{"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":313,"title":"Pythagorean perfect squares: find the square of the hypotenuse and the length of the other side","description":"Given the square root of a square number, *seed*, and a range, *n*, find the square number, *Z* as well as the other side, *y*, the square root of a square number i.e. return the hypotenuse squared as well as the length of the other side. Note that *n* is the number of squares to search through starting with one.\r\n\r\nHINT: Z = seed^2 + y^2 where Z = z^2, find Z first and then y. \r\n\r\nNote that Z, seed^2 and y^2 are all perfect squares.\r\n\r\n\u003e\u003e [z s] = findPerfectZ(3,6)\r\n\r\nz = 25\r\n\r\ns = 4\r\n\r\n\u003e\u003e","description_html":"\u003cp\u003eGiven the square root of a square number, \u003cb\u003eseed\u003c/b\u003e, and a range, \u003cb\u003en\u003c/b\u003e, find the square number, \u003cb\u003eZ\u003c/b\u003e as well as the other side, \u003cb\u003ey\u003c/b\u003e, the square root of a square number i.e. return the hypotenuse squared as well as the length of the other side. Note that \u003cb\u003en\u003c/b\u003e is the number of squares to search through starting with one.\u003c/p\u003e\u003cp\u003eHINT: Z = seed^2 + y^2 where Z = z^2, find Z first and then y.\u003c/p\u003e\u003cp\u003eNote that Z, seed^2 and y^2 are all perfect squares.\u003c/p\u003e\u003cp\u003e\u003e\u003e [z s] = findPerfectZ(3,6)\u003c/p\u003e\u003cp\u003ez = 25\u003c/p\u003e\u003cp\u003es = 4\u003c/p\u003e\u003cp\u003e\u003e\u003e\u003c/p\u003e","function_template":"function [Z,y] = findPerfectZ(seed,n)\r\n  Z = perfectZSquare \r\n  y = aside\r\nend","test_suite":"%%\r\n\r\nseed=3;n=6;\r\n\r\n[Z,y] = findPerfectZ(seed,n);\r\n\r\nZ_correct = 25; y_correct = 4;\r\n\r\nassert(isequal(Z,Z_correct));\r\n\r\nassert(isequal(y,y_correct));\r\n\r\n%%\r\n\r\nseed=5;n=15;\r\n\r\n[Z,y] = findPerfectZ(seed,n);\r\n\r\nZ_correct = 169; y_correct = 12;\r\n\r\nassert(isequal(Z,Z_correct));\r\n\r\nassert(isequal(y,y_correct));\r\n\r\n%%\r\n\r\nseed=4;n=6;\r\n\r\n[Z,y] = findPerfectZ(seed,n);\r\n\r\nZ_correct = 25; y_correct = 3;\r\n\r\nassert(isequal(Z,Z_correct));\r\n\r\nassert(isequal(y,y_correct));\r\n\r\n%%\r\n\r\nseed=12;n=15;\r\n\r\n[Z,y] = findPerfectZ(seed,n);\r\n\r\nZ_correct = 169; y_correct = 5;\r\n\r\nassert(isequal(Z,Z_correct));\r\n\r\nassert(isequal(y,y_correct));\r\n\r\n%%\r\n\r\nseed=6;n=9;\r\n\r\n[Z,y] = findPerfectZ(seed,n);\r\n\r\nZ_correct = 100; y_correct = 8;\r\n\r\nassert(isequal(Z,Z_correct));\r\n\r\nassert(isequal(y,y_correct));\r\n\r\n%%\r\n\r\nseed=8;n=9;\r\n\r\n[Z,y] = findPerfectZ(seed,n);\r\n\r\nZ_correct = 100; y_correct = 6;\r\n\r\nassert(isequal(Z,Z_correct));\r\n\r\nassert(isequal(y,y_correct));","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2012-02-12T06:59:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-12T06:59:40.000Z","updated_at":"2026-03-23T10:18:19.000Z","published_at":"2012-02-12T06:59:40.000Z","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 the square root of a square number,\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eseed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and a range,\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the square number,\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eZ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as well as the other side,\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the square root of a square number i.e. return the hypotenuse squared as well as the length of the other side. Note that\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of squares to search through starting with one.\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\u003eHINT: Z = seed^2 + y^2 where Z = z^2, find Z first and then y.\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\u003eNote that Z, seed^2 and y^2 are all perfect squares.\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\u003e\u0026gt;\u0026gt; [z s] = findPerfectZ(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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ez = 25\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\u003es = 4\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\u003e\u0026gt;\u0026gt;\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\\\" 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courtesy of \u003ca href = \"http://upload.wikimedia.org/wikipedia/commons/7/7c/Right_Angle_Triangle.svg\"\u003eWikipedia\u003c/a\u003e.\u003c/p\u003e","function_template":"function a = calculate_short_side(b, c)\r\n  a = \r\nend","test_suite":"%%\r\nb = 1;\r\nc = 2; \r\na_correct = sqrt(3);\r\ntolerance = 1e-12; \r\nassert(abs(calculate_short_side(b,c)-a_correct)\u003ctolerance);\r\n%%\r\nb = 4;\r\nc = 5;\r\na_correct = 3; \r\ntolerance = 1e-12; \r\nassert(abs(calculate_short_side(b,c)-a_correct)\u003ctolerance);\r\n%%\r\nb = 12;\r\nc = 13;\r\na_correct = 5; \r\ntolerance = 1e-12; \r\nassert(abs(calculate_short_side(b,c)-a_correct)\u003ctolerance);\r\n%%\r\nb = 8;\r\nc = 10;\r\na_correct = 6; \r\ntolerance = 1e-12; \r\nassert(abs(calculate_short_side(b,c)-a_correct)\u003ctolerance);","published":true,"deleted":false,"likes_count":62,"comments_count":17,"created_by":974,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8015,"test_suite_updated_at":"2013-11-29T09:41:22.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-08T23:06:44.000Z","updated_at":"2026-04-03T13:34:44.000Z","published_at":"2013-11-28T17:12:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml 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\"}]}"},{"id":2015,"title":"Length of the hypotenuse","description":"Given short sides of lengths a and b, calculate the length c of the hypotenuse of the right-angled triangle.\r\n\r\n\u003c\u003chttps://i.imgur.com/73mQn4N.png\u003e\u003e\r\n\r\nImage courtesy of \u003chttp://upload.wikimedia.org/wikipedia/commons/7/7c/Right_Angle_Triangle.svg Wikipedia\u003e.","description_html":"\u003cp\u003eGiven short sides of lengths a and b, calculate the length c of the hypotenuse of the right-angled triangle.\u003c/p\u003e\u003cimg src = \"https://i.imgur.com/73mQn4N.png\"\u003e\u003cp\u003eImage courtesy of \u003ca href = \"http://upload.wikimedia.org/wikipedia/commons/7/7c/Right_Angle_Triangle.svg\"\u003eWikipedia\u003c/a\u003e.\u003c/p\u003e","function_template":"function c = hypotenuse(a,b)\r\n  c = \r\nend","test_suite":"%%\r\na = 1;\r\nb = 2; \r\nc_correct = sqrt(5);\r\ntolerance = 1e-12 ; \r\nassert(abs(hypotenuse(a,b)-c_correct)\u003ctolerance);\r\n%%\r\na = 3;\r\nb = 4;\r\nc_correct = 5; \r\ntolerance = 1e-12 ; \r\nassert(abs(hypotenuse(a,b)-c_correct)\u003ctolerance);\r\n%%\r\na = 5;\r\nb = 12;\r\nc_correct = 13; \r\ntolerance = 1e-12 ; \r\nassert(abs(hypotenuse(a,b)-c_correct)\u003ctolerance);\r\n","published":true,"deleted":false,"likes_count":67,"comments_count":9,"created_by":974,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16509,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:11:28.000Z","updated_at":"2026-04-04T03:49:26.000Z","published_at":"2013-11-28T17:12:06.000Z","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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml 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\"}]}"},{"id":2307,"title":"length of string on cylinder","description":"A cylinder H cm high has a circumference of C cm. A string makes exactly N complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm? \r\n\r\n","description_html":"\u003cp\u003eA cylinder H cm high has a circumference of C cm. A string makes exactly N complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm?\u003c/p\u003e","function_template":"function ans = your_fcn_name(H,C,N)\r\n \r\nend","test_suite":"%%\r\nH=90\r\nC=20\r\nN=6\r\ny_correct =150;\r\nassert(isequal(your_fcn_name(H,C,N),y_correct))\r\n\r\n%%\r\nH=72\r\nC=16\r\nN=6\r\ny_correct =120;\r\nassert(isequal(your_fcn_name(H,C,N),y_correct))\r\n\r\n%%\r\nH=105\r\nC=20\r\nN=7\r\ny_correct =175;\r\nassert(isequal(your_fcn_name(H,C,N),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":17228,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":62,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-07T11:16:39.000Z","updated_at":"2026-03-16T12:43:40.000Z","published_at":"2014-05-07T11:16:39.000Z","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\",\"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\u003eA cylinder H cm high has a circumference of C cm. A string makes exactly N complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm?\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":2016,"title":"Area of an equilateral triangle ","description":"Calculate the area of an equilateral triangle of side x. \r\n\r\n\u003c\u003chttps://i.imgur.com/jlZDHhq.png\u003e\u003e\r\n\r\nImage courtesy of \u003chttp://upload.wikimedia.org/wikipedia/commons/e/e0/Equilateral-triangle.svg Wikipedia\u003e.","description_html":"\u003cp\u003eCalculate the area of an equilateral triangle of side x.\u003c/p\u003e\u003cimg src = \"https://i.imgur.com/jlZDHhq.png\"\u003e\u003cp\u003eImage courtesy of \u003ca href = \"http://upload.wikimedia.org/wikipedia/commons/e/e0/Equilateral-triangle.svg\"\u003eWikipedia\u003c/a\u003e.\u003c/p\u003e","function_template":"function y = equilateral_area(x)\r\n  y = x; \r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = sqrt(3)/4;\r\ntolerance = 1e-12;\r\nassert(abs(equilateral_area(x)-y_correct)\u003ctolerance)\r\n%%\r\nx = 2;\r\ny_correct = sqrt(3);\r\ntolerance = 1e-12;\r\nassert(abs(equilateral_area(x)-y_correct)\u003ctolerance)\r\n%%\r\nx = 3;\r\ny_correct = sqrt(3)*9/4;\r\ntolerance =1e-12;\r\nassert(abs(equilateral_area(x)-y_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":26,"comments_count":8,"created_by":974,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6803,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:21:11.000Z","updated_at":"2026-04-02T15:31:22.000Z","published_at":"2013-11-28T17:12:09.000Z","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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"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\u003eCalculate the area of an equilateral triangle of side 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\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eImage courtesy 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is the distance from point P(x,y) to the line Ax + By + C = 0?","description":"Given a point, P(x,y), find the distance from this point to a linear line.\r\n\r\nINPUTS: x, y, A, B, C\r\n\r\nOUTPUTS: d, the distance which of course should always be positive.\r\n    \r\n  EX:\r\n  \u003e\u003ex=2; y=2; A=2; B=2; C=-4;\r\n  \u003e\u003ed = normalLen(x,y,A,B,C)\r\n  d = 1.4142\r\n\r\n\r\n","description_html":"\u003cp\u003eGiven a point, P(x,y), find the distance from this point to a linear line.\u003c/p\u003e\u003cp\u003eINPUTS: x, y, A, B, C\u003c/p\u003e\u003cp\u003eOUTPUTS: d, the distance which of course should always be positive.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eEX:\r\n\u003e\u003ex=2; y=2; A=2; B=2; C=-4;\r\n\u003e\u003ed = normalLen(x,y,A,B,C)\r\nd = 1.4142\r\n\u003c/pre\u003e","function_template":"function d = normalLen(x,y,A,B,C)\r\n  d = x+y+[A,B,C]\r\nend","test_suite":"%% test 1\r\nx=2; y=2; A=2; B=2; C=-4;\r\ny_correct = 1.4142;\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)\u003c=1e-4)\r\n%% test 2\r\nx=3; y=4; A=3; B=4; C=5;\r\ny_correct = 6;\r\nassert(normalLen(x,y,A,B,C)-y_correct==0)\r\n%% test 3\r\nx=4; y=5; A=3; B=4; C=5;\r\ny_correct = 7.4;\r\ndisplay(normalLen(x,y,A,B,C))\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)\u003c1e-1)\r\n%% test 4\r\nx=0;y=12345;A=0;B=1;C=0;\r\ny_correct = 12345;\r\ndisplay(normalLen(x,y,A,B,C))\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)==0)\r\n%% test 5\r\nx=0;y=-12345;A=0;B=1;C=0;\r\ny_correct = 12345;\r\ndisplay(normalLen(x,y,A,B,C))\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)==0)\r\n\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":2,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":560,"test_suite_updated_at":"2013-01-26T00:45:07.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-03-05T04:51:25.000Z","updated_at":"2026-03-13T05:04:32.000Z","published_at":"2012-03-06T06:29:12.000Z","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 a point, P(x,y), find the distance from this point to a linear line.\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\u003eINPUTS: x, y, A, B, C\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\u003eOUTPUTS: d, the distance which of course should always be positive.\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[EX:\\n\u003e\u003ex=2; y=2; A=2; B=2; C=-4;\\n\u003e\u003ed = normalLen(x,y,A,B,C)\\nd = 1.4142]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2018,"title":"Side of a rhombus","description":"If a rhombus has diagonals of length x and x+1, then what is the length of its side, y? \r\n\r\n\u003c\u003chttps://imgur.com/x6hT6mm.png\u003e\u003e\r\n\r\nImage courtesy of \u003chttp://upload.wikimedia.org/wikipedia/commons/b/b5/Rhombus.svg Wikipedia\u003e.","description_html":"\u003cp\u003eIf a rhombus has diagonals of length x and x+1, then what is the length of its side, y?\u003c/p\u003e\u003cimg src = \"https://imgur.com/x6hT6mm.png\"\u003e\u003cp\u003eImage courtesy of \u003ca href = \"http://upload.wikimedia.org/wikipedia/commons/b/b5/Rhombus.svg\"\u003eWikipedia\u003c/a\u003e.\u003c/p\u003e","function_template":"function y = rhombus_side(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = sqrt(5)/2;\r\ntolerance = 1e-12; \r\nassert(abs(rhombus_side(x)-y_correct)\u003ctolerance)\r\n%%\r\nx = 3;\r\ny_correct = 5/2;\r\ntolerance = 1e-12; \r\nassert(abs(rhombus_side(x)-y_correct)\u003ctolerance)\r\n%%\r\nx = 2;\r\ny_correct = sqrt(13)/2;\r\ntolerance = 1e-12; \r\nassert(abs(rhombus_side(x)-y_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":28,"comments_count":1,"created_by":974,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5900,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:23:39.000Z","updated_at":"2026-04-02T15:30:51.000Z","published_at":"2013-11-28T17:12:17.000Z","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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml 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Triangles - find the height of the tree","description":"Given the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\r\n\r\n\r\nInputs: h1, x1, x2\r\n\r\nOutput: h2\r\n\r\nHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\r\n\r\nEX:\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\r\n\r\n\u003e\u003eh2=findHeight(x1,x2,h1)\r\n\r\nh2=6\r\n\r\n\u003e\u003e","description_html":"\u003cp\u003eGiven the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\u003c/p\u003e\u003cp\u003eInputs: h1, x1, x2\u003c/p\u003e\u003cp\u003eOutput: h2\u003c/p\u003e\u003cp\u003eHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\u003c/p\u003e\u003cp\u003eEX:\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\u003c/p\u003e\u003cp\u003e\u003e\u003eh2=findHeight(x1,x2,h1)\u003c/p\u003e\u003cp\u003eh2=6\u003c/p\u003e\u003cp\u003e\u003e\u003e\u003c/p\u003e","function_template":"function h2 = findHeight(x1,x2,h1)\r\n  h2 = heightoftree\r\nend","test_suite":"%%\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\r\ny_correct = 6;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 8;\r\nh1 = 3;\r\ny_correct = 9;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 12;\r\nh1 = 3;\r\ny_correct = 12;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 16;\r\nh1 = 3;\r\ny_correct = 15;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 20;\r\nh1 = 3;\r\ny_correct = 18;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 24;\r\nh1 = 3;\r\ny_correct = 21;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 12;\r\nh1 = 5;\r\ny_correct = 20;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 16;\r\nh1 = 10;\r\ny_correct = 50;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 2;\r\nx2 = 4;\r\nh1 = 5;\r\ny_correct = 15;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 3;\r\nx2 = 6;\r\nh1 = 4;\r\ny_correct = 12;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":6,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":469,"test_suite_updated_at":"2012-02-18T04:42:47.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-02-17T22:52:21.000Z","updated_at":"2026-03-13T05:26:44.000Z","published_at":"2012-02-18T04:42:47.000Z","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\",\"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\u003eGiven the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\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\u003eInputs: h1, x1, x2\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\u003eOutput: h2\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\u003eHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\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\u003eEX: x1 = 4; x2 = 4; h1 = 3;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003e\u003eh2=findHeight(x1,x2,h1)\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\u003eh2=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\u003e\u003e\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2017,"title":"Side of an equilateral triangle","description":"If an equilateral triangle has area A, then what is the length of each of its sides, x?\r\n\r\nImage courtesy of Wikipedia.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; 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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: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://upload.wikimedia.org/wikipedia/commons/e/e0/Equilateral-triangle.svg\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); 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\u003c tolerance)\r\n%%\r\nA = 2;\r\nx_correct = 2*sqrt(2)/sqrt(sqrt(3));\r\ntolerance = 1e-12; \r\nassert(abs(side_length(A) - x_correct) \u003c tolerance)\r\n","published":true,"deleted":false,"likes_count":32,"comments_count":4,"created_by":974,"edited_by":223089,"edited_at":"2026-03-22T08:15:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6875,"test_suite_updated_at":"2026-03-22T08:15:23.