{"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":"591f854d-af83-56ba-b281-b92de34c1928","task_key":"test--591f854d-af83-56ba-b281-b92de34c1928","task_revision_id":"1","upstream_id":"","short_description":"Let $S=\\{1,2, \\ldots, 2021\\}$, and let $\\mathcal{F}$ denote the set of functions…","config":"","split":"test","body":"{\"problem\":\"Let $S=\\\\{1,2, \\\\ldots, 2021\\\\}$, and let $\\\\mathcal{F}$ denote the set of functions $f: S \\\\rightarrow S$. For a function $f \\\\in \\\\mathcal{F}$, let $$T_{f}=\\\\left\\\\{f^{2021}(s): s \\\\in S\\\\right\\\\}$$ where $f^{2021}(s)$ denotes $f(f(\\\\cdots(f(s)) \\\\cdots))$ with 2021 copies of $f$. Compute the remainder when $$\\\\sum_{f \\\\in \\\\mathcal{F}}\\\\left|T_{f}\\\\right|$$ is divided by the prime 2017, where the sum is over all functions $f$ in $\\\\mathcal{F}$.\"}","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":[]}