uuid large_string | messages large list | expected_answer large_string | tools large list | source large_string | license large_string |
|---|---|---|---|---|---|
ultra_dsv4_cot_aops_rs0_000000001 | [
{
"role": "user",
"content": "Let \\( A' \\), \\( B' \\), and \\( C' \\) be the feet of the altitudes of a nonright triangle \\( ABC \\) issued from \\( A \\), \\( B \\), and \\( C \\) respectively. Let \\( D \\), \\( E \\), and \\( F \\) be the incenters of triangles \\( AB'C' \\), \\( BC'A' \\), and \\( C... | \( \frac{1}{2} \sqrt{\frac{(b+c-a)(c+a-b)(a+b-c)}{a+b+c}} \) | [] | nvidia/Nemotron-SFT-Math-v4 | cc-by-4.0 |
ultra_dsv4_cot_aops_rs0_000000003 | [{"role":"user","content":"Through the vertex of a regular quadrangular pyramid a cutting plane is d(...TRUNCATED) | $S=\frac{a^2\sqrt {\cos \alpha }}{4\sin\frac{\alpha }{2}\sin\varphi }$ | [] | nvidia/Nemotron-SFT-Math-v4 | cc-by-4.0 |
ultra_dsv4_cot_aops_rs0_000000007 | [{"role":"user","content":"Let $n$ be a natural number. We call a pair of numbers $annoying$ if thei(...TRUNCATED) | \displaystyle
\Big\lceil\frac{1+\pi(2n)-\pi(n)}{2}\Big\rceil | [] | nvidia/Nemotron-SFT-Math-v4 | cc-by-4.0 |
ultra_dsv4_cot_aops_rs0_000000010 | [{"role":"user","content":"The product of a two-digit number and 4 is equal to the product of the sa(...TRUNCATED) | 0 | [] | nvidia/Nemotron-SFT-Math-v4 | cc-by-4.0 |
ultra_dsv4_cot_aops_rs0_000000014 | [{"role":"user","content":"A local daily newspaper sells for $1.50/week with a circulation of 80,000(...TRUNCATED) | "p^{*}\\approx \\$1.53\\ \\text{per week},\\qquad a^{*}\\approx \\$460\\ \\text{per advertising page(...TRUNCATED) | [] | nvidia/Nemotron-SFT-Math-v4 | cc-by-4.0 |
ultra_dsv4_cot_aops_rs0_000000016 | [{"role":"user","content":"For which values of \\( n \\geq 3 \\) does the equation \\( x^n + y^n = z(...TRUNCATED) | n\text{ even, i.e. }n=2k\text{ with }k\ge2\;(n=4,6,8,\dots) | [] | nvidia/Nemotron-SFT-Math-v4 | cc-by-4.0 |
ultra_dsv4_cot_aops_rs0_000000019 | [{"role":"user","content":"Classify all finite groups of order $140$.\nPlease reason step by step, a(...TRUNCATED) | 11 | [] | nvidia/Nemotron-SFT-Math-v4 | cc-by-4.0 |
ultra_dsv4_cot_aops_rs0_000000021 | [{"role":"user","content":"There are eight seats at a round table, numbered one through eight. Four (...TRUNCATED) | 280 | [] | nvidia/Nemotron-SFT-Math-v4 | cc-by-4.0 |
ultra_dsv4_cot_aops_rs0_000000022 | [{"role":"user","content":"Find the value of \\( p \\) such that \\( x^3 + y^3 + z^3 - 3xyz \\ge p |(...TRUNCATED) | \( \sqrt{9+6\sqrt{3}} \) | [] | nvidia/Nemotron-SFT-Math-v4 | cc-by-4.0 |
ultra_dsv4_cot_aops_rs0_000000028 | [{"role":"user","content":"In square \\(ABCD\\) with side length 12, points \\(E\\), \\(G\\), and \\(...TRUNCATED) | 4\sqrt5 | [] | nvidia/Nemotron-SFT-Math-v4 | cc-by-4.0 |
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