{"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":264,"title":"Find the \"ordinary\" or Euclidean distance between A and Z","description":"A, B and Z define three points in the 3D _Euclidean_ space of the form:\r\nA = [x1;y1;0]; B = [x2;y2;0]; Z = [x2;y2;z];\r\n\r\nFind the *Euclidean distance* between A and Z where\r\n  \r\n  A = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\r\n  \r\n  \u003e\u003e euclidean(A,B,Z)\r\n  \r\n  ans = 5.830951894845301\r\n\r\nYour function should be able to handle 1 x 3 vectors or 3 x 1 vectors\r\nfor all input parameters: A,B and Z. Z need not be 1 x 3 if A and B are.\r\nSo 1x3,1x3,3x1 inputs, corresponding A, B and Z, are possible function\r\ninput vectors.\r\n\r\nHINT: use the Pythagorean formula.","description_html":"\u003cp\u003eA, B and Z define three points in the 3D \u003ci\u003eEuclidean\u003c/i\u003e space of the form:\r\nA = [x1;y1;0]; B = [x2;y2;0]; Z = [x2;y2;z];\u003c/p\u003e\u003cp\u003eFind the \u003cb\u003eEuclidean distance\u003c/b\u003e between A and Z where\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eA = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003e\u003e\u003e euclidean(A,B,Z)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eans = 5.830951894845301\r\n\u003c/pre\u003e\u003cp\u003eYour function should be able to handle 1 x 3 vectors or 3 x 1 vectors\r\nfor all input parameters: A,B and Z. Z need not be 1 x 3 if A and B are.\r\nSo 1x3,1x3,3x1 inputs, corresponding A, B and Z, are possible function\r\ninput vectors.\u003c/p\u003e\u003cp\u003eHINT: use the Pythagorean formula.\u003c/p\u003e","function_template":"function y = euclidean(A,B,Z)\r\n  y = findEuclid(A,B,Z);\r\nend","test_suite":"%%\r\nA = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [1;0;0]; B = [5;3;0]; Z=[5;3;3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0,0,0]; B = [4,3,0]; Z=[4,3,3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0;0;0]; B = [4;3;0]; Z=[4;3;3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0,3,0]; B = [4,0,0]; Z=[4,0,3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0;3;0]; B = [4;0;0]; Z=[4;0;3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0;3;0]; B = [4;0;0]; Z=[4;0;12];\r\ny_correct = 13;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":177,"test_suite_updated_at":"2012-02-12T03:40:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-05T23:24:30.000Z","updated_at":"2026-02-11T14:15:21.000Z","published_at":"2012-02-12T03:52:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA, B and Z define three points in the 3D\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEuclidean\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e space of the form: A = [x1;y1;0]; B = [x2;y2;0]; Z = [x2;y2;z];\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\u003eFind the\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\u003eEuclidean distance\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e between A and Z where\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 = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\\n\\n\u003e\u003e euclidean(A,B,Z)\\n\\nans = 5.830951894845301]]\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\u003eYour function should be able to handle 1 x 3 vectors or 3 x 1 vectors for all input parameters: A,B and Z. Z need not be 1 x 3 if A and B are. So 1x3,1x3,3x1 inputs, corresponding A, B and Z, are possible function input vectors.\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: use the Pythagorean formula.\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":57954,"title":"Easy Sequences 108: Enclosing a Circle with Primitive Pythagorean Triangles","description":"Pythagorean Triangle is a right triangle all sides of which are represented by integers. Examples are triangles with sides  and . \r\nWe say that pythagorean triangle is a primitive pythagorean triangle (PPT), if all of its sides are relatively prime. That is, if the sides of a pythagorean triangle are a, b and c, it is PPT if and only if: gcd(a,b) == 1 \u0026\u0026 gcd(a,c) == 1 \u0026\u0026 gcd(b,c) == 1.\r\nGiven a circle of radius R, find the dimensions of the PPT with the smallest area, that can enclose the circle, without touching the circle (i.e. no sides is a tangent of the circle, or crosses the circle). For example, in the figure below, if R = 12, the smallest pythagorean triangle that can enclose the circle without touching it is [39,52,65]. However this is not primitive since, gcd(39,52) = 13 ≠ 1. The correct smallest PPT is the triangle with dimensions: [48 55 73].\r\n                                                   \r\n-----------------------\r\nNOTE:   There can be more than one PPT with smallest area for the same value of R. For example if R = 4.5, there are two possible smallest area PPT: [20 21 29] and [12 35 37]. Both have an area of 210. In cases where there are more than one possible PPT's, the function should output the PPT with the least perimeter. So, for R = 4.5, the function output should be: [20 21 29].","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: 547px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 273.5px; transform-origin: 407px 273.5px; 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\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 is a right triangle all sides of which are represented by integers. Examples are triangles 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=\"50\" height=\"19\" style=\"width: 50px; 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 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIIAAAAmCAYAAAAIjkMFAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAgqADAAQAAAABAAAAJgAAAABj1f6GAAAF5ElEQVR4Ae2ZeagWVRiHTa5L1zQ12rTwKuoNKaUSy9QbWf7RrmkLRhspEkFJe1SgpZG2UNEiqFCWRRaaFNJGVEjWbdMkLSstRTJbECtbTOv5XebUYb6Z+WY7MhfOC889Z86cOef3vfOebW6HDt68B7wHvAe8B7wHvAe8B2o9sF9tUVvJcfx9NubeM5TPjLnni6vhgfnIaImRMpbyreF7DeGC4Hp/0sHwIWwLykyyw2R8WlkPfIayw0Lq+nF9DOjd1ljcjDCKmithArxY81R0QR+K+0bcUh8nwBlwesT9Moo60shk6AoLUjTYiTqnwFBQwG+CVdAKu8C1ZdUrPaNhBDSDRrT0vge/QBqbRqV5MAi+SvOA6igQ/oHxukhpEqZn4rg6ZTtZqsmhF8F6UL9PQz0bRoXVEKXzJ8oVtK4sj14NrpchSq8C4uiUYhUIamNgyvpt1bIGwpigkyixKtsJ3dtaLuePZpmJsBbsPusFgkaDRrz9TDivETYWyrS8ehsR8QlI40fwfJDamn+mrCfUs8RAaKj3dMr7N1Hvb5gLeyKeWUFZ2iks4vGaIi0xl8AcuADOhnqml7EQusA98DBshyaYAtdDJzgA9DuGQ1mWR6/6vhuOggthCRjrT0azxBDoBQrcpVC6ZZkRJGYvPFW6inQNTqKaGSFJM8LIoN7tMc1OtdpRMMvBLiyt3h50rsGjfVqUnU+h+d33RVUIlSXOCFqzitoNNKDRtjxIi7aX9flfUz5wFvU+B42yKFtAodlEyS9joiqVUJZW7wD6ehCWxfT5vVX+rZXPlS0aCDopXBz0rPXrR3gJNG13gyqZ1tEZoNkryjS61lg34upZVZxmtaG9I6EH851AOt9IqJfqVtFAuJZeOls99SavkbcItoCOdFUxnVqeqyPmD+v+Ritftaz2MucFou4i1ampkBUNhO303gpR053W2MWQFNXcrpQ1BWo2kK6rlLL/xTSS1TJ8LMwIIClmRQPhfrrXuVsbm35wGXwDtt3JhYleu7xq+UMQZL4hPF41cejRu9LpY2WQkrSddK5RpqgVDQTTv9bXzbAIdNy5Gf4CY9qgldWXabPsVEHcAJ/Co2U3XrA9zQJfgo7hmgmM6dvMQ6AlupC5eDl/omguTLeUNZM/ybquWvZwBN0G2iNcAbuhSrYLMaNhCJwDb4JtM7k42C7ImncRCEaDptcl5oJUS0cVTUdfzQBa3i6Fj6GK9h2i1oNOZafBVWD2ZgeSHwe5zWUgSNQLljKtwVU0jaYJoOVMR+D2YFqK54G9hGlJzm2uA8EeXTtyq3T3oGYAnWr0yfled904a/kVq+VeVj5z1nUg2OdyTW1VsnMRsxA0sm6tkrAMWt6l7t6gvjaTuc11IAwLlGk2eDu3yvIfPJUm9XFJexh9aIoyjbBZUTcqVNYTLeYdri2iS8cll3Zd0PiTpL876kibvSx2IpWXw2ugI6MZUWT/M325ewK0Wy/bsupN6v/M4OZq0reSKta7VyQQJtP4bJCzHgOdEmynTuVaI+8L0HcEV3ao1XBXKx+VHUrhCugGCkz9oylsvSkYBUqlv2xLq/cgOp4DXeAReB9s03FRn5f3wI2gDWTpJkeo4fEJLS8N6qieWAUtcDw8ACrbAH3AlQ2g4TVgNPxAvjmms8GUb7PqmmfiUv0nsszRK1lZ9F5padUAWwxaauXPSbAZtAebCGlsGpX0WwemqWzqpAmEEVTeClGOVPl0aAQX1pdGt4AcFO5fZZtAP9y217kI1026vsV+uGA+j94e9KnfGNao3/c1aBY+AtJaYiAUWRpaUdAEI+FI0EuXcL2EjbAbXJkCTX1msXFZKpdcN4/enWgYBCeDAklLwLqA30hLtSKBICF62e+Uqsg3ZntAU/+rdoGrfEdXDft225cHfCC0r/flTG29peFyetZ/vWz7gAt9jPFWXQ9MQVr4fw8teeQO56HwbtVcz8/ToH9mn3pgWcL7679PlfjOvAe8B7wHvAe8B7wHvAe8B9q/B/4Fw0JjrlWmBOQAAAAASUVORK5CYII=\" width=\"65\" height=\"19\" style=\"width: 65px; 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\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=\"\"\u003eWe say that pythagorean triangle is a \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; \"\u003eprimitive pythagorean triangle (PPT), \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=\"\"\u003eif all of its sides are relatively prime. That is, if the sides of a pythagorean triangle are \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ec\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, it is PPT if and only if: \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003egcd(a,b) == 1 \u0026amp;\u0026amp; gcd(a,c) == 1 \u0026amp;\u0026amp; gcd(b,c) == 1\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.