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:22:35.000Z","updated_at":"2026-04-04T19:05:04.000Z","published_at":"2013-11-28T17:12:13.000Z","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 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this triangle right-angled?","description":"Given three positive numbers a, b, c, where c is the largest number, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.","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: 233.5px 8px; transform-origin: 233.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven three positive numbers a, b, c, where c is the largest number, return\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: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etrue\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: 118px 8px; transform-origin: 118px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if the triangle with sides a, b and c is right-angled. Otherwise, return\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: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003efalse\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\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function flag = isRightAngled(a, b, c)\r\n  flag = false;\r\nend","test_suite":"%%\r\na = 3;\r\nb = 4;\r\nc = 5;\r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 2;\r\nb = 3;\r\nc = 4;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5;\r\nb = 12;\r\nc = 13;\r\nflag_correct = true; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 17;\r\nb = 19;\r\nc = 23;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 12;\r\nb = 35;\r\nc = 37;\r\nflag_correct = true; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 10*rand;\r\nb = a;\r\nc = a;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))","published":true,"deleted":false,"likes_count":38,"comments_count":7,"created_by":974,"edited_by":223089,"edited_at":"2023-05-04T07:40:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6416,"test_suite_updated_at":"2023-05-04T07:40:55.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:28:55.000Z","updated_at":"2026-04-02T15:26:12.000Z","published_at":"2013-11-28T17:12:28.000Z","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\u003eGiven three positive numbers a, b, c, where c is the largest number, return\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if the triangle with sides a, b and c is right-angled. Otherwise, return\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efalse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\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":2020,"title":"Area of an Isoceles Triangle","description":"An isosceles triangle has equal sides of length x and a base of length y. Find the area, A, of the triangle. \r\n\r\n\u003c\u003chttps://imgur.com/HVdn9p1.png\u003e\u003e\r\n\r\n\r\nImage courtesy of \u003chttp://upload.wikimedia.org/wikipedia/commons/8/8e/Triangle_isocele.svg Wikipedia\u003e.","description_html":"\u003cp\u003eAn isosceles triangle has equal sides of length x and a base of length y. Find the area, A, of the triangle.\u003c/p\u003e\u003cimg src = \"https://imgur.com/HVdn9p1.png\"\u003e\u003cp\u003eImage courtesy of \u003ca href = \"http://upload.wikimedia.org/wikipedia/commons/8/8e/Triangle_isocele.svg\"\u003eWikipedia\u003c/a\u003e.\u003c/p\u003e","function_template":"function A = isocelesArea(x,y)\r\n  A = \r\nend","test_suite":"%%\r\nx = 5;\r\ny = 8; \r\nA_correct = 12;\r\ntolerance = 1e-12; \r\nassert(abs(isocelesArea(x,y)-A_correct)\u003ctolerance)\r\n%%\r\nx = 2;\r\ny = 2; \r\nA_correct = sqrt(3);\r\ntolerance = 1e-12;\r\nassert(abs(isocelesArea(x,y)-A_correct)\u003ctolerance)\r\n%%\r\nx = 10;\r\ny = 2; \r\nA_correct = sqrt(99);\r\ntolerance = 1e-12; \r\nassert(abs(isocelesArea(x,y)-A_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":32,"comments_count":5,"created_by":974,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6116,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:27:15.000Z","updated_at":"2026-04-02T15:30:16.000Z","published_at":"2013-11-28T17:12:24.000Z","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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"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\u003eAn isosceles triangle has equal sides of length x and a base of length y. Find the area, A, of the triangle.\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eImage courtesy of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://upload.wikimedia.org/wikipedia/commons/8/8e/Triangle_isocele.svg\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\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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of a rectangle","description":"The longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width and length of the rectangle.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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: 428.625px 8px; transform-origin: 428.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width and length of the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [width, length] = findRectangleDimensions(x)\r\n  width = x;\r\n  length = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('findRectangleDimensions.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp');\r\nassert(~illegal)\r\n\r\n%%\r\nx = 1\r\nlength_correct = 3/sqrt(10);\r\nwidth_correct = 1/sqrt(10); \r\n[width, length] = findRectangleDimensions(x); \r\ntolerance = 1e-12; \r\nassert( abs(length-length_correct)\u003ctolerance \u0026\u0026 abs(width-width_correct)\u003ctolerance )\r\n\r\n%%\r\nx = 2;\r\nwidth_correct = 2/sqrt(10); \r\nlength_correct = 6/sqrt(10); \r\n[width, length] = findRectangleDimensions(x); \r\ntolerance = 1e-12;\r\nassert(abs(length-length_correct)\u003ctolerance \u0026\u0026 abs(width-width_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":49,"comments_count":11,"created_by":974,"edited_by":223089,"edited_at":"2026-03-22T08:23:37.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5781,"test_suite_updated_at":"2026-03-22T08:23:37.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:24:49.000Z","updated_at":"2026-04-03T13:48:18.000Z","published_at":"2013-11-28T17:12:20.000Z","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\u003eThe longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width and length of the rectangle.\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":44476,"title":"How many unique Pythagorean triples?","description":"For a given integer |n|, return all \u003chttps://en.wikipedia.org/wiki/Pythagorean_triple Pythagorean triples\u003e that inlude numbers smaller or equal to |n|.\r\n\r\nA Pythagorean triple consist of three positive integers |{a, b, c}| such that:\r\n\r\n a \u003c b \u003c c,\r\n a^2 + b^2 = c^2\r\n\r\nThe triples should be retured in a matrix with tree columns, where each row contains a different triple. Every row needs to be sorted in ascending order ( |a| in the first column, |b| in the second and |c| in the third), and the first column must also be sorted.\r\n\r\nExample:\r\n\r\n  Input:  n   = 16\r\n  Output: mat = [3,  4, 5\r\n                 5, 12, 13 \r\n                 6,  8, 10 \r\n                 9, 12, 15]\r\n\r\nIf |n| is not an integer, or it is smaller than 5, the function should return an empty matrix.","description_html":"\u003cp\u003eFor a given integer \u003ctt\u003en\u003c/tt\u003e, return all \u003ca href = \"https://en.wikipedia.org/wiki/Pythagorean_triple\"\u003ePythagorean triples\u003c/a\u003e that inlude numbers smaller or equal to \u003ctt\u003en\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eA Pythagorean triple consist of three positive integers \u003ctt\u003e{a, b, c}\u003c/tt\u003e such that:\u003c/p\u003e\u003cpre\u003e a \u0026lt; b \u0026lt; c,\r\n a^2 + b^2 = c^2\u003c/pre\u003e\u003cp\u003eThe triples should be retured in a matrix with tree columns, where each row contains a different triple. Every row needs to be sorted in ascending order ( \u003ctt\u003ea\u003c/tt\u003e in the first column, \u003ctt\u003eb\u003c/tt\u003e in the second and \u003ctt\u003ec\u003c/tt\u003e in the third), and the first column must also be sorted.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eInput:  n   = 16\r\nOutput: mat = [3,  4, 5\r\n               5, 12, 13 \r\n               6,  8, 10 \r\n               9, 12, 15]\r\n\u003c/pre\u003e\u003cp\u003eIf \u003ctt\u003en\u003c/tt\u003e is not an integer, or it is smaller than 5, the function should return an empty matrix.\u003c/p\u003e","function_template":"function mat = triples(n)\r\n    mat = [];\r\nend","test_suite":"%%\r\nfiletext = fileread('triples.m');\r\nassert(isempty(strfind(filetext, 'regexp')),'regexp hacks are forbidden')\r\n\r\n%%\r\nn = 1;\r\nmat_correct = [];\r\nassert(isequal(triples(n),mat_correct))\r\n\r\n%%\r\nn = 20.5;\r\nmat_correct = [];\r\nassert(isequal(triples(n),mat_correct))\r\n\r\n%%\r\nn = 15;\r\nmat_correct = [3,  4, 5; 5, 12, 13; 6,  8, 10; 9, 12, 15];\r\nassert(isequal(triples(n),mat_correct))\r\n\r\n%%\r\nn = 16;\r\nmat_correct = [3,  4, 5; 5, 12, 13; 6,  8, 10; 9, 12, 15];\r\nassert(isequal(triples(n),mat_correct))\r\n\r\n%%\r\nn = 100\r\nmat_correct = ...\r\n    [3     4     5;\r\n     5    12    13;\r\n     6     8    10;\r\n     7    24    25;\r\n     8    15    17;\r\n     9    12    15;\r\n     9    40    41;\r\n    10    24    26;\r\n    11    60    61;\r\n    12    16    20;\r\n    12    35    37;\r\n    13    84    85;\r\n    14    48    50;\r\n    15    20    25;\r\n    15    36    39;\r\n    16    30    34;\r\n    16    63    65;\r\n    18    24    30;\r\n    18    80    82;\r\n    20    21    29;\r\n    20    48    52;\r\n    21    28    35;\r\n    21    72    75;\r\n    24    32    40;\r\n    24    45    51;\r\n    24    70    74;\r\n    25    60    65;\r\n    27    36    45;\r\n    28    45    53;\r\n    28    96   100;\r\n    30    40    50;\r\n    30    72    78;\r\n    32    60    68;\r\n    33    44    55;\r\n    33    56    65;\r\n    35    84    91;\r\n    36    48    60;\r\n    36    77    85;\r\n    39    52    65;\r\n    39    80    89;\r\n    40    42    58;\r\n    40    75    85;\r\n    42    56    70;\r\n    45    60    75;\r\n    48    55    73;\r\n    48    64    80;\r\n    51    68    85;\r\n    54    72    90;\r\n    57    76    95;\r\n    60    63    87;\r\n    60    80   100;\r\n    65    72    97];\r\n\r\n%%\r\nn = 1000;\r\ns_correct = [881, 3];\r\nassert(isequal(size(triples(n)), s_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":140356,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":150,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-12-31T20:29:09.000Z","updated_at":"2026-02-24T14:05:30.000Z","published_at":"2017-12-31T20:29:09.000Z","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\u003eFor a given integer\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return all\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://en.wikipedia.org/wiki/Pythagorean_triple\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePythagorean triples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e that inlude numbers smaller or equal to\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:rFonts w:cs=\\\"monospace\\\"/\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\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\u003eA Pythagorean triple consist of three positive integers\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e{a, b, c}\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ a \u003c b \u003c c,\\n a^2 + b^2 = c^2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe triples should be retured in a matrix with tree columns, where each row contains a different triple. Every row needs to be sorted in ascending order (\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the first column,\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the second and\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the third), and the first column must also be sorted.\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:\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[Input:  n   = 16\\nOutput: mat = [3,  4, 5\\n               5, 12, 13 \\n               6,  8, 10 \\n               9, 12, 15]]]\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\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is not an integer, or it is smaller than 5, the function should return an empty matrix.\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":49582,"title":"Determine whether a square can be drawn on a grid of dots","description":null,"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: 444.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 222.233px; transform-origin: 407px 222.233px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; 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 42px; text-align: left; transform-origin: 384px 42px; 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: 382.358px 7.79167px; transform-origin: 382.358px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSuppose you have a regular grid of dots, each 1 unit apart. By connecting four dots arranged in a square of side 1, you can draw a square of area 1. Similarly, you can draw squares of area 4, 9, 16, 25, etc. As shown below, by connecting dots with diagonal lines, you can draw squares of area 2, 5, 10, 8, 13, and 17. Which squares can you draw by connecting dots on the grid with straight lines? \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: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \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: 301.708px 7.79167px; transform-origin: 301.708px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes an area and determines whether the square of that area can be drawn.\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: 0px 7.79167px; transform-origin: 0px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 291.467px; 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 145.733px; text-align: left; transform-origin: 384px 145.733px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://www.mathsisfun.com/activity/images/squares8.gif\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = squareOnGrid(A)\r\n  tf = false;\r\nend","test_suite":"%%\r\nassert(squareOnGrid(1))\r\n\r\n%%\r\nassert(squareOnGrid(2))\r\n\r\n%%\r\nassert(~squareOnGrid(3))\r\n\r\n%%\r\nassert(squareOnGrid(4))\r\n\r\n%%\r\nassert(squareOnGrid(5))\r\n\r\n%%\r\nassert(~squareOnGrid(6))\r\n\r\n%%\r\nassert(~squareOnGrid(7))\r\n\r\n%%\r\nassert(squareOnGrid(8))\r\n\r\n%%\r\nassert(squareOnGrid(9))\r\n\r\n%%\r\nassert(squareOnGrid(10))\r\n\r\n%%\r\nassert(~squareOnGrid(11))\r\n\r\n%%\r\nassert(~squareOnGrid(12))\r\n\r\n%%\r\nassert(squareOnGrid(13))\r\n\r\n%%\r\nassert(~squareOnGrid(14))\r\n\r\n%%\r\nassert(~squareOnGrid(15))\r\n\r\n%%\r\nassert(squareOnGrid(16))\r\n\r\n%%\r\nassert(squareOnGrid(17))\r\n\r\n%%\r\nassert(squareOnGrid(18))\r\n\r\n%%\r\nassert(~squareOnGrid(19))\r\n\r\n%%\r\nassert(squareOnGrid(20))\r\n\r\n%%\r\nassert(~squareOnGrid(21))\r\n\r\n%%\r\nassert(~squareOnGrid(42))\r\n\r\n%%\r\nassert(squareOnGrid(49))\r\n\r\n%%\r\nassert(~squareOnGrid(51))\r\n\r\n%%\r\nassert(squareOnGrid(53))\r\n\r\n%%\r\nassert(~squareOnGrid(63))\r\n\r\n%%\r\nassert(squareOnGrid(130))\r\n\r\n%%\r\nassert(squareOnGrid(281))\r\n\r\n%%\r\nassert(~squareOnGrid(283))\r\n\r\n%%\r\nfor k = 566:575\r\n    tf(k-565) = squareOnGrid(k);\r\nend\r\nassert(isequal(sum(tf),1))\r\n\r\n%%\r\nassert(~squareOnGrid(1323))\r\n\r\n%%\r\nassert(~squareOnGrid(2310))\r\n\r\n%%\r\nassert(~squareOnGrid(12768))\r\n\r\n%%\r\nassert(squareOnGrid(12769))\r\n\r\n%%\r\nassert(~squareOnGrid(19200))\r\n\r\n%%\r\nassert(~squareOnGrid(1514205))\r\n\r\n%%\r\nassert(squareOnGrid(2e7))\r\n\r\n%%\r\nassert(squareOnGrid(2^randi(20)))\r\n\r\n%%\r\nassert(~squareOnGrid(7^(2*randi(10)+1)))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2020-12-25T06:14:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-24T15:45:57.000Z","updated_at":"2021-01-01T19:18:37.000Z","published_at":"2020-12-24T16:01:03.000Z","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\u003eSuppose you have a regular grid of dots, each 1 unit apart. By connecting four dots arranged in a square of side 1, you can draw a square of area 1. Similarly, you can draw squares of area 4, 9, 16, 25, etc. As shown below, by connecting dots with diagonal lines, you can draw squares of area 2, 5, 10, 8, 13, and 17. Which squares can you draw by connecting dots on the grid with straight lines? \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes an area and determines whether the square of that area can be drawn.\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\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.gif\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.gif\",\"contentType\":\"image/gif\",\"content\":\"https://www.mathsisfun.com/activity/images/squares8.gif\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2308,"title":"rectangle in circle ","description":"In the figure below, the rectangle at the corner measures a cm x b cm. What is the radius of the circle in cm? \r\n\r\n\u003c\u003chttp://www.syvum.com/iosundry/contrib/teasers/circle1a.gif\u003e\u003e","description_html":"\u003cp\u003eIn the figure below, the rectangle at the corner measures a cm x b cm. What is the radius of the circle in cm?\u003c/p\u003e\u003cimg src = \"http://www.syvum.com/iosundry/contrib/teasers/circle1a.gif\"\u003e","function_template":"function y = your_fcn_name(a,b)\r\n  y = x;\r\nend","test_suite":"%%\r\na=6;\r\nb=12;\r\ny_correct=30\r\nassert(isequal(your_fcn_name(a,b),y_correct))\r\n\r\n%%\r\na=7;\r\nb=14;\r\ny_correct=35\r\nassert(isequal(your_fcn_name(a,b),y_correct))\r\n\r\n\r\n%%\r\na=3;\r\nb=6;\r\ny_correct=15\r\nassert(isequal(your_fcn_name(a,b),y_correct))\r\n\r\n%%\r\na=5;\r\nb=40;\r\ny_correct=65\r\nassert(isequal(your_fcn_name(a,b),y_correct))\r\n\r\n%%\r\na=5;\r\nb=90;\r\ny_correct=125\r\nassert(isequal(your_fcn_name(a,b),y_correct))\r\n\r\n%%\r\na=12;\r\nb=54;\r\ny_correct=102\r\nassert(isequal(your_fcn_name(a,b),y_correct))\r\n\r\n%%\r\na=16;\r\nb=18;\r\ny_correct=58\r\nassert(isequal(your_fcn_name(a,b),y_correct))\r\n\r\n%%\r\na=16;\r\nb=72;\r\ny_correct=136\r\nassert(isequal(your_fcn_name(a,b),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":17228,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":71,"test_suite_updated_at":"2014-05-12T07:30:16.000Z","rescore_all_solutions":false,"group_id":26,"created_at":"2014-05-07T11:30:17.000Z","updated_at":"2026-02-19T10:40:20.000Z","published_at":"2014-05-07T11:30:17.000Z","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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.gif\"}],\"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\u003eIn the figure below, the rectangle at the corner measures a cm x b cm. What is the radius of the circle in cm?