{"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":"a616c54d-3ce3-5844-b8d7-d7273db3a94e","task_key":"test--a616c54d-3ce3-5844-b8d7-d7273db3a94e","task_revision_id":"1","upstream_id":"","short_description":"Let $S$ be the set \\{1,2, \\ldots, 2012\\}. A perfectutation is a bijective…","config":"","split":"test","body":"{\"problem\":\"Let $S$ be the set \\\\{1,2, \\\\ldots, 2012\\\\}. A perfectutation is a bijective function $h$ from $S$ to itself such that there exists an $a \\\\in S$ such that $h(a) \\\\neq a$, and that for any pair of integers $a \\\\in S$ and $b \\\\in S$ such that $h(a) \\\\neq a, h(b) \\\\neq b$, there exists a positive integer $k$ such that $h^{k}(a)=b$. Let $n$ be the number of ordered pairs of perfectutations $(f, g)$ such that $f(g(i))=g(f(i))$ for all $i \\\\in S$, but $f \\\\neq g$. Find the remainder when $n$ is divided by 2011 .\"}","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":[]}