{"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":"c05b6133-c7aa-5de9-8cf3-57398f7b9803","task_key":"geometry--test--c05b6133-c7aa-5de9-8cf3-57398f7b9803","task_revision_id":"1","upstream_id":"","short_description":"A solid $5\\times 5\\times 5$ cube is composed of unit cubes. Each face of the…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"A solid $5\\\\times 5\\\\times 5$ cube is composed of unit cubes. Each face of the large, solid cube is partially painted with gray paint, as shown. [asy]\\n\\nfill((0,0)--(0,1)--(1,1)--(1,0)--cycle,gray);\\n\\nfill((0,4)--(0,5)--(1,5)--(1,4)--cycle,gray);\\n\\nfill((4,1)--(5,1)--(5,0)--(4,0)--cycle,gray);\\n\\nfill((1,2)--(2,2)--(2,1)--(1,1)--cycle,gray);\\n\\nfill((2,2)--(3,2)--(3,1)--(2,1)--cycle,gray);\\n\\nfill((3,2)--(4,2)--(4,1)--(3,1)--cycle,gray);\\n\\nfill((1,3)--(2,3)--(2,2)--(1,2)--cycle,gray);\\n\\nfill((3,3)--(4,3)--(4,2)--(3,2)--cycle,gray);\\n\\nfill((1,4)--(2,4)--(2,3)--(1,3)--cycle,gray);\\n\\nfill((2,4)--(3,4)--(3,3)--(2,3)--cycle,gray);\\n\\nfill((3,4)--(4,4)--(4,3)--(3,3)--cycle,gray);\\n\\nfill((4,5)--(5,5)--(5,4)--(4,4)--cycle,gray);\\n\\ndraw((0,0)--(0,1)--(1,1)--(1,0)--(0,0),rgb(0,0,0));\\n\\ndraw((0,1)--(0,2)--(1,2)--(1,1),rgb(0,0,0));\\n\\ndraw((0,2)--(0,3)--(1,3)--(1,2),rgb(0,0,0));\\n\\ndraw((0,3)--(0,4)--(1,4)--(1,3),rgb(0,0,0));\\n\\ndraw((0,4)--(0,5)--(1,5)--(1,4),rgb(0,0,0));\\n\\ndraw((1,0)--(1,1)--(2,1)--(2,0)--(1,0),rgb(0,0,0));\\n\\ndraw((2,1)--(3,1)--(3,0)--(2,0),rgb(0,0,0));\\n\\ndraw((3,1)--(4,1)--(4,0)--(3,0),rgb(0,0,0));\\n\\ndraw((4,1)--(5,1)--(5,0)--(4,0),rgb(0,0,0));\\n\\ndraw((1,2)--(2,2)--(2,1)--(1,1),rgb(0,0,0));\\n\\ndraw((2,2)--(3,2)--(3,1)--(2,1)--(2,2),rgb(0,0,0));\\n\\ndraw((3,2)--(4,2)--(4,1),rgb(0,0,0));\\n\\ndraw((4,2)--(5,2)--(5,1)--(4,1),rgb(0,0,0));\\n\\ndraw((1,3)--(2,3)--(2,2)--(1,2)--(1,3),rgb(0,0,0));\\n\\ndraw((2,3)--(3,3)--(3,2),rgb(0,0,0));\\n\\ndraw((3,3)--(4,3)--(4,2),rgb(0,0,0));\\n\\ndraw((4,3)--(5,3)--(5,2),rgb(0,0,0));\\n\\ndraw((1,4)--(2,4)--(2,3),rgb(0,0,0));\\n\\ndraw((2,4)--(3,4)--(3,3),rgb(0,0,0));\\n\\ndraw((3,4)--(4,4)--(4,3),rgb(0,0,0));\\n\\ndraw((4,4)--(5,4)--(5,3),rgb(0,0,0));\\n\\ndraw((1,5)--(2,5)--(2,4),rgb(0,0,0));\\n\\ndraw((2,5)--(3,5)--(3,4),rgb(0,0,0));\\n\\ndraw((3,5)--(4,5)--(4,4),rgb(0,0,0));\\n\\ndraw((4,5)--(5,5)--(5,4),rgb(0,0,0));\\n\\n[/asy] \\t \\tWhat fraction of the entire solid cube's unit cubes have no paint on them? Express your answer as a common fraction.\",\"type\":\"Geometry\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}