\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\"},{\"partUri\":\"/media/image1.gif\",\"contentType\":\"image/gif\",\"content\":\"data:image/gif;base64,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\"}]}"},{"id":2023,"title":"Is this triangle right-angled?","description":"Given any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.","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: 381.5px 8px; transform-origin: 381.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function flag = isRightAngled(a,b,c)\r\n  flag = false;\r\nend","test_suite":"%%\r\na = 3;\r\nb = 4;\r\nc = 5;\r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 3;\r\nb = 4;\r\nc = 6;\r\nflag_correct = false;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 3;\r\nb = 5;\r\nc = 4; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 4;\r\nb = 3; \r\nc = 5;\r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 4; \r\nb = 5;\r\nc = 3; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 3;\r\nc = 4; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 4;\r\nc = 3; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 12;\r\nc = 13; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 12;\r\nc = 11; \r\nflag_correct = false;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 10; \r\nb = 15;\r\nc = 20; \r\nflag_correct = false;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))","published":true,"deleted":false,"likes_count":38,"comments_count":5,"created_by":974,"edited_by":223089,"edited_at":"2023-01-29T06:52:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6564,"test_suite_updated_at":"2023-01-29T06:52:29.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:31:43.000Z","updated_at":"2026-04-04T19:09:09.000Z","published_at":"2013-11-28T17:12:35.000Z","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\u003eGiven any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.\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":49738,"title":"Determine whether a prime is Pythagorean","description":null,"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: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 369.1px 7.79167px; transform-origin: 369.1px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePythagorean primes get their name from the property that they can be written as the sum of two squares. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"13 = 2^2 + 3^2\" style=\"width: 78.5px; height: 19px;\" width=\"78.5\" height=\"19\"\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: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45964\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 45964\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 68.45px 7.79167px; transform-origin: 68.45px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked you to find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 185.167px 7.79167px; transform-origin: 185.167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth Pythagorean prime and two numbers whose squares will produce the prime. This problem merely asks you to determine whether a prime can be written as the sum of two squares. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 379.5px 7.79167px; transform-origin: 379.5px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a prime is Pythagorean. All input numbers in the tests are prime. Because some are large, they are given as strings. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isPythagoreanPrime(pstr)\r\n  tf = isprime(str2num(pstr));\r\nend","test_suite":"%%\r\npstr = '13';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '17';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '23';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '31';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '541';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '997';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '2459';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '36293';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '499979';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '5999681';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '69985649';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '87178291199';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '99194853094755497';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '900900900900990990990991';\r\nassert(~isPythagoreanPrime(pstr))\r\n    \r\n%%\r\npstr = '1066340417491710595814572169';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '845100400152152934331135470251';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '19134702400093278081449423917';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '10888869450418352160768000001';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '26525285981219105863630847999999';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '263130836933693530167218012159999999';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '8683317618811886495518194401279999999';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '56713727820156410577229101238628035243';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '62357403192785191176690552862561408838653121833643';\r\nassert(~isPythagoreanPrime(pstr))","published":true,"deleted":false,"likes_count":2,"comments_count":7,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":84,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-02T23:14:39.000Z","updated_at":"2026-01-06T08:06:28.000Z","published_at":"2021-01-02T23:21:49.000Z","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\u003ePythagorean primes get their name from the property that they can be written as the sum of two squares. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"13 = 2^2 + 3^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e13 = 2^2 + 3^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\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/45964\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 45964\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked you to find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth Pythagorean prime and two numbers whose squares will produce the prime. This problem merely asks you to determine whether a prime can be written as the sum of two squares. \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\u003eWrite a function to determine whether a prime is Pythagorean. All input numbers in the tests are prime. Because some are large, they are given as strings. \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":2022,"title":"Find a Pythagorean triple","description":"Given four different positive numbers, a, b, c and d, provided in increasing order: a \u003c b \u003c c \u003c d, find if any three of them comprise sides of a right-angled triangle. Return true if they do, otherwise return false .","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: 376.5px 8px; transform-origin: 376.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven four different positive numbers, a, b, c and d, provided in increasing order: a \u0026lt; b \u0026lt; c \u0026lt; d, find if any three of them comprise sides of a right-angled triangle. Return\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: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etrue\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: 86px 8px; transform-origin: 86px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if they do, otherwise return\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: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003efalse\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=\"\"\u003e .\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function flag = isTherePythagoreanTriple(a, b, c, d)\r\n  flag = false;\r\nend","test_suite":"%%\r\nfiletext = fileread('isTherePythagoreanTriple.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp');\r\nassert(~illegal)\r\n\r\n%%\r\na = 1;\r\nb = 2; \r\nc = 3;\r\nd = 4;\r\nflag_correct = false;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 2;\r\nb = 3; \r\nc = 4;\r\nd = 5;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 3;\r\nb = 4;  \r\nc = 5; \r\nd = 6;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 3;\r\nb = 4; \r\nc = 4.5;\r\nd = 5;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 2;\r\nb = 3;\r\nc = 5;\r\nd = 7;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),~flag_correct))\r\n%%\r\na = 1;\r\nb = 2;\r\nc = sqrt(5);\r\nd = 6;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 5;\r\nb = 7;\r\nc = 12;\r\nd = 13;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 5;\r\nb = 7;\r\nc = 11;\r\nd = 13;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),~flag_correct))","published":true,"deleted":false,"likes_count":48,"comments_count":12,"created_by":974,"edited_by":223089,"edited_at":"2023-03-13T17:24:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5084,"test_suite_updated_at":"2023-03-13T17:24:10.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:29:57.000Z","updated_at":"2026-04-02T15:27:25.000Z","published_at":"2013-11-28T17:12:31.000Z","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\u003eGiven four different positive numbers, a, b, c and d, provided in increasing order: a \u0026lt; b \u0026lt; c \u0026lt; d, find if any three of them comprise sides of a right-angled triangle. Return\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they do, otherwise return\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efalse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\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":45964,"title":"Compute the nth Pythagorean prime","description":"Pythagorean primes have the form p = 4n+1, where n is an integer, and they can be written as the sum of squares of two integers. More information is available at \u003chttps://en.wikipedia.org/wiki/Pythagorean_prime Wikipedia\u003e, \u003chttps://www.youtube.com/watch?v=yu_aqA7mw7E Numberphile\u003e, and the \u003chttps://oeis.org/A002144 Online Encyclopedia of Integer Sequences\u003e. \r\n\r\nCompute the nth Pythagorean prime p and two integers a and b such that p = a^2+b^2","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: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; 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: 109.3px 7.8px; transform-origin: 109.3px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePythagorean primes have the form \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = 4n+1\" style=\"width: 70px; height: 18px;\" width=\"70\" height=\"18\"\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: 24.9px 7.8px; transform-origin: 24.9px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 209.25px 7.8px; transform-origin: 209.25px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is an integer, and they can be written as the sum of squares of two integers. More information is available at\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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pythagorean_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWikipedia\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; 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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=yu_aqA7mw7E\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eNumberphile\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 27.2333px 7.8px; transform-origin: 27.2333px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the\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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A002144\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOnline Encyclopedia of Integer Sequences\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\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: 42.0167px 7.8px; transform-origin: 42.0167px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 68.85px 7.8px; transform-origin: 68.85px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth Pythagorean prime \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\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: 55.2333px 7.8px; transform-origin: 55.2333px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and two integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\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: 15.5667px 7.8px; transform-origin: 15.5667px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\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: 32.2833px 7.8px; transform-origin: 32.2833px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = a^2+b^2\" style=\"width: 72.5px; height: 19px;\" width=\"72.5\" height=\"19\"\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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [pp,a,b] = PythagoreanPrime(n)\r\n  pp = a^2+b^2;\r\nend","test_suite":"%%\r\nn = 1;\r\npp_correct = 5;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 5;\r\npp_correct = 37;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 25;\r\npp_correct = 257;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 125;\r\npp_correct = 1657;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 625;\r\npp_correct = 10313;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 3125;\r\npp_correct = 62497;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 15625;\r\npp_correct = 367229;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":98,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-19T01:58:26.000Z","updated_at":"2026-01-19T15:38:08.000Z","published_at":"2020-06-19T02:08:23.000Z","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\u003ePythagorean primes have the form \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 4n+1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 4n+1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer, and they can be written as the sum of squares of two integers. More information is available at\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://en.wikipedia.org/wiki/Pythagorean_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=yu_aqA7mw7E\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNumberphile\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and the\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://oeis.org/A002144\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOnline Encyclopedia of Integer Sequences\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth Pythagorean prime \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and two integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = a^2+b^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = a^2+b^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\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":2024,"title":"Triangle sequence ","description":"A sequence of triangles is constructed in the following way:\r\n1) the first triangle is Pythagoras' 3-4-5 triangle\r\n2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle\r\n3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.\r\nEach triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.\r\nWhat is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?","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: 234px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 117px; transform-origin: 407px 117px; 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: 185px 8px; transform-origin: 185px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA sequence of triangles is constructed in the following way:\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: 148.5px 8px; transform-origin: 148.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1) the first triangle is Pythagoras' 3-4-5 triangle\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 365.5px 8px; transform-origin: 365.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 368px 8px; transform-origin: 368px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.\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: 299px 8px; transform-origin: 299px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhat is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = triangle_sequence(n)\r\n  area = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('triangle_sequence.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n%%\r\nn = 1;\r\narea_correct = 25;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 2;\r\narea_correct = 41;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 3;\r\narea_correct = 66;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 9;\r\narea_correct = 1186;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 13;\r\narea_correct = 8129;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 22;\r\narea_correct = 617911;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 50;\r\narea_correct = 439116598409;\r\ntolerance = 1e-3;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)","published":true,"deleted":false,"likes_count":156,"comments_count":39,"created_by":974,"edited_by":223089,"edited_at":"2023-03-16T15:12:00.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5829,"test_suite_updated_at":"2023-03-16T15:12:00.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:39:45.000Z","updated_at":"2026-03-31T16:33:25.000Z","published_at":"2013-11-28T17:12:38.000Z","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\u003eA sequence of triangles is constructed in the following way:\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\u003e1) the first triangle is Pythagoras' 3-4-5 triangle\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\u003e2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle\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\u003e3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.\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\u003eEach triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.\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\u003eWhat is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?