{"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":"f4937414-671f-5112-8c43-19532a1aec5e","task_key":"test--f4937414-671f-5112-8c43-19532a1aec5e","task_revision_id":"4","upstream_id":"","short_description":"Let $\\{ z_n \\}_{n \\ge 1}$ be a sequence of complex numbers, whose odd terms are…","config":"","split":"test","body":"{\"problem\":\"Let $\\\\{ z_n \\\\}_{n \\\\ge 1}$ be a sequence of complex numbers, whose odd terms are real, even terms are purely imaginary, and for every positive integer $k$, $|z_k z_{k+1}|=2^k$. Denote $f_n=|z_1+z_2+\\\\cdots+z_n|,$ for $n=1,2,\\\\cdots$\\n(1) Find the minimum of $f_{2020}$.\\n(2) Find the minimum of $f_{2020} \\\\cdot f_{2021}$.\"}","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":[]}