{"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":52015,"title":"Logarithmically spaced vector creation using linspace","description":"Create a vector y containing n logarithmically spaced values between a and b, with a \u003c b. Avoid using logspace and use the linspace operator instead.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91px 8px; transform-origin: 91px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCreate a vector y containing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.5px 8px; transform-origin: 44.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003elogarithmically\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78px 8px; transform-origin: 78px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e spaced values between \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 134.5px 8px; transform-origin: 134.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, with a \u0026lt; b. Avoid using logspace and use the linspace operator instead.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(a,b,n) %% Do not change this line\r\n y = 1;\r\nend %% Do not change this line","test_suite":"%%\r\na = 1; b = 1000; n = 4;\r\ny_correct = [1 10 100 1000];\r\nassert(isequal(your_fcn_name(a,b,n),y_correct))\r\n%%\r\na = 2; b = 1024; n = 10;\r\ny_correct = [ 2 4 8 16 32 64 128 256 512 1024 ];\r\nassert(max(abs(your_fcn_name(a,b,n)-y_correct))\u003c1e-12)\r\n%%\r\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'logspace')),'logspace forbidden')\r\n%%\r\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'linspace'))==0,'use linspace')\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":428668,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-06T02:18:55.000Z","updated_at":"2026-02-16T16:36:07.000Z","published_at":"2021-06-06T02:18:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a vector y containing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elogarithmically\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e spaced values between \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, with a \u0026lt; b. Avoid using logspace and use the linspace operator instead.\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":1226,"title":"Non-zero bits in 10^n.","description":"Given an integer that is a power of 10, find the number of non-zero bits, k, in its binary representation.\r\nFor example:\r\nn = 1, 10^n = 1010, so k = 2.\r\nn = 5, 10^n = 11000011010100000, so k = 6.\r\nThe solution should work for arbitrarily large powers n, say at least till n = 100.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 142.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 71.4333px; transform-origin: 407px 71.4333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 320.5px 8px; transform-origin: 320.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an integer that is a power of 10, find the number of non-zero bits, k, in its binary representation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41px 8px; transform-origin: 41px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 20.4333px; transform-origin: 391px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 89.5px 8px; transform-origin: 89.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en = 1, 10^n = 1010, so k = 2.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 140.5px 8px; transform-origin: 140.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en = 5, 10^n = 11000011010100000, so k = 6.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 245.5px 8px; transform-origin: 245.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe solution should work for arbitrarily large powers n, say at least till n = 100.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function k = num_ones(n)\r\n k = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('num_ones.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assert') || ...\r\n contains(filetext, 'switch') || contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 0;\r\nk_correct = 1;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 1;\r\nk_correct = 2;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 2;\r\nk_correct = 3;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 5;\r\nk_correct = 6;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 10;\r\nk_correct = 11;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 15;\r\nk_correct = 20;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 22;\r\nk_correct = 25;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 23;\r\nk_correct = 27;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 45;\r\nk_correct = 53;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 100;\r\nk_correct = 105;\r\nassert(isequal(num_ones(n),k_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":8870,"edited_by":223089,"edited_at":"2023-01-09T11:26:33.000Z","deleted_by":null,"deleted_at":null,"solvers_count":40,"test_suite_updated_at":"2023-01-09T11:26:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-01-25T11:35:50.000Z","updated_at":"2023-01-09T11:26:33.000Z","published_at":"2013-01-25T11:38:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer that is a power of 10, find the number of non-zero bits, k, in its binary representation.