{"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":"8512ebae-eaa5-500a-9acf-4c1477055457","task_key":"default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f24","task_revision_id":"2","upstream_id":"https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_24","short_description":"Let $K$ be the number of sequences $A_1$, $A_2$, $\\dots$, $A_n$ such that $n$ is…","config":"default","split":"train","body":"{\"problem\":\"Let $K$ be the number of sequences $A_1$, $A_2$, $\\\\dots$, $A_n$ such that $n$ is a positive integer less than or equal to $10$, each $A_i$ is a subset of $\\\\{1, 2, 3, \\\\dots, 10\\\\}$, and $A_{i-1}$ is a subset of $A_i$ for each $i$ between $2$ and $n$, inclusive. For example, $\\\\{\\\\}$, $\\\\{5, 7\\\\}$, $\\\\{2, 5, 7\\\\}$, $\\\\{2, 5, 7\\\\}$, $\\\\{2, 5, 6, 7, 9\\\\}$ is one such sequence, with $n = 5$.What is the remainder when $K$ is divided by $10$?\"}","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":[]}