{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"omni-math","formal_name":"Omni-MATH","introduction":"Omni-MATH evaluates mathematical reasoning on Olympiad-level problems. Its official dataset contains 4,428 problems accompanied by domain and difficulty information.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/KbsdJames/Omni-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":"e6f54e41-a915-540d-9dbf-5ec08155fc5b","task_key":"test--e6f54e41-a915-540d-9dbf-5ec08155fc5b","task_revision_id":"1","upstream_id":"","short_description":"Regular hexagon $P_{1} P_{2} P_{3} P_{4} P_{5} P_{6}$ has side length 2. For $1…","config":"","split":"test","body":"{\"problem\":\"Regular hexagon $P_{1} P_{2} P_{3} P_{4} P_{5} P_{6}$ has side length 2. For $1 \\\\leq i \\\\leq 6$, let $C_{i}$ be a unit circle centered at $P_{i}$ and $\\\\ell_{i}$ be one of the internal common tangents of $C_{i}$ and $C_{i+2}$, where $C_{7}=C_{1}$ and $C_{8}=C_{2}$. Assume that the lines $\\\\{\\\\ell_{1}, \\\\ell_{2}, \\\\ell_{3}, \\\\ell_{4}, \\\\ell_{5}, \\\\ell_{6}\\\\}$ bound a regular hexagon. The area of this hexagon can be expressed as $\\\\sqrt{\\\\frac{a}{b}}$, where $a$ and $b$ are relatively prime positive integers. Compute $100 a+b$.\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}