\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:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 1, 10^n = 1010, so k = 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 5, 10^n = 11000011010100000, so k = 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\u003eThe solution should work for arbitrarily large powers n, say at least till n = 100.\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":711,"title":"What digit is it?","description":"The function you are being asked to write will take three numbers (n,x,q) as input. The object of the function is to determine what the qth digit (counting from the front) is of n^x.\r\n\r\nFor example, if the input is whatdigit(3,7,2), your function will need to determine the 2nd digit of 3^7. 3^7=2187, and the 2nd digit is 1. Therefore, the correct output will be y=1.\r\n\r\nAll digits will be positive integers, and there will always be at least q digits in n^x.","description_html":"\u003cp\u003eThe function you are being asked to write will take three numbers (n,x,q) as input. The object of the function is to determine what the qth digit (counting from the front) is of n^x.\u003c/p\u003e\u003cp\u003eFor example, if the input is whatdigit(3,7,2), your function will need to determine the 2nd digit of 3^7. 3^7=2187, and the 2nd digit is 1. Therefore, the correct output will be y=1.\u003c/p\u003e\u003cp\u003eAll digits will be positive integers, and there will always be at least q digits in n^x.\u003c/p\u003e","function_template":"function y = whatdigit(n,x,q)\r\n y = x+n+q;\r\nend","test_suite":"%%\r\nn=3;\r\nx=7;\r\nq=2;\r\ny_correct = 1;\r\nassert(isequal(whatdigit(n,x,q),y_correct))\r\n%%\r\nn=5;\r\nx=5;\r\nq=3;\r\ny_correct = 2;\r\nassert(isequal(whatdigit(n,x,q),y_correct))\r\n%%\r\nn=7;\r\nx=7;\r\nq=3;\r\ny_correct = 3;\r\nassert(isequal(whatdigit(n,x,q),y_correct))\r\n%%\r\nn=21;\r\nx=17;\r\nq=18;\r\ny_correct = 8;\r\nassert(isequal(whatdigit(n,x,q),y_correct))\r\n%%\r\nn=201;\r\nx=123;\r\nq=241;\r\ny_correct = 7;\r\nassert(isequal(whatdigit(n,x,q),y_correct))\r\n%%\r\nn=1;\r\nx=1;\r\nq=1;\r\ny_correct = 1;\r\nassert(isequal(whatdigit(n,x,q),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":40,"test_suite_updated_at":"2012-05-23T19:20:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-05-23T19:17:43.000Z","updated_at":"2025-06-23T22:16:57.000Z","published_at":"2012-05-23T19:20:16.000Z","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\u003eThe function you are being asked to write will take three numbers (n,x,q) as input. The object of the function is to determine what the qth digit (counting from the front) is of n^x.\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, if the input is whatdigit(3,7,2), your function will need to determine the 2nd digit of 3^7. 3^7=2187, and the 2nd digit is 1. Therefore, the correct output will be y=1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll digits will be positive integers, and there will always be at least q digits in n^x.\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":44782,"title":"Highest powers in factorials","description":"This is the inverse of the problem \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44747 Exponents in Factorials\u003e. Instead of being given a number and finding out the highest exponent it can be raised to for a given factorial, you'll be given a power, and you're being asked to find the highest number that can be raised to that power for a given factorial.\r\n\r\nFor example, n=7 and p=2. The highest perfect square (p=2) that can evenly divide 5040 (n=7, and 7!=5040) is 144, or 12^2. Therefore, your output should be y=12.\r\n\r\nAs before, you can assume that both n and power are integers greater than 1.","description_html":"\u003cp\u003eThis is the inverse of the problem \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44747\"\u003eExponents in Factorials\u003c/a\u003e. Instead of being given a number and finding out the highest exponent it can be raised to for a given factorial, you'll be given a power, and you're being asked to find the highest number that can be raised to that power for a given factorial.\u003c/p\u003e\u003cp\u003eFor example, n=7 and p=2. The highest perfect square (p=2) that can evenly divide 5040 (n=7, and 7!=5040) is 144, or 12^2. Therefore, your output should be y=12.\u003c/p\u003e\u003cp\u003eAs before, you can assume that both n and power are integers greater than 1.\u003c/p\u003e","function_template":"function y = biggest_power(n,p)\r\n y = n*p;\r\nend","test_suite":"%%\r\nn=7;p=2;y=biggest_power(n,p)\r\nassert(isequal(y,12));\r\n%%\r\nn=30;p=4;y=biggest_power(n,p)\r\nassert(isequal(y,60480));\r\n%%\r\nn=25;p=11;y=biggest_power(n,p)\r\nassert(isequal(y,4));\r\n%%\r\nn=1000;p=100;y=biggest_power(n,p)\r\nassert(isequal(y,7257600));\r\n%%\r\ns=0;\r\np=10;\r\nfor n=100:-1:20\r\n s(n-19)=biggest_power(n,p);\r\nend\r\nassert(isequal(sum(s),79641800));\r\nassert(isequal(numel(unique(s)),13));\r\nassert(isequal(floor(mean(s)),983232));\r\n%%\r\nn=100;\r\ns=0;\r\nfor p=30:-1:10\r\n s(p-9)=biggest_power(n,p);\r\nend\r\nassert(isequal(sum(s),14825664));\r\nassert(isequal(numel(unique(s)),7));\r\nassert(isequal(floor(mean(s)),705984));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":71,"created_at":"2018-11-08T14:45:39.000Z","updated_at":"2025-12-14T23:05:05.000Z","published_at":"2018-11-08T14:45:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the inverse of the problem\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/44747\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eExponents in Factorials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Instead of being given a number and finding out the highest exponent it can be raised to for a given factorial, you'll be given a power, and you're being asked to find the highest number that can be raised to that power for a given factorial.