{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"1a4a023b-ed4f-5e07-9ce1-d2bfdea39183","task_key":"counting~5fand~5fprobability--test--1a4a023b-ed4f-5e07-9ce1-d2bfdea39183","task_revision_id":"1","upstream_id":"","short_description":"For each integer $n$, let $f(n)$ be the sum of the elements of the $n$th row…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"For each integer $n$, let $f(n)$ be the sum of the elements of the $n$th row (i.e. the row with $n+1$ elements) of Pascal's triangle minus the sum of all the elements from previous rows. For example, \\\\[f(2) = \\\\underbrace{(1 + 2 + 1)}_{\\\\text{2nd row}} - \\\\underbrace{(1 + 1 + 1)}_{\\\\text{0th and 1st rows}} = 1. \\\\]What is the minimum value of $f(n)$ for $n \\\\ge 2015$?\",\"type\":\"Counting & Probability\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}