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[ { "role": "user", "content": "\n\nLet $a_0=5/2$ and $a_k=a^2_{k-1}-2$ for $k\\geq1.$ Compute\n\n$$\\prod\\limits_{k=0}^{\\infty}\\left(1-\\frac{1}{a_k}\\right)$$\n\nin closed form.The answer is in the form \\frac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.\n\nMake sure to use \\boxed{} fo...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 121, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.375, "pass_rate_total": 8, "pass_rate_passed": 3, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $a_0=5/2$ and $a_...
[ { "role": "user", "content": "\n\nA triangle has vertices $P=(-8,5)$, $Q=(-15,-19)$, and $R=(1,-7)$. The equation of the bisector of $\\angle P$ can be written in the form $ax+2y+c=0$. Find $a+c$.\n[asy] import graph; pointpen=black;pathpen=black+linewidth(0.7);pen f = fontsize(10); pair P=(-8,5),Q=(-15,-19...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 231, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nA triangle has vertic...
[ { "role": "user", "content": "\n\nIn a chess tournament, each of two players has only one game played. After 2 rounds, 5 players left the tournament. At the end of the tournament, it was found that the total number of games played is 100. How many players were there at the start of the tournament?\n\nMake s...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 84, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0, "pass_rate_total": 8, "pass_rate_passed": 0, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nIn a chess tournament, eac...
[ { "role": "user", "content": "Please solve the following math problem. Your final answer should be inside \\boxed{}.\n\n在椭圆中, $A$ 为长轴的一个端点, $B$ 为短轴的一个端点, $F_{1}, F_{2}$ 为两个焦点. 若 $$ \\overline{A F_{1}} \\cdot \\overline{A F_{2}}+\\overrightarrow{B F_{1}} \\cdot \\overrightarrow{B F_{2}}=0, $$ 求 $\\tan \\angl...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 159, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Please solve the followin...
[ { "role": "user", "content": "Solve this problem. Enclose your final answer in \\boxed{}.\n\nIn the following sequence of numbers, each term, starting with the third, is obtained by adding three times the previous term plus twice the term before that to the previous one:\n\n$$a_1, a_2, 78, a_4, a_5, 3438, a...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 139, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.625, "pass_rate_total": 8, "pass_rate_passed": 5, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve this problem. Enclo...
[ { "role": "user", "content": "Solve the given math problem. Make sure your answer is inside \\boxed{}.\n\nForty slips of paper numbered $1$ to $40$ are placed in a hat. Alice and Bob each draw one number from the hat without replacement, keeping their numbers hidden from each other. Alice says, \"I can't te...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 158, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve the given math prob...
[ { "role": "user", "content": "\n\nDefine the sequence of positive integers $\\{a_n\\}$ as follows:\n- Let $a_1=1$, $a_2=3$.\n- For each $n>2$, let $a_n$ be the result of expressing $a_{n-1}$ in base $n-1$, then reading the resulting numeral in base $n$, then adding $2$ (in base $n$).\n\nFor example:\n- $a_2...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 165, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.625, "pass_rate_total": 8, "pass_rate_passed": 5, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nDefine the sequence o...
[ { "role": "user", "content": "\n\nThere are positive integers $x$ and $y$ that satisfy the system of equations \n$$\\begin{align*} \\log_{10} x + 2 \\log_{10} (\\mathrm{gcd}(x,y)) &= 60\\\\ \\log_{10} y + 2 \\log_{10} (\\mathrm{lcm}(x,y)) &= 570. \\end{align*}$$\n Let $m$ be the number of (not necessarily d...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 174, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nThere are positive in...
[ { "role": "user", "content": "\n\nLet $m$ and $n$ be positive integers such that\n$$(m^3 -27)(n^3- 27) = 27(m^2n^2 + 27):$$\nFind the maximum possible value of $m^3 + n^3$.\n\nDon't forget to put your answer in \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 85, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.5, "pass_rate_total": 8, "pass_rate_passed": 4, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $m$ and $n$ be posit...
[ { "role": "user", "content": "Solve the given math problem. Make sure your answer is inside \\boxed{}.\n\nTriangle $ABC$ has side lengths $AB=120, BC=220$, and $AC=180$. Lines $\\ell_A, \\ell_B$, and $\\ell_C$ are drawn parallel to $\\overline{BC}, \\overline{AC}$, and $\\overline{AB}$, respectively, such t...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 165, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.625, "pass_rate_total": 8, "pass_rate_passed": 5, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve the given math prob...
[ { "role": "user", "content": "Please solve this math problem. Put your final answer inside \\boxed{}.\n\nThe keystone arch is an ancient architectural feature. It is composed of congruent isosceles trapezoids fitted together along the non-parallel sides, as shown. The bottom sides of the two end trapezoids ...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 128, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0, "pass_rate_total": 8, "pass_rate_passed": 0, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Please solve this math proble...
[ { "role": "user", "content": "Please solve the following math problem. Your final answer should be inside \\boxed{}.\n\nFill in numbers in the boxes below so that the sum of the entries in each three consecutive boxes is $2005$. What is the number that goes into the leftmost box?\n\n```\n\\begin{asy}\nsize(...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 184, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.75, "pass_rate_total": 8, "pass_rate_passed": 6, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Please solve the following...
[ { "role": "user", "content": "\n\nThrough a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is \\(m\\) times the area of the squar...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 114, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.5, "pass_rate_total": 8, "pass_rate_passed": 4, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nThrough a point on the ...
[ { "role": "user", "content": "Find the solution to this math problem. Put your answer in \\boxed{}.\n\nZack keeps cutting the interval $[0, 1]$ of the number line, each time cutting at a uniformly random point in the interval, until the interval is cut into pieces, none of which have length greater than $\\...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 115, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.75, "pass_rate_total": 8, "pass_rate_passed": 6, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Find the solution to this ...
