\r\n%% \r\nnn = [6, 30, 22, 126, 16, 124, 120, 118, 116, 114, 112, 110, 100, 98];\r\nii = [4, 28,  6, 100,  4,  20,  24,  12,  44,  28,  36,  36,  30, 48];\r\nidx = randi(length(nn)); % random index\r\nn = nn(idx) % number of elements\r\nj = ii(idx) % number of shuffles to get back to the initial arrangement for n elements\r\nx = randperm(n); % array of n elements\r\ny_correct = x;\r\nfor i = 1:j\r\n    y_correct = perfect_shuffle(y_correct);\r\nend\r\nassert(isequal(y_correct, x));\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-05T08:41:11.000Z","updated_at":"2026-03-05T12:25:49.000Z","published_at":"2024-05-05T08:41:11.000Z","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 call \\\"perfect shuffle\\\" the process of cutting a deck of cards into two equal halves, and then perfectly interleaving them: one card from the left stack, one card from the right stack, one card from the left stack, and so on.\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 \\\"deck\\\" be an array with an even number of elements. Write a function \\\"perfect_shuffle(deck)\\\" that returns a new array constructed according to this shuffle.\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\u003eFor example, perfect_shuffle([1, 2, 3, 4, 5, 6]) should return [1, 4, 2, 5, 3, 6].\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\u003eRemark: For an array of 1024 elements, after 10 shuffles, we get back to the initial arrangement.\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":2482,"title":"Card Game","description":"This is an overly simplified and highly modified version of card game Twenty-Nine.\r\n\r\nA deck of 100 unique cards (hypothetical) is randomly shuffled and divided into two equal parts. One is given to you and one to bot. Bot plays a card first. Then, you play a card. If your card is higher, you win that round. This is repeated until all cards are played.\r\n\r\nBot plays cards randomly and it will always play the first card. Your task is to devise a strategy so that your routine wins 75 percent or more rounds. Your function will be provided with two inputs, the card played by the bot and cards left to you.\r\n\r\n(This is partially dependent on luck. I might change the winning condition (75 percent or more wins currently) depending on performance without re-scoring.)","description_html":"\u003cp\u003eThis is an overly simplified and highly modified version of card game Twenty-Nine.\u003c/p\u003e\u003cp\u003eA deck of 100 unique cards (hypothetical) is randomly shuffled and divided into two equal parts. One is given to you and one to bot. Bot plays a card first. Then, you play a card. If your card is higher, you win that round. This is repeated until all cards are played.\u003c/p\u003e\u003cp\u003eBot plays cards randomly and it will always play the first card. Your task is to devise a strategy so that your routine wins 75 percent or more rounds. Your function will be provided with two inputs, the card played by the bot and cards left to you.\u003c/p\u003e\u003cp\u003e(This is partially dependent on luck. I might change the winning condition (75 percent or more wins currently) depending on performance without re-scoring.)\u003c/p\u003e","function_template":"function y = call(a,b)\r\n\r\n% a is the card played by bot\r\n% b are the cards left to you\r\n% example: \r\n% a=4\r\n% b=[10 21 31 4 5 62 7]\r\n% may be, play 7 (y = 7) to win this round\r\n\r\n\r\nend","test_suite":"%%\r\n\r\nfor i=1:randi(1000)\r\n    vec = randperm(100);\r\nend\r\n\r\nvec = randperm(100);\r\n\r\na = vec(1:50);    % given to bot\r\nb = vec(51:100);  % given to player\r\n\r\nyou = 0;\r\nbot = 0;\r\n\r\nfor i = 1:50\r\n    c = call(a(1),b);\r\n    if ~ismember(c,b)\r\n        while(1)\r\n        end\r\n    end\r\n    \r\n    \r\n    if c\u003ea(1)\r\n        you = you + 1;\r\n    else\r\n        bot = bot + 1;\r\n    end\r\n    b(b==c)=[];\r\n    a(1)=[];\r\nend\r\n\r\nif you\u003cfloor(50*0.75)\r\n    while(1)\r\n        disp('not enough wins');\r\n    end\r\nend ","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":112,"test_suite_updated_at":"2014-08-04T18:12:30.000Z","rescore_all_solutions":false,"group_id":15,"created_at":"2014-08-04T16:49:44.000Z","updated_at":"2026-04-01T19:01:18.000Z","published_at":"2014-08-04T16:49:44.000Z","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 an overly simplified and highly modified version of card game Twenty-Nine.\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 deck of 100 unique cards (hypothetical) is randomly shuffled and divided into two equal parts. One is given to you and one to bot. Bot plays a card first. Then, you play a card. If your card is higher, you win that round. This is repeated until all cards are played.