\u003c/span\u003e\u003c/span\u003e\u003c/div\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a circle of radius \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eR\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, find the dimensions of 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePPT with the smallest area, that can enclose the circle, without touching the circle \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(i.e. no sides is a tangent of the circle, or crosses the circle).\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; \"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, in the figure below, if\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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e R = 12\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, the smallest pythagorean triangle that can enclose the circle without touching it is \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[39,52,65]\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. However this is not primitive since, \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003egcd(39,52) = 13 ≠ 1\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. The correct smallest PPT is the triangle with dimensions: \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[48 55 73]\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.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 208px; font-family: Helvetica, Arial, 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data-image-state=\"image-loaded\"\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\u003c/div\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:  \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 There can be more than one PPT with smallest area for the same value of \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eR\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; \"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example if \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eR = 4.5\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, there are two possible smallest area PPT: \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[20 21 29] \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=\"\"\u003eand \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[12 35 37]\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. Both have an area of \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e210\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. \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; \"\u003eIn cases where there are more than one possible PPT's, the function should output the PPT with the least perimeter.\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 So, for \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eR = 4.5\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, the function output should be: \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[20 21 29]\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.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Ts = minPPTs(R)\r\n  y = x;\r\nend","test_suite":"%%\r\nR = [4.5, 12];\r\nTs = arrayfun(@minPPTs,R,'uni',0);\r\nTs_correct = {[20 21 29] [48 55 73]};\r\nassert(isequal(Ts,Ts_correct))\r\n%%\r\nR = 50;\r\nTs_correct = [160 231 281];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = 100;\r\nTs_correct = [336 377 505];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = 200:50:800;\r\nPs = arrayfun(@(r) sum(minPPTs(r)),R)\r\nPs_correct = [2378 3008 3570 4240 4902 5368 6030 6432 7100 7592 8374 8848 9396];\r\nassert(isequal(Ps,Ps_correct))\r\n%%\r\nR = 900;\r\nTs_correct = [3045 3172 4397];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = 1000;\r\nTs_correct = [3255 3712 4937];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = [123 1234 12345 123456];\r\nTs = arrayfun(@minPPTs,R,'uni',0);\r\nTs_correct = {[429 460 629] [4176 4343 6025] [42036 42427 59725] [417543 425776 596345]};\r\nassert(isequal(Ts,Ts_correct))\r\n%%\r\nR = randi([100000,1000000])\r\nTs = minPPTs(R);\r\nr = prod(Ts(1:2)) / sum(Ts)\r\nassert(gcd(Ts(1),Ts(2))==1)\r\nassert(isequal(sqrt(sum(Ts(1:2).^2)),Ts(3)))\r\nassert((r\u003eR) \u0026\u0026 ((r-R)/R\u003c0.0005))\r\n%%\r\nR = 1000000;\r\nTs_correct = [3404505 3424952 4829177];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nfiletext = fileread('minPPTs.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":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-12T18:05:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-06T11:52:42.000Z","updated_at":"2023-04-12T18:05:02.000Z","published_at":"2023-04-12T18:05:02.000Z","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: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 is a right triangle all sides of which are represented by integers. Examples are triangles 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[3\\\\ 4\\\\ 5]\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\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[5\\\\ 12\\\\ 13]\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\u003eWe say that pythagorean triangle is a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprimitive pythagorean triangle (PPT), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eif all of its sides are relatively prime. That is, if the sides of a pythagorean triangle are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\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, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\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 and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\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, it is PPT if and only if: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egcd(a,b) == 1 \u0026amp;\u0026amp; gcd(a,c) == 1 \u0026amp;\u0026amp; gcd(b,c) == 1\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\u003eGiven a circle of radius \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\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the dimensions of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePPT with the smallest area, that can enclose the circle, without touching the circle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(i.e. no sides is a tangent of the circle, or crosses the circle).