{"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":"f8d20723-8164-535e-b987-b27a5bb3b793","task_key":"default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f23","task_revision_id":"2","upstream_id":"https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_23","short_description":"Let $x_0,x_1,x_2,\\dotsc$ be a sequence of numbers, where each $x_k$ is either…","config":"default","split":"train","body":"{\"problem\":\"Let $x_0,x_1,x_2,\\\\dotsc$ be a sequence of numbers, where each $x_k$ is either $0$ or $1$. For each positive integer $n$, define \\n\\\\[S_n = \\\\sum_{k=0}^{n-1} x_k 2^k\\\\]\\nSuppose $7S_n \\\\equiv 1 \\\\pmod{2^n}$ for all $n \\\\geq 1$. What is the value of the sum  \\n\\\\[x_{2019} + 2x_{2020} + 4x_{2021} + 8x_{2022}?\\\\]\"}","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":[]}