[ { "role": "user", "content": "\n\nLet $(1+\\sqrt{2})^{2012}=a+b\\sqrt{2}$, where $a$ and $b$ are integers. Find the greatest common divisor of $b$ and $81$.\n\nMake sure to use \\boxed{} for your answer." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 69, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $(1+\\sqrt{2})^{20...
[ { "role": "user", "content": "\n\nGiven an integer $n>1$, let $S_{n}$ be the group of permutations of the numbers $1,2, \\\\ldots, n$. Two players, A and B, play the following game. Taking turns, they select elements (one element at a time) from the group $S_{n}$. It is forbidden to select an element that h...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 159, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.625, "pass_rate_total": 8, "pass_rate_passed": 5, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nGiven an integer $n>1...
[ { "role": "user", "content": "Find the solution to this math problem. Put your answer in \\boxed{}.\n\nCall a positive integer $n$ [i]tubular [/i] if for any two distinct primes $p$ and $q$ dividing $n, (p + q) | n$. Find the number of tubular numbers less than $100,000$. (Integer powers of primes, includin...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 116, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.25, "pass_rate_total": 8, "pass_rate_passed": 2, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Find the solution to this ...
[ { "role": "user", "content": "Solve this problem. Enclose your final answer in \\boxed{}.\n\nFind the largest $n$ for which there exists a sequence $(a_0, a_1, \\ldots, a_n)$ of non-zero digits such that, for each $k$, $1 \\le k \\le n$, the $k$-digit number $\\overline{a_{k-1} a_{k-2} \\ldots a_0} = a_{k-1...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 181, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.25, "pass_rate_total": 8, "pass_rate_passed": 2, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve this problem. Enclos...
[ { "role": "user", "content": "\n\nLet $\\{a,b,c,d,e,f,g,h,i\\}$ be a permutation of $\\{1,2,3,4,5,6,7,8,9\\}$ such that $\\gcd(c,d)=\\gcd(f,g)=1$ and\n\\[(10a+b)^{c/d}=e^{f/g}.\\]\nGiven that $h>i$, evaluate $10h+i$.\n\nMake sure to use \\boxed{} for your answer." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 109, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.25, "pass_rate_total": 8, "pass_rate_passed": 2, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $\\{a,b,c,d,e,f,g,...
[ { "role": "user", "content": "\n\nThe diagram shows a regular pentagon $ABCDE$ and a square $ABFG$. Find the degree measure of $\\angle FAD$.\n\nDon't forget to put your answer in \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 49, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.125, "pass_rate_total": 8, "pass_rate_passed": 1, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nThe diagram shows a re...
[ { "role": "user", "content": "\n\nThe numbers $2^0, 2^1, \\dots , 2{}^1{}^5, 2{}^1{}^6 = 65536$ are written on a blackboard. You repeatedly take two numbers on the blackboard, subtract one form the other, erase them both, and write the result of the subtraction on the blackboard. What is the largest possibl...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 122, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.625, "pass_rate_total": 8, "pass_rate_passed": 5, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nThe numbers $2^0, 2^1...
[ { "role": "user", "content": "Solve the given math problem. Make sure your answer is inside \\boxed{}.\n\nEach number from the set $\\{1, 2, 3, 4, 5, 6, 7\\}$ must be written in each circle of the diagram, so that the sum of any three aligned numbers is the same (e.g., $A+D+E = D+C+B$). What number cannot b...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 104, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.25, "pass_rate_total": 8, "pass_rate_passed": 2, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve the given math probl...
[ { "role": "user", "content": "\n\nHow many ways are there to put 9 differently colored beads on a $3\\times3$ grid if the purple bead and the green bead cannot be adjacent (either horizontally, vertically, or diagonally), and rotations and reflections of the grid are considered the same?\n\nDon't forget to ...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 76, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.375, "pass_rate_total": 8, "pass_rate_passed": 3, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nHow many ways are ther...
[ { "role": "user", "content": "Please solve the following math problem. Your final answer should be inside \\boxed{}.\n\n$A$ store normally sells windows at $100$ each. This week the store is offering one free window for each purchase of four. Dave needs seven windows and Doug needs eight windows. How much w...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 134, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.5, "pass_rate_total": 8, "pass_rate_passed": 4, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Please solve the following ...
[ { "role": "user", "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\n给定实数 $a 、 b(a>b>0)$ ,将长为 $a$ 、宽为 $b$ 的矩形放入一个正方形内(包含边界)。问正方形的边至少为多长? 若 $a \\geqslant(\\sqrt{2}+1) b$, 则原始答案的形式为$\\frac{\\sqrt{m}}{n}(a+b)$,请给出m+n的值。" } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 122, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve the following math ...
[ { "role": "user", "content": "\n\nFind the least positive integer $m$ such that $m^2 - m + 11$ is a product of at least four not necessarily distinct primes.\n\nYour final answer should be in \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 53, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.375, "pass_rate_total": 8, "pass_rate_passed": 3, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nFind the least positiv...
[ { "role": "user", "content": "Solve the given math problem. Make sure your answer is inside \\boxed{}.\n\nNinth and tenth graders participated in a chess tournament. There were ten times as many tenth graders as ninth graders. The total score of tenth graders was 4.5 times that of the ninth graders. What wa...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 81, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.5, "pass_rate_total": 8, "pass_rate_passed": 4, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve the given math problem...
[ { "role": "user", "content": "\n\nLet $\\{a,b,c,d,e,f,g,h,i\\}$ be a permutation of $\\{1,2,3,4,5,6,7,8,9\\}$ such that $\\gcd(c,d)=\\gcd(f,g)=1$ and\n\\[(10a+b)^{c/d}=e^{f/g}.\\]\nGiven that $h>i$, evaluate $10h+i$.\n\nMake sure to use \\boxed{} for your answer." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 109, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.25, "pass_rate_total": 8, "pass_rate_passed": 2, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $\\{a,b,c,d,e,f,g,...
