{"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":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"6a8d4a5e-aa45-5157-9d8e-fa94486d7fc0","task_key":"test--6a8d4a5e-aa45-5157-9d8e-fa94486d7fc0","task_revision_id":"3","upstream_id":"","short_description":"Define the sequences $(a_n),(b_n)$ by","config":"","split":"test","body":"{\"problem\":\"Define the sequences $(a_n),(b_n)$ by\\n\\\\begin{align*}\\n& a_n, b_n > 0, \\\\forall n\\\\in\\\\mathbb{N_+} \\\\\\\\ \\n& a_{n+1} = a_n - \\\\frac{1}{1+\\\\sum_{i=1}^n\\\\frac{1}{a_i}} \\\\\\\\ \\n& b_{n+1} = b_n + \\\\frac{1}{1+\\\\sum_{i=1}^n\\\\frac{1}{b_i}}\\n\\\\end{align*}\\n1) If $a_{100}b_{100} = a_{101}b_{101}$, find the value of $a_1-b_1$;\\n2) If $a_{100} = b_{99}$, determine which is larger between $a_{100}+b_{100}$ and $a_{101}+b_{101}$.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}