{"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":"f3136877-2cc1-553e-9412-a7ddb869f2dd","task_key":"test--f3136877-2cc1-553e-9412-a7ddb869f2dd","task_revision_id":"1","upstream_id":"","short_description":"Let $S$ be the set of $10$-tuples of non-negative integers that have sum $2019$.…","config":"","split":"test","body":"{\"problem\":\"Let $S$ be the set of $10$-tuples of non-negative integers that have sum $2019$. For any tuple in $S$, if one of the numbers in the tuple is $\\\\geq 9$, then we can subtract $9$ from it, and add $1$ to the remaining numbers in the tuple. Call thus one operation. If for $A,B\\\\in S$ we can get from $A$ to $B$ in finitely many operations, then denote $A\\\\rightarrow B$.\\n\\n(1) Find the smallest integer $k$, such that if the minimum number in $A,B\\\\in S$ respectively are both $\\\\geq k$, then $A\\\\rightarrow B$ implies $B\\\\rightarrow A$.\\n\\n(2) For the $k$ obtained in (1), how many tuples can we pick from $S$, such that any two of these tuples $A,B$ that are distinct, $A\\\\not\\\\rightarrow B$.\"}","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":[]}