{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"429637ad-e5ec-549c-a05b-a4d38f91cbd4","task_key":"counting~5fand~5fprobability--test--429637ad-e5ec-549c-a05b-a4d38f91cbd4","task_revision_id":"1","upstream_id":"","short_description":"A diagonal of a polyhedron is a line segment connecting two non-adjacent…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"A diagonal of a polyhedron is a line segment connecting two non-adjacent vertices. How many diagonals does a pentagonal prism have? [asy]\\nimport three;\\nsize(100);\\ndefaultpen(linewidth(0.7));\\ncurrentprojection = orthographic(-0.2,-1,2/3);\\n\\nvoid drawPentagon (real h)\\n{\\n\\npath3 y;\\n\\ny=(0,0,h)--(3,0,h)--(5,3,h)--(3,6,h)--(0,5,h)--cycle;\\n\\ndraw(surface(y),white,nolight);\\n\\ndraw(y);\\n}\\n\\nvoid drawRectangle(triple a, triple b, real h)\\n{\\n\\npath3 y;\\n\\ny=a--b--b+(0,0,h)--a+(0,0,h)--cycle;\\n\\ndraw(surface(y),white,black,nolight);\\n}\\n\\ndrawRectangle((0,0,0),(0,5,0),4);\\ndrawRectangle((0,0,0),(3,0,0),4);\\ndrawRectangle((3,0,0),(5,3,0),4);\\ndrawPentagon(4);\\n\\n//import three; currentprojection = orthographic(25,150,100); //defaultpen(linewidth(0.8)); size(100);\\n//void nGon(int numSides, real height){\\n//real angle = 360/numSides;\\n//for(int i = 0; i < numSides; ++i){\\n//draw(dir(angle*i,0)--dir(angle*(i + 1),0));\\n//draw((dir(angle*i,0) + (0,0,height))--(dir(angle*(i + 1),0) + (0,0,height)));\\n//draw(dir(angle*i,0)--(dir(angle*i,0) + (0,0,height)));\\n// }\\n//}\\n//nGon(5,2);\\n[/asy]\",\"type\":\"Counting & Probability\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}