{"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":"4caacf63-915d-5c64-bac9-6a19671ccd67","task_key":"test--4caacf63-915d-5c64-bac9-6a19671ccd67","task_revision_id":"1","upstream_id":"","short_description":"For each positive real number $\\alpha$, define $$ \\lfloor\\alpha…","config":"","split":"test","body":"{\"problem\":\"For each positive real number $\\\\alpha$, define $$ \\\\lfloor\\\\alpha \\\\mathbb{N}\\\\rfloor:=\\\\{\\\\lfloor\\\\alpha m\\\\rfloor \\\\mid m \\\\in \\\\mathbb{N}\\\\} $$ Let $n$ be a positive integer. A set $S \\\\subseteq\\\\{1,2, \\\\ldots, n\\\\}$ has the property that: for each real $\\\\beta>0$, $$ \\\\text { if } S \\\\subseteq\\\\lfloor\\\\beta \\\\mathbb{N}\\\\rfloor \\\\text {, then }\\\\{1,2, \\\\ldots, n\\\\} \\\\subseteq\\\\lfloor\\\\beta \\\\mathbb{N}\\\\rfloor $$ Determine, with proof, the smallest possible size of $S$.\"}","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":[]}