{"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":"bc54c3d9-3c1c-5161-89f8-69c44ee9b39d","task_key":"test--bc54c3d9-3c1c-5161-89f8-69c44ee9b39d","task_revision_id":"1","upstream_id":"","short_description":"Let $S = \\left\\{ 1,2,\\dots,n \\right\\}$, where $n \\ge 1$. Each of the $2^n$…","config":"","split":"test","body":"{\"problem\":\"Let $S = \\\\left\\\\{ 1,2,\\\\dots,n \\\\right\\\\}$, where $n \\\\ge 1$. Each of the $2^n$ subsets of $S$ is to be colored red or blue. (The subset itself is assigned a color and not its individual elements.) For any set $T \\\\subseteq S$, we then write $f(T)$ for the number of subsets of $T$ that are blue.\\n\\nDetermine the number of colorings that satisfy the following condition: for any subsets $T_1$ and $T_2$ of $S$, \\\\[ f(T_1)f(T_2) = f(T_1 \\\\cup T_2)f(T_1 \\\\cap T_2). \\\\]\"}","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":[]}