{"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":"8582f6f2-d602-5df6-bc9b-e02af6a16f44","task_key":"default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f22","task_revision_id":"2","upstream_id":"https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_22","short_description":"Ant Amelia starts on the number line at $0$ and crawls in the following manner.…","config":"default","split":"train","body":"{\"problem\":\"Ant Amelia starts on the number line at $0$ and crawls in the following manner. For $n=1,2,3,$ Amelia chooses a time duration $t_n$ and an increment $x_n$ independently and uniformly at random from the interval $(0,1).$ During the $n$th step of the process, Amelia moves $x_n$ units in the positive direction, using up $t_n$ minutes. If the total elapsed time has exceeded $1$ minute during the $n$th step, she stops at the end of that step; otherwise, she continues with the next step, taking at most $3$ steps in all. What is the denominator plus the numerator of thethe probability that Amelia’s position when she stops will be greater than $1$?\"}","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":[]}