{"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":"a3e02f33-3dfc-5ece-b4ad-866bf32cd5e1","task_key":"test--a3e02f33-3dfc-5ece-b4ad-866bf32cd5e1","task_revision_id":"1","upstream_id":"","short_description":"In the game of Galactic Dominion, players compete to amass cards, each of which…","config":"","split":"test","body":"{\"problem\":\"In the game of Galactic Dominion, players compete to amass cards, each of which is worth a certain number of points. Say you are playing a version of this game with only two kinds of cards, planet cards and hegemon cards. Each planet card is worth 2010 points, and each hegemon card is worth four points per planet card held. You start with no planet cards and no hegemon cards, and, on each turn, starting at turn one, you take either a planet card or a hegemon card, whichever is worth more points given the hand you currently hold. Define a sequence $\\\\left\\\\{a_{n}\\\\right\\\\}$ for all positive integers $n$ by setting $a_{n}$ to be 0 if on turn $n$ you take a planet card and 1 if you take a hegemon card. What is the smallest value of $N$ such that the sequence $a_{N}, a_{N+1}, \\\\ldots$ is necessarily periodic (meaning that there is a positive integer $k$ such that $a_{n+k}=a_{n}$ for all $\\\\left.n \\\\geq N\\\\right)$ ?\"}","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":[]}