\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":46701,"title":"Compute the nth Naerogahtyp emirp","description":null,"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: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 6.60833px 8.05px; transform-origin: 6.60833px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45964-compute-the-nth-pythagorean-prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePythagorean prime\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 311.542px 8.05px; transform-origin: 311.542px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a prime number that can be written as the sum of two squares. For example, 13 is a Pythagorean prime because it is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 95.5px; height: 19px;\" width=\"95.5\" height=\"19\"\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: 139.508px 8.05px; transform-origin: 139.508px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In a similar way, a Naerogahtyp emirp is an \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46624-list-the-emirps\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eemirp\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 117.833px 8.05px; transform-origin: 117.833px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that can be written as the sum of two \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46676-list-the-erauqs\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"perspective-origin: 21.4px 8.05px; transform-origin: 21.4px 8.05px; \"\u003eerauqs\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 3.88333px 8.05px; transform-origin: 3.88333px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \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: 156.233px 8.05px; transform-origin: 156.233px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find the nth Naerogahtyp emirp.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ne = NaerogahtypEmirp(n)\r\n  ne = f(n);\r\nend","test_suite":"%%\r\nn = 1;\r\nne_correct = 1061;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = 2;\r\nne_correct = 1069;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = 5;\r\nne_correct = 15053;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = 10;\r\nne_correct = 102769;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = 29;\r\nne_correct = 1508621;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = 53;\r\nne_correct = 11364701;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = 101;\r\nne_correct = 106684421;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = 197;\r\nne_correct = 153918421;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = [17 31 67];\r\nfor k = 1:3\r\n    ne(k) = NaerogahtypEmirp(n(k));\r\nend\r\nsum_correct = 102944443;\r\nassert(isequal(sum(ne),sum_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-06T21:38:21.000Z","updated_at":"2025-11-17T17:22:23.000Z","published_at":"2020-10-20T04:54:59.000Z","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\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45964-compute-the-nth-pythagorean-prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePythagorean prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a prime number that can be written as the sum of two squares. For example, 13 is a Pythagorean prime because it is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4+9=2^2+3^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. In a similar way, a Naerogahtyp emirp is an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46624-list-the-emirps\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eemirp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e that can be written as the sum of two \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46676-list-the-erauqs\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eerauqs\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find the nth Naerogahtyp emirp.\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":57998,"title":"Easy Sequences 111: Repnums as Hypotenuse of Pythagorean Triangles","description":"The number  belongs to a class of numbers called Repunit Numbers, in which all digits are . \r\nFor this problem, we'll define a superset of the repunit numbers which we shall call repnums, which are composed of repeated numbers. That is, if we denote repnums by , then  is the number to be repeated and   is the number of repetitions. Hence,  , ,  and so on.\r\nWe can see from the figure below that  can be a hypotenuse of a right triangle with integer sides (Pythagorean Triangle).\r\n                                                        \r\nIn fact, this is the only Pythagorean triangle that can be formed with hypotenuse equal to . There is also only one Pythagorean triangle with hypotenuse equal to , that is the triangle with sides , while there are seven Pythagorean triangles with hypotenures of , with legs as follows:\r\n        \r\nCreate the function, , that counts the number of Pythagorean triangles that can be formed with hypotenuse equal to .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; 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; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 435px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 217.5px; transform-origin: 407px 217.5px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"25.5\" height=\"18\" style=\"width: 25.5px; height: 18px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e belongs to a class of numbers called \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Repunit\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRepunit Numbers,\u003c/span\u003e\u003c/span\u003e\u003c/a\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=\"\"\u003e in which all digits are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor this problem, we'll define a superset of the repunit numbers which we shall call \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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003erepnums\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, which are composed of repeated numbers. That is, if we denote repnums by \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the number to be repeated and  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the number of repetitions. Hence,  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"87\" height=\"19\" style=\"width: 87px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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src=\"data:image/png;base64,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\" width=\"214.5\" height=\"19\" style=\"width: 214.5px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and so on.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe can see from the figure below that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFwAAAAmCAYAAABJVvz/AAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAXKADAAQAAAABAAAAJgAAAADSajFxAAAF0klEQVRoBe2YeYhWVRjGpzSzLKFJoUxrtKhAKC0sWmz5xxYlCLfSirHUAqVCihYwJaiINiGIwPSfLGjB9ohokTFGKG2TFqKaIVuMLC3Lcsrq98x33zpz5px77zdzP+f74D7wzD3vct7z3vc7252mphJlBcoKlBUoK1BWoKxAQ1RgDll+CQ9uiGx7JjkXsR2O7alOl/bxzEcjN3s6V/wHYTv8Bv7hGvrQXkSfB+ECuCqj/77Y9eMMhY9k+PbVfCgdL4Tj4XC4EW6An8AQBqN8Dk6Cp8EvYNVYTo8tUIXN4jZ8NOClUAWpBqfi3AXvyOikuJdAvbTyWQNrgXkE/RGG3nkFen9iWg4H0XgXvgc1GfoEBVch3MG1dGZCzbIbYRt07ZuQj4R5cAhOnfAZGHsR6afDzdAdpxYF1ztpjF/hE/AVuAO64y5DjmEUhq0wa5XG+nfrtazcAWcHvM9Fp23F/NbRjhUQ0394ltafUNtXDFra8rsMPg9tjKILfjixd8FX4QhoGELjemjjfmiGyPPaxPfKiD1Trdlqg+k5NdJjiec3JeJnaptNK02R4zkDH8ul6ILfTuy34f6RPD5yxk472LWd6FzTKtE2E4X2yBD0gnnwmuc0wZN98apEkbV3u/30ErWCCt0Kd0cG+D7Ra39Py0Mr/X44DM6CUcQKHu3gGfZ4svazGMZgOAdq1nTCesBNJPFxJBH9GDrcBW05WZPw5W7Pyg+YNHs/+lvwU7yQHZ7sirq3arzXXWUdt6eR24FQs1xbZxZ0k9LhORkeE3PuT8F14Cx1AnfR1gEXwwWJoREKrkP7UfgTnARVyDx4M3HShSKIvhRch8c8qOBjk6habjfAtBlu18bYEk5CDejjMEa/C+qGdABsho9By51mKj5NrGNSvQJGdVARjRtpvwh1yd/l6GVvg1m3E10XdTDJX/fwanA+zpZH0bcUN4/FCLqu2ljucwv61NtHEmhR0n91Ivd65J3hKpL2pYlQv7ywAY6DZ0EdKmkYiVF32z1wR5rjANpWMfbxUAflzdC9lYxGvgVmQbcZQf5VwZ/huofvB1Vk++VVPM2+PDgRJ/XblsfZ89lbM9wbtqkFha699r6f+Q4B2XJ9J2DrVuWd4XLWcpsJf5AA1PdxqFmeBZstQ7Mc68jeSS4XQ723oPfUKk2Drf6/Yk7VFFwxvoZz4N8SgLaatVDXpzToK0wYBnW/bRTsJNH2JNlBPNO+NuWm/zgKqlMQ1RZcQbTMbnOiabtY6cihpr7EbGVYUiG/etStT5LaztP26FieIxJDoQVXzDvhS0lwPTTrr3PkUNOSGBUy1rHOJsjmHDnq20Swd61Izt/YDPeX/WCnj5o6SC6HHRIS3MtTN5YY9CUmTK48cv/VlTIvdLBPgzOgtq/+QvGmJEFW5Ahm7/9BDt8eLmci2ems54Ie1v+Fk2j+Ds13K+0WGIK+3uT3QsiYomvFZvGfTvGTSV+65ruJ9nApUzAbmz5ydOWzA891vxVB8da5ykhb24nONp1XsYkc7DoarbYLS1zP9+F4GJpt8z3f75DPg/4L6ND5Fv4M/RWDKohxaDVbLBedA8cFPSsv2eX4qs+siK+p9UFjsb+i3Qq1LUyED0HZ3oBZhyUu3Tc4+d8jIS/W4GgJhJ6xj5bVgX6/BQa9O/G7ImBzVUcgqBiaMX4e0nXAq6GPp1C4/st9B09e4vlb31/QvwX1g4UmGepe0GVC/U/oZRlARQtja4Z/DvPOclyrwrF4z4V6eR3mWdCK0dZyDZwKj4J5i4xrN87mr8Z7siLW19/pSXLza5jWw8TW9pO1hxeVQhuBNIn21nhV530fPXbCCVX3TO+gw+oBqO3sonTXwqxLibQbnlxYxBoE0nayHupE1yFdFBYSqBMW/UPG8rOta3HMoZ70uka1Q91CBhWUmJZ0c0GxssKcgYO+oJdlOdaTfQjJ6CNFW0GjQYft6Y2WdJlvWYGyAmUFygqUFWiYCvwLNaZWwXCKJFMAAAAASUVORK5CYII=\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e can be a hypotenuse of a right triangle with integer sides (\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pythagorean_triple\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePythagorean Triangle\u003c/span\u003e\u003c/span\u003e\u003c/a\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=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 129px; 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 64.5px; text-align: left; transform-origin: 384px 64.5px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                                        \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"254\" height=\"123\" style=\"vertical-align: baseline;width: 254px;height: 123px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn fact, this is the only Pythagorean triangle that can be formed with hypotenuse equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. There is also only one Pythagorean triangle with hypotenuse equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, that is the triangle with sides \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"140\" height=\"19\" style=\"width: 140px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, while there are seven Pythagorean triangles with hypotenures of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"53.5\" height=\"19\" style=\"width: 53.5px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, with legs as follows:\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" width=\"620.5\" height=\"19\" style=\"width: 620.5px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCreate the function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, that counts the number of Pythagorean triangles that can be formed with hypotenuse equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFwAAAAmCAYAAABJVvz/AAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAXKADAAQAAAABAAAAJgAAAADSajFxAAAGOUlEQVRoBe2YaWxWRRSGqaKiuKIxAbXSSkoMiYJEDSoVYl3igjEKajHGhRoNKmr0p4BGjBui8Y+BlF9AgibuSzQVtSb4QwE1EjVsNVhF0SDiRpHq+5R7kmE6d77v3n61S+6bvJ0z55zZzp05M1+HDClQRKCIQBGBIgJFBIoIDIgINGqWm8UjBsRs95/kTFVXizX7q+O1Ks98iuojPJ1b/VeVHWK7+LdryCHPVpvnxCaxOUf7vm4yVBN4VTxTnCRuEjNjvlpsFQlsKf4sHwa8XjxAzIKz5dwhLsjSqB/6Hq45rRXXicPyzo9dTyDcgHN0poukgAfEVtG1r1G9WiwHx8ipTXxZ9E+YVAMOozTjbWKPTuk4deAG9NpAGKZKR1oxvw8klxPAV+S3RyR9DRbcrYUQh1vyLojdaoGkvCylo/s8v4tS/EzNCaG/JaYYJCXphHvtd5E0k4q03EtQykGL5zTeq/vVWxPFQM/d/ro46U+Lw8UZvtGtpwXc9YnJez0j+SwNJ8kwRVwvtomDDW8lC7optjCeNj3BWV7jLV7drfJu5QO/5ypLyGNlbxBrRV5EraLhWAmcGC7hx8SdYl4cp4YTEm5QyYUOThavELlv3hBjc/9Kdi7PyeIYcaNYNtiNpBVjKIePlJ0fLeazW3KNmIYPZcB3WpqDoyfQLOAf0frn2BJkgJ2cabZ5KHNgodp8J1o/lGwMcLNITnZtvLljWCEj/k0xp5AtFnB+FTKZr0WbTKfku8QYtsiIP1+/FMiFdSInYpFo4/BaYjduEtntHOMfxdCGkLok+HDk3A6RMfaInBheHXxsxn5btPHvkBzDXBnxfTjmFLL5Af9UThypteKfok2AkoWXep1UyYcTgD8LyoLT5WzjPSv5JfF98SCxEqCfXSJjrBKvElmjrWmOZBv/EskxzJYR36Uxp5DNDzg7yt3RdLparAk1DuiOl4427BqCnwX47xBt0cgnZOmghG+90/czkn8Tb3DaNDt20mgM18nIPN+NOYVsfsA5suyEj0Vb+F7Jpb64XLpgu5R/B+SBe6zvzNNBpM0jstmavpW82PP9JrF/6elDVeJBX5+EjOjIkeWC/MbP++1JA9quEGuTeqzg8gHD9hWZ/3KaDKSwSsJSB32S9u5xOq+WXJfU33H0aeKhiYGTHESWgNMBN3qj2ElFIB+TUw+jEkF7Yhuu8pCIX5qJF4phkgkVKHn1THT6uV0y+dvgfoxy0oS9oohTEFkDTict4lynN9LFEqceEgmYnQybVMgvpOMN7I43OeSUU9egdhYDArrK6+fCpM78yzlZvKBARQNOh4+KbyIkYNfPsUpKaZMYlWIPqYdKuUz8TPwicahkwN0dzIXpgg9xQaL4SOVfrjFFHpnoba0pbt3VY6Syi4Tyyu4uXelks+NHjq8P+JlqeeJ7rynKKB+SDxftieIi0eZULRlcKt7WJe37w8V+uXiNSPoqha1yoM+fRD6uC1KNjXd/YmhWOSWRQ8U6KWnTEDLGdOclDW3AphTnM6Tny5vfNsmjxRAIDn6vh4yJrlYlflyufGQuH35aA97HNg4vlVPFX8SpouE1CeazRvKRZgiUtDffxQE7l6fZJ0heIG4QjxJDIJ10iu0ip6NssJtIFzYYJUd6nFgl+pglhev7g+oXi3Zjm/+BEr4Xd4r+bjIf23F/SMHknzCDyqNF+9GF/VfxKdHAIjtEdy4zzBgo3YByKnwwtvVFSmHep/lOTn26ZPyfdHQlxWVJIxvIL1lkCEul9H0Jio/HpcDvRt+Q1NcndnyWi/5OYSfaOCsl8xFdvKiK2Snnu0ZPfkF1fJinvzlw5aTx0fFh154jxtAiI76xjxJr3yu20eqVnbJRDO1yXjCkkLFiCJywejH2NKyTfabI4hvFnoBTzVihD+L2e74qjMdH7He4WjNicrN6cWbPq+/tYiyHV3L4VnXGJvq/xss894VqsUscn7llvAEpiNcMaWJa3LVi1gfV025xYsV67IWOSCdcRORGLulKgSdim1jpD5k2P0tdvJr6PXhGrRY/F/3LL+/kOdIj8jbO2O5c+fMLdF7Gdn3qfrBG50eK/xrp00mVOTgXe6mXS5ldFW5FBIoIFBEoIlBEoIhAtwj8B7kYiuSPD/PFAAAAAElFTkSuQmCC\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = C(x,n)\r\n  c = C(x,n);\r\nend\r\n\r\n","test_suite":"%%\r\nx = (1:5).^2; n = [3,5,2,3,2];\r\nc_correct = [1,1,0,4,7];\r\nassert(isequal(arrayfun(@(i) C(x(i),n(i)),1:5),c_correct))\r\n%%\r\ns_correct = 26;\r\nassert(isequal(sum(arrayfun(@(i) C(i,i),1:9)),s_correct))\r\n%%\r\nx = 1; n = 15;\r\nc_correct = 13;\r\nassert(isequal(C(x,n),c_correct))\r\n%%\r\nx = 123; n = 6;\r\nc_correct = 4;\r\nassert(isequal(C(x,n),c_correct))\r\n%%\r\nx = 1234; n = 4;\r\nc_correct = 121;\r\nassert(isequal(C(x,n),c_correct))\r\n%%\r\nx = 12345; n = 2;\r\nc_correct = 1;\r\nassert(isequal(C(x,n),c_correct))\r\n%%\r\nx = 123456789;\r\nc_correct = 1;\r\nassert(isequal(C(x,1)+C(x,2),c_correct))\r\n%%\r\nx = 3; n = 17;\r\nc_correct = 1;\r\nassert(isequal(C(x,n),c_correct))\r\n%%\r\nx = 35; n = 10;\r\nc_correct = 121;\r\nassert(isequal(C(x,n),c_correct))\r\n%%\r\nx = 5; n = 24;\r\nc_correct = 3280;\r\nassert(isequal(C(x,n),c_correct))\r\n%%\r\nx = 101:200;\r\nc = arrayfun(@(i) C(i,4),x);\r\ns_correct = [30 13 22 23];\r\nassert(isequal(floor([mean(c) mode(c) median(c) std(c)]),s_correct))\r\n%%\r\nfiletext = fileread('C.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'assignin') || contains(filetext, 'evalin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-27T05:38:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2023-04-27T05:33:05.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-18T10:54:53.000Z","updated_at":"2023-04-27T05:38:35.000Z","published_at":"2023-04-26T22:30:53.000Z","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\u003eThe number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e111\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e belongs to a class of numbers called \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Repunit\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRepunit Numbers,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in which all digits are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, we'll define a superset of the repunit numbers which we shall call \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003erepnums\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which are composed of repeated numbers. That is, if we denote repnums by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(x,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the number to be repeated and  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of repetitions. Hence,  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(1,3)=111\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(25,2)=2525\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(123,6)=123123123123123123\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e 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\u003eWe can see from the figure below that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(1,3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be a hypotenuse of a right triangle with integer sides (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pythagorean_triple\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePythagorean Triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"123\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"254\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eIn fact, this is the only Pythagorean triangle that can be formed with hypotenuse equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(1,3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. There is also only one Pythagorean triangle with hypotenuse equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(4,5)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, that is the triangle with sides \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[9756,\\\\ 43360, \\\\ 44444]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, while there are seven Pythagorean triangles with hypotenures of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(25,2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, with legs as follows:\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        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{\\\\ [213,\\\\ 2516]\\\\ [500,\\\\ 2475]\\\\ [707,\\\\ 2424]\\\\ [1085,\\\\ 2280]\\\\ [1173,\\\\ 2236]\\\\ [1515,\\\\ 2020]\\\\ [1680,\\\\ 1885]\\\\ \\\\}\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCreate the function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{C}(x,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, that counts the number of Pythagorean triangles that can be formed with hypotenuse equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" 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perfect squares: find the square of the hypotenuse and the length of the other side","description":"Given the square root of a square number, *seed*, and a range, *n*, find the square number, *Z* as well as the other side, *y*, the square root of a square number i.e. return the hypotenuse squared as well as the length of the other side. Note that *n* is the number of squares to search through starting with one.\r\n\r\nHINT: Z = seed^2 + y^2 where Z = z^2, find Z first and then y. \r\n\r\nNote that Z, seed^2 and y^2 are all perfect squares.