{"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":61290,"title":"20 Points create 23 Segments of four points","description":"By placing 20 points create a graph that has 23 segments that each traverse 4 points. A Cheat Solution Image (press play/stop) that is missing one segment. Given 6 starting segment end-points find the remaining 14 points. Also provide a matrix of the 23 segments giving starting and ending points from the point matrix. The maximum point position error from its segments must be less than 0.01.\r\nThis figure provides context to find six new points directly.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(33, 33, 33); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 464px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 232px; transform-origin: 468.5px 232px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 31.5px; text-align: left; transform-origin: 444.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eBy placing 20 points create a graph that has 23 segments that each traverse 4 points. A \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=fMNmrBZyeQE\u0026amp;t=5438s\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration: none; text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eCheat Solution Image (press play/stop)\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 that is missing one segment. Given 6 starting segment end-points find the remaining 14 points. Also provide a matrix of the 23 segments giving starting and ending points from the point matrix. The maximum point position error from its segments must be less than 0.01.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis figure provides context to find six new points 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [m,segments]=Manga20(m,segments)\r\n %[xi,yi]=L_intersect(x1,y1,x2,y2,x3,y3,x4,y4) % L1(P1 P2) L2(P3 P4)\r\n %m has Points 1,2,5,18,19,20 Pre-filled\r\n \r\n%Create Pts 4 and 3 using [P1 P20 P2 P5]\r\n[xi,yi]=L_intersect(m(1,1),m(1,2),m(20,1),m(20,2), ...\r\n                    m(2,1),m(2,2),m( 5,1),m( 5,2));\r\nm(3,:)=[-xi yi]; % Symmetry exists around Y-axis\r\nm(4,:)=[xi yi];\r\n\r\n%Create Pts 10 and 13 using [P1 P20 P5 P19]\r\n\r\n%m(10,:)=[-xi yi];\r\n%m(13,:)=[xi yi];\r\n\r\n%Create Pts 11 and 12 using [P5 P18 Px Py]\r\n\r\n%m(11,:)=[-xi yi];\r\n%m(12,:)=[xi yi];\r\n\r\n%Create Pts 16 and 17 using [P5 P19 Px Py]\r\n\r\n%m(16,:)=[-xi yi];\r\n%m(17,:)=[xi yi];\r\n\r\n%Create Pts 14 and 15 using [P4 P19 Px Py]\r\n\r\n%m(14,:)=[-xi yi];\r\n%m(15,:)=[xi yi];\r\n\r\n%Create Pts 7 and 8 using [P1 P17 Px Py]\r\n\r\n%m(7,:)=[-xi yi];\r\n%m(8,:)=[xi yi];\r\n\r\n%Create Pt 6 using [P1 P19 Px Py]\r\n%m(6,:)=[xi yi]; %xi=0\r\n\r\n%Create Pt 9 using [P1 P19 Px Py]\r\n%m(9,:)=[xi yi]; % xi=0\r\n\r\n\r\n%segments=[1 18;1  16;1 19;1  17;1 20;\r\n%   ...