{"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":"a59ecf7d-49f7-5302-a7cb-8d24036f72a4","task_key":"test--a59ecf7d-49f7-5302-a7cb-8d24036f72a4","task_revision_id":"1","upstream_id":"","short_description":"Call a subset $S$ of $\\{1, 2, \\dots, n\\}$ \\emph{mediocre} if it has the…","config":"","split":"test","body":"{\"problem\":\"Call a subset $S$ of $\\\\{1, 2, \\\\dots, n\\\\}$ \\\\emph{mediocre} if it has the following property:\\nWhenever $a$ and $b$ are elements of $S$ whose average is an integer, that average is also\\nan element of $S$. Let $A(n)$ be the number of mediocre subsets of $\\\\{1,2,\\\\dots,n\\\\}$.\\n[For instance, every subset of $\\\\{1,2,3\\\\}$ except $\\\\{1,3\\\\}$ is mediocre, so $A(3) =7$.]\\nFind all positive integers $n$ such that $A(n+2) - 2A(n+1) + A(n) = 1$.\"}","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":[]}