{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"amc","formal_name":"AMC (AIMO validation set)","introduction":"83 AMC 12 problems assembled by Project Numina as a validation set for the AIMO competition. They sit a step below AIME in difficulty, which makes them a useful lower rung on the same scale.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/AI-MO/aimo-validation-amc","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"2d701f58-1285-5fdc-8958-607838ed0eb8","task_key":"default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f25","task_revision_id":"2","upstream_id":"https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_25","short_description":"A circle with integer radius $r$ is centered at $(r, r)$. Distinct line segments…","config":"default","split":"train","body":"{\"problem\":\"A circle with integer radius $r$ is centered at $(r, r)$. Distinct line segments of length $c_i$ connect points $(0, a_i)$ to $(b_i, 0)$ for $1 \\\\le i \\\\le 14$ and are tangent to the circle, where $a_i$, $b_i$, and $c_i$ are all positive integers and $c_1 \\\\le c_2 \\\\le \\\\cdots \\\\le c_{14}$. What is the ratio $\\\\frac{c_{14}}{c_1}$ for the least possible value of $r$?\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/AI-MO/aimo-validation-amc","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}