{"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":"fc4e8fb1-b3ce-5c72-8d58-f044b2ef0890","task_key":"precalculus--test--fc4e8fb1-b3ce-5c72-8d58-f044b2ef0890","task_revision_id":"1","upstream_id":"","short_description":"Let $\\mathbf{v}_1,$ $\\mathbf{v}_2,$ $\\dots,$ $\\mathbf{v}_k$ be unit vectors such…","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Let $\\\\mathbf{v}_1,$ $\\\\mathbf{v}_2,$ $\\\\dots,$ $\\\\mathbf{v}_k$ be unit vectors such that\\n\\\\[\\\\mathbf{v}_1 + \\\\mathbf{v}_2 + \\\\dots + \\\\mathbf{v}_k = \\\\begin{pmatrix} 6 \\\\\\\\ -5 \\\\end{pmatrix}.\\\\]Find the smallest possible value of $k.$\\n\\nNote: A unit vector is a vector of magnitude 1.\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}