\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\u003eBot plays cards randomly and it will always play the first card. Your task is to devise a strategy so that your routine wins 75 percent or more rounds. Your function will be provided with two inputs, the card played by the bot and cards left to you.\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(This is partially dependent on luck. I might change the winning condition (75 percent or more wins currently) depending on performance without re-scoring.)\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":46813,"title":"Card games","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: 20.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.4px; transform-origin: 407px 10.4px; 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 10.4px; 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=\"\"\u003ehow many outputs will a shuffled deck of 52 cards have?\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 =8.0658e+67;\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":430136,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2020-10-16T20:35:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-16T20:34:00.000Z","updated_at":"2026-02-18T21:54:27.000Z","published_at":"2020-10-16T20:35:35.000Z","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\u003ehow many outputs will a shuffled deck of 52 cards have?\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":60216,"title":"Perfect shuffle","description":"We call \"perfect shuffle\" the process of cutting a deck of cards into two equal halves, and then perfectly interleaving them: one card from the left stack, one card from the right stack, one card from the left stack, and so on.\r\nLet \"deck\" be an array with an even number of elements. Write a function \"perfect_shuffle(deck)\" that returns a new array constructed according to this shuffle.\r\nFor example, perfect_shuffle([1, 2, 3, 4, 5, 6]) should return [1, 4, 2, 5, 3, 6].\r\nRemark: For an array of 1024 elements, after 10 shuffles, we get back to the initial arrangement.","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: 153.026px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 441.989px 76.5057px; transform-origin: 441.996px 76.5128px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.017px; 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: 418.991px 21.0085px; text-align: left; transform-origin: 418.999px 21.0085px; white-space-collapse: preserve; 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe call \"perfect shuffle\" the process of cutting a deck of cards into two equal halves, and then perfectly interleaving them: one card from the left stack, one card from the right stack, one card from the left stack, and so on.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.017px; 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: 418.991px 21.0085px; text-align: left; transform-origin: 418.999px 21.0085px; white-space-collapse: preserve; 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \"deck\" be an array with an even number of elements. Write a function \"perfect_shuffle(deck)\" that returns a new array constructed according to this shuffle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; 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: 418.991px 10.4972px; text-align: left; transform-origin: 418.999px 10.5043px; white-space-collapse: preserve; 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, perfect_shuffle([1, 2, 3, 4, 5, 6]) should return [1, 4, 2, 5, 3, 6].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; 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: 418.991px 10.4972px; text-align: left; transform-origin: 418.999px 10.5043px; white-space-collapse: preserve; 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; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRemark: For an array of 1024 elements, after 10 shuffles, we get back to the initial arrangement.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = perfect_shuffle(x)\r\n  \r\nend","test_suite":"%%  \r\nx = [1, 2, 3, 4, 5, 6];\r\ny_correct = [1, 4, 2, 5, 3, 6];\r\ny = perfect_shuffle(x);\r\nassert(isequal(y, y_correct));\r\n\r\n%%  \r\nx = [1, 4, 2, 5, 3, 6];\r\ny_correct = [1, 5, 4, 3, 2, 6];\r\ny = perfect_shuffle(x);\r\nassert(isequal(y, y_correct));\r\n\r\n%%  \r\nx = [10, 20, 30, 40, 50, 60, 70, 80];\r\ny_correct = [10, 50, 20, 60, 30, 70, 40, 80];\r\ny = perfect_shuffle(x);\r\nassert(isequal(y, y_correct));\r\n\r\n%% \r\nx = randperm(6);\r\ny_correct = x;\r\nfor i = 1:4\r\n    y_correct = perfect_shuffle(y_correct);\r\nend\r\nassert(isequal(y_correct, x));\r\n\r\n%% \r\nx = randperm(1024);\r\ny_correct = x;\r\nfor i = 1:10\r\n    y_correct = perfect_shuffle(y_correct);\r\nend\r\nassert(isequal(y_correct, x));\r\n\r\n\r\n%% \r\nnn = [6, 30, 22, 126, 16, 124, 120, 118, 116, 114, 112, 110, 100, 98];\r\nii = [4, 28,  6, 100,  4,  20,  24,  12,  44,  28,  36,  36,  30, 48];\r\nidx = randi(length(nn)); % random index\r\nn = nn(idx) % number of elements\r\nj = ii(idx) % number of shuffles to get back to the initial arrangement for n elements\r\nx = randperm(n); % array of n elements\r\ny_correct = x;\r\nfor i = 1:j\r\n    y_correct = perfect_shuffle(y_correct);\r\nend\r\nassert(isequal(y_correct, x));\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":208445,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-05T08:41:11.000Z","updated_at":"2026-03-05T12:25:49.000Z","published_at":"2024-05-05T08:41:11.000Z","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 call \\\"perfect shuffle\\\" the process of cutting a deck of cards into two equal halves, and then perfectly interleaving them: one card from the left stack, one card from the right stack, one card from the left stack, and so on.\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 \\\"deck\\\" be an array with an even number of elements. Write a function \\\"perfect_shuffle(deck)\\\" that returns a new array constructed according to this shuffle.\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\u003eFor example, perfect_shuffle([1, 2, 3, 4, 5, 6]) should return [1, 4, 2, 5, 3, 6].\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\u003eRemark: For an array of 1024 elements, after 10 shuffles, we get back to the initial arrangement.\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":2482,"title":"Card Game","description":"This is an overly simplified and highly modified version of card game Twenty-Nine.\r\n\r\nA deck of 100 unique cards (hypothetical) is randomly shuffled and divided into two equal parts. One is given to you and one to bot. Bot plays a card first. Then, you play a card. If your card is higher, you win that round. This is repeated until all cards are played.\r\n\r\nBot plays cards randomly and it will always play the first card. Your task is to devise a strategy so that your routine wins 75 percent or more rounds. Your function will be provided with two inputs, the card played by the bot and cards left to you.\r\n\r\n(This is partially dependent on luck. I might change the winning condition (75 percent or more wins currently) depending on performance without re-scoring.)","description_html":"\u003cp\u003eThis is an overly simplified and highly modified version of card game Twenty-Nine.\u003c/p\u003e\u003cp\u003eA deck of 100 unique cards (hypothetical) is randomly shuffled and divided into two equal parts. One is given to you and one to bot. Bot plays a card first. Then, you play a card. If your card is higher, you win that round. This is repeated until all cards are played.\u003c/p\u003e\u003cp\u003eBot plays cards randomly and it will always play the first card. Your task is to devise a strategy so that your routine wins 75 percent or more rounds. Your function will be provided with two inputs, the card played by the bot and cards left to you.\u003c/p\u003e\u003cp\u003e(This is partially dependent on luck. I might change the winning condition (75 percent or more wins currently) depending on performance without re-scoring.)\u003c/p\u003e","function_template":"function y = call(a,b)\r\n\r\n% a is the card played by bot\r\n% b are the cards left to you\r\n% example: \r\n% a=4\r\n% b=[10 21 31 4 5 62 7]\r\n% may be, play 7 (y = 7) to win this round\r\n\r\n\r\nend","test_suite":"%%\r\n\r\nfor i=1:randi(1000)\r\n    vec = randperm(100);\r\nend\r\n\r\nvec = randperm(100);\r\n\r\na = vec(1:50);    % given to bot\r\nb = vec(51:100);  % given to player\r\n\r\nyou = 0;\r\nbot = 0;\r\n\r\nfor i = 1:50\r\n    c = call(a(1),b);\r\n    if ~ismember(c,b)\r\n        while(1)\r\n        end\r\n    end\r\n    \r\n    \r\n    if c\u003ea(1)\r\n        you = you + 1;\r\n    else\r\n        bot = bot + 1;\r\n    end\r\n    b(b==c)=[];\r\n    a(1)=[];\r\nend\r\n\r\nif you\u003cfloor(50*0.75)\r\n    while(1)\r\n        disp('not enough wins');\r\n    end\r\nend ","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":112,"test_suite_updated_at":"2014-08-04T18:12:30.000Z","rescore_all_solutions":false,"group_id":15,"created_at":"2014-08-04T16:49:44.000Z","updated_at":"2026-04-01T19:01:18.000Z","published_at":"2014-08-04T16:49:44.000Z","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 an overly simplified and highly modified version of card game Twenty-Nine.\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 deck of 100 unique cards (hypothetical) is randomly shuffled and divided into two equal parts. 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