[ { "role": "user", "content": "\n\n在一个社交网站上有 2022 名用户,其中一些是朋友,朋友关系是相互且永久的. 从现在开始,两名陌生用户只有至少有两个公共朋友,才允许他们成为朋友. 问:初始时至少需要有多少对朋友,才能使得最终任两名用户都成为朋友?\n\nRemember to put your final answer inside \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 86, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0, "pass_rate_total": 8, "pass_rate_passed": 0, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\n在一个社交网站上有 2022 名用户,其中一些是朋友...
[ { "role": "user", "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nRandom sequences $a_1, a_2, . . .$ and $b_1, b_2, . . .$ are chosen so that every element in each sequence is chosen independently and uniformly from the set $\\{0, 1, 2, 3, . ....
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 155, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.125, "pass_rate_total": 8, "pass_rate_passed": 1, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve the following math ...
[ { "role": "user", "content": "Please solve this math problem. Put your final answer inside \\boxed{}.\n\nEach triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. The hypotenuse of the larger triangle is 16 centimeters. What is the number of centimet...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 451, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Please solve this math pr...
[ { "role": "user", "content": "Solve this problem. Enclose your final answer in \\boxed{}.\n\nLet $ABCD$ be a parallelogram with an area of 160. The diagonals $AC$ and $BD$ intersect at point $E$. Point $P$ is on the line segment $\\overline{AE}$ such that $EC = 4EP$. If the line $DP$ intersects $AB$ at poin...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 109, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.75, "pass_rate_total": 8, "pass_rate_passed": 6, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve this problem. Enclos...
[ { "role": "user", "content": "Solve the math problem below. Your answer should be placed inside \\boxed{}.\n\n给定正整数 $a$. 求函数 $f(x)=\\min \\{\\|x\\|,\\|a x\\|\\}$ 的最大值.($\\|x\\|$ 表示实数 $x$ 到与它最近整数的距离: $\\min \\{s, t\\}$ 表示实数 $s, t$ 中较小的数.)请提供当 $a = 3$ 时,最大值的形式为 \\frac{m}{n},请给出 m + n 的值。" } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 136, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0, "pass_rate_total": 8, "pass_rate_passed": 0, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve the math problem below....
[ { "role": "user", "content": "\n\nLet $ x$ be a real number such that the five numbers $ \\cos(2 \\pi x)$, $ \\cos(4 \\pi x)$, $ \\cos(8 \\pi x)$, $ \\cos(16 \\pi x)$, and $ \\cos(32 \\pi x)$ are all nonpositive. What is the smallest possible positive value of $ x$?The answer is in the form \frac{m}{n}, wh...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 138, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.75, "pass_rate_total": 8, "pass_rate_passed": 6, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $ x$ be a real num...
[ { "role": "user", "content": "\n\n有 2018 人围坐在圆桌旁玩游戏. 开始时,将 K 张牌任意发给这些人,可能有人没获得牌. 在每一轮中,选择某人从与他相邻两人的牌中各抽取一张牌,能这样做的前提是这两人都有牌. 若无法选出这样的人则游戏结束. 求 K 的最大值,使得无论开始时如何发牌以及接下来每一轮如何选人,有限轮后游戏一定会结束.\n\nMake sure to use \\boxed{} for your answer." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 118, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.5, "pass_rate_total": 8, "pass_rate_passed": 4, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\n有 2018 人围坐在圆桌旁玩游戏. 开始时,...
[ { "role": "user", "content": "\n\nIf integers $m$, $n$, and $k$ satisfy the equation $m^2 + n^2 + 1 = kmn$, what values can $k$ have?\n\nPlease enclose your answer in \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 58, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.25, "pass_rate_total": 8, "pass_rate_passed": 2, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nIf integers $m$, $n$, a...
[ { "role": "user", "content": "Work through this math problem and place your final answer in \\boxed{}.\n\nThere are $2024$ people, consisting of knights and liars, and some of them are friends. Each person was asked how many friends they have, and the possible answers were $0, 1, \\ldots, 2023$. Every knigh...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 107, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0, "pass_rate_total": 8, "pass_rate_passed": 0, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Work through this math proble...
[ { "role": "user", "content": "Solve the given math problem. Make sure your answer is inside \\boxed{}.\n\n若 \\triangle ABC 的内角 A,B,C 满足 \\sin A=\\cos B=\\tan C,求 \\cos^3A+\\cos^2A-\\cos A 的值.原始的答案是\\frac{m}{n}的形式,其中m、n是互质的。请给出最终m + n的值" } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 93, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve the given math probl...
[ { "role": "user", "content": "Find the solution to this math problem. Put your answer in \\boxed{}.\n\nFind the number of positive integers less than 100 that are divisors of 300." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 48, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Find the solution to this ...
[ { "role": "user", "content": "Please solve the following math problem. Your final answer should be inside \\boxed{}.\n\nMichael is celebrating his fifteenth birthday today. How many Sundays have there been in his lifetime?" } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 46, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.375, "pass_rate_total": 8, "pass_rate_passed": 3, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Please solve the following...
[ { "role": "user", "content": "\n\nGiven that $x, y,$ and $z$ are real numbers that satisfy:\n\\begin{align*} x &= \\sqrt{y^2-\\frac{1}{16}}+\\sqrt{z^2-\\frac{1}{16}}, \\\\ y &= \\sqrt{z^2-\\frac{1}{25}}+\\sqrt{x^2-\\frac{1}{25}}, \\\\ z &= \\sqrt{x^2 - \\frac 1{36}}+\\sqrt{y^2-\\frac 1{36}}, \\end{align*}\n...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 191, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.5, "pass_rate_total": 8, "pass_rate_passed": 4, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nGiven that $x, y,$ and ...
[ { "role": "user", "content": "\n\nLet $\\lfloor x \\rfloor$ be the greatest integer less than or equal to $x$. Determine the number of real solutions to the equation:\n\n$$4x^2 - 40 \\lfloor x \\rfloor + 51 = 0$$\n\nFill in the blank with the number of real solutions.\n\nRemember to put your final answer in...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 89, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $\\lfloor x \\rflo...
[ { "role": "user", "content": "\n\nLet $N$ be the second smallest positive integer that is divisible by every positive integer less than $7$. What is the sum of the digits of $N$?\n\nRemember to put your final answer inside \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 55, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $N$ be the second ...