\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\u003eFor example, n=7 and p=2. The highest perfect square (p=2) that can evenly divide 5040 (n=7, and 7!=5040) is 144, or 12^2. Therefore, your output should be y=12.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs before, you can assume that both n and power are integers greater than 1.\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":1106,"title":"I've got the power! (Inspired by Project Euler problem 29)","description":"Consider all integer combinations of a^b and b^a for the integer values 2 ≤ a ≤ 4 and 2 ≤ b ≤ 5:\r\n\r\n 2^2=4, 2^3=8, 2^4=16, 2^5=32\r\n 3^2=9, 3^3=27, 3^4=81, 3^5=243\r\n 4^2=16, 4^3=64, 4^4=256, 4^5=1024\r\n 5^2=25, 5^3=125, 5^4=625\r\n\r\nIf they are then placed in numerical order, with any repeats removed, we get the following sequence of 14 distinct terms:\r\n\r\n4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024\r\n\r\nGiven two values for x and y, find the unique, sorted sequence given by the values a^b and b^a for 2≤a≤x and 2≤b≤y.","description_html":"\u003cp\u003eConsider all integer combinations of a^b and b^a for the integer values 2 ≤ a ≤ 4 and 2 ≤ b ≤ 5:\u003c/p\u003e\u003cpre\u003e 2^2=4, 2^3=8, 2^4=16, 2^5=32\r\n 3^2=9, 3^3=27, 3^4=81, 3^5=243\r\n 4^2=16, 4^3=64, 4^4=256, 4^5=1024\r\n 5^2=25, 5^3=125, 5^4=625\u003c/pre\u003e\u003cp\u003eIf they are then placed in numerical order, with any repeats removed, we get the following sequence of 14 distinct terms:\u003c/p\u003e\u003cp\u003e4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024\u003c/p\u003e\u003cp\u003eGiven two values for x and y, find the unique, sorted sequence given by the values a^b and b^a for 2≤a≤x and 2≤b≤y.\u003c/p\u003e","function_template":"function z = euler029(x,y)\r\n z = x+y;\r\nend","test_suite":"%%\r\nassert(isequal(euler029(5,5),[4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125]));\r\n%%\r\nassert(isequal(euler029(4,15),[4\t8\t9\t16\t25\t27\t32\t36\t49\t64\t81\t100\t121\t125\t128\t144\t169\t196\t216\t225\t243\t256\t343\t512\t625\t729\t1000\t1024\t1296\t1331\t1728\t2048\t2187\t2197\t2401\t2744\t3375\t4096\t6561\t8192\t10000\t14641\t16384\t19683\t20736\t28561\t32768\t38416\t50625\t59049\t65536\t177147\t262144\t531441\t1048576\t1594323\t4194304\t4782969\t14348907\t16777216\t67108864\t268435456\t1073741824]));\r\n%%\r\nassert(isequal(euler029(10,10),[4,8,9,16,25,27,32,36,49,64,81,100,125,128,216,243,256,343,512,625,729,1000,1024,1296,2187,2401,3125,4096,6561,7776,10000,15625,16384,16807,19683,32768,46656,59049,65536,78125,100000,117649,262144,279936,390625,531441,823543,1000000,1048576,1679616,1953125,2097152,4782969,5764801,9765625,10000000,10077696,16777216,40353607,43046721,60466176,100000000,134217728,282475249,387420489,1000000000,1073741824,3486784401,10000000000]));\r\n%%\r\na=ceil(rand*80)+2\r\nb=ceil(rand*80)+2\r\nassert(isequal(euler029(a,b),euler029(b,a)))\r\n%%\r\nassert(isequal(euler029(30,2),[4,8,9,16,25,32,36,49,64,81,100,121,128,144,169,196,225,256,289,324,361,400,441,484,512,529,576,625,676,729,784,841,900,1024,2048,4096,8192,16384,32768,65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,33554432,67108864,134217728,268435456,536870912,1073741824]))","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":143,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-12-07T17:27:47.000Z","updated_at":"2026-03-09T19:34:22.000Z","published_at":"2012-12-07T17:27:47.000Z","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\u003eConsider all integer combinations of a^b and b^a for the integer values 2 ≤ a ≤ 4 and 2 ≤ b ≤ 5:\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[ 2^2=4, 2^3=8, 2^4=16, 2^5=32\\n 3^2=9, 3^3=27, 3^4=81, 3^5=243\\n 4^2=16, 4^3=64, 4^4=256, 4^5=1024\\n 5^2=25, 5^3=125, 5^4=625]]\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\u003eIf they are then placed in numerical order, with any repeats removed, we get the following sequence of 14 distinct terms:\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\u003e4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024\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\u003eGiven two values for x and y, find the unique, sorted sequence given by the values a^b and b^a for 2≤a≤x and 2≤b≤y.