\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, in the figure below, if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e R = 12\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the smallest pythagorean triangle that can enclose the circle without touching it is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[39,52,65]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. However this is not primitive since, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egcd(39,52) = 13 ≠ 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The correct smallest PPT is the triangle with dimensions: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[48 55 73]\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\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=\\\"202\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"354\\\"/\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\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e There can be more than one PPT with smallest area for the same value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR = 4.5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, there are two possible smallest area PPT: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[20 21 29] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[12 35 37]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Both have an area of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e210\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\u003eIn cases where there are more than one possible PPT's, the function should output the PPT with the least perimeter.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e So, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR = 4.5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the function output should be: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[20 21 29]\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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.jpeg\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.jpeg\",\"contentType\":\"image/jpeg\",\"content\":\"data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4REARXhpZgAATU0AKgAAAAgABAE7AAIAAAASAAAISodpAAQAAAABAAAIXJydAAEAAAAkAAAQ1OocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFJhbW9uIFZpbGxhbWFuZ2NhAAAFkAMAAgAAABQAABCqkAQAAgAAABQAABC+kpEAAgAAAAMwMgAAkpIAAgAAAAMwMgAA6hwABwAACAwAAAieAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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Sequences 106: Counting Pythagorean Triangles inside a Circle","description":"Pythagorean Triangle is a right triangle all sides of which are represented by integers. Examples are triangles with sides  and .\r\nOur goal in this exercise is to write a function that outputs the maximum number of unique pythagorean triangles that can fit inside a circle of radius , with overlaps are allowed.\r\n                                                                \r\nFor example if , the following unique pythagorean triangles can fit inside the circle: , , , , , and . Hence, for , the function should return .\r\n--------------------\r\nNOTE: Unique means that congruent triangles, even if rotated or reflected, are counted only once.","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: 400px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 200px; transform-origin: 407px 200px; 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\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 is a right triangle all sides of which are represented by integers. Examples are triangles with sides \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=\"65\" height=\"19\" style=\"width: 65px; 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\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=\"\"\u003eOur goal in this exercise is to \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; \"\u003ewrite a function that outputs the maximum number of \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; text-decoration-line: underline; \"\u003eunique\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; \"\u003e pythagorean triangles that can fit inside a circle of radius \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);\"\u003eR\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 overlaps are allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 187px; 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 93.5px; text-align: left; transform-origin: 384px 93.5px; 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=\"195\" height=\"181\" style=\"vertical-align: baseline;width: 195px;height: 181px\" 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\" data-image-state=\"image-loaded\"\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=\"\"\u003eFor example if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18\" style=\"width: 46.5px; 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, the following unique pythagorean triangles can fit inside the circle: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"50\" height=\"19\" style=\"width: 50px; 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 src=\"data:image/png;base64,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\" width=\"65\" height=\"19\" style=\"width: 65px; 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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Hence, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF0AAAAkCAYAAADrXDbKAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAXaADAAQAAAABAAAAJAAAAAAvDKlSAAAD7ElEQVRoBe1YS2xOQRQuRRCPhIh32tCI0MRGWXglVBGPpUSiSRPRDRFLLDTCohssWHhUVEmkxCMRQgTRFW28LaQhJKh6tQiNN9+X3NOcjPnvP39H2v+2c5Ivc+bMmXNnvjv33HNvTk6QwEBgIDAQGAgMBAYCA0liIDdJi+2EtebjGluBW0AbkE4mwmEZUAqsAIYDX4BWwEuOYPaHGDRj7B5wGlgN9AeSJuOx4P3Ad+APUADESV8MVgDizzka1eh7H+g8BGk0AlehvwbYAbxRYzegjwCSIGOxyL3AN0CTlo70g4a/niv6Gfj0A7zkImZLwJtGpGHoP1XjJD4JcgqL3A4wPfwAZH9xpC+M/B6iXQDwyR4KlAD3AYnBlqnHS15jtgRk3jNlLQwyzna06ZDlfZIo648j/RL8XgAjLfsZANtjQOLstvg4m6aqQAw40zKz2PBZavHJZhOfTiErFemD4MNUtCpmI3xqJM5tm19vm9Fi46Mj0gKlQTqqnax0qk1Gvzt0J2ATdcCJmM3cUWO/lZ6xqvN5rWU2Xxj1gNzhBxafbDe5nHSXPfApER6sN8flpPNFMVddjTlNCx+5A0BRZGQZtTHSe2KTrzZ9Vuntap92LbUyB0N8QYjwLT8LyAMKgXKAHwWUVwD7V9hxFNb38xx949xWYjCT68bF8hlbHk1m4cG9/SMupC8yZtUYfd6E88AFgB9S/CLLRAbDmSWnr/CDpatlIBYgL9kN0L/aFuRCeomauAf6cWAbwHqVchXwqUcrMf8kA3kKP927WiqwAH4YMpdb87nLAsfASV4KbJlWKCRZ7L+gj6Mx4eL7Ip2O/fOprwd0Os6YljLMEHI/Qpcngy3zt4xtgZ508SGdh+4l8AQYlY6IdNWLTi3XEOxnFJDtURW8TOk9TR2CDZ+LNl2MttmHAN6Qt4Cc5nVGsClqjD6zjXHXLt/w7/8D+B/ERzpy0plGrgPvAPLhLcxRQjjbSZaIeqGHLOMupstw0tfpqL7Y5WIxPnovBTF+MsRqiVXbJ6BIjJa2DLYZ2i45WttE16XicxgbZUC1h6HLfxjWySyTMi0ZKzEnG6qXXliHqzALHAPmA0uABsAm/KjcB0yzDdpsd2GUU1drc4CNvzTblN/6FH5JMD9T+yiMWTBvTlXk24S22oIa2PgPhpVdHZBWcuGxGRDC2T4CSLBNeMfFtwU6c2smp8YWszNt3C9/W8ge2O4EmD5ssgtG7ZtOL7UF0TZ+HTJH2QKxBt2knSOdJJv+PAlJEKa2z4C5fvZZIvMfuxZ+p9h8U9la4e9Vs+uLBz0wEBgIDAQGAgOBgcBAYCAwEBgIDHQrBv4CRnU6xYXt/JUAAAAASUVORK5CYII=\" width=\"46.5\" height=\"18\" style=\"width: 46.5px; 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, the function should return \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);\"\u003e6\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: 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\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=\"font-weight: 700; \"\u003eNOTE:\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 Unique means that congruent triangles, even if rotated or reflected, are counted only once.