{"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":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"c3ba8b2a-9da5-5029-bed5-a51e17e9d2aa","task_key":"test--c3ba8b2a-9da5-5029-bed5-a51e17e9d2aa","task_revision_id":"4","upstream_id":"","short_description":"Let $C=\\{ z \\in \\mathbb{C} : |z|=1 \\}$ be the unit circle on the complex plane.…","config":"","split":"test","body":"{\"problem\":\"Let $C=\\\\{ z \\\\in \\\\mathbb{C} : |z|=1 \\\\}$ be the unit circle on the complex plane. Let $z_1, z_2, \\\\ldots, z_{240} \\\\in C$ (not necessarily different) be $240$ complex numbers, satisfying the following two conditions:\\n(1) For any open arc $\\\\Gamma$ of length $\\\\pi$ on $C$, there are at most $200$ of $j ~(1 \\\\le j \\\\le 240)$ such that $z_j \\\\in \\\\Gamma$.\\n(2) For any open arc $\\\\gamma$ of length $\\\\pi/3$ on $C$, there are at most $120$ of  $j ~(1 \\\\le j \\\\le 240)$ such that $z_j \\\\in \\\\gamma$.\\n\\nFind the maximum of $|z_1+z_2+\\\\ldots+z_{240}|$.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}