[ { "role": "user", "content": "\n\nLet $S$ be the set of points $(x, y)$ in the Cartesian plane that satisfy\n\\[\\Big|\\big| |x|-2\\big|-1\\Big|+\\Big|\\big| |y|-2\\big|-1\\Big|=1.\\]What is the total length of all the lines that make up $S$?The answer is in the form k\\sqrt{m}+n,. Please provide the value ...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 119, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.75, "pass_rate_total": 8, "pass_rate_passed": 6, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $S$ be the set of ...
[ { "role": "user", "content": "\n\nKimberly borrows $1000$ dollars from Lucy, who charged interest of $5\\%$ per month (which compounds monthly). What is the least integer number of months after which Kimberly will owe more than twice as much as she borrowed?\n\nMake sure to use \\boxed{} for your answer." ...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 75, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nKimberly borrows $1000...
[ { "role": "user", "content": "\n\nHow many positive integers less than $555$ are either a perfect cube or a perfect square?\n\nRemember to put your final answer inside \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 42, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nHow many positive inte...
[ { "role": "user", "content": "Work through this math problem and place your final answer in \\boxed{}.\n\nIn parallelogram $ABCD$, the longer side is twice the shorter side. Let $XYZW$ be the quadrilateral formed by the internal bisectors of the angles of $ABCD$. If the area of $XYZW$ is $10$, find the area...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 86, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Work through this math pro...
[ { "role": "user", "content": "\n\nDetermine the smallest positive integer $N$ such that there exist 6 distinct integers $a_1, a_2, a_3, a_4, a_5, a_6 > 0$ satisfying:\n\n1. $N = a_1 + a_2 + a_3 + a_4 + a_5 + a_6$\n2. $N - a_i$ is a perfect square for $i = 1,2,3,4,5,6$.\n\nDon't forget to put your answer in ...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 129, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.25, "pass_rate_total": 8, "pass_rate_passed": 2, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nDetermine the smallest...
[ { "role": "user", "content": "Solve the given math problem. Make sure your answer is inside \\boxed{}.\n\nA convex equilateral pentagon with side length $2$ has two right angles. The greatest possible area of the pentagon is $m + \\sqrt{n}$, where $m$ and $n$ are positive integers. Find $100m + n$." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 82, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.25, "pass_rate_total": 8, "pass_rate_passed": 2, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve the given math proble...
[ { "role": "user", "content": "\n\n将一枚均匀的股子独立投郑三次, 所得的点数依次记为 $x, y, z$, 则事件 \" $\\mathrm{C}_{7}^{x}<\\mathrm{C}_{7}^{y}<\\mathrm{C}_{7}^{2}$ \"发生的概率为 $\\qquad$。原始的答案是\\frac{m}{n}的形式,其中m、n是互质的。请给出最终m + n的值\n\nYour final answer should be in \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 114, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.25, "pass_rate_total": 8, "pass_rate_passed": 2, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\n将一枚均匀的股子独立投郑三次, 所得的点数依...
[ { "role": "user", "content": "Solve the math problem below. Your answer should be placed inside \\boxed{}.\n\nLet $p_1, p_2, \\ldots, p_{25}$ are primes which don’t exceed 2004. Find the largest integer $T$ such that every positive integer $\\leq T$ can be expressed as sums of distinct divisors of $(p_1\\cd...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 113, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.375, "pass_rate_total": 8, "pass_rate_passed": 3, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve the math problem be...
[ { "role": "user", "content": "Solve this problem. Enclose your final answer in \\boxed{}.\n\nA unit cube is cut twice to form three triangular prisms, two of which are congruent, as shown in Figure 1. The cube is then cut in the same manner along the dashed lines shown in Figure 2. This creates nine pieces....
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 520, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.125, "pass_rate_total": 8, "pass_rate_passed": 1, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve this problem. Enclo...
[ { "role": "user", "content": "\n\nFind the number of permutations of the letters $AAABBBCCC$ where no letter appears in a position that originally contained that letter. For example, count the permutations $BBBCCCAAA$ and $CBCAACBBA$ but not the permutation $CABCACBAB$.\n\nPlease enclose your answer in \\bo...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 77, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nFind the number of per...
[ { "role": "user", "content": "Solve this problem. Enclose your final answer in \\boxed{}.\n\nSuppose that $p$ is the unique monic polynomial of minimal degree such that its coefficients are rational numbers and one of its roots is $\\sin \\frac{2\\pi}{7} + \\cos \\frac{4\\pi}{7}$. If $p(1) = \\frac{a}{b}$, ...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 111, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.375, "pass_rate_total": 8, "pass_rate_passed": 3, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve this problem. Enclo...
[ { "role": "user", "content": "\n\nLet $P$ be the product of all non-zero digits of the positive integer $n$. For example, $P(4) = 4$, $P(50) = 5$, $P(123) = 6$, $P(2009) = 18$. \nFind the value of the sum: $P(1) + P(2) + \\ldots + P(2008) + P(2009)$.\n\nDon't forget to put your answer in \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 126, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $P$ be the produc...
[ { "role": "user", "content": "\n\nLet $ ABC$ be a triangle with $ BC \\equal{} 2007$, $ CA \\equal{} 2008$, $ AB \\equal{} 2009$. Let $ \\omega$ be an excircle of $ ABC$ that touches the line segment $ BC$ at $ D$, and touches extensions of lines $ AC$ and $ AB$ at $ E$ and $ F$, respectively (so that $ C$ ...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 179, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.125, "pass_rate_total": 8, "pass_rate_passed": 1, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $ ABC$ be a trian...
[ { "role": "user", "content": "\n\n(a) Find a solution that is not identically zero, of the homogeneous linear differential equation $$( 3x^2+x-1 ){y}''- ( 9x^2+9x-2 ){y}'+( 18x+3 )y=0$$ Intelligent guessing of the form of a solution may be helpful. \n(b) Let $y=f(x)$ be the solution of the nonhomogeneous di...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 221, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.75, "pass_rate_total": 8, "pass_rate_passed": 6, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\n(a) Find a solution th...
