{"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":"44a5da69-a628-5e31-b2e2-1b03b9aaa1ea","task_key":"test--44a5da69-a628-5e31-b2e2-1b03b9aaa1ea","task_revision_id":"1","upstream_id":"","short_description":"Let $ \\left(a_{n}\\right)$ be the sequence of reals defined by $…","config":"","split":"test","body":"{\"problem\":\"Let $ \\\\left(a_{n}\\\\right)$ be the sequence of reals defined by $ a_{1}=\\\\frac{1}{4}$ and the recurrence $ a_{n}= \\\\frac{1}{4}(1+a_{n-1})^{2}, n\\\\geq 2$. Find the minimum real $ \\\\lambda$ such that for any non-negative reals $ x_{1},x_{2},\\\\dots,x_{2002}$, it holds\\r\\n\\\\[ \\\\sum_{k=1}^{2002}A_{k}\\\\leq \\\\lambda a_{2002}, \\\\]\\r\\nwhere $  A_{k}= \\\\frac{x_{k}-k}{(x_{k}+\\\\cdots+x_{2002}+\\\\frac{k(k-1)}{2}+1)^{2}}, k\\\\geq 1$.\"}","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":[]}