{"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":"489e9e7d-f17c-5c4e-a1f1-f582cdd7511f","task_key":"test--489e9e7d-f17c-5c4e-a1f1-f582cdd7511f","task_revision_id":"1","upstream_id":"","short_description":"[i]Version 1[/i]. Let $n$ be a positive integer, and set $N=2^{n}$. Determine…","config":"","split":"test","body":"{\"problem\":\"[i]Version 1[/i]. Let $n$ be a positive integer, and set $N=2^{n}$. Determine the smallest real number $a_{n}$ such that, for all real $x$,\\n\\\\[\\n\\\\sqrt[N]{\\\\frac{x^{2 N}+1}{2}} \\\\leqslant a_{n}(x-1)^{2}+x .\\n\\\\]\\n[i]Version 2[/i]. For every positive integer $N$, determine the smallest real number $b_{N}$ such that, for all real $x$,\\n\\\\[\\n\\\\sqrt[N]{\\\\frac{x^{2 N}+1}{2}} \\\\leqslant b_{N}(x-1)^{2}+x .\\n\\\\]\"}","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":[]}