{"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":"7d3bae48-a872-57b8-a304-edb2d1d0a8a6","task_key":"test--7d3bae48-a872-57b8-a304-edb2d1d0a8a6","task_revision_id":"1","upstream_id":"","short_description":"Given real numbers $b_0, b_1, \\dots, b_{2019}$ with $b_{2019} \\neq 0$, let…","config":"","split":"test","body":"{\"problem\":\"Given real numbers $b_0, b_1, \\\\dots, b_{2019}$ with $b_{2019} \\\\neq 0$, let $z_1,z_2,\\\\dots,z_{2019}$ be the roots in the complex plane of the polynomial \\\\[ P(z) = \\\\sum_{k=0}^{2019} b_k z^k. \\\\] Let $\\\\mu = (|z_1| + \\\\cdots + |z_{2019}|)/2019$ be the average of the distances from $z_1,z_2,\\\\dots,z_{2019}$ to the origin. Determine the largest constant $M$ such that $\\\\mu \\\\geq M$ for all choices of $b_0,b_1,\\\\dots, b_{2019}$ that satisfy \\\\[ 1 \\\\leq b_0 < b_1 < b_2 < \\\\cdots < b_{2019} \\\\leq 2019. \\\\]\"}","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":[]}