{"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":"f424cf63-61da-5d57-92af-694e59b96737","task_key":"test--f424cf63-61da-5d57-92af-694e59b96737","task_revision_id":"1","upstream_id":"","short_description":"One day, there is a Street Art Show at somewhere, and there are some spectators…","config":"","split":"test","body":"{\"problem\":\"One day, there is a Street Art Show at somewhere, and there are some spectators around. We consider this place as an Euclidean plane. Let $K$ be the center of the show. And name the spectators by $A_{1}, A_{2}, \\\\ldots, A_{n}, \\\\ldots$ They pick their positions $P_{1}, P_{2}, \\\\ldots, P_{n}, \\\\ldots$ one by one. The positions need to satisfy the following three conditions simultaneously. (i) The distance between $K$ and $A_{n}$ is no less than 10 meters, that is, $K P_{n} \\\\geq 10 \\\\mathrm{~m}$ holds for any positive integer $n$. (ii) The distance between $A_{n}$ and any previous spectator is no less than 1 meter, that is, $P_{m} P_{n} \\\\geq 1 \\\\mathrm{~m}$ holds for any $n \\\\geq 2$ and any $1 \\\\leq m \\\\leq n-1$. (iii) $A_{n}$ always choose the position closest to $K$ that satisfies (i) and (ii), that is, $K P_{n}$ reaches its minimum possible value. If there are more than one point that satisfy (i) and (ii) and have the minimum distance to $K, A_{n}$ may choose any one of them. For example, $A_{1}$ is not restricted by (ii), so he may choose any point on the circle $C$ which is centered at $K$ with radius 10 meters. For $A_{2}$, since there are lots of points on $C$ which are at least 1 meter apart from $P_{1}$, he may choose anyone of them. (1) Which of the following statement is true? (A) There exist positive real numbers $c_{1}, c_{2}$ such that for any positive integer $n$, no matter how $A_{1}, A_{2}, \\\\ldots, A_{n}$ choose their positions, $c_{1} \\\\leq K P_{n} \\\\leq c_{2}$ always hold (unit: meter); (B) There exist positive real numbers $c_{1}, c_{2}$ such that for any positive integer $n$, no matter how $A_{1}, A_{2}, \\\\ldots, A_{n}$ choose their positions, $c_{1} \\\\sqrt{n} \\\\leq K P_{n} \\\\leq c_{2} \\\\sqrt{n}$ always hold (unit: meter); (C) There exist positive real numbers $c_{1}, c_{2}$ such that for any positive integer $n$, no matter how $A_{1}, A_{2}, \\\\ldots, A_{n}$ choose their positions, $c_{1} n \\\\leq K P_{n} \\\\leq c_{2} n$ always hold (unit: meter); (D) There exist positive real numbers $c_{1}, c_{2}$ such that for any positive integer $n$, no matter how $A_{1}, A_{2}, \\\\ldots, A_{n}$ choose their positions, $c_{1} n^{2} \\\\leq K P_{n} \\\\leq c_{2} n^{2}$ always hold (unit: meter).\"}","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":[]}