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = cPTIC(R)\r\n    n = 0;\r\n    for (a=1; a++; a \u003c= R)\r\n        for (b=1; b++; b \u003c= R)\r\n            if (a^2 + b^2 == R)\r\n                n++;\r\n            end\r\n        end\r\n    end\r\nend","test_suite":"%%\r\nR = 12:25;\r\nn_correct = [6 9 9 11 11 12 13 14 16 17 17 18 18 20];\r\nassert(isequal(cPTIC(R),n_correct))\r\n%%\r\nR = 50;\r\nn_correct = 52;\r\nassert(isequal(cPTIC(R),n_correct))\r\n%%\r\nR = [150:-1:110 100:210 123 789 456 1234];\r\nu = unique(cPTIC(R),'stable');\r\ns = [length(u) sum(u) sum(diff(u))];\r\ns_correct = [96 24978 2325];\r\nassert(isequal(s,s_correct))\r\n%%\r\nR = pi.^(1:10);\r\nn_correct = [1 5 27 120 494 1892 7055 25605 91342 321029];\r\nassert(isequal(cPTIC(R),n_correct))\r\n%%\r\nR = exp(15);\r\nn_correct = 14903353;\r\nassert(isequal(cPTIC(R),n_correct))\r\n%%\r\nR = 10.^(1:6);\r\nn_correct = [6 127 1981 27175 344889 4181998];\r\nassert(isequal(cPTIC(R),n_correct))\r\n%%\r\nR = 1:12345678;\r\nn = diff(cPTIC(R));\r\nz = find(n==0);\r\ns = [numel(z) sum(z)]\r\ns_correct = [698208 4158131344543];\r\nassert(isequal(s,s_correct))\r\n%%\r\nR = 1e7:1e5:1e8;\r\nn = cPTIC(R);\r\ns = floor([mean(n) median(n) mode(n) std(n)])\r\ns_correct = [302290670 300165731 49149097 149658811];\r\nassert(isequal(s,s_correct))\r\n%%\r\nR = 123456789;\r\nn_correct = 705546798;\r\nassert(isequal(cPTIC(R),n_correct))\r\n%%\r\nfiletext = fileread('cPTIC.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":1,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-11T17:43:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":"2023-04-11T17:43:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-06T09:45:58.000Z","updated_at":"2023-04-11T17:43:13.000Z","published_at":"2023-04-08T15:03:35.000Z","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: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 is a right triangle all sides of which are represented by integers. Examples are triangles 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[3\\\\ 4\\\\ 5]\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\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[5\\\\ 12\\\\ 13]\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\u003eOur goal in this exercise is to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewrite a function that outputs the maximum number of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunique\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e pythagorean triangles that can fit inside a circle of radius \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\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, with overlaps are allowed.\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=\\\"181\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"195\\\"/\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\u003eFor example if \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\u003eR=12\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the following unique pythagorean triangles can fit inside the circle: \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[3\\\\ 4\\\\ 5]\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[5\\\\ 12\\\\ 13]\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[6\\\\ 8\\\\ 10]\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[8\\\\ 15\\\\  17]\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[9\\\\ 12\\\\ 15]\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\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[12\\\\ 16\\\\ 20]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Hence, for \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\u003eR=12\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the function should return \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\u003e6\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\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Unique means that congruent triangles, even if rotated or reflected, are counted only 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the \"ordinary\" or Euclidean distance between A and Z","description":"A, B and Z define three points in the 3D _Euclidean_ space of the form:\r\nA = [x1;y1;0]; B = [x2;y2;0]; Z = [x2;y2;z];\r\n\r\nFind the *Euclidean distance* between A and Z where\r\n  \r\n  A = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\r\n  \r\n  \u003e\u003e euclidean(A,B,Z)\r\n  \r\n  ans = 5.830951894845301\r\n\r\nYour function should be able to handle 1 x 3 vectors or 3 x 1 vectors\r\nfor all input parameters: A,B and Z. Z need not be 1 x 3 if A and B are.\r\nSo 1x3,1x3,3x1 inputs, corresponding A, B and Z, are possible function\r\ninput vectors.\r\n\r\nHINT: use the Pythagorean formula.","description_html":"\u003cp\u003eA, B and Z define three points in the 3D \u003ci\u003eEuclidean\u003c/i\u003e space of the form:\r\nA = [x1;y1;0]; B = [x2;y2;0]; Z = [x2;y2;z];\u003c/p\u003e\u003cp\u003eFind the \u003cb\u003eEuclidean distance\u003c/b\u003e between A and Z where\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eA = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003e\u003e\u003e euclidean(A,B,Z)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eans = 5.830951894845301\r\n\u003c/pre\u003e\u003cp\u003eYour function should be able to handle 1 x 3 vectors or 3 x 1 vectors\r\nfor all input parameters: A,B and Z. Z need not be 1 x 3 if A and B are.\r\nSo 1x3,1x3,3x1 inputs, corresponding A, B and Z, are possible function\r\ninput vectors.\u003c/p\u003e\u003cp\u003eHINT: use the Pythagorean formula.\u003c/p\u003e","function_template":"function y = euclidean(A,B,Z)\r\n  y = findEuclid(A,B,Z);\r\nend","test_suite":"%%\r\nA = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [1;0;0]; B = [5;3;0]; Z=[5;3;3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0,0,0]; B = [4,3,0]; Z=[4,3,3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0;0;0]; B = [4;3;0]; Z=[4;3;3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0,3,0]; B = [4,0,0]; Z=[4,0,3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0;3;0]; B = [4;0;0]; Z=[4;0;3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0;3;0]; B = [4;0;0]; Z=[4;0;12];\r\ny_correct = 13;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":177,"test_suite_updated_at":"2012-02-12T03:40:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-05T23:24:30.000Z","updated_at":"2026-02-11T14:15:21.000Z","published_at":"2012-02-12T03:52:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA, B and Z define three points in the 3D\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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEuclidean\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e space of the form: A = [x1;y1;0]; B = [x2;y2;0]; Z = [x2;y2;z];\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\u003eFind the\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\u003eEuclidean distance\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e between A and Z where\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 = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\\n\\n\u003e\u003e euclidean(A,B,Z)\\n\\nans = 5.830951894845301]]\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\u003eYour function should be able to handle 1 x 3 vectors or 3 x 1 vectors for all input parameters: A,B and Z. Z need not be 1 x 3 if A and B are. So 1x3,1x3,3x1 inputs, corresponding A, B and Z, are possible function input vectors.