[ { "role": "user", "content": "\n\n在世界杯足球赛前,F 国教练为了考察 A_1, A_2, \\cdots, A_7 这七名队员,准备让他们在三场训练比赛(每场 90 分钟)中都上场. 假设在比赛的任何时刻,这些队员中有且仅有一人在场上,且 A_1,A_2,A_3,A_4 每人上场的总时间(以分钟为单位)均能被 7 整除,A_5,A_6,A_7 每人上场的总时间(以分钟为单位)均能被 13 整除. 如果每场换人次数不限,那么,按每名队员上场的总时间计算,共有多少种不同的情况?\n\nYour final answer should be in \\boxed{}." } ...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 173, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.625, "pass_rate_total": 8, "pass_rate_passed": 5, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\n在世界杯足球赛前,F 国教练为了考察 A_...
[ { "role": "user", "content": "\n\nIf $\\frac{m}{n} = \\frac{4}{3}$ and $\\frac{r}{t} = \\frac{9}{14}$, find the value of $\\frac{3mr - nt}{4nt - 7mr}$. The original answer is in \\frac{a}{b} format, please give the value of a + b.\n\nPlease enclose your answer in \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 97, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.75, "pass_rate_total": 8, "pass_rate_passed": 6, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nIf $\\frac{m}{n} = \\fr...
[ { "role": "user", "content": "Please solve the following math problem. Your final answer should be inside \\boxed{}.\n\n设函数 f:\\{1,2,\\cdots,2019\\}\\rightarrow\\{-1,1\\},满足对任意 1\\leq k\\leq 2019,存在 1\\leq l\\leq 2019,使得\\ds{i:(l-i)(i-k)\\geq0}{}f(i)\\leq0.求 \\ds{i=1}{2019}f(i) 的最大值." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 130, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.375, "pass_rate_total": 8, "pass_rate_passed": 3, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Please solve the followin...
[ { "role": "user", "content": "\n\nThere are $22$ chairs around a round table. Find the minimum number $n$ such that for any group of $n$ people sitting at the table, there will always be two people with exactly $2$ or $8$ chairs between them.\n\nPlease enclose your answer in \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 73, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.25, "pass_rate_total": 8, "pass_rate_passed": 2, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nThere are $22$ chairs a...
[ { "role": "user", "content": "Please solve the following math problem. Your final answer should be inside \\boxed{}.\n\n已知正四棱雉 $\\Gamma$ 的高 $h=3$, 侧面与底面所成角 $\\theta=\\frac{\\pi}{3}$ 。先在正四棱雉 $\\Gamma$ 内放入一个内切球 $O_{1}$, 然后依次放入球 $O_{2}, O_{3}, \\cdots$, 使得后放入的各球均与前一个球及正四棱雉 $\\Gamma$的四个侧面都相切。则放入所有球的体积之和的原始答案为$\...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 155, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Please solve the followin...
[ { "role": "user", "content": "\n\nIf the remainder is $2013$ when a polynomial with coefficients from the set $\\{0,1,2,3,4,5\\}$ is divided by $x-6$, find the least possible value of the coefficient of $x$ in this polynomial.\n\nDon't forget to put your answer in \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 79, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nIf the remainder is $2...
[ { "role": "user", "content": "\n\nIn $\\triangle ABC$, $AC=BC$, and $m\\angle BAC=40^\\circ$. What is the number of degrees in angle $x$? [asy]\nsize(80);\ndraw((0,0)--(7,0));\ndraw((0,0)--(3,2)--(6,0));\nlabel(\"$A$\",(0,0),W);\nlabel(\"$B$\",(6,0),S);\nlabel(\"$C$\",(3,2),N);\nlabel(\"$x$\",(6,0),NE);\n[/...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 145, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.125, "pass_rate_total": 8, "pass_rate_passed": 1, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nIn $\\triangle ABC$, ...
[ { "role": "user", "content": "\n\n设 $E, F, G$ 分别是正四面体 $A B C D$ 的棱 $A B, B C, C D$ 的中点,求二面角 $C-F G-E$ 的大小。如果答案为 $\\pi-\\operatorname{arccot} x$,其原始答案的形式为\\frac{k\\sqrt{n}}{m},请计算k+m+n的值。\n\nPlease enclose your answer in \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 107, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\n设 $E, F, G$ 分别是正四面体 $...
[ { "role": "user", "content": "Solve the math problem below. Your answer should be placed inside \\boxed{}.\n\nVitya cut the chessboard along the borders of the cells into pieces of the same perimeter. It turned out that not all of the received parts are equal. What is the largest possible number of parts th...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 75, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0, "pass_rate_total": 8, "pass_rate_passed": 0, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve the math problem below. ...
[ { "role": "user", "content": "\n\nLet $ABCD$ be a parallelogram with area $15$. Points $P$ and $Q$ are the projections of $A$ and $C,$ respectively, onto the line $BD;$ and points $R$ and $S$ are the projections of $B$ and $D,$ respectively, onto the line $AC.$ See the figure, which also shows the relative ...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 433, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.75, "pass_rate_total": 8, "pass_rate_passed": 6, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $ABCD$ be a parall...
[ { "role": "user", "content": "\n\nJerry purchased some stock for $ \\$14,400$ at the same time that Susan purchased a bond for $ \\$6,250$. Jerry’s investment went up $20$ percent the first year, fell $10$ percent the second year, and rose another $20$ percent the third year. Susan’s investment grew at a co...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 127, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.375, "pass_rate_total": 8, "pass_rate_passed": 3, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nJerry purchased some ...
[ { "role": "user", "content": "\n\nLet $S$ be the sum of all real $x$ such that $4^x = x^4$. Find the nearest integer to $S$.\n\nDon't forget to put your answer in \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 55, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.625, "pass_rate_total": 8, "pass_rate_passed": 5, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $S$ be the sum of ...
[ { "role": "user", "content": "\n\nSuppose $a_1$, $a_2$, $\\ldots$, $a_{10}$ are nonnegative integers such that \\[\\sum_{k=1}^{10}a_k=15 \\text{ and } \\sum_{k=1}^{10}ka_k = 80.\\] Let $M$ and $m$ denote the maximum and minimum respectively of $\\sum_{k=1}^{10}k^2a_k$. Compute $M-m$.\n\nYour final answer sh...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 126, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.5, "pass_rate_total": 8, "pass_rate_passed": 4, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nSuppose $a_1$, $a_2$, $...
[ { "role": "user", "content": "\n\nFind the number of integers $x$ which satisfy the equation $(x^2-5x+5)^{x+5}=1$.\n\nMake sure to use \\boxed{} for your answer." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 51, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nFind the number of int...
[ { "role": "user", "content": "\n\nA right circular cone has base radius $r$ and height $h$. The cone lies on its side on a flat table. As the cone rolls on the surface of the table without slipping, the point where the cone's base meets the table traces a circular arc centered at the point where the vertex ...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 157, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.375, "pass_rate_total": 8, "pass_rate_passed": 3, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nA right circular cone...
