{"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":"47490048-d134-5a0f-8a14-be4985214c00","task_key":"test--47490048-d134-5a0f-8a14-be4985214c00","task_revision_id":"1","upstream_id":"","short_description":"Let $k$ and $s$ be positive integers such that $s<(2k + 1)^2$. Initially, one…","config":"","split":"test","body":"{\"problem\":\"Let $k$ and $s$ be positive integers such that $s<(2k + 1)^2$. Initially, one cell out of an $n \\\\times n$ grid is coloured green. On each turn, we pick some green cell $c$ and colour green some $s$ out of the $(2k + 1)^2$ cells in the $(2k + 1) \\\\times (2k + 1)$ square centred at $c$. No cell may be coloured green twice. We say that $s$ is $k-sparse$ if there exists some positive number $C$ such that, for every positive integer $n$, the total number of green cells after any number of turns is always going to be at most $Cn$. Find, in terms of $k$, the least $k$-sparse integer $s$.\\n\\n[I]\"}","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":[]}