{"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":"47bbf39c-2f67-563f-8fac-4f9b36057e44","task_key":"test--47bbf39c-2f67-563f-8fac-4f9b36057e44","task_revision_id":"3","upstream_id":"","short_description":"Let $p_1,p_2,p_3,...$ be the prime numbers listed in increasing order, and let…","config":"","split":"test","body":"{\"problem\":\"Let $p_1,p_2,p_3,...$ be the prime numbers listed in increasing order, and let $x_0$ be a real number between $0$ and $1$ . For positive integer $k$ , define\\n$x_{k}=\\\\begin{cases}0&\\\\text{ if }x_{k-1}=0\\\\\\\\ \\\\left\\\\{\\\\frac{p_{k}}{x_{k-1}}\\\\right\\\\}&\\\\text{ if }x_{k-1}\\\\ne0\\\\end{cases}$ \\nwhere $\\\\{x\\\\}$ denotes the fractional part of $x$ . (The fractional part of $x$ is given by $x-\\\\lfloor{x}\\\\rfloor$ where $\\\\lfloor{x}\\\\rfloor$ is the greatest integer less than or equal to $x$ .) Find, with proof, all $x_0$ satisfying $0<x_0<1$ for which the sequence $x_0,x_1,x_2,...$ eventually becomes $0$ .\"}","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":[]}