[ { "role": "user", "content": "\n\nLeaving his house at noon, Jim walks at a constant rate of $4$ miles per hour along a $4$ mile square route returning to his house at $1$ PM. At a randomly chosen time between noon and $1$ PM, Sally chooses a random location along Jim's route and begins running at a constan...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 163, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.75, "pass_rate_total": 8, "pass_rate_passed": 6, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLeaving his house at n...
[ { "role": "user", "content": "\n\nHarold has $3$ red checkers and $3$ black checkers. Find the number of distinct ways that Harold can place these checkers in stacks. Two ways of stacking checkers are the same if each stack of the \frst way matches a corresponding stack in the second way in both size and co...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 147, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.375, "pass_rate_total": 8, "pass_rate_passed": 3, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nHarold has $3$ red ch...
[ { "role": "user", "content": "\n\nLet $ABCDEF$ be a regular hexagon with side length 10 inscribed in a circle $\\omega$. $X$, $Y$, and $Z$ are points on $\\omega$ such that $X$ is on minor arc $AB$, $Y$ is on minor arc $CD$, and $Z$ is on minor arc $EF$, where $X$ may coincide with $A$ or $B$ (and similarly...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 133, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $ABCDEF$ be a reg...
[ { "role": "user", "content": "\n\nKelvin the Frog likes numbers whose digits strictly decrease, but numbers that violate this condition in at most one place are good enough. In other words, if $d_i$ denotes the $i$th digit, then $d_i\\le d_{i+1}$ for at most one value of $i$. For example, Kelvin likes the n...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 137, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nKelvin the Frog likes...
[ { "role": "user", "content": "\n\n数列 \\{a_n\\} 定义如下:设 \\df{(2n)!}{n!(n+2024)!} 写成既约分数后的分母为 A(n),a_n 等于 2A(n) 的最大质因数,则 a_n 的最大值等于__________.\n\nDon't forget to put your answer in \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 86, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.125, "pass_rate_total": 8, "pass_rate_passed": 1, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\n数列 \\{a_n\\} 定义如下:设 \\...
[ { "role": "user", "content": "\n\nAna has \\(22\\) coins. She can take from her friends either \\(6\\) coins or \\(18\\) coins, or she can give \\(12\\) coins to her friends. She can perform these operations as many times as she wants. Find the least number of coins Ana can have.\n\nRemember to put your fin...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 82, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nAna has \\(22\\) coins...
[ { "role": "user", "content": "Solve this problem. Enclose your final answer in \\boxed{}.\n\n设 $f(x)$ 是定义在 $\\mathbf{R}$ 上的函数, 对任意实数 $x$ 有 $f(x+3) \\cdot f(x-4)=-1$. 又当 $0 \\leqslant x<7$ 时, $f(x)=\\log _{2}(9-x)$, 则 $f(-100)$ 的值为 \\qquad. 原始答案是以-\\frac{m}{n}的形式给出的,请提供m + n的值。" } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 138, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0, "pass_rate_total": 8, "pass_rate_passed": 0, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve this problem. Enclose y...
[ { "role": "user", "content": "Find the solution to this math problem. Put your answer in \\boxed{}.\n\nRose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular regions in her flower bed are as shown in the figure. She ...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 354, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.625, "pass_rate_total": 8, "pass_rate_passed": 5, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Find the solution to this...
[ { "role": "user", "content": "\n\n设函数$$f(x)=\\cos 2 x+2 \\sqrt{3} \\sin x^{\\circ} \\cos x(x \\in \\mathbf{R})$$的最大值为 $M$, 最小正周期为 $T$ 。(1) 求 $M 、 T$ 的值, 并写出函数 $f(x)$ 的单调递增区间;(2)若 10 个互不相等的正数 $x_{i}(i=1,2$, $\\cdots, 10)$ 满足 $f\\left(x_{i}\\right)=M$ ,且 $x_{i}<10 \\pi$ ,请给出满足条件的\\frac{m\\pi}{n}形式的答案中m+n的值。\n...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 181, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.5, "pass_rate_total": 8, "pass_rate_passed": 4, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\n设函数$$f(x)=\\cos 2 x+2 \...
[ { "role": "user", "content": "\n\nLet $S$ be a subset of the natural numbers such that $0 \\in S$, and for all $n \\in \\mathbb{N}$, if $n$ is in $S$, then both $2n+1$ and $3n+2$ are in $S$. What is the smallest number of elements $S$ can have in the range $\\{0,1,\\ldots, 2019\\}$?\n\nDon't forget to put y...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 116, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.625, "pass_rate_total": 8, "pass_rate_passed": 5, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $S$ be a subset o...
[ { "role": "user", "content": "\n\nLet $\\mathbf{u}$ and $\\mathbf{v}$ be unit vectors, and let $\\mathbf{w}$ be a vector such that $\\mathbf{u} \\times \\mathbf{v} + \\mathbf{u} = \\mathbf{w}$ and $\\mathbf{w} \\times \\mathbf{u} = \\mathbf{v}.$ Compute $\\mathbf{u} \\cdot (\\mathbf{v} \\times \\mathbf{w})...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 129, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $\\mathbf{u}$ and...
[ { "role": "user", "content": "Solve the given math problem. Make sure your answer is inside \\boxed{}.\n\nFor a natural number $p$, one can move between two points with integer coordinates if the distance between them equals $p$. Find all prime numbers $p$ for which it is possible to reach the point $(2002,...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 87, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.375, "pass_rate_total": 8, "pass_rate_passed": 3, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve the given math probl...
[ { "role": "user", "content": "Please solve this math problem. Put your final answer inside \\boxed{}.\n\nConsider the following sequence \\(\\left(a_{n}\\right)_{n=1}^{\\infty}=(1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,1, \\ldots)\\). Find all pairs \\((\\alpha, \\beta)\\) of positive real numbers such that \\(\\lim _...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 156, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0, "pass_rate_total": 8, "pass_rate_passed": 0, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Please solve this math proble...
[ { "role": "user", "content": "\n\nLet $a_1,a_2,\\ldots, a_{2013}$ be a permutation of the numbers from $1$ to $2013$. Let $A_n = \\frac{a_1 + a_2 + \\cdots + a_n}{n}$ for $n = 1,2,\\ldots, 2013$. If the smallest possible difference between the largest and smallest values of $A_1,A_2,\\ldots, A_{2013}$ is $\...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 157, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $a_1,a_2,\\ldots,...