\r\n\r\n\u003e\u003e [z s] = findPerfectZ(3,6)\r\n\r\nz = 25\r\n\r\ns = 4\r\n\r\n\u003e\u003e","description_html":"\u003cp\u003eGiven the square root of a square number, \u003cb\u003eseed\u003c/b\u003e, and a range, \u003cb\u003en\u003c/b\u003e, find the square number, \u003cb\u003eZ\u003c/b\u003e as well as the other side, \u003cb\u003ey\u003c/b\u003e, the square root of a square number i.e. return the hypotenuse squared as well as the length of the other side. Note that \u003cb\u003en\u003c/b\u003e is the number of squares to search through starting with one.\u003c/p\u003e\u003cp\u003eHINT: Z = seed^2 + y^2 where Z = z^2, find Z first and then y.\u003c/p\u003e\u003cp\u003eNote that Z, seed^2 and y^2 are all perfect squares.\u003c/p\u003e\u003cp\u003e\u003e\u003e [z s] = findPerfectZ(3,6)\u003c/p\u003e\u003cp\u003ez = 25\u003c/p\u003e\u003cp\u003es = 4\u003c/p\u003e\u003cp\u003e\u003e\u003e\u003c/p\u003e","function_template":"function [Z,y] = findPerfectZ(seed,n)\r\n  Z = perfectZSquare \r\n  y = aside\r\nend","test_suite":"%%\r\n\r\nseed=3;n=6;\r\n\r\n[Z,y] = findPerfectZ(seed,n);\r\n\r\nZ_correct = 25; y_correct = 4;\r\n\r\nassert(isequal(Z,Z_correct));\r\n\r\nassert(isequal(y,y_correct));\r\n\r\n%%\r\n\r\nseed=5;n=15;\r\n\r\n[Z,y] = findPerfectZ(seed,n);\r\n\r\nZ_correct = 169; y_correct = 12;\r\n\r\nassert(isequal(Z,Z_correct));\r\n\r\nassert(isequal(y,y_correct));\r\n\r\n%%\r\n\r\nseed=4;n=6;\r\n\r\n[Z,y] = findPerfectZ(seed,n);\r\n\r\nZ_correct = 25; y_correct = 3;\r\n\r\nassert(isequal(Z,Z_correct));\r\n\r\nassert(isequal(y,y_correct));\r\n\r\n%%\r\n\r\nseed=12;n=15;\r\n\r\n[Z,y] = findPerfectZ(seed,n);\r\n\r\nZ_correct = 169; y_correct = 5;\r\n\r\nassert(isequal(Z,Z_correct));\r\n\r\nassert(isequal(y,y_correct));\r\n\r\n%%\r\n\r\nseed=6;n=9;\r\n\r\n[Z,y] = findPerfectZ(seed,n);\r\n\r\nZ_correct = 100; y_correct = 8;\r\n\r\nassert(isequal(Z,Z_correct));\r\n\r\nassert(isequal(y,y_correct));\r\n\r\n%%\r\n\r\nseed=8;n=9;\r\n\r\n[Z,y] = findPerfectZ(seed,n);\r\n\r\nZ_correct = 100; y_correct = 6;\r\n\r\nassert(isequal(Z,Z_correct));\r\n\r\nassert(isequal(y,y_correct));","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2012-02-12T06:59:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-12T06:59:40.000Z","updated_at":"2026-03-23T10:18:19.000Z","published_at":"2012-02-12T06:59:40.000Z","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 the square root of a square number,\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eseed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and a range,\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the square number,\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eZ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as well as the other side,\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the square root of a square number i.e. return the hypotenuse squared as well as the length of the other side. Note that\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of squares to search through starting with one.\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\u003eHINT: Z = seed^2 + y^2 where Z = z^2, find Z first and then y.\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\u003eNote that Z, seed^2 and y^2 are all perfect squares.\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\u003e\u0026gt;\u0026gt; [z s] = findPerfectZ(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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ez = 25\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\u003es = 4\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\u003e\u0026gt;\u0026gt;\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":1974,"title":"Length of a short side ","description":"Calculate the length of the short side, a, of a right-angled triangle with hypotenuse of length c, and other short side of length b.  \r\n\r\n\u003c\u003chttps://i.imgur.com/73mQn4N.png\u003e\u003e\r\n\r\nImage courtesy of \u003chttp://upload.wikimedia.org/wikipedia/commons/7/7c/Right_Angle_Triangle.svg Wikipedia\u003e.","description_html":"\u003cp\u003eCalculate the length of the short side, a, of a right-angled triangle with hypotenuse of length c, and other short side of length b.\u003c/p\u003e\u003cimg src = \"https://i.imgur.com/73mQn4N.png\"\u003e\u003cp\u003eImage courtesy of \u003ca href = \"http://upload.wikimedia.org/wikipedia/commons/7/7c/Right_Angle_Triangle.svg\"\u003eWikipedia\u003c/a\u003e.\u003c/p\u003e","function_template":"function a = calculate_short_side(b, c)\r\n  a = \r\nend","test_suite":"%%\r\nb = 1;\r\nc = 2; \r\na_correct = sqrt(3);\r\ntolerance = 1e-12; \r\nassert(abs(calculate_short_side(b,c)-a_correct)\u003ctolerance);\r\n%%\r\nb = 4;\r\nc = 5;\r\na_correct = 3; \r\ntolerance = 1e-12; \r\nassert(abs(calculate_short_side(b,c)-a_correct)\u003ctolerance);\r\n%%\r\nb = 12;\r\nc = 13;\r\na_correct = 5; \r\ntolerance = 1e-12; \r\nassert(abs(calculate_short_side(b,c)-a_correct)\u003ctolerance);\r\n%%\r\nb = 8;\r\nc = 10;\r\na_correct = 6; \r\ntolerance = 1e-12; \r\nassert(abs(calculate_short_side(b,c)-a_correct)\u003ctolerance);","published":true,"deleted":false,"likes_count":62,"comments_count":17,"created_by":974,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8015,"test_suite_updated_at":"2013-11-29T09:41:22.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-08T23:06:44.000Z","updated_at":"2026-04-03T13:34:44.000Z","published_at":"2013-11-28T17:12:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml 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\"}]}"},{"id":2015,"title":"Length of the hypotenuse","description":"Given short sides of lengths a and b, calculate the length c of the hypotenuse of the right-angled triangle.\r\n\r\n\u003c\u003chttps://i.imgur.com/73mQn4N.png\u003e\u003e\r\n\r\nImage courtesy of \u003chttp://upload.wikimedia.org/wikipedia/commons/7/7c/Right_Angle_Triangle.svg Wikipedia\u003e.","description_html":"\u003cp\u003eGiven short sides of lengths a and b, calculate the length c of the hypotenuse of the right-angled triangle.\u003c/p\u003e\u003cimg src = \"https://i.imgur.com/73mQn4N.png\"\u003e\u003cp\u003eImage courtesy of \u003ca href = \"http://upload.wikimedia.org/wikipedia/commons/7/7c/Right_Angle_Triangle.svg\"\u003eWikipedia\u003c/a\u003e.\u003c/p\u003e","function_template":"function c = hypotenuse(a,b)\r\n  c = \r\nend","test_suite":"%%\r\na = 1;\r\nb = 2; \r\nc_correct = sqrt(5);\r\ntolerance = 1e-12 ; \r\nassert(abs(hypotenuse(a,b)-c_correct)\u003ctolerance);\r\n%%\r\na = 3;\r\nb = 4;\r\nc_correct = 5; \r\ntolerance = 1e-12 ; \r\nassert(abs(hypotenuse(a,b)-c_correct)\u003ctolerance);\r\n%%\r\na = 5;\r\nb = 12;\r\nc_correct = 13; \r\ntolerance = 1e-12 ; \r\nassert(abs(hypotenuse(a,b)-c_correct)\u003ctolerance);\r\n","published":true,"deleted":false,"likes_count":67,"comments_count":9,"created_by":974,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16509,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:11:28.000Z","updated_at":"2026-04-04T03:49:26.000Z","published_at":"2013-11-28T17:12:06.000Z","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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml 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\"}]}"},{"id":2307,"title":"length of string on cylinder","description":"A cylinder H cm high has a circumference of C cm. A string makes exactly N complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm? \r\n\r\n","description_html":"\u003cp\u003eA cylinder H cm high has a circumference of C cm. A string makes exactly N complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm?\u003c/p\u003e","function_template":"function ans = your_fcn_name(H,C,N)\r\n \r\nend","test_suite":"%%\r\nH=90\r\nC=20\r\nN=6\r\ny_correct =150;\r\nassert(isequal(your_fcn_name(H,C,N),y_correct))\r\n\r\n%%\r\nH=72\r\nC=16\r\nN=6\r\ny_correct =120;\r\nassert(isequal(your_fcn_name(H,C,N),y_correct))\r\n\r\n%%\r\nH=105\r\nC=20\r\nN=7\r\ny_correct =175;\r\nassert(isequal(your_fcn_name(H,C,N),y_correct))","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":17228,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":62,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-07T11:16:39.000Z","updated_at":"2026-03-16T12:43:40.000Z","published_at":"2014-05-07T11:16:39.000Z","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\",\"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\u003eA cylinder H cm high has a circumference of C cm. A string makes exactly N complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm?\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":2016,"title":"Area of an equilateral triangle ","description":"Calculate the area of an equilateral triangle of side x. \r\n\r\n\u003c\u003chttps://i.imgur.com/jlZDHhq.png\u003e\u003e\r\n\r\nImage courtesy of \u003chttp://upload.wikimedia.org/wikipedia/commons/e/e0/Equilateral-triangle.svg Wikipedia\u003e.","description_html":"\u003cp\u003eCalculate the area of an equilateral triangle of side x.\u003c/p\u003e\u003cimg src = \"https://i.imgur.com/jlZDHhq.png\"\u003e\u003cp\u003eImage courtesy of \u003ca href = \"http://upload.wikimedia.org/wikipedia/commons/e/e0/Equilateral-triangle.svg\"\u003eWikipedia\u003c/a\u003e.\u003c/p\u003e","function_template":"function y = equilateral_area(x)\r\n  y = x; \r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = sqrt(3)/4;\r\ntolerance = 1e-12;\r\nassert(abs(equilateral_area(x)-y_correct)\u003ctolerance)\r\n%%\r\nx = 2;\r\ny_correct = sqrt(3);\r\ntolerance = 1e-12;\r\nassert(abs(equilateral_area(x)-y_correct)\u003ctolerance)\r\n%%\r\nx = 3;\r\ny_correct = sqrt(3)*9/4;\r\ntolerance =1e-12;\r\nassert(abs(equilateral_area(x)-y_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":26,"comments_count":8,"created_by":974,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6803,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:21:11.000Z","updated_at":"2026-04-02T15:31:22.000Z","published_at":"2013-11-28T17:12:09.000Z","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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"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\u003eCalculate the area of an equilateral triangle of side 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\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eImage courtesy 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is the distance from point P(x,y) to the line Ax + By + C = 0?","description":"Given a point, P(x,y), find the distance from this point to a linear line.\r\n\r\nINPUTS: x, y, A, B, C\r\n\r\nOUTPUTS: d, the distance which of course should always be positive.\r\n    \r\n  EX:\r\n  \u003e\u003ex=2; y=2; A=2; B=2; C=-4;\r\n  \u003e\u003ed = normalLen(x,y,A,B,C)\r\n  d = 1.4142\r\n\r\n\r\n","description_html":"\u003cp\u003eGiven a point, P(x,y), find the distance from this point to a linear line.\u003c/p\u003e\u003cp\u003eINPUTS: x, y, A, B, C\u003c/p\u003e\u003cp\u003eOUTPUTS: d, the distance which of course should always be positive.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eEX:\r\n\u003e\u003ex=2; y=2; A=2; B=2; C=-4;\r\n\u003e\u003ed = normalLen(x,y,A,B,C)\r\nd = 1.4142\r\n\u003c/pre\u003e","function_template":"function d = normalLen(x,y,A,B,C)\r\n  d = x+y+[A,B,C]\r\nend","test_suite":"%% test 1\r\nx=2; y=2; A=2; B=2; C=-4;\r\ny_correct = 1.4142;\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)\u003c=1e-4)\r\n%% test 2\r\nx=3; y=4; A=3; B=4; C=5;\r\ny_correct = 6;\r\nassert(normalLen(x,y,A,B,C)-y_correct==0)\r\n%% test 3\r\nx=4; y=5; A=3; B=4; C=5;\r\ny_correct = 7.4;\r\ndisplay(normalLen(x,y,A,B,C))\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)\u003c1e-1)\r\n%% test 4\r\nx=0;y=12345;A=0;B=1;C=0;\r\ny_correct = 12345;\r\ndisplay(normalLen(x,y,A,B,C))\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)==0)\r\n%% test 5\r\nx=0;y=-12345;A=0;B=1;C=0;\r\ny_correct = 12345;\r\ndisplay(normalLen(x,y,A,B,C))\r\nassert(abs(normalLen(x,y,A,B,C)-y_correct)==0)\r\n\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":2,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":560,"test_suite_updated_at":"2013-01-26T00:45:07.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-03-05T04:51:25.000Z","updated_at":"2026-03-13T05:04:32.000Z","published_at":"2012-03-06T06:29:12.000Z","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 a point, P(x,y), find the distance from this point to a linear line.\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\u003eINPUTS: x, y, A, B, C\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\u003eOUTPUTS: d, the distance which of course should always be positive.\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[EX:\\n\u003e\u003ex=2; y=2; A=2; B=2; C=-4;\\n\u003e\u003ed = normalLen(x,y,A,B,C)\\nd = 1.4142]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2018,"title":"Side of a rhombus","description":"If a rhombus has diagonals of length x and x+1, then what is the length of its side, y? \r\n\r\n\u003c\u003chttps://imgur.com/x6hT6mm.png\u003e\u003e\r\n\r\nImage courtesy of \u003chttp://upload.wikimedia.org/wikipedia/commons/b/b5/Rhombus.svg Wikipedia\u003e.","description_html":"\u003cp\u003eIf a rhombus has diagonals of length x and x+1, then what is the length of its side, y?\u003c/p\u003e\u003cimg src = \"https://imgur.com/x6hT6mm.png\"\u003e\u003cp\u003eImage courtesy of \u003ca href = \"http://upload.wikimedia.org/wikipedia/commons/b/b5/Rhombus.svg\"\u003eWikipedia\u003c/a\u003e.\u003c/p\u003e","function_template":"function y = rhombus_side(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = sqrt(5)/2;\r\ntolerance = 1e-12; \r\nassert(abs(rhombus_side(x)-y_correct)\u003ctolerance)\r\n%%\r\nx = 3;\r\ny_correct = 5/2;\r\ntolerance = 1e-12; \r\nassert(abs(rhombus_side(x)-y_correct)\u003ctolerance)\r\n%%\r\nx = 2;\r\ny_correct = sqrt(13)/2;\r\ntolerance = 1e-12; \r\nassert(abs(rhombus_side(x)-y_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":28,"comments_count":1,"created_by":974,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5900,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:23:39.000Z","updated_at":"2026-04-02T15:30:51.000Z","published_at":"2013-11-28T17:12:17.000Z","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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml 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Triangles - find the height of the tree","description":"Given the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\r\n\r\n\r\nInputs: h1, x1, x2\r\n\r\nOutput: h2\r\n\r\nHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\r\n\r\nEX:\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\r\n\r\n\u003e\u003eh2=findHeight(x1,x2,h1)\r\n\r\nh2=6\r\n\r\n\u003e\u003e","description_html":"\u003cp\u003eGiven the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\u003c/p\u003e\u003cp\u003eInputs: h1, x1, x2\u003c/p\u003e\u003cp\u003eOutput: h2\u003c/p\u003e\u003cp\u003eHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\u003c/p\u003e\u003cp\u003eEX:\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\u003c/p\u003e\u003cp\u003e\u003e\u003eh2=findHeight(x1,x2,h1)\u003c/p\u003e\u003cp\u003eh2=6\u003c/p\u003e\u003cp\u003e\u003e\u003e\u003c/p\u003e","function_template":"function h2 = findHeight(x1,x2,h1)\r\n  h2 = heightoftree\r\nend","test_suite":"%%\r\nx1 = 4;\r\nx2 = 4;\r\nh1 = 3;\r\ny_correct = 6;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 8;\r\nh1 = 3;\r\ny_correct = 9;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 12;\r\nh1 = 3;\r\ny_correct = 12;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 16;\r\nh1 = 3;\r\ny_correct = 15;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 20;\r\nh1 = 3;\r\ny_correct = 18;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 24;\r\nh1 = 3;\r\ny_correct = 21;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 12;\r\nh1 = 5;\r\ny_correct = 20;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 4;\r\nx2 = 16;\r\nh1 = 10;\r\ny_correct = 50;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 2;\r\nx2 = 4;\r\nh1 = 5;\r\ny_correct = 15;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n%%\r\nx1 = 3;\r\nx2 = 6;\r\nh1 = 4;\r\ny_correct = 12;\r\nassert(isequal(findHeight(x1,x2,h1),y_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":6,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":469,"test_suite_updated_at":"2012-02-18T04:42:47.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-02-17T22:52:21.000Z","updated_at":"2026-03-13T05:26:44.000Z","published_at":"2012-02-18T04:42:47.000Z","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\",\"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\u003eGiven the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Please note that the angle, phi, is the acute angle measured from the ground to an observer's line of sight aimed to the sucessive peaks of the power pole and the tree, in that order. Also the distance from the observer to the power pole is x1, also a given. x2 is the distance between the tree and the power pole. In all tests x1 is always a multiple of x2.\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\u003eInputs: h1, x1, x2\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\u003eOutput: h2\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\u003eHINT: find phi, given h1 and x1. Phi may be measured in degrees or radians. Note that default trig functions in MATLAB operate in radians.\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\u003eEX: x1 = 4; x2 = 4; h1 = 3;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003e\u003eh2=findHeight(x1,x2,h1)\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\u003eh2=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\u003e\u003e\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2017,"title":"Side of an equilateral triangle","description":"If an equilateral triangle has area A, then what is the length of each of its sides, x?\r\n\r\nImage courtesy of Wikipedia.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; 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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: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://upload.wikimedia.org/wikipedia/commons/e/e0/Equilateral-triangle.svg\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); 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\u003c tolerance)\r\n%%\r\nA = 2;\r\nx_correct = 2*sqrt(2)/sqrt(sqrt(3));\r\ntolerance = 1e-12; \r\nassert(abs(side_length(A) - x_correct) \u003c tolerance)\r\n","published":true,"deleted":false,"likes_count":32,"comments_count":4,"created_by":974,"edited_by":223089,"edited_at":"2026-03-22T08:15:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6875,"test_suite_updated_at":"2026-03-22T08:15:23.