{"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":"bb3c3aa8-0a92-5075-8c89-25ab77fa7da2","task_key":"test--bb3c3aa8-0a92-5075-8c89-25ab77fa7da2","task_revision_id":"1","upstream_id":"","short_description":"In three-dimensional space, let $S$ be the region of points $(x, y, z)$…","config":"","split":"test","body":"{\"problem\":\"In three-dimensional space, let $S$ be the region of points $(x, y, z)$ satisfying $-1 \\\\leq z \\\\leq 1$. Let $S_{1}, S_{2}, \\\\ldots, S_{2022}$ be 2022 independent random rotations of $S$ about the origin ( $0,0,0$). The expected volume of the region $S_{1} \\\\cap S_{2} \\\\cap \\\\cdots \\\\cap S_{2022}$ can be expressed as $\\\\frac{a \\\\pi}{b}$, for relatively prime positive integers $a$ and $b$. 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":[]}