[ { "role": "user", "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nThe members of a distinguished committee were choosing a president, and each member gave one vote to one of the $27$ candidates. For each candidate, the exact percentage of vote...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 101, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.75, "pass_rate_total": 8, "pass_rate_passed": 6, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Solve the following math p...
[ { "role": "user", "content": "Please solve this math problem. Put your final answer inside \\boxed{}.\n\nA stairway with three steps has three risers that are each 8 inches high and three treads that are each 10 inches deep. What is the area, in square inches, of this figure that is the side panel of the st...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 294, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Please solve this math pr...
[ { "role": "user", "content": "\n\nFind the sum of all possible $n$ such that $n$ is a positive integer and there exist real numbers $a, b, c$ such that for every integer $m$, the quantity \\( \\frac{2013m^3 + am^2 + bm + c}{n} \\) is an integer.\n\nMake sure to use \\boxed{} for your answer." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 90, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0, "pass_rate_total": 8, "pass_rate_passed": 0, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nFind the sum of all possib...
[ { "role": "user", "content": "Work through this math problem and place your final answer in \\boxed{}.\n\nFind the number of pairs $(n,C)$ of positive integers such that $C\\leq 100$ and $n^2+n+C$ is a perfect square." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 62, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0, "pass_rate_total": 8, "pass_rate_passed": 0, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Work through this math problem...
[ { "role": "user", "content": "Please solve the following math problem. Your final answer should be inside \\boxed{}.\n\n给定正整数 $n(n \\geqslant 2)$. 已知 $2 n$ 个正实数 $a_{1}, a_{2}, \\cdots, a_{2 n}$, 满足: \n$$ \n\\sum_{k=1}^{n} a_{2 k-1} \\cdot \\sum_{k=1}^{n} a_{2 k}=\\prod_{k=1}^{n} a_{2 k-1}+\\prod_{k=1}^{n}...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 215, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Please solve the followin...
[ { "role": "user", "content": "\n\nThe graphs of the equations\n$y=k, \\qquad y=\\sqrt{3}x+2k, \\qquad y=-\\sqrt{3}x+2k,$\nare drawn in the coordinate plane for $k=-10,-9,-8,\\ldots,9,10.\\,$ These 63 lines cut part of the plane into equilateral triangles of side $2/\\sqrt{3}.\\,$ How many such triangles are...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 118, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0, "pass_rate_total": 8, "pass_rate_passed": 0, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nThe graphs of the equatio...
[ { "role": "user", "content": "\n\nA \"chaisri\" figure is a triangle where the three vertices are vertices of a regular $2019$-gon. Two different chaisri figures may be formed by different regular $2019$-gons.\n\nA \"thubkaew\" figure is a convex polygon that can be dissected into multiple chaisri figures, ...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 135, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nA \"chaisri\" figure ...
[ { "role": "user", "content": "\n\nHow many integers $-11 \\leq n \\leq 11$ satisfy $(n-2)(n+4)(n + 8)<0$?\n\nYour final answer should be in \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 56, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.625, "pass_rate_total": 8, "pass_rate_passed": 5, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nHow many integers $-11...
[ { "role": "user", "content": "\n\nDetermine the largest integer $n$ such that $2^n$ divides the decimal representation given by some permutation of the digits $2$, $0$, $1$, and $5$. For example, $2^1$ divides $2150$. Note: The number may start with $0$.\n\nRemember to put your final answer inside \\boxed{}...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 84, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nDetermine the largest ...
[ { "role": "user", "content": "\n\nThe average (arithmetic mean) age of a group consisting of doctors and lawyers is 40. If the doctors average 35 years old and the lawyers average 50 years old, what is the ratio of the number of doctors to the number of lawyers? Express your answer as a simplified ratio in ...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 101, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.75, "pass_rate_total": 8, "pass_rate_passed": 6, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nThe average (arithmeti...
[ { "role": "user", "content": "\n\nFind all real values of $x$ such that $$\\frac{2x^2-3x}{x^2-x} + 5x -11 = \\frac{3x^2+5x+2}{x^2-1}.$$Enter all the solutions, separated by commas.The answer is in the form \frac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.\n\nYour final answer should be in...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 116, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0, "pass_rate_total": 8, "pass_rate_passed": 0, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nFind all real values of $...
[ { "role": "user", "content": "\n\nLet $x$ be a real number such that $3 \\sin^4 x - 2 \\cos^6 x = -\\frac{17}{25}$. Then, $3 \\cos^4 x - 2 \\sin^6 x = \\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $10m + n$.\n\nYour final answer should be in \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 105, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nLet $x$ be a real num...
[ { "role": "user", "content": "\n\nFind all positive integers $n$ such that the number $\\frac{(2n)!+1}{n!+1}$ is a positive integer.\n\nRemember to put your final answer inside \\boxed{}." } ]
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 51, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.75, "pass_rate_total": 8, "pass_rate_passed": 6, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "\n\nFind all positive integ...
[ { "role": "user", "content": "Work through this math problem and place your final answer in \\boxed{}.\n\n已知正四棱雉 $\\Gamma$ 的高为 3, 侧面与底面所成角为 $\\frac{\\pi}{3}$ 。先在 $\\Gamma$ 内放入一个内切球 $O_{1}$, 然后依次放入球 $O_{2}, O_{3}, O_{4}, \\cdots$, 使得后放入的各球与前一个球及 $\\Gamma$ 的四个侧面均相切,则放入的所有球的体积之和的原始答案为$\\frac{m\\pi}{n}$,请给出$m +...
{ "data_type": "nemotron_math_dapo17k", "num_tokens": 144, "agent_ref": { "type": "responses_api_agents", "name": "math_with_judge_simple_agent" }, "pass_rate": 0.875, "pass_rate_total": 8, "pass_rate_passed": 7, "dataset": "nano_v3_sft_profiled_dapo17k", "question": "Work through this math pr...
End of preview. Expand in Data Studio

