{"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":"fa3afeea-039b-5d7c-ac5a-80a6b17e5beb","task_key":"test--fa3afeea-039b-5d7c-ac5a-80a6b17e5beb","task_revision_id":"1","upstream_id":"","short_description":"Let $k$ and $n$ be positive integers and let $$ S=\\left\\{\\left(a_{1}, \\ldots,…","config":"","split":"test","body":"{\"problem\":\"Let $k$ and $n$ be positive integers and let $$ S=\\\\left\\\\{\\\\left(a_{1}, \\\\ldots, a_{k}\\\\right) \\\\in \\\\mathbb{Z}^{k} \\\\mid 0 \\\\leq a_{k} \\\\leq \\\\cdots \\\\leq a_{1} \\\\leq n, a_{1}+\\\\cdots+a_{k}=k\\\\right\\\\} $$ Determine, with proof, the value of $$ \\\\sum_{\\\\left(a_{1}, \\\\ldots, a_{k}\\\\right) \\\\in S}\\\\binom{n}{a_{1}}\\\\binom{a_{1}}{a_{2}} \\\\cdots\\\\binom{a_{k-1}}{a_{k}} $$ in terms of $k$ and $n$, where the sum is over all $k$-tuples $\\\\left(a_{1}, \\\\ldots, a_{k}\\\\right)$ in $S$.\"}","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":[]}