\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: use the Pythagorean formula.\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":57954,"title":"Easy Sequences 108: Enclosing a Circle with Primitive Pythagorean Triangles","description":"Pythagorean Triangle is a right triangle all sides of which are represented by integers. Examples are triangles with sides  and . \r\nWe say that pythagorean triangle is a primitive pythagorean triangle (PPT), if all of its sides are relatively prime. That is, if the sides of a pythagorean triangle are a, b and c, it is PPT if and only if: gcd(a,b) == 1 \u0026\u0026 gcd(a,c) == 1 \u0026\u0026 gcd(b,c) == 1.\r\nGiven a circle of radius R, find the dimensions of the PPT with the smallest area, that can enclose the circle, without touching the circle (i.e. no sides is a tangent of the circle, or crosses the circle). For example, in the figure below, if R = 12, the smallest pythagorean triangle that can enclose the circle without touching it is [39,52,65]. However this is not primitive since, gcd(39,52) = 13 ≠ 1. The correct smallest PPT is the triangle with dimensions: [48 55 73].\r\n                                                   \r\n-----------------------\r\nNOTE:   There can be more than one PPT with smallest area for the same value of R. For example if R = 4.5, there are two possible smallest area PPT: [20 21 29] and [12 35 37]. Both have an area of 210. In cases where there are more than one possible PPT's, the function should output the PPT with the least perimeter. So, for R = 4.5, the function output should be: [20 21 29].","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: 547px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 273.5px; transform-origin: 407px 273.5px; 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\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 is a right triangle all sides of which are represented by integers. Examples are triangles 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=\"50\" height=\"19\" style=\"width: 50px; 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 \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"65\" height=\"19\" style=\"width: 65px; 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\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=\"\"\u003eWe say that pythagorean triangle is a \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; \"\u003eprimitive pythagorean triangle (PPT), \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=\"\"\u003eif all of its sides are relatively prime. That is, if the sides of a pythagorean triangle are \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003ec\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, it is PPT if and only if: \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003egcd(a,b) == 1 \u0026amp;\u0026amp; gcd(a,c) == 1 \u0026amp;\u0026amp; gcd(b,c) == 1\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.\u003c/span\u003e\u003c/span\u003e\u003c/div\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a circle of radius \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eR\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, find the dimensions of 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePPT with the smallest area, that can enclose the circle, without touching the circle \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(i.e. no sides is a tangent of the circle, or crosses the circle).\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; \"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, in the figure below, if\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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e R = 12\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, the smallest pythagorean triangle that can enclose the circle without touching it is \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[39,52,65]\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. However this is not primitive since, \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003egcd(39,52) = 13 ≠ 1\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. The correct smallest PPT is the triangle with dimensions: \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[48 55 73]\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.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 208px; 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 104px; text-align: left; transform-origin: 384px 104px; 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=\"354\" height=\"202\" style=\"vertical-align: baseline;width: 354px;height: 202px\" 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data-image-state=\"image-loaded\"\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\u003c/div\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE:  \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 There can be more than one PPT with smallest area for the same value of \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eR\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; \"\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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example if \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eR = 4.5\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, there are two possible smallest area PPT: \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[20 21 29] \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=\"\"\u003eand \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[12 35 37]\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. Both have an area of \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e210\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. \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; \"\u003eIn cases where there are more than one possible PPT's, the function should output the PPT with the least perimeter.\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 So, for \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eR = 4.5\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, the function output should be: \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-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003e[20 21 29]\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.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Ts = minPPTs(R)\r\n  y = x;\r\nend","test_suite":"%%\r\nR = [4.5, 12];\r\nTs = arrayfun(@minPPTs,R,'uni',0);\r\nTs_correct = {[20 21 29] [48 55 73]};\r\nassert(isequal(Ts,Ts_correct))\r\n%%\r\nR = 50;\r\nTs_correct = [160 231 281];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = 100;\r\nTs_correct = [336 377 505];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = 200:50:800;\r\nPs = arrayfun(@(r) sum(minPPTs(r)),R)\r\nPs_correct = [2378 3008 3570 4240 4902 5368 6030 6432 7100 7592 8374 8848 9396];\r\nassert(isequal(Ps,Ps_correct))\r\n%%\r\nR = 900;\r\nTs_correct = [3045 3172 4397];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = 1000;\r\nTs_correct = [3255 3712 4937];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nR = [123 1234 12345 123456];\r\nTs = arrayfun(@minPPTs,R,'uni',0);\r\nTs_correct = {[429 460 629] [4176 4343 6025] [42036 42427 59725] [417543 425776 596345]};\r\nassert(isequal(Ts,Ts_correct))\r\n%%\r\nR = randi([100000,1000000])\r\nTs = minPPTs(R);\r\nr = prod(Ts(1:2)) / sum(Ts)\r\nassert(gcd(Ts(1),Ts(2))==1)\r\nassert(isequal(sqrt(sum(Ts(1:2).