{"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":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"db6d7e21-aee1-5809-aeb1-7e5ee78b0088","task_key":"test--db6d7e21-aee1-5809-aeb1-7e5ee78b0088","task_revision_id":"4","upstream_id":"","short_description":"Let $\\lfloor \\bullet \\rfloor$ denote the floor function. For nonnegative…","config":"","split":"test","body":"{\"problem\":\"Let $\\\\lfloor \\\\bullet \\\\rfloor$ denote the floor function. For nonnegative integers $a$ and $b$, their [i]bitwise xor[/i], denoted $a \\\\oplus b$, is the unique nonnegative integer such that $$ \\\\left \\\\lfloor \\\\frac{a}{2^k}  \\\\right \\\\rfloor+ \\\\left\\\\lfloor\\\\frac{b}{2^k} \\\\right\\\\rfloor - \\\\left\\\\lfloor \\\\frac{a\\\\oplus b}{2^k}\\\\right\\\\rfloor$$ is even for every $k \\\\ge 0$. Find all positive integers $a$ such that for any integers $x>y\\\\ge 0$, we have \\\\[ x\\\\oplus ax \\\\neq y \\\\oplus ay. \\\\]\\n\\n[i]Carl Schildkraut[/i]\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}