{"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":"ee33508b-a6ec-5b91-aa13-f417500d9537","task_key":"test--ee33508b-a6ec-5b91-aa13-f417500d9537","task_revision_id":"1","upstream_id":"","short_description":"Let $\\mathbb{Z}^n$ be the integer lattice in $\\mathbb{R}^n$. Two points in…","config":"","split":"test","body":"{\"problem\":\"Let $\\\\mathbb{Z}^n$ be the integer lattice in $\\\\mathbb{R}^n$. Two points in $\\\\mathbb{Z}^n$ are called \\\\emph{neighbors} if they differ by exactly $1$ in one coordinate and are equal in all other coordinates. For which integers $n \\\\geq 1$ does there exist a set of points $S \\\\subset \\\\mathbb{Z}^n$ satisfying the following two conditions? \\\\begin{enumerate} \\\\item[(1)] If $p$ is in $S$, then none of the neighbors of $p$ is in $S$. \\\\item[(2)] If $p \\\\in \\\\mathbb{Z}^n$ is not in $S$, then exactly one of the neighbors of $p$ is in $S$. \\\\end{enumerate}\"}","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":[]}