\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":3077,"title":"Big numbers, least significant digits","description":"Given two numbers, x and n, return the last d digits of the number that is calculated by x^n. In all cases, d will be the number of digits in x. Keep in mind that the n values in the examples are small, however the test suite values may be much larger. Also, any leading zeros in the final answer should be discounted (If d = 2 and the number ends in 01, just report 1) \r\n\r\nExample #1:\r\n\r\n* x = 23 (therefore d = 2)\r\n* n = 2;\r\n* 23^2 = 529;\r\n* function will return 29\r\n\r\nExample #2:\r\n\r\n* x = 123; (therefore d = 3)\r\n* n = 3;\r\n* 123^3 = 1860867;\r\n* function should return 867","description_html":"\u003cp\u003eGiven two numbers, x and n, return the last d digits of the number that is calculated by x^n. In all cases, d will be the number of digits in x. Keep in mind that the n values in the examples are small, however the test suite values may be much larger. Also, any leading zeros in the final answer should be discounted (If d = 2 and the number ends in 01, just report 1)\u003c/p\u003e\u003cp\u003eExample #1:\u003c/p\u003e\u003cul\u003e\u003cli\u003ex = 23 (therefore d = 2)\u003c/li\u003e\u003cli\u003en = 2;\u003c/li\u003e\u003cli\u003e23^2 = 529;\u003c/li\u003e\u003cli\u003efunction will return 29\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eExample #2:\u003c/p\u003e\u003cul\u003e\u003cli\u003ex = 123; (therefore d = 3)\u003c/li\u003e\u003cli\u003en = 3;\u003c/li\u003e\u003cli\u003e123^3 = 1860867;\u003c/li\u003e\u003cli\u003efunction should return 867\u003c/li\u003e\u003c/ul\u003e","function_template":"function y = findLeastInBig(x,n)\r\n y = x + n;\r\nend","test_suite":"%%\r\nx = 23;\r\nn = 2\r\ny_correct = 29;\r\nassert(isequal(findLeastInBig(x,n),y_correct))\r\n\r\n%%\r\nx = 123;\r\nn = 3;\r\ny_correct = 867;\r\nassert(isequal(findLeastInBig(x,n),y_correct))\r\n\r\n%%\r\nx = 9876;\r\nn = 1024;\r\ny_correct = 1376;\r\nassert(isequal(findLeastInBig(x,n),y_correct))\r\n\r\n%%\r\nx = 1234;\r\nn = 45;\r\ny_correct = 7824;\r\nassert(isequal(findLeastInBig(x,n),y_correct))\r\n\r\n%%\r\nx = 201;\r\nn = 100;\r\ny_correct = 1;\r\nassert(isequal(findLeastInBig(x,n),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":3096,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":106,"test_suite_updated_at":"2015-03-13T13:02:34.000Z","rescore_all_solutions":false,"group_id":45,"created_at":"2015-03-12T15:02:27.000Z","updated_at":"2026-01-15T14:46:42.000Z","published_at":"2015-03-12T15:03:19.000Z","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 two numbers, x and n, return the last d digits of the number that is calculated by x^n. In all cases, d will be the number of digits in x. Keep in mind that the n values in the examples are small, however the test suite values may be much larger. Also, any leading zeros in the final answer should be discounted (If d = 2 and the number ends in 01, just report 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample #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\u003ex = 23 (therefore d = 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\u003en = 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\u003e23^2 = 529;\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\u003efunction will return 29\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\u003eExample #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\u003ex = 123; (therefore d = 3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 3;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e123^3 = 1860867;\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\u003efunction should return 867\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":2910,"title":"Mersenne Primes vs. All Primes","description":"A Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. \u003chttps://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes Problem 525\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\r\n\r\nFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.","description_html":"\u003cp\u003eA Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes\"\u003eProblem 525\u003c/a\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\u003c/p\u003e\u003cp\u003eFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.\u003c/p\u003e","function_template":"function [y,f] = Mersenne_prime_comp(n)\r\n y = 1;\r\n f = 0;\r\nend","test_suite":"%%\r\nn = 1e2;\r\ny_correct = 3;\r\nf_correct = 3/25;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(isequal(f,f_correct))\r\n\r\n%%\r\nn = 1e3;\r\ny_correct = 4;\r\nf_correct = 0.023809523809524;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e4;\r\ny_correct = 5;\r\nf_correct = 0.004068348250610;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e5;\r\ny_correct = 5;\r\nf_correct = 5.212677231025855e-04;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e6;\r\ny_correct = 7;\r\nf_correct = 8.917424647761727e-05;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":2,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":846,"test_suite_updated_at":"2015-02-01T04:14:08.000Z","rescore_all_solutions":false,"group_id":29,"created_at":"2015-02-01T03:56:07.000Z","updated_at":"2026-04-01T10:02:01.000Z","published_at":"2015-02-01T04:14:08.000Z","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 Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number.\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/525-mersenne-primes\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 525\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\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\u003eFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.