{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"omni-math","formal_name":"Omni-MATH","introduction":"Omni-MATH evaluates mathematical reasoning on Olympiad-level problems. Its official dataset contains 4,428 problems accompanied by domain and difficulty information.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/KbsdJames/Omni-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":"111c2917-eddc-5d28-88c1-50b49a5d9baa","task_key":"test--111c2917-eddc-5d28-88c1-50b49a5d9baa","task_revision_id":"1","upstream_id":"","short_description":"Let $a_{1}, a_{2}, \\ldots, a_{2005}$ be real numbers such that…","config":"","split":"test","body":"{\"problem\":\"Let $a_{1}, a_{2}, \\\\ldots, a_{2005}$ be real numbers such that $$\\\\begin{array}{ccccccccccc} a_{1} \\\\cdot 1 & + & a_{2} \\\\cdot 2 & + & a_{3} \\\\cdot 3 & + & \\\\cdots & + & a_{2005} \\\\cdot 2005 & = & 0 \\\\\\\\ a_{1} \\\\cdot 1^{2} & + & a_{2} \\\\cdot 2^{2} & + & a_{3} \\\\cdot 3^{2} & + & \\\\cdots & + & a_{2005} \\\\cdot 2005^{2} & = & 0 \\\\\\\\ a_{1} \\\\cdot 1^{3} & + & a_{2} \\\\cdot 2^{3} & + & a_{3} \\\\cdot 3^{3} & + & \\\\cdots & + & a_{2005} \\\\cdot 2005^{3} & = & 0 \\\\\\\\ \\\\vdots & & \\\\vdots & & \\\\vdots & & & & \\\\vdots & & \\\\vdots \\\\\\\\ a_{1} \\\\cdot 1^{2004} & + & a_{2} \\\\cdot 2^{2004} & + & a_{3} \\\\cdot 3^{2004} & + & \\\\cdots & + & a_{2005} \\\\cdot 2005^{2004} & = & 0 \\\\end{array}$$ and $$a_{1} \\\\cdot 1^{2005}+a_{2} \\\\cdot 2^{2005}+a_{3} \\\\cdot 3^{2005}+\\\\cdots+a_{2005} \\\\cdot 2005^{2005}=1$$ What is the value of $a_{1}$?\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}