{"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":"85e9cff5-67fd-5890-b028-965b99a62a79","task_key":"counting~5fand~5fprobability--test--85e9cff5-67fd-5890-b028-965b99a62a79","task_revision_id":"1","upstream_id":"","short_description":"Set $R$ is a set of rectangles such that (1) only the grid points shown here are…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Set $R$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. If $R$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $R$ are squares? Express your answer as a common fraction. [asy]import graph;\\nsize(50);\\nfor(int i = 0; i<5; ++i)\\nfor(int j = 0; j<5; ++j)\\nfill(Circle((i,j),.1));\\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":[]}