{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"aime-2024","formal_name":"AIME 2024","introduction":"The 30 problems of the 2024 American Invitational Mathematics Examination (AIME I and II). Every answer is an integer from 0 to 999, with no options and no partial credit. It is a frequent reference point for reasoning models.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/Maxwell-Jia/AIME_2024","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"0a6c5622-8934-597c-b002-a856d62bbfd0","task_key":"default--train--0a6c5622-8934-597c-b002-a856d62bbfd0","task_revision_id":"2","upstream_id":"","short_description":"AIME 2024 train 0a6c5622-8934-597c-b002-a856d62bbfd0","config":"default","split":"train","body":"{\"Problem\":\"Let $O(0,0), A(\\\\tfrac{1}{2}, 0),$ and $B(0, \\\\tfrac{\\\\sqrt{3}}{2})$ be points in the coordinate plane. Let $\\\\mathcal{F}$ be the family of segments $\\\\overline{PQ}$ of unit length lying in the first quadrant with $P$ on the $x$-axis and $Q$ on the $y$-axis. There is a unique point $C$ on $\\\\overline{AB}$, distinct from $A$ and $B$, that does not belong to any segment from $\\\\mathcal{F}$ other than $\\\\overline{AB}$. Then $OC^2 = \\\\tfrac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p + q$.\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/Maxwell-Jia/AIME_2024","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}