\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":52015,"title":"Logarithmically spaced vector creation using linspace","description":"Create a vector y containing n logarithmically spaced values between a and b, with a \u003c b. Avoid using logspace and use the linspace operator instead.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 91px 8px; transform-origin: 91px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCreate a vector y containing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.5px 8px; transform-origin: 44.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003elogarithmically\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78px 8px; transform-origin: 78px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e spaced values between \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 134.5px 8px; transform-origin: 134.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, with a \u0026lt; b. Avoid using logspace and use the linspace operator instead.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(a,b,n) %% Do not change this line\r\n y = 1;\r\nend %% Do not change this line","test_suite":"%%\r\na = 1; b = 1000; n = 4;\r\ny_correct = [1 10 100 1000];\r\nassert(isequal(your_fcn_name(a,b,n),y_correct))\r\n%%\r\na = 2; b = 1024; n = 10;\r\ny_correct = [ 2 4 8 16 32 64 128 256 512 1024 ];\r\nassert(max(abs(your_fcn_name(a,b,n)-y_correct))\u003c1e-12)\r\n%%\r\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'logspace')),'logspace forbidden')\r\n%%\r\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'linspace'))==0,'use linspace')\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":428668,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-06-06T02:18:55.000Z","updated_at":"2026-02-16T16:36:07.000Z","published_at":"2021-06-06T02:18:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a vector y containing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elogarithmically\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e spaced values between \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, with a \u0026lt; b. Avoid using logspace and use the linspace operator instead.\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":1226,"title":"Non-zero bits in 10^n.","description":"Given an integer that is a power of 10, find the number of non-zero bits, k, in its binary representation.\r\nFor example:\r\nn = 1, 10^n = 1010, so k = 2.\r\nn = 5, 10^n = 11000011010100000, so k = 6.\r\nThe solution should work for arbitrarily large powers n, say at least till n = 100.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 142.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 71.4333px; transform-origin: 407px 71.4333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 320.5px 8px; transform-origin: 320.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an integer that is a power of 10, find the number of non-zero bits, k, in its binary representation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 41px 8px; transform-origin: 41px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 20.4333px; transform-origin: 391px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 89.5px 8px; transform-origin: 89.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en = 1, 10^n = 1010, so k = 2.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 140.5px 8px; transform-origin: 140.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en = 5, 10^n = 11000011010100000, so k = 6.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 245.5px 8px; transform-origin: 245.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe solution should work for arbitrarily large powers n, say at least till n = 100.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function k = num_ones(n)\r\n k = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('num_ones.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assert') || ...\r\n contains(filetext, 'switch') || contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 0;\r\nk_correct = 1;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 1;\r\nk_correct = 2;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 2;\r\nk_correct = 3;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 5;\r\nk_correct = 6;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 10;\r\nk_correct = 11;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 15;\r\nk_correct = 20;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 22;\r\nk_correct = 25;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 23;\r\nk_correct = 27;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 45;\r\nk_correct = 53;\r\nassert(isequal(num_ones(n),k_correct))\r\n\r\n%%\r\nn = 100;\r\nk_correct = 105;\r\nassert(isequal(num_ones(n),k_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":8870,"edited_by":223089,"edited_at":"2023-01-09T11:26:33.000Z","deleted_by":null,"deleted_at":null,"solvers_count":40,"test_suite_updated_at":"2023-01-09T11:26:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-01-25T11:35:50.000Z","updated_at":"2023-01-09T11:26:33.000Z","published_at":"2013-01-25T11:38:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer that is a power of 10, find the number of non-zero bits, k, in its binary representation.