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:22:35.000Z","updated_at":"2026-04-04T19:05:04.000Z","published_at":"2013-11-28T17:12:13.000Z","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 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this triangle right-angled?","description":"Given three positive numbers a, b, c, where c is the largest number, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.","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: 233.5px 8px; transform-origin: 233.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven three positive numbers a, b, c, where c is the largest number, return\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: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etrue\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: 118px 8px; transform-origin: 118px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if the triangle with sides a, b and c is right-angled. Otherwise, return\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: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003efalse\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\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function flag = isRightAngled(a, b, c)\r\n  flag = false;\r\nend","test_suite":"%%\r\na = 3;\r\nb = 4;\r\nc = 5;\r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 2;\r\nb = 3;\r\nc = 4;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5;\r\nb = 12;\r\nc = 13;\r\nflag_correct = true; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 17;\r\nb = 19;\r\nc = 23;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 12;\r\nb = 35;\r\nc = 37;\r\nflag_correct = true; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n\r\n%%\r\na = 10*rand;\r\nb = a;\r\nc = a;\r\nflag_correct = false; \r\nassert(isequal(isRightAngled(a,b,c),flag_correct))","published":true,"deleted":false,"likes_count":38,"comments_count":7,"created_by":974,"edited_by":223089,"edited_at":"2023-05-04T07:40:55.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6416,"test_suite_updated_at":"2023-05-04T07:40:55.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:28:55.000Z","updated_at":"2026-04-02T15:26:12.000Z","published_at":"2013-11-28T17:12:28.000Z","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\u003eGiven three positive numbers a, b, c, where c is the largest number, return\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if the triangle with sides a, b and c is right-angled. Otherwise, return\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efalse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\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":2020,"title":"Area of an Isoceles Triangle","description":"An isosceles triangle has equal sides of length x and a base of length y. Find the area, A, of the triangle. \r\n\r\n\u003c\u003chttps://imgur.com/HVdn9p1.png\u003e\u003e\r\n\r\n\r\nImage courtesy of \u003chttp://upload.wikimedia.org/wikipedia/commons/8/8e/Triangle_isocele.svg Wikipedia\u003e.","description_html":"\u003cp\u003eAn isosceles triangle has equal sides of length x and a base of length y. Find the area, A, of the triangle.\u003c/p\u003e\u003cimg src = \"https://imgur.com/HVdn9p1.png\"\u003e\u003cp\u003eImage courtesy of \u003ca href = \"http://upload.wikimedia.org/wikipedia/commons/8/8e/Triangle_isocele.svg\"\u003eWikipedia\u003c/a\u003e.\u003c/p\u003e","function_template":"function A = isocelesArea(x,y)\r\n  A = \r\nend","test_suite":"%%\r\nx = 5;\r\ny = 8; \r\nA_correct = 12;\r\ntolerance = 1e-12; \r\nassert(abs(isocelesArea(x,y)-A_correct)\u003ctolerance)\r\n%%\r\nx = 2;\r\ny = 2; \r\nA_correct = sqrt(3);\r\ntolerance = 1e-12;\r\nassert(abs(isocelesArea(x,y)-A_correct)\u003ctolerance)\r\n%%\r\nx = 10;\r\ny = 2; \r\nA_correct = sqrt(99);\r\ntolerance = 1e-12; \r\nassert(abs(isocelesArea(x,y)-A_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":32,"comments_count":5,"created_by":974,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6116,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:27:15.000Z","updated_at":"2026-04-02T15:30:16.000Z","published_at":"2013-11-28T17:12:24.000Z","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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"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\u003eAn isosceles triangle has equal sides of length x and a base of length y. Find the area, A, of the triangle.\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eImage courtesy of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://upload.wikimedia.org/wikipedia/commons/8/8e/Triangle_isocele.svg\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\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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of a rectangle","description":"The longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width and length of the rectangle.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 21px; transform-origin: 468.5px 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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\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: 428.625px 8px; transform-origin: 428.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width and length of the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [width, length] = findRectangleDimensions(x)\r\n  width = x;\r\n  length = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('findRectangleDimensions.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp');\r\nassert(~illegal)\r\n\r\n%%\r\nx = 1\r\nlength_correct = 3/sqrt(10);\r\nwidth_correct = 1/sqrt(10); \r\n[width, length] = findRectangleDimensions(x); \r\ntolerance = 1e-12; \r\nassert( abs(length-length_correct)\u003ctolerance \u0026\u0026 abs(width-width_correct)\u003ctolerance )\r\n\r\n%%\r\nx = 2;\r\nwidth_correct = 2/sqrt(10); \r\nlength_correct = 6/sqrt(10); \r\n[width, length] = findRectangleDimensions(x); \r\ntolerance = 1e-12;\r\nassert(abs(length-length_correct)\u003ctolerance \u0026\u0026 abs(width-width_correct)\u003ctolerance)\r\n","published":true,"deleted":false,"likes_count":49,"comments_count":11,"created_by":974,"edited_by":223089,"edited_at":"2026-03-22T08:23:37.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5781,"test_suite_updated_at":"2026-03-22T08:23:37.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:24:49.000Z","updated_at":"2026-04-03T13:48:18.000Z","published_at":"2013-11-28T17:12:20.000Z","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\u003eThe longer side of a rectangle is three times the length of the shorter side. If the length of the diagonal is x, find the width and length of the rectangle.\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":44476,"title":"How many unique Pythagorean triples?","description":"For a given integer |n|, return all \u003chttps://en.wikipedia.org/wiki/Pythagorean_triple Pythagorean triples\u003e that inlude numbers smaller or equal to |n|.\r\n\r\nA Pythagorean triple consist of three positive integers |{a, b, c}| such that:\r\n\r\n a \u003c b \u003c c,\r\n a^2 + b^2 = c^2\r\n\r\nThe triples should be retured in a matrix with tree columns, where each row contains a different triple. Every row needs to be sorted in ascending order ( |a| in the first column, |b| in the second and |c| in the third), and the first column must also be sorted.\r\n\r\nExample:\r\n\r\n  Input:  n   = 16\r\n  Output: mat = [3,  4, 5\r\n                 5, 12, 13 \r\n                 6,  8, 10 \r\n                 9, 12, 15]\r\n\r\nIf |n| is not an integer, or it is smaller than 5, the function should return an empty matrix.","description_html":"\u003cp\u003eFor a given integer \u003ctt\u003en\u003c/tt\u003e, return all \u003ca href = \"https://en.wikipedia.org/wiki/Pythagorean_triple\"\u003ePythagorean triples\u003c/a\u003e that inlude numbers smaller or equal to \u003ctt\u003en\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eA Pythagorean triple consist of three positive integers \u003ctt\u003e{a, b, c}\u003c/tt\u003e such that:\u003c/p\u003e\u003cpre\u003e a \u0026lt; b \u0026lt; c,\r\n a^2 + b^2 = c^2\u003c/pre\u003e\u003cp\u003eThe triples should be retured in a matrix with tree columns, where each row contains a different triple. Every row needs to be sorted in ascending order ( \u003ctt\u003ea\u003c/tt\u003e in the first column, \u003ctt\u003eb\u003c/tt\u003e in the second and \u003ctt\u003ec\u003c/tt\u003e in the third), and the first column must also be sorted.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eInput:  n   = 16\r\nOutput: mat = [3,  4, 5\r\n               5, 12, 13 \r\n               6,  8, 10 \r\n               9, 12, 15]\r\n\u003c/pre\u003e\u003cp\u003eIf \u003ctt\u003en\u003c/tt\u003e is not an integer, or it is smaller than 5, the function should return an empty matrix.\u003c/p\u003e","function_template":"function mat = triples(n)\r\n    mat = [];\r\nend","test_suite":"%%\r\nfiletext = fileread('triples.m');\r\nassert(isempty(strfind(filetext, 'regexp')),'regexp hacks are forbidden')\r\n\r\n%%\r\nn = 1;\r\nmat_correct = [];\r\nassert(isequal(triples(n),mat_correct))\r\n\r\n%%\r\nn = 20.5;\r\nmat_correct = [];\r\nassert(isequal(triples(n),mat_correct))\r\n\r\n%%\r\nn = 15;\r\nmat_correct = [3,  4, 5; 5, 12, 13; 6,  8, 10; 9, 12, 15];\r\nassert(isequal(triples(n),mat_correct))\r\n\r\n%%\r\nn = 16;\r\nmat_correct = [3,  4, 5; 5, 12, 13; 6,  8, 10; 9, 12, 15];\r\nassert(isequal(triples(n),mat_correct))\r\n\r\n%%\r\nn = 100\r\nmat_correct = ...\r\n    [3     4     5;\r\n     5    12    13;\r\n     6     8    10;\r\n     7    24    25;\r\n     8    15    17;\r\n     9    12    15;\r\n     9    40    41;\r\n    10    24    26;\r\n    11    60    61;\r\n    12    16    20;\r\n    12    35    37;\r\n    13    84    85;\r\n    14    48    50;\r\n    15    20    25;\r\n    15    36    39;\r\n    16    30    34;\r\n    16    63    65;\r\n    18    24    30;\r\n    18    80    82;\r\n    20    21    29;\r\n    20    48    52;\r\n    21    28    35;\r\n    21    72    75;\r\n    24    32    40;\r\n    24    45    51;\r\n    24    70    74;\r\n    25    60    65;\r\n    27    36    45;\r\n    28    45    53;\r\n    28    96   100;\r\n    30    40    50;\r\n    30    72    78;\r\n    32    60    68;\r\n    33    44    55;\r\n    33    56    65;\r\n    35    84    91;\r\n    36    48    60;\r\n    36    77    85;\r\n    39    52    65;\r\n    39    80    89;\r\n    40    42    58;\r\n    40    75    85;\r\n    42    56    70;\r\n    45    60    75;\r\n    48    55    73;\r\n    48    64    80;\r\n    51    68    85;\r\n    54    72    90;\r\n    57    76    95;\r\n    60    63    87;\r\n    60    80   100;\r\n    65    72    97];\r\n\r\n%%\r\nn = 1000;\r\ns_correct = [881, 3];\r\nassert(isequal(size(triples(n)), s_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":140356,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":150,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-12-31T20:29:09.000Z","updated_at":"2026-02-24T14:05:30.000Z","published_at":"2017-12-31T20:29:09.000Z","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\u003eFor a given integer\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return all\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://en.wikipedia.org/wiki/Pythagorean_triple\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePythagorean triples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e that inlude numbers smaller or equal to\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:rFonts w:cs=\\\"monospace\\\"/\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\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\u003eA Pythagorean triple consist of three positive integers\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e{a, b, c}\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e such that:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ a \u003c b \u003c c,\\n a^2 + b^2 = c^2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe triples should be retured in a matrix with tree columns, where each row contains a different triple. Every row needs to be sorted in ascending order (\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the first column,\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the second and\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the third), and the first column must also be sorted.\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:\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[Input:  n   = 16\\nOutput: mat = [3,  4, 5\\n               5, 12, 13 \\n               6,  8, 10 \\n               9, 12, 15]]]\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\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:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is not an integer, or it is smaller than 5, the function should return an empty matrix.\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":49582,"title":"Determine whether a square can be drawn on a grid of dots","description":null,"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: 444.467px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 222.233px; transform-origin: 407px 222.233px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; 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 42px; text-align: left; transform-origin: 384px 42px; 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: 382.358px 7.79167px; transform-origin: 382.358px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSuppose you have a regular grid of dots, each 1 unit apart. By connecting four dots arranged in a square of side 1, you can draw a square of area 1. Similarly, you can draw squares of area 4, 9, 16, 25, etc. As shown below, by connecting dots with diagonal lines, you can draw squares of area 2, 5, 10, 8, 13, and 17. Which squares can you draw by connecting dots on the grid with straight lines? \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: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \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: 301.708px 7.79167px; transform-origin: 301.708px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes an area and determines whether the square of that area can be drawn.\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: 0px 7.79167px; transform-origin: 0px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 291.467px; 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 145.733px; text-align: left; transform-origin: 384px 145.733px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline\" src=\"https://www.mathsisfun.com/activity/images/squares8.gif\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = squareOnGrid(A)\r\n  tf = false;\r\nend","test_suite":"%%\r\nassert(squareOnGrid(1))\r\n\r\n%%\r\nassert(squareOnGrid(2))\r\n\r\n%%\r\nassert(~squareOnGrid(3))\r\n\r\n%%\r\nassert(squareOnGrid(4))\r\n\r\n%%\r\nassert(squareOnGrid(5))\r\n\r\n%%\r\nassert(~squareOnGrid(6))\r\n\r\n%%\r\nassert(~squareOnGrid(7))\r\n\r\n%%\r\nassert(squareOnGrid(8))\r\n\r\n%%\r\nassert(squareOnGrid(9))\r\n\r\n%%\r\nassert(squareOnGrid(10))\r\n\r\n%%\r\nassert(~squareOnGrid(11))\r\n\r\n%%\r\nassert(~squareOnGrid(12))\r\n\r\n%%\r\nassert(squareOnGrid(13))\r\n\r\n%%\r\nassert(~squareOnGrid(14))\r\n\r\n%%\r\nassert(~squareOnGrid(15))\r\n\r\n%%\r\nassert(squareOnGrid(16))\r\n\r\n%%\r\nassert(squareOnGrid(17))\r\n\r\n%%\r\nassert(squareOnGrid(18))\r\n\r\n%%\r\nassert(~squareOnGrid(19))\r\n\r\n%%\r\nassert(squareOnGrid(20))\r\n\r\n%%\r\nassert(~squareOnGrid(21))\r\n\r\n%%\r\nassert(~squareOnGrid(42))\r\n\r\n%%\r\nassert(squareOnGrid(49))\r\n\r\n%%\r\nassert(~squareOnGrid(51))\r\n\r\n%%\r\nassert(squareOnGrid(53))\r\n\r\n%%\r\nassert(~squareOnGrid(63))\r\n\r\n%%\r\nassert(squareOnGrid(130))\r\n\r\n%%\r\nassert(squareOnGrid(281))\r\n\r\n%%\r\nassert(~squareOnGrid(283))\r\n\r\n%%\r\nfor k = 566:575\r\n    tf(k-565) = squareOnGrid(k);\r\nend\r\nassert(isequal(sum(tf),1))\r\n\r\n%%\r\nassert(~squareOnGrid(1323))\r\n\r\n%%\r\nassert(~squareOnGrid(2310))\r\n\r\n%%\r\nassert(~squareOnGrid(12768))\r\n\r\n%%\r\nassert(squareOnGrid(12769))\r\n\r\n%%\r\nassert(~squareOnGrid(19200))\r\n\r\n%%\r\nassert(~squareOnGrid(1514205))\r\n\r\n%%\r\nassert(squareOnGrid(2e7))\r\n\r\n%%\r\nassert(squareOnGrid(2^randi(20)))\r\n\r\n%%\r\nassert(~squareOnGrid(7^(2*randi(10)+1)))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2020-12-25T06:14:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-24T15:45:57.000Z","updated_at":"2021-01-01T19:18:37.000Z","published_at":"2020-12-24T16:01:03.000Z","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\u003eSuppose you have a regular grid of dots, each 1 unit apart. By connecting four dots arranged in a square of side 1, you can draw a square of area 1. Similarly, you can draw squares of area 4, 9, 16, 25, etc. As shown below, by connecting dots with diagonal lines, you can draw squares of area 2, 5, 10, 8, 13, and 17. Which squares can you draw by connecting dots on the grid with straight lines? \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes an area and determines whether the square of that area can be drawn.\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\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.gif\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.gif\",\"contentType\":\"image/gif\",\"content\":\"https://www.mathsisfun.com/activity/images/squares8.gif\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2308,"title":"rectangle in circle ","description":"In the figure below, the rectangle at the corner measures a cm x b cm. What is the radius of the circle in cm? \r\n\r\n\u003c\u003chttp://www.syvum.com/iosundry/contrib/teasers/circle1a.gif\u003e\u003e","description_html":"\u003cp\u003eIn the figure below, the rectangle at the corner measures a cm x b cm. What is the radius of the circle in cm?