{"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":"645533d4-4b22-59ca-8ebe-9259b727a057","task_key":"default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f17","task_revision_id":"2","upstream_id":"https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_17","short_description":"Suppose $a$ is a real number such that the equation \\[a\\cdot(\\sin{x}+\\sin{(2x)})…","config":"default","split":"train","body":"{\"problem\":\"Suppose $a$ is a real number such that the equation \\\\[a\\\\cdot(\\\\sin{x}+\\\\sin{(2x)}) = \\\\sin{(3x)}\\\\]\\nhas more than one solution in the interval $(0, \\\\pi)$. The set of all such $a$ that can be written\\nin the form \\\\[(p,q) \\\\cup (q,r),\\\\]\\nwhere $p, q,$ and $r$ are real numbers with $p < q< r$. What is $p+q+r$?\"}","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":[]}