{"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":"886965c6-3232-5ef0-a9e0-195c7d17875b","task_key":"test--886965c6-3232-5ef0-a9e0-195c7d17875b","task_revision_id":"1","upstream_id":"","short_description":"Let $S$ be a set of positive integers satisfying the following two conditions: -…","config":"","split":"test","body":"{\"problem\":\"Let $S$ be a set of positive integers satisfying the following two conditions: - For each positive integer $n$, at least one of $n, 2 n, \\\\ldots, 100 n$ is in $S$. - If $a_{1}, a_{2}, b_{1}, b_{2}$ are positive integers such that $\\\\operatorname{gcd}\\\\left(a_{1} a_{2}, b_{1} b_{2}\\\\right)=1$ and $a_{1} b_{1}, a_{2} b_{2} \\\\in S$, then $a_{2} b_{1}, a_{1} b_{2} \\\\in S$ Suppose that $S$ has natural density $r$. Compute the minimum possible value of $\\\\left\\\\lfloor 10^{5} r\\\\right\\\\rfloor$. Note: $S$ has natural density $r$ if $\\\\frac{1}{n}|S \\\\cap\\\\{1, \\\\ldots, n\\\\}|$ approaches $r$ as $n$ approaches $\\\\infty$.\"}","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":[]}