\r\n%13 18];\r\n \r\nend % Manga20\r\n\r\nfunction [xi,yi]=L_intersect(x1,y1,x2,y2,x3,y3,x4,y4)\r\n%Line Seg12 intersect to Seg34\r\n%No parallel check\r\n denominator = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4);\r\n xi = ((x1*y2 - y1*x2)*(x3-x4) - (x1-x2)*(x3*y4 - y3*x4)) / denominator;\r\n yi = ((x1*y2 - y1*x2)*(y3-y4) - (y1-y2)*(x3*y4 - y3*x4)) / denominator;\r\nend % L_intersect","test_suite":"%%\r\n%Given Six Points Arranged Top Left to Bottom Right\r\n%Only four values are required to define the solution\r\n%a=14.40;b=11.5/2;c=10.80;d=15.3/2+.016;    %0.000626114178873 errmax\r\n%a=14.40;b=11.5/2;c=10.80;d=15.3/2+.0166;   %0.000062608967868 errmax\r\n a=14.40;b=11.5/2;c=10.80;d=15.3/2+15/900;  %0.000000000000005 errmax\r\n%Not sure if this is an exact solution due to eps limits\r\n%Do not know an exact solution with zero error \r\nm=inf(20,2);\r\nm(1,:)=[0 a];\r\nm(2,:)=[-b c];\r\nm(5,:)=[b c];\r\nm(18,:)=[-d 0];\r\nm(19,:)=[0 0];\r\nm(20,:)=[d 0]; % d 7.666...\r\n\r\nsegments=inf(23,2);\r\nsegments(1,:)=[1 18]; %Segments from initial 6 points\r\nsegments(3,:)=[1 19]; %These values may be changed\r\nsegments(5,:)=[1 20];\r\nsegments(6,:)=[2  5];\r\nsegments(8,:)=[2 20];\r\nsegments(9,:)=[2 19];\r\nsegments(19,:)=[5 18];\r\nsegments(20,:)=[5 19];\r\n\r\n [m,segments]=Manga20(m,segments);\r\n \r\n m=unique(m,'rows','stable');\r\n segments=unique(segments,'rows','stable');\r\n Pass=size(m,1)==20;\r\n Pass=Pass \u0026\u0026 size(segments,1)==23;\r\n \r\n fprintf('m\\n')\r\n for i=1:size(m,1)\r\n  fprintf('Idx:%i  %.5f %.5f\\n',i,m(i,:));\r\n end\r\n fprintf('\\nsegments\\n')\r\n for i=1:size(segments,1)\r\n  fprintf('Idx:%i  %i %i\\n',i,segments(i,:));\r\n end\r\n fprintf('\\n');\r\n \r\nf=figure(1);clf;\r\nw=9; h=15;\r\nplot([-w;w;w;-w;-w],[-1;-1;h;h;-1],'k','linewidth',2);hold on\r\nxticks([]);yticks([]); %Ticks/Labels off\r\naxis equal;axis tight;\r\n\r\nfor k=1:size(segments,1)\r\n plot([m(segments(k,1),1);m(segments(k,2),1)], ...\r\n      [m(segments(k,1),2);m(segments(k,2),2)],'k','linewidth',2);\r\nend\r\nfor k=1:size(m,1)\r\n plot(m(k,1),m(k,2),'.r','MarkerSize',10);\r\nend\r\n\r\n \r\n %Calc errmax by looping over segments and evaluating 4th max distant point\r\n errmax=0;\r\nfor seg=1:23 %\r\n x1=m(segments(seg,1),1);\r\n x2=m(segments(seg,2),1);\r\n y1=m(segments(seg,1),2);\r\n y2=m(segments(seg,2),2);\r\n xmin=min(x1,x2)-.01; xmax=max(x1,x2)+.01;\r\n ymin=min(y1,y2)-.01; ymax=max(y1,y2)+.01;\r\n \r\n if x1==x2\r\n  Lm=inf;\r\n  Lb=x1; %Give x vertical line\r\n else % Non-Vertical\r\n  Lm = (y2-y1)/(x2-x1); %Slope\r\n  Lb = y1 - Lm*x1; % Intercept\r\n end\r\n \r\n %Determine simple dy error when assert x value to segment\r\n %Distance from segment is unnecessary given allowed tolerance\r\n if Lm==inf\r\n  ve=abs(m(:,1)-Lb)+double(m(:,2)\u003cymin | m(:,2)\u003eymax);\r\n  ves=sort(ve);\r\n%  ves=sort(abs(m(:,1)-Lb));\r\n  ves4=ves(4); % Fourth dx error from segment\r\n  if ves4\u003e0.01\r\n   fprintf('Error Exceed in Segment %i   Error:%.3f\\n',seg,ves4)\r\n  end\r\n  if ves(5)\u003c0.1\r\n   fprintf('No Pass: Five Points in Segment  %i\\n',seg)\r\n   Pass=0;\r\n  end\r\n  errmax=max(errmax,ves4);\r\n else\r\n  v=m(:,1)*Lm+Lb;\r\n  ve=abs([v-m(:,2)])+double(m(:,1)\u003cxmin | m(:,1)\u003exmax | m(:,2)\u003cymin | m(:,2)\u003eymax);\r\n  verrs=sort(ve);\r\n%  verrs=sort(abs([v-m(:,2)]));\r\n  ves4=verrs(4); % Simple fourth dy error of point from segment\r\n  if ves4\u003e0.01\r\n   fprintf('Error Exceed in Segment %i   Error:%.3f\\n',seg,ves4)\r\n  end\r\n  if verrs(5)\u003c0.1\r\n   fprintf('No Pass: Five Points in Segment  %i\\n',seg)\r\n   Pass=0;\r\n  end\r\n  errmax=max(errmax,ves4);\r\n end\r\nend % seg 1:23\r\nfprintf('errmax: %.15f\\n',errmax)\r\n \r\n \r\n Pass=Pass \u0026\u0026 errmax\u003c0.01; %The 6 starting points can create a solution with errmax \u003c1e-14\r\n \r\nassert(Pass)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":3097,"edited_by":3097,"edited_at":"2026-03-23T13:04:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2026-03-23T13:04:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-20T17:45:44.000Z","updated_at":"2026-03-23T13:04:36.000Z","published_at":"2026-03-20T19:10:00.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBy placing 20 points create a graph that has 23 segments that each traverse 4 points. 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":61290,"title":"20 Points create 23 Segments of four points","description":"By placing 20 points create a graph that has 23 segments that each traverse 4 points. A Cheat Solution Image (press play/stop) that is missing one segment. Given 6 starting segment end-points find the remaining 14 points. Also provide a matrix of the 23 segments giving starting and ending points from the point matrix. The maximum point position error from its segments must be less than 0.01.\r\nThis figure provides context to find six new points directly.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(33, 33, 33); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 464px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 232px; transform-origin: 468.5px 232px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 31.5px; text-align: left; transform-origin: 444.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eBy placing 20 points create a graph that has 23 segments that each traverse 4 points. A \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.youtube.com/watch?v=fMNmrBZyeQE\u0026amp;t=5438s\"\u003e\u003cspan style=\"border-block-end-color: rgb(0, 91, 130); border-block-start-color: rgb(0, 91, 130); border-bottom-color: rgb(0, 91, 130); border-inline-end-color: rgb(0, 91, 130); border-inline-start-color: rgb(0, 91, 130); border-left-color: rgb(0, 91, 130); border-right-color: rgb(0, 91, 130); border-top-color: rgb(0, 91, 130); caret-color: rgb(0, 91, 130); color: rgb(0, 91, 130); column-rule-color: rgb(0, 91, 130); outline-color: rgb(0, 91, 130); text-decoration: none; text-decoration-color: rgb(0, 91, 130); text-emphasis-color: rgb(0, 91, 130); \"\u003e\u003cspan style=\"\"\u003eCheat Solution Image (press play/stop)\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 that is missing one segment. Given 6 starting segment end-points find the remaining 14 points. Also provide a matrix of the 23 segments giving starting and ending points from the point matrix. The maximum point position error from its segments must be less than 0.01.