{"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":"d75715d6-a824-5f9c-94f2-03352854f92b","task_key":"intermediate~5falgebra--test--d75715d6-a824-5f9c-94f2-03352854f92b","task_revision_id":"1","upstream_id":"","short_description":"For every positive integer $n$, let $\\text{mod}_5 (n)$ be the remainder obtained…","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"For every positive integer $n$, let $\\\\text{mod}_5 (n)$ be the remainder obtained when $n$ is divided by 5. Define a function $f: \\\\{0,1,2,3,\\\\dots\\\\} \\\\times \\\\{0,1,2,3,4\\\\} \\\\to \\\\{0,1,2,3,4\\\\}$ recursively as follows:\\n\\n\\\\[f(i,j) = \\\\begin{cases}\\\\text{mod}_5 (j+1) & \\\\text{ if } i = 0 \\\\text{ and } 0 \\\\le j \\\\le 4 \\\\text{,}\\\\\\\\ f(i-1,1) & \\\\text{ if } i \\\\ge 1 \\\\text{ and } j = 0 \\\\text{, and} \\\\\\\\ f(i-1, f(i,j-1)) & \\\\text{ if } i \\\\ge 1 \\\\text{ and } 1 \\\\le j \\\\le 4. \\\\end{cases}\\\\]What is $f(2015,2)$?\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}