\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:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 1, 10^n = 1010, so k = 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 5, 10^n = 11000011010100000, so k = 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\u003eThe solution should work for arbitrarily large powers n, say at least till n = 100.\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":711,"title":"What digit is it?","description":"The function you are being asked to write will take three numbers (n,x,q) as input. The object of the function is to determine what the qth digit (counting from the front) is of n^x.\r\n\r\nFor example, if the input is whatdigit(3,7,2), your function will need to determine the 2nd digit of 3^7. 3^7=2187, and the 2nd digit is 1. Therefore, the correct output will be y=1.\r\n\r\nAll digits will be positive integers, and there will always be at least q digits in n^x.","description_html":"\u003cp\u003eThe function you are being asked to write will take three numbers (n,x,q) as input. The object of the function is to determine what the qth digit (counting from the front) is of n^x.\u003c/p\u003e\u003cp\u003eFor example, if the input is whatdigit(3,7,2), your function will need to determine the 2nd digit of 3^7. 3^7=2187, and the 2nd digit is 1. Therefore, the correct output will be y=1.\u003c/p\u003e\u003cp\u003eAll digits will be positive integers, and there will always be at least q digits in n^x.\u003c/p\u003e","function_template":"function y = whatdigit(n,x,q)\r\n y = x+n+q;\r\nend","test_suite":"%%\r\nn=3;\r\nx=7;\r\nq=2;\r\ny_correct = 1;\r\nassert(isequal(whatdigit(n,x,q),y_correct))\r\n%%\r\nn=5;\r\nx=5;\r\nq=3;\r\ny_correct = 2;\r\nassert(isequal(whatdigit(n,x,q),y_correct))\r\n%%\r\nn=7;\r\nx=7;\r\nq=3;\r\ny_correct = 3;\r\nassert(isequal(whatdigit(n,x,q),y_correct))\r\n%%\r\nn=21;\r\nx=17;\r\nq=18;\r\ny_correct = 8;\r\nassert(isequal(whatdigit(n,x,q),y_correct))\r\n%%\r\nn=201;\r\nx=123;\r\nq=241;\r\ny_correct = 7;\r\nassert(isequal(whatdigit(n,x,q),y_correct))\r\n%%\r\nn=1;\r\nx=1;\r\nq=1;\r\ny_correct = 1;\r\nassert(isequal(whatdigit(n,x,q),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":40,"test_suite_updated_at":"2012-05-23T19:20:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-05-23T19:17:43.000Z","updated_at":"2025-06-23T22:16:57.000Z","published_at":"2012-05-23T19:20:16.000Z","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\u003eThe function you are being asked to write will take three numbers (n,x,q) as input. The object of the function is to determine what the qth digit (counting from the front) is of n^x.\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, if the input is whatdigit(3,7,2), your function will need to determine the 2nd digit of 3^7. 3^7=2187, and the 2nd digit is 1. Therefore, the correct output will be y=1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll digits will be positive integers, and there will always be at least q digits in n^x.\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":44782,"title":"Highest powers in factorials","description":"This is the inverse of the problem \u003chttps://www.mathworks.com/matlabcentral/cody/problems/44747 Exponents in Factorials\u003e. Instead of being given a number and finding out the highest exponent it can be raised to for a given factorial, you'll be given a power, and you're being asked to find the highest number that can be raised to that power for a given factorial.\r\n\r\nFor example, n=7 and p=2. The highest perfect square (p=2) that can evenly divide 5040 (n=7, and 7!=5040) is 144, or 12^2. Therefore, your output should be y=12.\r\n\r\nAs before, you can assume that both n and power are integers greater than 1.","description_html":"\u003cp\u003eThis is the inverse of the problem \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/44747\"\u003eExponents in Factorials\u003c/a\u003e. Instead of being given a number and finding out the highest exponent it can be raised to for a given factorial, you'll be given a power, and you're being asked to find the highest number that can be raised to that power for a given factorial.\u003c/p\u003e\u003cp\u003eFor example, n=7 and p=2. The highest perfect square (p=2) that can evenly divide 5040 (n=7, and 7!=5040) is 144, or 12^2. Therefore, your output should be y=12.\u003c/p\u003e\u003cp\u003eAs before, you can assume that both n and power are integers greater than 1.\u003c/p\u003e","function_template":"function y = biggest_power(n,p)\r\n y = n*p;\r\nend","test_suite":"%%\r\nn=7;p=2;y=biggest_power(n,p)\r\nassert(isequal(y,12));\r\n%%\r\nn=30;p=4;y=biggest_power(n,p)\r\nassert(isequal(y,60480));\r\n%%\r\nn=25;p=11;y=biggest_power(n,p)\r\nassert(isequal(y,4));\r\n%%\r\nn=1000;p=100;y=biggest_power(n,p)\r\nassert(isequal(y,7257600));\r\n%%\r\ns=0;\r\np=10;\r\nfor n=100:-1:20\r\n s(n-19)=biggest_power(n,p);\r\nend\r\nassert(isequal(sum(s),79641800));\r\nassert(isequal(numel(unique(s)),13));\r\nassert(isequal(floor(mean(s)),983232));\r\n%%\r\nn=100;\r\ns=0;\r\nfor p=30:-1:10\r\n s(p-9)=biggest_power(n,p);\r\nend\r\nassert(isequal(sum(s),14825664));\r\nassert(isequal(numel(unique(s)),7));\r\nassert(isequal(floor(mean(s)),705984));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":26,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":71,"created_at":"2018-11-08T14:45:39.000Z","updated_at":"2025-12-14T23:05:05.000Z","published_at":"2018-11-08T14:45:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the inverse of the problem\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/44747\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eExponents in Factorials\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Instead of being given a number and finding out the highest exponent it can be raised to for a given factorial, you'll be given a power, and you're being asked to find the highest number that can be raised to that power for a given factorial.