{"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":"e5662f82-4e9c-567c-8801-77aeb621c6ce","task_key":"precalculus--test--e5662f82-4e9c-567c-8801-77aeb621c6ce","task_revision_id":"1","upstream_id":"","short_description":"The distances from a point $P$ to five of the vertices of a regular octahedron…","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"The distances from a point $P$ to five of the vertices of a regular octahedron are 3, 7, 8, 9, and 11.  Find the distance from $P$ to the sixth vertex.\\n\\n[asy]\\nimport three;\\n\\nsize(125);\\ncurrentprojection = perspective(6,3,1);\\n\\ntriple A, B, C, D, E, F, P;\\n\\nA = (1,0,0);\\nB = (-1,0,0);\\nC = (0,1,0);\\nD = (0,-1,0);\\nE = (0,0,1);\\nF = (0,0,-1);\\nP = (1.2,1.5,1);\\n\\ndraw(A--P,red);\\ndraw(B--P,red);\\ndraw(C--P,red);\\ndraw(D--P,red);\\ndraw(E--P,red);\\ndraw(F--P,red);\\n\\ndraw(A--C);\\ndraw(A--D);\\ndraw(A--E);\\ndraw(A--F);\\ndraw(C--E--D--F--cycle);\\ndraw(D--B--C,dashed);\\ndraw(B--C,dashed);\\ndraw(B--D,dashed);\\ndraw(B--E,dashed);\\ndraw(B--F,dashed);\\n\\nlabel(\\\"$P$\\\", P, NE);\\n[/asy]\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}