\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; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis figure provides context to find six new points directly.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 362px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 181px; text-align: left; transform-origin: 444.5px 181px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"487\" height=\"356\" style=\"vertical-align: baseline;width: 487px;height: 356px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [m,segments]=Manga20(m,segments)\r\n %[xi,yi]=L_intersect(x1,y1,x2,y2,x3,y3,x4,y4) % L1(P1 P2) L2(P3 P4)\r\n %m has Points 1,2,5,18,19,20 Pre-filled\r\n \r\n%Create Pts 4 and 3 using [P1 P20 P2 P5]\r\n[xi,yi]=L_intersect(m(1,1),m(1,2),m(20,1),m(20,2), ...\r\n                    m(2,1),m(2,2),m( 5,1),m( 5,2));\r\nm(3,:)=[-xi yi]; % Symmetry exists around Y-axis\r\nm(4,:)=[xi yi];\r\n\r\n%Create Pts 10 and 13 using [P1 P20 P5 P19]\r\n\r\n%m(10,:)=[-xi yi];\r\n%m(13,:)=[xi yi];\r\n\r\n%Create Pts 11 and 12 using [P5 P18 Px Py]\r\n\r\n%m(11,:)=[-xi yi];\r\n%m(12,:)=[xi yi];\r\n\r\n%Create Pts 16 and 17 using [P5 P19 Px Py]\r\n\r\n%m(16,:)=[-xi yi];\r\n%m(17,:)=[xi yi];\r\n\r\n%Create Pts 14 and 15 using [P4 P19 Px Py]\r\n\r\n%m(14,:)=[-xi yi];\r\n%m(15,:)=[xi yi];\r\n\r\n%Create Pts 7 and 8 using [P1 P17 Px Py]\r\n\r\n%m(7,:)=[-xi yi];\r\n%m(8,:)=[xi yi];\r\n\r\n%Create Pt 6 using [P1 P19 Px Py]\r\n%m(6,:)=[xi yi]; %xi=0\r\n\r\n%Create Pt 9 using [P1 P19 Px Py]\r\n%m(9,:)=[xi yi]; % xi=0\r\n\r\n\r\n%segments=[1 18;1  16;1 19;1  17;1 20;\r\n%   ...\r\n%13 18];\r\n \r\nend % Manga20\r\n\r\nfunction [xi,yi]=L_intersect(x1,y1,x2,y2,x3,y3,x4,y4)\r\n%Line Seg12 intersect to Seg34\r\n%No parallel check\r\n denominator = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4);\r\n xi = ((x1*y2 - y1*x2)*(x3-x4) - (x1-x2)*(x3*y4 - y3*x4)) / denominator;\r\n yi = ((x1*y2 - y1*x2)*(y3-y4) - (y1-y2)*(x3*y4 - y3*x4)) / denominator;\r\nend % L_intersect","test_suite":"%%\r\n%Given Six Points Arranged Top Left to Bottom Right\r\n%Only four values are required to define the solution\r\n%a=14.40;b=11.5/2;c=10.80;d=15.3/2+.016;    %0.000626114178873 errmax\r\n%a=14.40;b=11.5/2;c=10.80;d=15.3/2+.0166;   %0.000062608967868 errmax\r\n a=14.40;b=11.5/2;c=10.80;d=15.3/2+15/900;  %0.000000000000005 errmax\r\n%Not sure if this is an exact solution due to eps limits\r\n%Do not know an exact solution with zero error \r\nm=inf(20,2);\r\nm(1,:)=[0 a];\r\nm(2,:)=[-b c];\r\nm(5,:)=[b c];\r\nm(18,:)=[-d 0];\r\nm(19,:)=[0 0];\r\nm(20,:)=[d 0]; % d 7.666...