^2)),Ts(3)))\r\nassert((r\u003eR) \u0026\u0026 ((r-R)/R\u003c0.0005))\r\n%%\r\nR = 1000000;\r\nTs_correct = [3404505 3424952 4829177];\r\nassert(isequal(minPPTs(R),Ts_correct))\r\n%%\r\nfiletext = fileread('minPPTs.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":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-12T18:05:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-06T11:52:42.000Z","updated_at":"2023-04-12T18:05:02.000Z","published_at":"2023-04-12T18:05:02.000Z","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: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 is a right triangle all sides of which are represented by integers. Examples are triangles 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[3\\\\ 4\\\\ 5]\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\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[5\\\\ 12\\\\ 13]\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\u003eWe say that pythagorean triangle is a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eprimitive pythagorean triangle (PPT), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eif all of its sides are relatively prime. That is, if the sides of a pythagorean triangle are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\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, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\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 and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\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, it is PPT if and only if: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egcd(a,b) == 1 \u0026amp;\u0026amp; gcd(a,c) == 1 \u0026amp;\u0026amp; gcd(b,c) == 1\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\u003eGiven a circle of radius \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\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the dimensions of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePPT with the smallest area, that can enclose the circle, without touching the circle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(i.e. no sides is a tangent of the circle, or crosses the circle).\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, in the figure below, if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e R = 12\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the smallest pythagorean triangle that can enclose the circle without touching it is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[39,52,65]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. However this is not primitive since, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003egcd(39,52) = 13 ≠ 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The correct smallest PPT is the triangle with dimensions: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[48 55 73]\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\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=\\\"202\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"354\\\"/\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\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e There can be more than one PPT with smallest area for the same value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR = 4.5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, there are two possible smallest area PPT: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[20 21 29] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[12 35 37]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Both have an area of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e210\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\u003eIn cases where there are more than one possible PPT's, the function should output the PPT with the least perimeter.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e So, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR = 4.5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the function output should be: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[20 21 29]\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\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.jpeg\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.jpeg\",\"contentType\":\"image/jpeg\",\"content\":\"data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4REARXhpZgAATU0AKgAAAAgABAE7AAIAAAASAAAISodpAAQAAAABAAAIXJydAAEAAAAkAAAQ1OocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFJhbW9uIFZpbGxhbWFuZ2NhAAAFkAMAAgAAABQAABCqkAQAAgAAABQAABC+kpEAAgAAAAMwMgAAkpIAAgAAAAMwMgAA6hwABwAACAwAAAieAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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Sequences 106: Counting Pythagorean Triangles inside a Circle","description":"Pythagorean Triangle is a right triangle all sides of which are represented by integers. Examples are triangles with sides  and .\r\nOur goal in this exercise is to write a function that outputs the maximum number of unique pythagorean triangles that can fit inside a circle of radius , with overlaps are allowed.\r\n                                                                \r\nFor example if , the following unique pythagorean triangles can fit inside the circle: , , , , , and . Hence, for , the function should return .\r\n--------------------\r\nNOTE: Unique means that congruent triangles, even if rotated or reflected, are counted only once.","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: 400px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 200px; transform-origin: 407px 200px; 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\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 is a right triangle all sides of which are represented by integers. Examples are triangles with sides \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=\"65\" height=\"19\" style=\"width: 65px; 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\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=\"\"\u003eOur goal in this exercise is to \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; \"\u003ewrite a function that outputs the maximum number of \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; text-decoration-line: underline; \"\u003eunique\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; \"\u003e pythagorean triangles that can fit inside a circle of radius \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);\"\u003eR\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 overlaps are allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 187px; 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 93.5px; text-align: left; transform-origin: 384px 93.5px; 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=\"195\" height=\"181\" style=\"vertical-align: baseline;width: 195px;height: 181px\" 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\" data-image-state=\"image-loaded\"\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=\"\"\u003eFor example if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18\" style=\"width: 46.5px; 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, the following unique pythagorean triangles can fit inside the circle: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"50\" height=\"19\" style=\"width: 50px; 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 src=\"data:image/png;base64,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\" width=\"65\" height=\"19\" style=\"width: 65px; 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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Hence, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46.5\" height=\"18\" style=\"width: 46.5px; 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, the function should return \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);\"\u003e6\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: 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\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=\"font-weight: 700; \"\u003eNOTE:\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 Unique means that congruent triangles, even if rotated or reflected, are counted only once.