\u003c/p\u003e\u003cimg src = \"http://www.syvum.com/iosundry/contrib/teasers/circle1a.gif\"\u003e","function_template":"function y = your_fcn_name(a,b)\r\n  y = x;\r\nend","test_suite":"%%\r\na=6;\r\nb=12;\r\ny_correct=30\r\nassert(isequal(your_fcn_name(a,b),y_correct))\r\n\r\n%%\r\na=7;\r\nb=14;\r\ny_correct=35\r\nassert(isequal(your_fcn_name(a,b),y_correct))\r\n\r\n\r\n%%\r\na=3;\r\nb=6;\r\ny_correct=15\r\nassert(isequal(your_fcn_name(a,b),y_correct))\r\n\r\n%%\r\na=5;\r\nb=40;\r\ny_correct=65\r\nassert(isequal(your_fcn_name(a,b),y_correct))\r\n\r\n%%\r\na=5;\r\nb=90;\r\ny_correct=125\r\nassert(isequal(your_fcn_name(a,b),y_correct))\r\n\r\n%%\r\na=12;\r\nb=54;\r\ny_correct=102\r\nassert(isequal(your_fcn_name(a,b),y_correct))\r\n\r\n%%\r\na=16;\r\nb=18;\r\ny_correct=58\r\nassert(isequal(your_fcn_name(a,b),y_correct))\r\n\r\n%%\r\na=16;\r\nb=72;\r\ny_correct=136\r\nassert(isequal(your_fcn_name(a,b),y_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":17228,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":71,"test_suite_updated_at":"2014-05-12T07:30:16.000Z","rescore_all_solutions":false,"group_id":26,"created_at":"2014-05-07T11:30:17.000Z","updated_at":"2026-02-19T10:40:20.000Z","published_at":"2014-05-07T11:30:17.000Z","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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.gif\"}],\"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\u003eIn the figure below, the rectangle at the corner measures a cm x b cm. What is the radius of the circle in cm?\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:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\"},{\"partUri\":\"/media/image1.gif\",\"contentType\":\"image/gif\",\"content\":\"data:image/gif;base64,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\"}]}"},{"id":2023,"title":"Is this triangle right-angled?","description":"Given any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.","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: 381.5px 8px; transform-origin: 381.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function flag = isRightAngled(a,b,c)\r\n  flag = false;\r\nend","test_suite":"%%\r\na = 3;\r\nb = 4;\r\nc = 5;\r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 3;\r\nb = 4;\r\nc = 6;\r\nflag_correct = false;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 3;\r\nb = 5;\r\nc = 4; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 4;\r\nb = 3; \r\nc = 5;\r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 4; \r\nb = 5;\r\nc = 3; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 3;\r\nc = 4; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 4;\r\nc = 3; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 12;\r\nc = 13; \r\nflag_correct = true;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 5; \r\nb = 12;\r\nc = 11; \r\nflag_correct = false;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))\r\n%%\r\na = 10; \r\nb = 15;\r\nc = 20; \r\nflag_correct = false;\r\nassert(isequal(isRightAngled(a,b,c),flag_correct))","published":true,"deleted":false,"likes_count":38,"comments_count":5,"created_by":974,"edited_by":223089,"edited_at":"2023-01-29T06:52:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6564,"test_suite_updated_at":"2023-01-29T06:52:29.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:31:43.000Z","updated_at":"2026-04-04T19:09:09.000Z","published_at":"2013-11-28T17:12:35.000Z","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\u003eGiven any three positive numbers a, b, c, return true if the triangle with sides a, b and c is right-angled. Otherwise, return false.\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":49738,"title":"Determine whether a prime is Pythagorean","description":null,"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: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 369.1px 7.79167px; transform-origin: 369.1px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePythagorean primes get their name from the property that they can be written as the sum of two squares. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ0AAAAmCAYAAADeK5lgAAADX0lEQVR4nO2b3ZWCMBCFbw90QAM0QAVWYAd2QAe2YA2WQA+2YA224D6Ee4gYyA9DCO585+RhXYQkczOZmSCgKIqiKIqiKEoIDYAWQL13RzLQDq3auyP/lTOAF4C31a74TfFd8TnOF4ALVHxZOQF4wng5/k0B3vbq1EZcAdxhFlMFIzaK77xjv/4dD4yCIyeMXuBXPEAFM54p9Hz92gdQyTH8WjzD8bSe67qZz+kBjiC6ENs1MItpSgszzkfqw2uYLeGN79Xrohqun8YzT/iNVSodvsfDGC1GQJyHUpGyHUUXHUqwA/bDfaKrYNT9gjFIB7Pf2/c4mvAe+Bab3XqECa/BKNQSkbQd4zqXF5zlNDz0hM9J94muhxHq1AgNxtWzep/PSAfTZzsTq/Ht+UKExO+UurVK2q6PuNYJJ94nuhZmZcxBr+kKPEukwnIGxi0kZEwMuKNWvodQRxCCpO04L6sWV6joTlgOOnmf5OAyMxcsGwII3wXuw/0kkRSdlO0qfJaKkgkVnQ+uFunJ34oOYVmqb246bFObkxSdj1Db9RCqzUmIjttLaNB9FDg3c7HaGW5vmVJ+mpJLdKG2u8EtyqT+rRUds6I70ie6wlgfW9Ok64X0AC5hneEuj1SQSaZyiC7Udje4vXkz87mXVNFV+D5/7JFmeDtoX9Okt/Yn3KUEuzjaTxrPJdeypehibNdZ/5+25P6liI7ZEB88PQyOFV4D96Bim2T2SGFNvVyFcexzTSLE2Ep0Mbbz2SU5lpWI6aarxpcVHoEextNtdcRnH7m5mn2ovnTdWnaxnVT2WmPsfMlF0hAuMGPYMp5yeZrYJlUTzW47KdEBn+9d5Uj1t4DHWZJbtYsrlrcuzqMrbmST9EpZbScpOntbiE1KSsheeSS0teBCyL14U22XxBaii3X7JWSvJQkO2E90WY4xJUV3Hu4T+6bF3tkrY5ql79Mb5yK36FJtl4Sk6JjxHSmeY4F07sVMckPe17Nziy6r7UJFx0Bz7oU/Vu9L2Z5CsN8x6xYai745M3JJ0RVluxpj1f2N5dU+feGzx2gUHqUc0cOFxou5X86UFF0Rtqsxn7LPHezyl0D2tdfhsyP+RoIeLLTlXlCSovs12ykbQU+kolAURVEURVEURVEURVEUJYo/LpHxrbfjoqEAAAAASUVORK5CYII=\" alt=\"13 = 2^2 + 3^2\" style=\"width: 78.5px; height: 19px;\" width=\"78.5\" height=\"19\"\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: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45964\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 45964\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 68.45px 7.79167px; transform-origin: 68.45px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked you to find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 185.167px 7.79167px; transform-origin: 185.167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth Pythagorean prime and two numbers whose squares will produce the prime. This problem merely asks you to determine whether a prime can be written as the sum of two squares. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 379.5px 7.79167px; transform-origin: 379.5px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to determine whether a prime is Pythagorean. All input numbers in the tests are prime. Because some are large, they are given as strings. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function tf = isPythagoreanPrime(pstr)\r\n  tf = isprime(str2num(pstr));\r\nend","test_suite":"%%\r\npstr = '13';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '17';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '23';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '31';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '541';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '997';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '2459';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '36293';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '499979';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '5999681';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '69985649';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '87178291199';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '99194853094755497';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '900900900900990990990991';\r\nassert(~isPythagoreanPrime(pstr))\r\n    \r\n%%\r\npstr = '1066340417491710595814572169';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '845100400152152934331135470251';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '19134702400093278081449423917';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '10888869450418352160768000001';\r\nassert(isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '26525285981219105863630847999999';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '263130836933693530167218012159999999';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '8683317618811886495518194401279999999';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '56713727820156410577229101238628035243';\r\nassert(~isPythagoreanPrime(pstr))\r\n\r\n%%\r\npstr = '62357403192785191176690552862561408838653121833643';\r\nassert(~isPythagoreanPrime(pstr))","published":true,"deleted":false,"likes_count":2,"comments_count":7,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":84,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-01-02T23:14:39.000Z","updated_at":"2026-01-06T08:06:28.000Z","published_at":"2021-01-02T23:21:49.000Z","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\u003ePythagorean primes get their name from the property that they can be written as the sum of two squares. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"13 = 2^2 + 3^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e13 = 2^2 + 3^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\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/45964\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 45964\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked you to find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth Pythagorean prime and two numbers whose squares will produce the prime. This problem merely asks you to determine whether a prime can be written as the sum of two squares. \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\u003eWrite a function to determine whether a prime is Pythagorean. All input numbers in the tests are prime. Because some are large, they are given as strings. \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":2022,"title":"Find a Pythagorean triple","description":"Given four different positive numbers, a, b, c and d, provided in increasing order: a \u003c b \u003c c \u003c d, find if any three of them comprise sides of a right-angled triangle. Return true if they do, otherwise return false .","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: 376.5px 8px; transform-origin: 376.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven four different positive numbers, a, b, c and d, provided in increasing order: a \u0026lt; b \u0026lt; c \u0026lt; d, find if any three of them comprise sides of a right-angled triangle. Return\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: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etrue\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: 86px 8px; transform-origin: 86px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if they do, otherwise return\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: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003efalse\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=\"\"\u003e .\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function flag = isTherePythagoreanTriple(a, b, c, d)\r\n  flag = false;\r\nend","test_suite":"%%\r\nfiletext = fileread('isTherePythagoreanTriple.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp');\r\nassert(~illegal)\r\n\r\n%%\r\na = 1;\r\nb = 2; \r\nc = 3;\r\nd = 4;\r\nflag_correct = false;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 2;\r\nb = 3; \r\nc = 4;\r\nd = 5;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 3;\r\nb = 4;  \r\nc = 5; \r\nd = 6;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 3;\r\nb = 4; \r\nc = 4.5;\r\nd = 5;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 2;\r\nb = 3;\r\nc = 5;\r\nd = 7;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),~flag_correct))\r\n%%\r\na = 1;\r\nb = 2;\r\nc = sqrt(5);\r\nd = 6;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 5;\r\nb = 7;\r\nc = 12;\r\nd = 13;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),flag_correct))\r\n%%\r\na = 5;\r\nb = 7;\r\nc = 11;\r\nd = 13;\r\nflag_correct = true;\r\nassert(isequal(isTherePythagoreanTriple(a, b, c, d),~flag_correct))","published":true,"deleted":false,"likes_count":48,"comments_count":12,"created_by":974,"edited_by":223089,"edited_at":"2023-03-13T17:24:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5084,"test_suite_updated_at":"2023-03-13T17:24:10.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:29:57.000Z","updated_at":"2026-04-02T15:27:25.000Z","published_at":"2013-11-28T17:12:31.000Z","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\u003eGiven four different positive numbers, a, b, c and d, provided in increasing order: a \u0026lt; b \u0026lt; c \u0026lt; d, find if any three of them comprise sides of a right-angled triangle. Return\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if they do, otherwise return\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:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efalse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\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":45964,"title":"Compute the nth Pythagorean prime","description":"Pythagorean primes have the form p = 4n+1, where n is an integer, and they can be written as the sum of squares of two integers. More information is available at \u003chttps://en.wikipedia.org/wiki/Pythagorean_prime Wikipedia\u003e, \u003chttps://www.youtube.com/watch?v=yu_aqA7mw7E Numberphile\u003e, and the \u003chttps://oeis.org/A002144 Online Encyclopedia of Integer Sequences\u003e. \r\n\r\nCompute the nth Pythagorean prime p and two integers a and b such that p = a^2+b^2","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: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; 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: 109.3px 7.8px; transform-origin: 109.3px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePythagorean primes have the form \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = 4n+1\" style=\"width: 70px; height: 18px;\" width=\"70\" height=\"18\"\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: 24.9px 7.8px; transform-origin: 24.9px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 209.25px 7.8px; transform-origin: 209.25px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is an integer, and they can be written as the sum of squares of two integers. More information is available at\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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pythagorean_prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWikipedia\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; 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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=yu_aqA7mw7E\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eNumberphile\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 27.2333px 7.8px; transform-origin: 27.2333px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the\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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://oeis.org/A002144\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eOnline Encyclopedia of Integer Sequences\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\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: 42.0167px 7.8px; transform-origin: 42.0167px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCompute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 68.85px 7.8px; transform-origin: 68.85px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth Pythagorean prime \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\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: 55.2333px 7.8px; transform-origin: 55.2333px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and two integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\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: 15.5667px 7.8px; transform-origin: 15.5667px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\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: 32.2833px 7.8px; transform-origin: 32.2833px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"p = a^2+b^2\" style=\"width: 72.5px; height: 19px;\" width=\"72.5\" height=\"19\"\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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [pp,a,b] = PythagoreanPrime(n)\r\n  pp = a^2+b^2;\r\nend","test_suite":"%%\r\nn = 1;\r\npp_correct = 5;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 5;\r\npp_correct = 37;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 25;\r\npp_correct = 257;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 125;\r\npp_correct = 1657;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 625;\r\npp_correct = 10313;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 3125;\r\npp_correct = 62497;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)\r\n\r\n%%\r\nn = 15625;\r\npp_correct = 367229;\r\n[pp1,a1,b1] = PythagoreanPrime(n);\r\nassert(isequal(pp1,pp_correct))\r\nassert(a1 == floor(a1) \u0026\u0026 b1 == floor(b1) \u0026\u0026 a1^2+b1^2 == pp1)","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":98,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-06-19T01:58:26.000Z","updated_at":"2026-01-19T15:38:08.000Z","published_at":"2020-06-19T02:08:23.000Z","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\u003ePythagorean primes have the form \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = 4n+1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = 4n+1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer, and they can be written as the sum of squares of two integers. More information is available at\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://en.wikipedia.org/wiki/Pythagorean_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.youtube.com/watch?v=yu_aqA7mw7E\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eNumberphile\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and the\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://oeis.org/A002144\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eOnline Encyclopedia of Integer Sequences\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCompute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth Pythagorean prime \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and two integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p = a^2+b^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep = a^2+b^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\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":2024,"title":"Triangle sequence ","description":"A sequence of triangles is constructed in the following way:\r\n1) the first triangle is Pythagoras' 3-4-5 triangle\r\n2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle\r\n3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.\r\nEach triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.\r\nWhat is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?","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: 234px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 117px; transform-origin: 407px 117px; 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: 185px 8px; transform-origin: 185px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA sequence of triangles is constructed in the following way:\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: 148.5px 8px; transform-origin: 148.