{"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":"52f92730-d7b3-58a9-b3be-d4d71d8145b5","task_key":"test--52f92730-d7b3-58a9-b3be-d4d71d8145b5","task_revision_id":"1","upstream_id":"","short_description":"Let $S=\\left\\{p_{1} p_{2} \\cdots p_{n} \\mid p_{1}, p_{2}, \\ldots, p_{n}\\right.$…","config":"","split":"test","body":"{\"problem\":\"Let $S=\\\\left\\\\{p_{1} p_{2} \\\\cdots p_{n} \\\\mid p_{1}, p_{2}, \\\\ldots, p_{n}\\\\right.$ are distinct primes and $\\\\left.p_{1}, \\\\ldots, p_{n}<30\\\\right\\\\}$. Assume 1 is in $S$. Let $a_{1}$ be an element of $S$. We define, for all positive integers $n$ : $$ \\\\begin{gathered} a_{n+1}=a_{n} /(n+1) \\\\quad \\\\text { if } a_{n} \\\\text { is divisible by } n+1 \\\\\\\\ a_{n+1}=(n+2) a_{n} \\\\quad \\\\text { if } a_{n} \\\\text { is not divisible by } n+1 \\\\end{gathered} $$ How many distinct possible values of $a_{1}$ are there such that $a_{j}=a_{1}$ for infinitely many $j$ '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":[]}