\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\u003eFor example, n=7 and p=2. The highest perfect square (p=2) that can evenly divide 5040 (n=7, and 7!=5040) is 144, or 12^2. Therefore, your output should be y=12.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs before, you can assume that both n and power are integers greater than 1.\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":1106,"title":"I've got the power! (Inspired by Project Euler problem 29)","description":"Consider all integer combinations of a^b and b^a for the integer values 2 ≤ a ≤ 4 and 2 ≤ b ≤ 5:\r\n\r\n 2^2=4, 2^3=8, 2^4=16, 2^5=32\r\n 3^2=9, 3^3=27, 3^4=81, 3^5=243\r\n 4^2=16, 4^3=64, 4^4=256, 4^5=1024\r\n 5^2=25, 5^3=125, 5^4=625\r\n\r\nIf they are then placed in numerical order, with any repeats removed, we get the following sequence of 14 distinct terms:\r\n\r\n4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024\r\n\r\nGiven two values for x and y, find the unique, sorted sequence given by the values a^b and b^a for 2≤a≤x and 2≤b≤y.","description_html":"\u003cp\u003eConsider all integer combinations of a^b and b^a for the integer values 2 ≤ a ≤ 4 and 2 ≤ b ≤ 5:\u003c/p\u003e\u003cpre\u003e 2^2=4, 2^3=8, 2^4=16, 2^5=32\r\n 3^2=9, 3^3=27, 3^4=81, 3^5=243\r\n 4^2=16, 4^3=64, 4^4=256, 4^5=1024\r\n 5^2=25, 5^3=125, 5^4=625\u003c/pre\u003e\u003cp\u003eIf they are then placed in numerical order, with any repeats removed, we get the following sequence of 14 distinct terms:\u003c/p\u003e\u003cp\u003e4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024\u003c/p\u003e\u003cp\u003eGiven two values for x and y, find the unique, sorted sequence given by the values a^b and b^a for 2≤a≤x and 2≤b≤y.\u003c/p\u003e","function_template":"function z = euler029(x,y)\r\n z = x+y;\r\nend","test_suite":"%%\r\nassert(isequal(euler029(5,5),[4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125]));\r\n%%\r\nassert(isequal(euler029(4,15),[4\t8\t9\t16\t25\t27\t32\t36\t49\t64\t81\t100\t121\t125\t128\t144\t169\t196\t216\t225\t243\t256\t343\t512\t625\t729\t1000\t1024\t1296\t1331\t1728\t2048\t2187\t2197\t2401\t2744\t3375\t4096\t6561\t8192\t10000\t14641\t16384\t19683\t20736\t28561\t32768\t38416\t50625\t59049\t65536\t177147\t262144\t531441\t1048576\t1594323\t4194304\t4782969\t14348907\t16777216\t67108864\t268435456\t1073741824]));\r\n%%\r\nassert(isequal(euler029(10,10),[4,8,9,16,25,27,32,36,49,64,81,100,125,128,216,243,256,343,512,625,729,1000,1024,1296,2187,2401,3125,4096,6561,7776,10000,15625,16384,16807,19683,32768,46656,59049,65536,78125,100000,117649,262144,279936,390625,531441,823543,1000000,1048576,1679616,1953125,2097152,4782969,5764801,9765625,10000000,10077696,16777216,40353607,43046721,60466176,100000000,134217728,282475249,387420489,1000000000,1073741824,3486784401,10000000000]));\r\n%%\r\na=ceil(rand*80)+2\r\nb=ceil(rand*80)+2\r\nassert(isequal(euler029(a,b),euler029(b,a)))\r\n%%\r\nassert(isequal(euler029(30,2),[4,8,9,16,25,32,36,49,64,81,100,121,128,144,169,196,225,256,289,324,361,400,441,484,512,529,576,625,676,729,784,841,900,1024,2048,4096,8192,16384,32768,65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,33554432,67108864,134217728,268435456,536870912,1073741824]))","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":143,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-12-07T17:27:47.000Z","updated_at":"2026-03-09T19:34:22.000Z","published_at":"2012-12-07T17:27:47.000Z","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\u003eConsider all integer combinations of a^b and b^a for the integer values 2 ≤ a ≤ 4 and 2 ≤ b ≤ 5:\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[ 2^2=4, 2^3=8, 2^4=16, 2^5=32\\n 3^2=9, 3^3=27, 3^4=81, 3^5=243\\n 4^2=16, 4^3=64, 4^4=256, 4^5=1024\\n 5^2=25, 5^3=125, 5^4=625]]\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\u003eIf they are then placed in numerical order, with any repeats removed, we get the following sequence of 14 distinct terms:\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\u003e4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024\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\u003eGiven two values for x and y, find the unique, sorted sequence given by the values a^b and b^a for 2≤a≤x and 2≤b≤y.