\r\n\r\nsegments=inf(23,2);\r\nsegments(1,:)=[1 18]; %Segments from initial 6 points\r\nsegments(3,:)=[1 19]; %These values may be changed\r\nsegments(5,:)=[1 20];\r\nsegments(6,:)=[2  5];\r\nsegments(8,:)=[2 20];\r\nsegments(9,:)=[2 19];\r\nsegments(19,:)=[5 18];\r\nsegments(20,:)=[5 19];\r\n\r\n [m,segments]=Manga20(m,segments);\r\n \r\n m=unique(m,'rows','stable');\r\n segments=unique(segments,'rows','stable');\r\n Pass=size(m,1)==20;\r\n Pass=Pass \u0026\u0026 size(segments,1)==23;\r\n \r\n fprintf('m\\n')\r\n for i=1:size(m,1)\r\n  fprintf('Idx:%i  %.5f %.5f\\n',i,m(i,:));\r\n end\r\n fprintf('\\nsegments\\n')\r\n for i=1:size(segments,1)\r\n  fprintf('Idx:%i  %i %i\\n',i,segments(i,:));\r\n end\r\n fprintf('\\n');\r\n \r\nf=figure(1);clf;\r\nw=9; h=15;\r\nplot([-w;w;w;-w;-w],[-1;-1;h;h;-1],'k','linewidth',2);hold on\r\nxticks([]);yticks([]); %Ticks/Labels off\r\naxis equal;axis tight;\r\n\r\nfor k=1:size(segments,1)\r\n plot([m(segments(k,1),1);m(segments(k,2),1)], ...\r\n      [m(segments(k,1),2);m(segments(k,2),2)],'k','linewidth',2);\r\nend\r\nfor k=1:size(m,1)\r\n plot(m(k,1),m(k,2),'.r','MarkerSize',10);\r\nend\r\n\r\n \r\n %Calc errmax by looping over segments and evaluating 4th max distant point\r\n errmax=0;\r\nfor seg=1:23 %\r\n x1=m(segments(seg,1),1);\r\n x2=m(segments(seg,2),1);\r\n y1=m(segments(seg,1),2);\r\n y2=m(segments(seg,2),2);\r\n xmin=min(x1,x2)-.01; xmax=max(x1,x2)+.01;\r\n ymin=min(y1,y2)-.01; ymax=max(y1,y2)+.01;\r\n \r\n if x1==x2\r\n  Lm=inf;\r\n  Lb=x1; %Give x vertical line\r\n else % Non-Vertical\r\n  Lm = (y2-y1)/(x2-x1); %Slope\r\n  Lb = y1 - Lm*x1; % Intercept\r\n end\r\n \r\n %Determine simple dy error when assert x value to segment\r\n %Distance from segment is unnecessary given allowed tolerance\r\n if Lm==inf\r\n  ve=abs(m(:,1)-Lb)+double(m(:,2)\u003cymin | m(:,2)\u003eymax);\r\n  ves=sort(ve);\r\n%  ves=sort(abs(m(:,1)-Lb));\r\n  ves4=ves(4); % Fourth dx error from segment\r\n  if ves4\u003e0.01\r\n   fprintf('Error Exceed in Segment %i   Error:%.3f\\n',seg,ves4)\r\n  end\r\n  if ves(5)\u003c0.1\r\n   fprintf('No Pass: Five Points in Segment  %i\\n',seg)\r\n   Pass=0;\r\n  end\r\n  errmax=max(errmax,ves4);\r\n else\r\n  v=m(:,1)*Lm+Lb;\r\n  ve=abs([v-m(:,2)])+double(m(:,1)\u003cxmin | m(:,1)\u003exmax | m(:,2)\u003cymin | m(:,2)\u003eymax);\r\n  verrs=sort(ve);\r\n%  verrs=sort(abs([v-m(:,2)]));\r\n  ves4=verrs(4); % Simple fourth dy error of point from segment\r\n  if ves4\u003e0.01\r\n   fprintf('Error Exceed in Segment %i   Error:%.3f\\n',seg,ves4)\r\n  end\r\n  if verrs(5)\u003c0.1\r\n   fprintf('No Pass: Five Points in Segment  %i\\n',seg)\r\n   Pass=0;\r\n  end\r\n  errmax=max(errmax,ves4);\r\n end\r\nend % seg 1:23\r\nfprintf('errmax: %.15f\\n',errmax)\r\n \r\n \r\n Pass=Pass \u0026\u0026 errmax\u003c0.01; %The 6 starting points can create a solution with errmax \u003c1e-14\r\n \r\nassert(Pass)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":3097,"edited_by":3097,"edited_at":"2026-03-23T13:04:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":"2026-03-23T13:04:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-20T17:45:44.000Z","updated_at":"2026-03-23T13:04:36.000Z","published_at":"2026-03-20T19:10:00.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBy placing 20 points create a graph that has 23 segments that each traverse 4 points. 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