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = cPTIC(R)\r\n    n = 0;\r\n    for (a=1; a++; a \u003c= R)\r\n        for (b=1; b++; b \u003c= R)\r\n            if (a^2 + b^2 == R)\r\n                n++;\r\n            end\r\n        end\r\n    end\r\nend","test_suite":"%%\r\nR = 12:25;\r\nn_correct = [6 9 9 11 11 12 13 14 16 17 17 18 18 20];\r\nassert(isequal(cPTIC(R),n_correct))\r\n%%\r\nR = 50;\r\nn_correct = 52;\r\nassert(isequal(cPTIC(R),n_correct))\r\n%%\r\nR = [150:-1:110 100:210 123 789 456 1234];\r\nu = unique(cPTIC(R),'stable');\r\ns = [length(u) sum(u) sum(diff(u))];\r\ns_correct = [96 24978 2325];\r\nassert(isequal(s,s_correct))\r\n%%\r\nR = pi.^(1:10);\r\nn_correct = [1 5 27 120 494 1892 7055 25605 91342 321029];\r\nassert(isequal(cPTIC(R),n_correct))\r\n%%\r\nR = exp(15);\r\nn_correct = 14903353;\r\nassert(isequal(cPTIC(R),n_correct))\r\n%%\r\nR = 10.^(1:6);\r\nn_correct = [6 127 1981 27175 344889 4181998];\r\nassert(isequal(cPTIC(R),n_correct))\r\n%%\r\nR = 1:12345678;\r\nn = diff(cPTIC(R));\r\nz = find(n==0);\r\ns = [numel(z) sum(z)]\r\ns_correct = [698208 4158131344543];\r\nassert(isequal(s,s_correct))\r\n%%\r\nR = 1e7:1e5:1e8;\r\nn = cPTIC(R);\r\ns = floor([mean(n) median(n) mode(n) std(n)])\r\ns_correct = [302290670 300165731 49149097 149658811];\r\nassert(isequal(s,s_correct))\r\n%%\r\nR = 123456789;\r\nn_correct = 705546798;\r\nassert(isequal(cPTIC(R),n_correct))\r\n%%\r\nfiletext = fileread('cPTIC.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":1,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-11T17:43:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":"2023-04-11T17:43:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-06T09:45:58.000Z","updated_at":"2023-04-11T17:43:13.000Z","published_at":"2023-04-08T15:03:35.000Z","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: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 is a right triangle all sides of which are represented by integers. Examples are triangles 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[3\\\\ 4\\\\ 5]\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\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[5\\\\ 12\\\\ 13]\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\u003eOur goal in this exercise is to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewrite a function that outputs the maximum number of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eunique\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e pythagorean triangles that can fit inside a circle of radius \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\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, with overlaps are allowed.\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=\\\"181\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"195\\\"/\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\u003eFor example if \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\u003eR=12\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the following unique pythagorean triangles can fit inside the circle: \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[3\\\\ 4\\\\ 5]\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[5\\\\ 12\\\\ 13]\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[6\\\\ 8\\\\ 10]\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[8\\\\ 15\\\\  17]\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[9\\\\ 12\\\\ 15]\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\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[12\\\\ 16\\\\ 20]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Hence, for \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\u003eR=12\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the function should return \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\u003e6\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\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Unique means that congruent triangles, even if rotated or reflected, are counted only 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2jkX1Vhgj8jXdNNxaTsxYecIVoyqR5opq67rqj5d8QeP/ABH4l3JqOoyLbt/y7Qfu48ehA6/jmubq/rmkzaFr17plz/rLWZo84+8AeG/EYP41Qr5OcpuXvvU/oLC06FOklh4pReqsrIKKKKg6QooooAKKKKACiip7K0l1DULeztxmW4lWJB6sxwP50bilJRV3se8fDrR/7M+DV7cOuJdQgnuGz127Cq/oufxri69p1Cyi03wRdWVuMRW2nPEg9ljIH8q8Wr9HymHs6PL2P5kz/EvF4yVd/abfyvp+AUUUV7B4Bp6Brc+g6ql1Dlk+7LHn76+n19K9os7yG/s4rq1cPDKu5WFeCV1vgfxN/ZN59gvXxZztwxPET+v0Pf8AOvOxuG9pHnjujvweI9nLklsz1SiiivCPbCiiigArgviH4Bl1x4vEHhmT7H4kscPDKh2+eB/Ax9ewJ+h46d7RUTgpqzN8PiKmHqKpTev5+T8jkPh545TxjpMiXcf2XWLFvKvbUjBVhxuAPOCQeOxyPc9fXlnxF8PX3hvXI/iD4STFzb/8hK2X7s8XdiPoOfoG6gmu/wDDfiGx8U6Db6tpcm6GZeVP3o27q3oR/wDXqKcnfkluvxOvGUIOKxNBe5Lp/K+3+XkalFFFbHmhRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABVbUNQttK024v7+VYba3jMkkjdgKs15R8RLufxr410/4f6XIwt1YXOqyofuIOQp+gIP1ZPSs6k+SN1udmDw/1iryydorVvslv/XcZ4G0+6+IHjKbx7rsTJY27GLSLV+ihT9/8Oef7xP8AdFetVBZWdvp1jDZ2USw28CCOONRwqgYAqeinDkXmGMxP1ipdK0Vol2X9b+YVS1f/AJB7f7w/nV2qOsf8g8/7wrDG/wC7VPRmFH+JH1Ofooor4E9sKsWl5JaSbk5U/eX1qvRV06kqclODs0KUVJWZ1NvcR3MQeI5HcdxUtcvbXMlrKHjP1HY10VrdR3cW+M8/xKeor7HAZhHErllpL8/Q8mtQdN3Wx4n8dvD32fVLPXoEwl0vkTkD+NRlSfquR/wGvJa+rPHPh8eJvBt/pyqDOU8yD2kXlfz6fQmvlMggkEYI6g1x4+lyVeZbM/WeEsd9ZwHspP3qeny6f5fIKKKK88+vCiiigAooooAK7v4PaP8A2r8QreZ1zFYRtctkcZHyr/48wP4Vwle7/AjR/s3h2/1aRcPeTiJCf7iDqP8AgTH/AL5rrwdPnrRXbU8DiPF/VcsqyW8lyr56flc9F1//AJFrU/8Ar0l/9ANeHV7jr/8AyLWp/wDXpL/6Aa8Or9Ay74JH865h8UQooor1DzQooooA9N8B+J/t1uNLvnzcwr+6Zj/rEHb6j+X0rtK8Ct7iW0uY57dzHLGwZGHUEV7L4a1+LxBpazrhZ0ws8Y/hb1+h7V4eNw3I/aR2Z7WDxHOuSW6NiiiivNPQCiiigBGUOpVwGUjBBGQRXj0Y/wCFRfEwRjMfhXX2+XJ+W1l/oAT/AN8nvtr2KsLxl4WtvGHhe60m6wrON0EpGfKkH3W/ofYmsqsHJXjutj0MDiI0punV+Cekv0fqtzdorzv4T+KLq9sLnwvr+Y9a0Q+S6ueZIgcBvfHAz3G0969EqoTU48yOfE4eWGqulLp+K6P5hRRRVnOFFFFABRRRQAUUUUAFFFFABRRRQBieMPEsHhLwreavcYYwpiGM/wDLSQ8Kv59fbNcv8IvDVxp+hz+IdZy+r64/2iV3HzLGTlR7ZzuP1A7Vk+OifHHxU0fwbEd9hp/+m6jjp0ztP/ASB/20r1kAAAAYA6AVhH36jl0Wnz6nrVf9lwcaS+Kp7z/w/ZXz3+4KKKK3PJCqGsf8eH/AhV+qGs/8eH/AxXHjv91n6M1o/wARGBRRRXwR7YUUUUAFSwTyW8okiOCP1qKiqjJxfNF2Ymk1ZnS2d7HeR5Xhx95fSvm74qeHv7A8eXYiTbbXv+lQ4HA3H5h+DZ49MV7fFK8MgeNtrDoa5f4u6amv+DU1KJMXmlvvdR3ibAbH0O0+2DX0EcasXR5Knxr8T1OHa7wOYx/kn7r8n0/HT5ng1FFFcp+vBRRRQAUUUUAHWvrPwho/9g+D9M00rteG3XzB/tn5m/8AHia+b/AGj/25480qzZd0YmEso7bE+Yg/XGPxr6pr2csp6Sn8j8143xfvUsKvOT/JfqZ+v/8AItan/wBekv8A6Aa8Or3HX/8AkWtT/wCvSX/0A14dX2WXfBI/IMw+KIUUUV6h5oUUUUAFaega3PoOqpdQ5ZPuyx5++vcfX0rMoqZRUlyvYcZOLuj3qyvINQs4rq1cPFKu5WH+etT15X4H8Tf2TefYbx8Wc7cMTxE/r9D3/OvVK+bxFB0Z8vTofRUKyrQv1Ciiiuc3CiiigDyb4l203g7xrpPj/To2MQcWupog++hGAT9VyPqqV6rbXEV3axXNtIskMyCSN16MpGQR+FU9e0a28Q6DeaTfDMF3EY2OOVPZh7g4I+lcJ8HNXuo7DUfCOrn/AE/QZzEuT96Ik4x6gEH8CtYL3KlukvzPWn/tWCU/tUtH5xe33PT0aPS6KKK3PJCiiigAooooAKKKKACiiigAqlrGqQaLot5qd3/qbSFpnA6kKM4HuelXa81+Nuozf8IzY+HbHm81y8SBUz1UMCf/AB4oPxNZ1JckHI68HQ+sYiFJ7N6+nX8Bvwa0q4m03UfF2qjN/rtw0gJ/hiDHp6Atn8AtemVU0nTodI0ez062/wBVaQJCnHUKAM/pXmQ+JOoaH4q1Ozv0+22Md7MqjpJGocgBT3A9D+YrnnWp4WMVU6nTVjUzCvUqU/kvLZL7j1iiszRPEWmeILbztLuVlwPnjPDp9V/r0rTrqjKM1zRd0ebKMoPlkrMKz9Z/48R/vj+taFZ+tf8AHiv/AF0H8jXJj/8AdZ+hpR/iIwaKKK+DPaCiiigAooooAKjuII7q1lt5hujmRo3X1UjBH5GpKKNhptO6Pm3V9Ol0jWLqwn+/byFM/wB4dj+IwfxqnXo/xc0byr611iJflnHkzEf3hyp/EZH/AAGvOK9WnLmimfsOXYpYvCwrdWtfXqFFFFWd4UUUUAev/ATR999qesyLxEi20R92O5vyAX869trjvhVo/wDY/wAO9PDLtluwbqTjrv8Au/8AjoWuxr6jCU/Z0Yo/Cs/xf1vMqs1snZei0/4Jn6//AMi1qf8A16S/+gGvDq9x1/8A5FrU/wDr0l/9ANeHV9Hl3wSPi8w+KIUUUV6h5oUUUUAFFFFABXpvgLxP9utxpV8+biFf3LMf9Yg7fUfy+leZVJb3EtrcRz27mOWNgyMOoIrCvRVaHKzahWdGfMj32isfwzr8XiDSlnGFuI/lnjH8Lev0NbFfNSi4ScZbn0UZKcVJBRRWfrVib/S5Y01G4011BZbqBwpjx3OeCPUGoexpFJySbsaFeT+Lv+KL+M+i+Jk+Sx1hfsV6ewbhdx/DYf8AgBrhNc+IPj7w1rf2CHxIdRikAa3nFkmLhSSAV3Jk8gjIJGRwTXoOv+HfEXiL4M3p8XzJNq8afboYo4lTyNgzsOOrFdwPucdq45VVVTUU7rU+lo5fLATjOtOLhU93S97PrZpbaM9Sormfh3rzeJPAGl6hK++cxeVMe5dDtJP1xn8a6auuMlJJo+drUpUakqct02vuCiiiqMgooooAKKKKACiiigAryph/wlf7RGG+az8NWmcdjKR/PL/+Q69TkkWKJpJGCoilmJ7AV5h8E431C28Q+J5xiXVtRYjPZVy385CPwrCprKMfn9x6uC/d0K1fqlyr1lp+SZ6jXzl4n/5G7WP+v6f/ANGGvo2vnLxP/wAjdrH/AF/T/wDow15Wcfw4+p0ZL/En6FG0u7ixuUuLOeSCZDlXjYgivSvDXxYI2W3iWPI6C7iX/wBCUfzH5V5fRXi0MTVoO8H/AJHvV8LSxCtUX+Z9N2d7bahapc2U8c8Lj5XjbINVNb/48k/66D+RrwHRfEGp6Bdefpd00WT86dUf6r0NekWPxJsdbs47bUUFjdhxkk/u34PQ9vofzr1a2Y06+GnCWkrHz88sq0KilHWP4mzRQDkZHIor5c1CiiigAooooAKKKKAMfxXo413wzeWIGZWTfD7OvI/Pp+NfPJBBIIwR1Br6erwj4haL/Y/i648tdsF3/pEeOgz94f8AfWfwxXXhpbxPtuFsXaU8LLrqv1/Q5iiiiu0+7Cr2iaY+s69Y6bFnddTpFkdgTgn8BzVGvR/gjo/2/wAbvfuuY9PgZwf9tvlH6Fj+Fa0Ye0qKPc4MyxSweDqV/wCVO3r0/E+goYkt4I4YVCRxqFRR2AGAKfRRX1h/PzbbuxskaSxtHKiujgqysMhgeoIqj/YGj/8AQJsf/AZP8K0KKpSktmS4p7oz/wCwNH/6BNj/AOAyf4Uf2Bo//QJsf/AZP8K0KKftJ9yeSPYz/wCwNH/6BNj/AOAyf4Uf2Bo//QJsf/AZP8K0KKPaT7hyR7Gf/YGj/wDQJsf/AAGT/Cj+wNH/AOgTY/8AgMn+FaFFHtJ9w5I9jP8A7A0f/oE2P/gMn+FH9gaP/wBAmx/8Bk/wrQrOg1u1v3uotKb7XNbAgkKwiLjI2eZjbnIwQMkdxS9pJdSo0VJXUSxa6bY2Ls9lZW9uzDDGKJUJH4CotS1mx0nyheysJJiRFDHG0kkhGM7UUFjjIzgcZqFbO/1HS5IdalW2kkfONNmdCicfL5nDE9csAvB7dav2ttFZ2sdvbqViiXagLFiB9TyfxqHKUtTVRpw0evp/n/wCtK2qtqsaQR2kdgozJK7s0jn+6qgAL25JP0otdJgtdQnvfMuJribILTTsyopOdqrnao4HQZ9c1eoosLndrLQ5BPBMd78SbnxVrCrKbdI4dOhPIjAXJkPvuLYHbr1xjrnVXRkcBlYYII4IpaKUYqOxdWtOrbmeySXkkeV/B120XV/FHhCYkHT70zQAnlkb5c/TCof+BV6pXlWqj/hHv2jNLvE+SHXbMwTH+84BA/VIq9VrKjpFx7M78z9+rGv/ADxT+ez/ABQUUUVueUFFFFABRRRQAUUUUAc58QtROlfDvXLpThhaPGp9Gf5AfzYVS+FOnf2Z8L9FjIw0sJuGPr5jFx+hFZPx1vPs3wxmhB/4+7qKH64Jf/2Su60iz/s7Q7GyAwLa3jhx/uqB/SsFrWfkvzPUl7mXRX802/8AwFJfqXK+cvE//I3ax/1/T/8Aow19G185eJ/+Ru1j/r+n/wDRhrys4/hx9TpyX+JP0MuiiivnD6YKKKKANrRfFWoaMVRH8+2HWGQ8D6Ht/KvQtG8TafrShYZPKuMcwScN+Hr+FeR0qsVYMpIIOQR2qZRTOarhoVNdme5UV5xovjq7stsOphruEcb8/vF/Hv8Aj+dd5p+qWeq2/nWM6yr3A6r9R2rFxaPLqUJ09y3RRRUmIUUUUAFcR8UtG/tDwyt9EuZrB95x3RuG/ofwNdvUdxBHdWstvOu+KVCjqe4IwRVQlyyTOvB4mWFxEK0ej/Dr+B8y0Vc1jTZNH1m60+b71vIUz/eHY/iMH8ap16qd9T9khOM4qUdmFfQfwQ0f7D4Kk1B1xJqE5YH1RPlH67/zr59jRpZFjjBZ2IVQO5NfUPhhhoWj2emNzDBEseR2IHJ/E5NdOFxFKhWTqdT43jCtJYKNCG8n+C/4NjqqKRWDqGUgg8gjvS19TufkQUUUUAFFFFABRVFdYsn1ZtMilMt0gzIkcbMIuM/OwGFJBGASCc8VHbpqt5DdJqYhskkXZCLSUvIg5yxcgDPTAA49TSuuhp7NpXloWNQ1Kz0q1+0ahOsMe4KCcksx6KoHLH2HNV7i51O5W0bSIIFhmUPJLeb0aJeOPKwCWIJ4JXGOfSqsep+HPDYOnz61aW0qne6XuoAyknnJMjbuavWGuaTqjlNM1SyvGHVbe4SQj8iajmTdrm3sZwjzqDa7taW/rzA6TA+rjUZZbmSVBiONp28qPjBIQHbkgnkgnmr1FFXZI55SctwooopkhRRRQAUUUUAeWfGwf2d/wi/iFeG07U1BYehw/wD7Sr1Pr0rgPjZZi6+Fd/JjJtpYZR/32FP6Ma6zwzdnUPCek3hO43FlDKT7sgP9awjpVku9mepW9/AUpfyuUfyf6s06KKK3PLCiiigAooooAKKKKAPLfjf/AKTaeGdN6i61ZMj1wNv/ALPXqVeXfFj9542+H8H9/Vcn6CSHP869RrCH8Sfy/I9TFaYPDr/E/wDya36BXzl4n/5G7WP+v6f/ANGGvo2vnLxP/wAjdrH/AF/T/wDow15Wcfw4+p05L/En6GXRRRXzh9MFFFFABRRRQAVNa3dxZXCz2kzwyL0ZDioaKA33O90Tx8j7YdaTY3QXEY4P1Hb8Pyrs4ZoriFZYJFkjYZV0OQfxrw+tDStbv9Gm32UxVSctG3KN9R/XrWcoJ7HDVwcZaw0PY6K5vRfGlhqe2K6xaXJ4w5+Rj7H+h/WukrJprc82cJQdpIKKKKRB5T8XNF8q9tdYiX5Zh5MxH94cqfxGR/wGvN6+h/FWjjXfDN5YgZkZN0Xs45X9Rj8a+eCCrEMMEcEHtXoYeXNC3Y/TOG8X7fB+ylvDT5dP8vkdJ8P9M/tPxpZKy5jt2Nw/tt5H/j22veq80+D+mbba/wBTdeXYQRn2HzN/Nfyr0LUNRttLtDcXkmxNwRR3dicBQO5JrnrvmnZHy/EVd18f7OP2Ul893+djWsNQa0ba+WiPUenuK345FljDxsGU9CK5OiHxDb6XqMVnJKXlnwRbopdsE43EAHaOvJwOK9PLsylRfsqmsfy/4B8jWwzqawWp11Q3d3b2NpJc3kyQQRLueSRsKo9zVS0uNRutQkdo7WPTlBEZWRnlkPHJGAEHXj5j9Kfpukw6aJTHLcTyzEGSW5naRmI6dThRz0UAe1fVxkpK8djznBR+J/1+n4kL6ldX2lx3Ph+3SZpX2g3vmQBV5+fBXcRxwMDOeuOafPpCX01rPfzzs9uFbyoZnjiZwc7ioPPPQMSK0aKq19w9pb4NPzCiiimZHg3iHTLTWf2i5NP1KHzrWeSJZI9xXcPsynqCD2qp8TdA0nwZ4i0p/CEr214dzvBHMztEwK7CMkkZy3HtU3ivRrfxD+0FPpV68qQXMkSu0RAYD7Op4JBHb0qKTSYPhd8VLJb2KO+0yUq8U1xGCyITgsOwZT39PTNeBNX57r7W/bU/W8PUcfq3LUbaoJ+z6T93ve1/K19D0XXPiJqXhu4jg1Tw7y6gpKt3hZOOcfJwfUdqy/8AhdH/AFAf/Jz/AOwr0TVtIsdd017PUYRNC4yD3U9mU9jXhvi7wbe+FrvL5nsZDiK4A/8AHW9D/OvWqOpDVPQ/n3NKmY4WTq053h6LT8NvM67/AIXR/wBQH/yc/wDsKP8AhdH/AFAf/Jz/AOwry6isfbT7ng/21j/+fn4L/I9R/wCF0f8AUB/8nP8A7Cj/AIXR/wBQH/yc/wDsK8uoo9tPuH9tY/8A5+fgv8j1H/hdH/UB/wDJz/7Cj/hdH/UB/wDJz/7CvLqKPbT7h/bWP/5+fgv8j17WdfHjT4O+I7trP7L5UUieX5nmZ2Kr5zgev6VtfDCc3Hwx0Jyc4tQn/fJK/wBK5Lwkgk+CnilG6NHdj/yXWuh+Djl/hLopbriYflPIK2g26ib7fqfpmX1Z1sjjUm7vnX4xf+R29FFFdJgFFFFABRRRQAUUUUAeXfFP/konw7/7CL/+jIK9Rry34vjyvEngW7/546sOfTLxn/2WvUqwp/xJ/L8j1MV/umHflL/0phXzl4n/AORu1j/r+n/9GGvo2vnLxP8A8jdrH/X9P/6MNeVnH8OPqdOS/wASfoZdFFFfOH0wUUUUAFFFFABRRRQAUUUUAFb2i+LtQ0jbEzfabYf8spDyo/2T2/lWDRSaT3JlCM1aSPX9I8RafrSf6LLtlxloX4Yfh3/CtSvDkdo3DxsUZTkMpwQa67RPHtxbbYdXU3EXQSr99fr6/wA6ylT7Hm1cG1rA9Drwn4h6N/Y/i64Ma4gu/wDSI8dBn7w/76z+BFe3WOoWupW4nsZ1mjPdTyPYjqKwvGXhdfEkenkAb7e6Uv7xMQHH8j+FVRnyS1O3JMcsDi71NItWf6fiP8LwW/hrwHaNfOsCRwefO78bS3zHP0zj8K8n1n4gNrnjiwvZV26XYXCvbwOxUcHh3wCc5x0BwOBnv7tPbQXUBhuoI5oj1jkQMp/A1ly+EPDk/wDrNC076i2QH8wKulVhFuUldsxoY2lGrOtWi3KV/lfcdDEmv6PbSz3oljf52NhMyRyD03A7iB9RnuO1aqqEUKowAMCqGl6Fpui7xpVqtqsnLJGx2k+u3OM+9aFYSavpsebUkm7R2LFpeSWkm5OVP3l9a6K3uI7mISRHI7juK5Wpra6ktZd8Z+oPQ16mAzGWGfJPWP5HDXoKorrc6iiobW6ju4t8Z57qeoqavsITjUipRd0zymnF2YUUUVYjiZ/hyJvicPF/9qEYZW+yfZ/SMR/f3e2elWPH3gKDxzZ2iNefYri1clJhF5mVI5XGR3APXtXXUVj7Cm4uNtHqz0lmmMjVp1lP3qa5Yuy0S0ttr87lLRrGXTNEs7G4uTdyW0KxNOU2mTaMZxk/zqe8s7fULOS1vYVmglXa6OMgipqK1SSVjzqknUbc9b7/ADPDvG3gG48OSNeWAafTWP3urQ+ze3v/AJPG19QyRpLG0cqK6MCGVhkEehFeReOfhy+m+ZqegxtJactLbjlofceq/qPp05KlG2sT4rNMmdK9bDr3eq7enl+R53RRRXMfMBRRRQB6Z4RYL8FvFDNwBHdk/wDgOtb/AMGuPhJov/bf/wBHyVy+gyiH4E+KWJxkXC/99QoP612HwniMPwr0NSMZhZvzkY/1rqp/GvT9T9eyr/kQQ/xL/wBJf+Z2FFFFdZAUUUUAFFFFABRRRQB5b8eQYPCuk6ggy1pqkbcdhsY/zUV6irB1DKcgjIPrXCfGix+2/CzUmAy1s0Uy/g4B/Qmuk8I3v9peC9GvCctNYws3+9sGf1zWEdKsl3SPUre/l9KX8spL77M2K+cvE/8AyN2sf9f0/wD6MNfRtfOXif8A5G7WP+v6f/0Ya8rOP4cfU6cl/iT9DLooor5w+mCiiigAooooAKKKKACiiigAooooAKKKKALFlf3WnXAnspnhkHdT19iO9d1onj2CfbDrCiCToJlHyH6jt/L6V57RScUzKpRhUXvI9xjkSWNZInV0YZVlOQR9adXj+keINQ0WTNpLmInLQvyjfh2+or0DRPGGn6ttikP2W5PHlyHhj7Hv/OsZQaPLq4adPVao6CiiioOUKKKKAJYJ5LeUSRHBH610Nnex3keV4cfeX0rmafFK8MgeNtrDvXpYHHzwsrPWL3X+Rz1qKqLzOroqpY36XaY+7IOq/wBRVuvs6VWFWCnB3TPJlFxdmFZ+ta7p3h7T2vNWuVgiHCg8s59FHUmuX8Z/E3TvDfmWdhtvtSHBjB+SI/7ZHf8A2Rz64rw/Wdc1HxBqDXmq3Lzynpn7qD0UdAK8/FZhCj7sNZfgjelQc9XsfRPhLxfYeL9PlubFWieGQpJDIRuUfwnjsR+uR2rfr5j8I+Jrjwr4giv4MvEfkuIgf9Yh6j69x7ivpWxvbfUrCG8spBLBOgeNx3BrTA4v6xC0viRNalyPTYnooor0DA8z8c/DcT+Zqnh2ILLy01oo4b1KD19u/b38pZSrFWBBBwQR0r6irhfHHw9h11X1DSVWHUQMunRZ/r6N79+/qOapRvrE+WzTJlO9bDLXqu/p/keLUVJcW81rcSQXMbRSxsVdHGCp9CKjrkPjWmnZnYfaRa/s9+IjnBkvBGPfcYQf0zXq3ge2Nn4B0KAjDLp8O4ehKAn9TXh+sTs3wei02E/vr/XxGq+oESn+e2vomCFba2igjGEjQIo9gMV00dZ37JH69gP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