\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":3077,"title":"Big numbers, least significant digits","description":"Given two numbers, x and n, return the last d digits of the number that is calculated by x^n. In all cases, d will be the number of digits in x. Keep in mind that the n values in the examples are small, however the test suite values may be much larger. Also, any leading zeros in the final answer should be discounted (If d = 2 and the number ends in 01, just report 1) \r\n\r\nExample #1:\r\n\r\n* x = 23 (therefore d = 2)\r\n* n = 2;\r\n* 23^2 = 529;\r\n* function will return 29\r\n\r\nExample #2:\r\n\r\n* x = 123; (therefore d = 3)\r\n* n = 3;\r\n* 123^3 = 1860867;\r\n* function should return 867","description_html":"\u003cp\u003eGiven two numbers, x and n, return the last d digits of the number that is calculated by x^n. In all cases, d will be the number of digits in x. Keep in mind that the n values in the examples are small, however the test suite values may be much larger. Also, any leading zeros in the final answer should be discounted (If d = 2 and the number ends in 01, just report 1)\u003c/p\u003e\u003cp\u003eExample #1:\u003c/p\u003e\u003cul\u003e\u003cli\u003ex = 23 (therefore d = 2)\u003c/li\u003e\u003cli\u003en = 2;\u003c/li\u003e\u003cli\u003e23^2 = 529;\u003c/li\u003e\u003cli\u003efunction will return 29\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eExample #2:\u003c/p\u003e\u003cul\u003e\u003cli\u003ex = 123; (therefore d = 3)\u003c/li\u003e\u003cli\u003en = 3;\u003c/li\u003e\u003cli\u003e123^3 = 1860867;\u003c/li\u003e\u003cli\u003efunction should return 867\u003c/li\u003e\u003c/ul\u003e","function_template":"function y = findLeastInBig(x,n)\r\n y = x + n;\r\nend","test_suite":"%%\r\nx = 23;\r\nn = 2\r\ny_correct = 29;\r\nassert(isequal(findLeastInBig(x,n),y_correct))\r\n\r\n%%\r\nx = 123;\r\nn = 3;\r\ny_correct = 867;\r\nassert(isequal(findLeastInBig(x,n),y_correct))\r\n\r\n%%\r\nx = 9876;\r\nn = 1024;\r\ny_correct = 1376;\r\nassert(isequal(findLeastInBig(x,n),y_correct))\r\n\r\n%%\r\nx = 1234;\r\nn = 45;\r\ny_correct = 7824;\r\nassert(isequal(findLeastInBig(x,n),y_correct))\r\n\r\n%%\r\nx = 201;\r\nn = 100;\r\ny_correct = 1;\r\nassert(isequal(findLeastInBig(x,n),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":3096,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":106,"test_suite_updated_at":"2015-03-13T13:02:34.000Z","rescore_all_solutions":false,"group_id":45,"created_at":"2015-03-12T15:02:27.000Z","updated_at":"2026-01-15T14:46:42.000Z","published_at":"2015-03-12T15:03:19.000Z","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 two numbers, x and n, return the last d digits of the number that is calculated by x^n. In all cases, d will be the number of digits in x. Keep in mind that the n values in the examples are small, however the test suite values may be much larger. Also, any leading zeros in the final answer should be discounted (If d = 2 and the number ends in 01, just report 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample #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\u003ex = 23 (therefore d = 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\u003en = 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\u003e23^2 = 529;\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\u003efunction will return 29\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\u003eExample #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\u003ex = 123; (therefore d = 3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 3;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e123^3 = 1860867;\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\u003efunction should return 867\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":2910,"title":"Mersenne Primes vs. All Primes","description":"A Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. \u003chttps://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes Problem 525\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\r\n\r\nFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.","description_html":"\u003cp\u003eA Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes\"\u003eProblem 525\u003c/a\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\u003c/p\u003e\u003cp\u003eFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.\u003c/p\u003e","function_template":"function [y,f] = Mersenne_prime_comp(n)\r\n y = 1;\r\n f = 0;\r\nend","test_suite":"%%\r\nn = 1e2;\r\ny_correct = 3;\r\nf_correct = 3/25;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(isequal(f,f_correct))\r\n\r\n%%\r\nn = 1e3;\r\ny_correct = 4;\r\nf_correct = 0.023809523809524;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e4;\r\ny_correct = 5;\r\nf_correct = 0.004068348250610;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e5;\r\ny_correct = 5;\r\nf_correct = 5.212677231025855e-04;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e6;\r\ny_correct = 7;\r\nf_correct = 8.917424647761727e-05;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":2,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":846,"test_suite_updated_at":"2015-02-01T04:14:08.000Z","rescore_all_solutions":false,"group_id":29,"created_at":"2015-02-01T03:56:07.000Z","updated_at":"2026-04-01T10:02:01.000Z","published_at":"2015-02-01T04:14:08.000Z","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 Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number.\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/525-mersenne-primes\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 525\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\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\u003eFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.\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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