{"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":"ec909461-7393-593c-93af-bc2bc01b7dc9","task_key":"test--ec909461-7393-593c-93af-bc2bc01b7dc9","task_revision_id":"1","upstream_id":"","short_description":"Let $\\mathcal{C}$ be the hyperbola $y^{2}-x^{2}=1$. Given a point $P_{0}$ on the…","config":"","split":"test","body":"{\"problem\":\"Let $\\\\mathcal{C}$ be the hyperbola $y^{2}-x^{2}=1$. Given a point $P_{0}$ on the $x$-axis, we construct a sequence of points $\\\\left(P_{n}\\\\right)$ on the $x$-axis in the following manner: let $\\\\ell_{n}$ be the line with slope 1 passing through $P_{n}$, then $P_{n+1}$ is the orthogonal projection of the point of intersection of $\\\\ell_{n}$ and $\\\\mathcal{C}$ onto the $x$-axis. (If $P_{n}=0$, then the sequence simply terminates.) Let $N$ be the number of starting positions $P_{0}$ on the $x$-axis such that $P_{0}=P_{2008}$. Determine the remainder of $N$ when divided by 2008.\"}","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":[]}