{"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":"85031697-9ecf-5312-ba59-8470c023517e","task_key":"default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f23","task_revision_id":"2","upstream_id":"https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_23","short_description":"Let $h_n$ and $k_n$ be the unique relatively prime positive integers such that…","config":"default","split":"train","body":"{\"problem\":\"Let $h_n$ and $k_n$ be the unique relatively prime positive integers such that \\\\[\\\\frac{1}{1}+\\\\frac{1}{2}+\\\\frac{1}{3}+\\\\cdots+\\\\frac{1}{n}=\\\\frac{h_n}{k_n}.\\\\] Let $L_n$ denote the least common multiple of the numbers $1, 2, 3, \\\\ldots, n$. For how many integers with $1\\\\le{n}\\\\le{22}$ is $k_n<L_n$?\"}","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":[]}