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1) the first triangle is Pythagoras' 3-4-5 triangle\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 365.5px 8px; transform-origin: 365.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 368px 8px; transform-origin: 368px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.\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: 299px 8px; transform-origin: 299px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhat is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function area = triangle_sequence(n)\r\n  area = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('triangle_sequence.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n%%\r\nn = 1;\r\narea_correct = 25;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 2;\r\narea_correct = 41;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 3;\r\narea_correct = 66;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 9;\r\narea_correct = 1186;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 13;\r\narea_correct = 8129;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 22;\r\narea_correct = 617911;\r\ntolerance = 1e-6;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)\r\n%%\r\nn = 50;\r\narea_correct = 439116598409;\r\ntolerance = 1e-3;\r\nassert(abs(triangle_sequence(n)-area_correct)\u003ctolerance)","published":true,"deleted":false,"likes_count":156,"comments_count":39,"created_by":974,"edited_by":223089,"edited_at":"2023-03-16T15:12:00.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5829,"test_suite_updated_at":"2023-03-16T15:12:00.000Z","rescore_all_solutions":false,"group_id":7,"created_at":"2013-11-27T20:39:45.000Z","updated_at":"2026-03-31T16:33:25.000Z","published_at":"2013-11-28T17:12:38.000Z","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\u003eA sequence of triangles is constructed in the following way:\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\u003e1) the first triangle is Pythagoras' 3-4-5 triangle\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\u003e2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle\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\u003e3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.\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\u003eEach triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.\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\u003eWhat is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?\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":46701,"title":"Compute the nth Naerogahtyp emirp","description":null,"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: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 6.60833px 8.05px; transform-origin: 6.60833px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45964-compute-the-nth-pythagorean-prime\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ePythagorean prime\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 311.542px 8.05px; transform-origin: 311.542px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a prime number that can be written as the sum of two squares. For example, 13 is a Pythagorean prime because it is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 95.5px; height: 19px;\" width=\"95.5\" height=\"19\"\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: 139.508px 8.05px; transform-origin: 139.508px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. In a similar way, a Naerogahtyp emirp is an \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46624-list-the-emirps\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eemirp\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 117.833px 8.05px; transform-origin: 117.833px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that can be written as the sum of two \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46676-list-the-erauqs\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"perspective-origin: 21.4px 8.05px; transform-origin: 21.4px 8.05px; \"\u003eerauqs\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 3.88333px 8.05px; transform-origin: 3.88333px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \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: 156.233px 8.05px; transform-origin: 156.233px 8.05px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find the nth Naerogahtyp emirp.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ne = NaerogahtypEmirp(n)\r\n  ne = f(n);\r\nend","test_suite":"%%\r\nn = 1;\r\nne_correct = 1061;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = 2;\r\nne_correct = 1069;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = 5;\r\nne_correct = 15053;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = 10;\r\nne_correct = 102769;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = 29;\r\nne_correct = 1508621;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = 53;\r\nne_correct = 11364701;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = 101;\r\nne_correct = 106684421;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = 197;\r\nne_correct = 153918421;\r\nassert(isequal(NaerogahtypEmirp(n),ne_correct))\r\n\r\n%%\r\nn = [17 31 67];\r\nfor k = 1:3\r\n    ne(k) = NaerogahtypEmirp(n(k));\r\nend\r\nsum_correct = 102944443;\r\nassert(isequal(sum(ne),sum_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-06T21:38:21.000Z","updated_at":"2025-11-17T17:22:23.000Z","published_at":"2020-10-20T04:54:59.000Z","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\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45964-compute-the-nth-pythagorean-prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePythagorean prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a prime number that can be written as the sum of two squares. For example, 13 is a Pythagorean prime because it is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4+9=2^2+3^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. In a similar way, a Naerogahtyp emirp is an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46624-list-the-emirps\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eemirp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e that can be written as the sum of two \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46676-list-the-erauqs\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eerauqs\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find the nth Naerogahtyp emirp.\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":57998,"title":"Easy Sequences 111: Repnums as Hypotenuse of Pythagorean Triangles","description":"The number  belongs to a class of numbers called Repunit Numbers, in which all digits are . \r\nFor this problem, we'll define a superset of the repunit numbers which we shall call repnums, which are composed of repeated numbers. That is, if we denote repnums by , then  is the number to be repeated and   is the number of repetitions. Hence,  , ,  and so on.\r\nWe can see from the figure below that  can be a hypotenuse of a right triangle with integer sides (Pythagorean Triangle).\r\n                                                        \r\nIn fact, this is the only Pythagorean triangle that can be formed with hypotenuse equal to . There is also only one Pythagorean triangle with hypotenuse equal to , that is the triangle with sides , while there are seven Pythagorean triangles with hypotenures of , with legs as follows:\r\n        \r\nCreate the function, , that counts the number of Pythagorean triangles that can be formed with hypotenuse equal to .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; 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; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 435px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 217.5px; transform-origin: 407px 217.5px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"25.5\" height=\"18\" style=\"width: 25.5px; height: 18px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e belongs to a class of numbers called \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Repunit\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRepunit Numbers,\u003c/span\u003e\u003c/span\u003e\u003c/a\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=\"\"\u003e in which all digits are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor this problem, we'll define a superset of the repunit numbers which we shall call \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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003erepnums\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, which are composed of repeated numbers. That is, if we denote repnums by \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFwAAAAmCAYAAABJVvz/AAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAXKADAAQAAAABAAAAJgAAAADSajFxAAAGOUlEQVRoBe2YaWxWRRSGqaKiuKIxAbXSSkoMiYJEDSoVYl3igjEKajHGhRoNKmr0p4BGjBui8Y+BlF9AgibuSzQVtSb4QwE1EjVsNVhF0SDiRpHq+5R7kmE6d77v3n61S+6bvJ0z55zZzp05M1+HDClQRKCIQBGBIgJFBIoIDIgINGqWm8UjBsRs95/kTFVXizX7q+O1Ks98iuojPJ1b/VeVHWK7+LdryCHPVpvnxCaxOUf7vm4yVBN4VTxTnCRuEjNjvlpsFQlsKf4sHwa8XjxAzIKz5dwhLsjSqB/6Hq45rRXXicPyzo9dTyDcgHN0poukgAfEVtG1r1G9WiwHx8ipTXxZ9E+YVAMOozTjbWKPTuk4deAG9NpAGKZKR1oxvw8klxPAV+S3RyR9DRbcrYUQh1vyLojdaoGkvCylo/s8v4tS/EzNCaG/JaYYJCXphHvtd5E0k4q03EtQykGL5zTeq/vVWxPFQM/d/ro46U+Lw8UZvtGtpwXc9YnJez0j+SwNJ8kwRVwvtomDDW8lC7optjCeNj3BWV7jLV7drfJu5QO/5ypLyGNlbxBrRV5EraLhWAmcGC7hx8SdYl4cp4YTEm5QyYUOThavELlv3hBjc/9Kdi7PyeIYcaNYNtiNpBVjKIePlJ0fLeazW3KNmIYPZcB3WpqDoyfQLOAf0frn2BJkgJ2cabZ5KHNgodp8J1o/lGwMcLNITnZtvLljWCEj/k0xp5AtFnB+FTKZr0WbTKfku8QYtsiIP1+/FMiFdSInYpFo4/BaYjduEtntHOMfxdCGkLok+HDk3A6RMfaInBheHXxsxn5btPHvkBzDXBnxfTjmFLL5Af9UThypteKfok2AkoWXep1UyYcTgD8LyoLT5WzjPSv5JfF98SCxEqCfXSJjrBKvElmjrWmOZBv/EskxzJYR36Uxp5DNDzg7yt3RdLparAk1DuiOl4427BqCnwX47xBt0cgnZOmghG+90/czkn8Tb3DaNDt20mgM18nIPN+NOYVsfsA5suyEj0Vb+F7Jpb64XLpgu5R/B+SBe6zvzNNBpM0jstmavpW82PP9JrF/6elDVeJBX5+EjOjIkeWC/MbP++1JA9quEGuTeqzg8gHD9hWZ/3KaDKSwSsJSB32S9u5xOq+WXJfU33H0aeKhiYGTHESWgNMBN3qj2ElFIB+TUw+jEkF7Yhuu8pCIX5qJF4phkgkVKHn1THT6uV0y+dvgfoxy0oS9oohTEFkDTict4lynN9LFEqceEgmYnQybVMgvpOMN7I43OeSUU9egdhYDArrK6+fCpM78yzlZvKBARQNOh4+KbyIkYNfPsUpKaZMYlWIPqYdKuUz8TPwicahkwN0dzIXpgg9xQaL4SOVfrjFFHpnoba0pbt3VY6Syi4Tyyu4uXelks+NHjq8P+JlqeeJ7rynKKB+SDxftieIi0eZULRlcKt7WJe37w8V+uXiNSPoqha1yoM+fRD6uC1KNjXd/YmhWOSWRQ8U6KWnTEDLGdOclDW3AphTnM6Tny5vfNsmjxRAIDn6vh4yJrlYlflyufGQuH35aA97HNg4vlVPFX8SpouE1CeazRvKRZgiUtDffxQE7l6fZJ0heIG4QjxJDIJ10iu0ip6NssJtIFzYYJUd6nFgl+pglhev7g+oXi3Zjm/+BEr4Xd4r+bjIf23F/SMHknzCDyqNF+9GF/VfxKdHAIjtEdy4zzBgo3YByKnwwtvVFSmHep/lOTn26ZPyfdHQlxWVJIxvIL1lkCEul9H0Jio/HpcDvRt+Q1NcndnyWi/5OYSfaOCsl8xFdvKiK2Snnu0ZPfkF1fJinvzlw5aTx0fFh154jxtAiI76xjxJr3yu20eqVnbJRDO1yXjCkkLFiCJywejH2NKyTfabI4hvFnoBTzVihD+L2e74qjMdH7He4WjNicrN6cWbPq+/tYiyHV3L4VnXGJvq/xss894VqsUscn7llvAEpiNcMaWJa3LVi1gfV025xYsV67IWOSCdcRORGLulKgSdim1jpD5k2P0tdvJr6PXhGrRY/F/3LL+/kOdIj8jbO2O5c+fMLdF7Gdn3qfrBG50eK/xrp00mVOTgXe6mXS5ldFW5FBIoIFBEoIlBEoIhAtwj8B7kYiuSPD/PFAAAAAElFTkSuQmCC\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the number to be repeated and  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is the number of repetitions. Hence,  \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"87\" height=\"19\" style=\"width: 87px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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src=\"data:image/png;base64,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\" width=\"214.5\" height=\"19\" style=\"width: 214.5px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and so on.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe can see from the figure below that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e can be a hypotenuse of a right triangle with integer sides (\u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Pythagorean_triple\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePythagorean Triangle\u003c/span\u003e\u003c/span\u003e\u003c/a\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=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 129px; 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 64.5px; text-align: left; transform-origin: 384px 64.5px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                                        \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"254\" height=\"123\" style=\"vertical-align: baseline;width: 254px;height: 123px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn fact, this is the only Pythagorean triangle that can be formed with hypotenuse equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. There is also only one Pythagorean triangle with hypotenuse equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, that is the triangle with sides \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"140\" height=\"19\" style=\"width: 140px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, while there are seven Pythagorean triangles with hypotenures of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"53.5\" height=\"19\" style=\"width: 53.5px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, with legs as follows:\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" width=\"620.5\" height=\"19\" style=\"width: 620.5px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCreate the function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, that counts the number of Pythagorean triangles that can be formed with hypotenuse equal to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = C(x,n)\r\n  c = C(x,n);\r\nend\r\n\r\n","test_suite":"%%\r\nx = (1:5).^2; n = [3,5,2,3,2];\r\nc_correct = [1,1,0,4,7];\r\nassert(isequal(arrayfun(@(i) C(x(i),n(i)),1:5),c_correct))\r\n%%\r\ns_correct = 26;\r\nassert(isequal(sum(arrayfun(@(i) C(i,i),1:9)),s_correct))\r\n%%\r\nx = 1; n = 15;\r\nc_correct = 13;\r\nassert(isequal(C(x,n),c_correct))\r\n%%\r\nx = 123; n = 6;\r\nc_correct = 4;\r\nassert(isequal(C(x,n),c_correct))\r\n%%\r\nx = 1234; n = 4;\r\nc_correct = 121;\r\nassert(isequal(C(x,n),c_correct))\r\n%%\r\nx = 12345; n = 2;\r\nc_correct = 1;\r\nassert(isequal(C(x,n),c_correct))\r\n%%\r\nx = 123456789;\r\nc_correct = 1;\r\nassert(isequal(C(x,1)+C(x,2),c_correct))\r\n%%\r\nx = 3; n = 17;\r\nc_correct = 1;\r\nassert(isequal(C(x,n),c_correct))\r\n%%\r\nx = 35; n = 10;\r\nc_correct = 121;\r\nassert(isequal(C(x,n),c_correct))\r\n%%\r\nx = 5; n = 24;\r\nc_correct = 3280;\r\nassert(isequal(C(x,n),c_correct))\r\n%%\r\nx = 101:200;\r\nc = arrayfun(@(i) C(i,4),x);\r\ns_correct = [30 13 22 23];\r\nassert(isequal(floor([mean(c) mode(c) median(c) std(c)]),s_correct))\r\n%%\r\nfiletext = fileread('C.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'assignin') || contains(filetext, 'evalin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-27T05:38:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2023-04-27T05:33:05.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-18T10:54:53.000Z","updated_at":"2023-04-27T05:38:35.000Z","published_at":"2023-04-26T22:30:53.000Z","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\u003eThe number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e111\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e belongs to a class of numbers called \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Repunit\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRepunit Numbers,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in which all digits are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, we'll define a superset of the repunit numbers which we shall call \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003erepnums\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which are composed of repeated numbers. That is, if we denote repnums by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(x,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the number to be repeated and  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of repetitions. Hence,  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(1,3)=111\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(25,2)=2525\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(123,6)=123123123123123123\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e 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\u003eWe can see from the figure below that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(1,3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e can be a hypotenuse of a right triangle with integer sides (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Pythagorean_triple\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePythagorean Triangle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"123\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"254\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\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\u003eIn fact, this is the only Pythagorean triangle that can be formed with hypotenuse equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(1,3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. There is also only one Pythagorean triangle with hypotenuse equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(4,5)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, that is the triangle with sides \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[9756,\\\\ 43360, \\\\ 44444]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, while there are seven Pythagorean triangles with hypotenures of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(25,2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, with legs as follows:\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        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{\\\\ [213,\\\\ 2516]\\\\ [500,\\\\ 2475]\\\\ [707,\\\\ 2424]\\\\ [1085,\\\\ 2280]\\\\ [1173,\\\\ 2236]\\\\ [1515,\\\\ 2020]\\\\ [1680,\\\\ 1885]\\\\ \\\\}\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCreate the function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{C}(x,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, that counts the number of Pythagorean triangles that can be formed with hypotenuse equal to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" 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