{"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":"179961cd-80dd-5415-8772-a133e05732d5","task_key":"default--train--179961cd-80dd-5415-8772-a133e05732d5","task_revision_id":"2","upstream_id":"","short_description":"AIME 2024 train 179961cd-80dd-5415-8772-a133e05732d5","config":"default","split":"train","body":"{\"Problem\":\"Torus $T$ is the surface produced by revolving a circle with radius $3$ around an axis in the plane of the circle that is a distance $6$ from the center of the circle (so like a donut). Let $S$ be a sphere with a radius $11$. When $T$ rests on the inside of $S$, it is internally tangent to $S$ along a circle with radius $r_i$, and when $T$ rests on the outside of $S$, it is externally tangent to $S$ along a circle with radius $r_o$. The difference $r_i-r_o$ can be written as $\\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\"}","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":[]}