{"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":"8462f740-3082-5871-820e-f8c3178b9625","task_key":"test--8462f740-3082-5871-820e-f8c3178b9625","task_revision_id":"3","upstream_id":"","short_description":"Given a positive integer $n \\ge 2$. Find all $n$-tuples of positive integers…","config":"","split":"test","body":"{\"problem\":\"Given a positive integer $n \\\\ge 2$. Find all $n$-tuples of positive integers $(a_1,a_2,\\\\ldots,a_n)$, such that $1<a_1 \\\\le a_2 \\\\le a_3 \\\\le \\\\cdots \\\\le a_n$, $a_1$ is odd, and\\n(1) $M=\\\\frac{1}{2^n}(a_1-1)a_2 a_3 \\\\cdots a_n$ is a positive integer;\\n(2) One can pick $n$-tuples of integers $(k_{i,1},k_{i,2},\\\\ldots,k_{i,n})$ for $i=1,2,\\\\ldots,M$ such that for any $1 \\\\le i_1 <i_2 \\\\le M$, there exists $j \\\\in \\\\{1,2,\\\\ldots,n\\\\}$ such that $k_{i_1,j}-k_{i_2,j} \\\\not\\\\equiv 0, \\\\pm 1 \\\\pmod{a_j}$.\"}","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":[]}