Nemotron Nano RL Math 22K

Nemotron Nano RL Math 22K is a 22,056-example English mathematical reasoning dataset prepared for reinforcement learning with verifiable rewards (RLVR). It contains the DAPO-Math and Skywork math profiling components identified in the metadata of NVIDIA's Nemotron-3-Nano-RL-Training-Blend, represented in a compact prompt / label / metadata JSONL schema.

Each example contains a ready-to-use user prompt, a reference answer, and empirical pass-rate metadata from repeated model generations. The dataset contains problems and answer targets, not model responses or chain-of-thought traces.

Dataset summary

Property Value
Examples 22,056
Split train only
File nemotron-nano-rl-math-22k.jsonl
Format UTF-8 JSON Lines; one object per line
File size 24,183,051 bytes (about 23.1 MiB)
Unique metadata.question values 18,235
Prompt shape One user message per example
Token count (metadata.num_tokens) median 112; mean 125.3; 95th percentile 225; range 30–2,600
SHA-256 ab380cbae419b244a96ec818503eaaef40e8fbd0b01ed33569d5b8356f946cde

All 22,056 lines parse as JSON and contain the top-level fields prompt, label, and metadata.

Composition

Component metadata.data_type Examples Share Unique question texts
DAPO-Math profile nemotron_math_dapo17k 10,224 46.35% 6,403
Skywork math profile (excluding Omni-Math) nemotron_math_skywork_no_omni 11,832 53.65% 11,832
Total 22,056 100% 18,235

The corresponding internal dataset identifiers are nano_v3_sft_profiled_dapo17k and nano_v3_sft_profiled_skywork_no_omni.

The DAPO component contains 3,821 repeated occurrences of a metadata.question value; no question appears more than twice. The Skywork component has no repeated metadata.question values, and there is no exact question-text overlap between the two components. Repeated question text does not necessarily imply byte-identical records because prompts and profiling metadata can differ.

Upstream sources

Data structure

Each line follows this structure:

{
  "prompt": [
    {
      "role": "user",
      "content": "Solve the problem ... Put your answer in \\boxed{}."
    }
  ],
  "label": "",
  "metadata": {
    "data_type": "nemotron_math_dapo17k",
    "num_tokens": 121,
    "agent_ref": {
      "type": "responses_api_agents",
      "name": "math_with_judge_simple_agent"
    },
    "pass_rate": 0.375,
    "pass_rate_total": 8,
    "pass_rate_passed": 3,
    "dataset": "nano_v3_sft_profiled_dapo17k",
    "question": "...",
    "expected_answer": "10"
  }
}

Fields

  • prompt: A list containing exactly one user message. All prompts request a final answer using LaTeX \\boxed{} formatting.
  • label: A compatibility field. It is an empty string in every record and must not be used as the reference answer.
  • metadata.data_type: Reward/data routing identifier for the DAPO or Skywork component.
  • metadata.num_tokens: Precomputed token count for the prompt.
  • metadata.agent_ref: Verifier/agent configuration; all rows use responses_api_agents with math_with_judge_simple_agent.
  • metadata.pass_rate: Fraction of profiled generations that passed the verifier.
  • metadata.pass_rate_total: Number of profiled generations (8 or 16).
  • metadata.pass_rate_passed: Number of generations that passed.
  • metadata.dataset: Internal upstream component name.
  • metadata.question: Source question text before or alongside prompt templating.
  • metadata.expected_answer: Reference answer used for verification. This is the target field for training and evaluation.

For the DAPO component, prompt[0].content equals metadata.question. For the Skywork component, the prompt includes an answer-format instruction template around the source question, so consumers should use prompt as the canonical model input.

The file also contains 432 prompts with embedded Asymptote ([asy] ... [/asy]) diagram source.

Difficulty profiling

The pass-rate fields are internally consistent for every record:

pass_rate == pass_rate_passed / pass_rate_total
Component Generation counts Median pass rate Mean pass rate Range
DAPO-Math 8 for all 10,224 records 0.625 0.557 0–0.875
Skywork math 8 for 8,978 records; 16 for 2,854 records 0.250 0.363 0–0.9375
All records 0.500 0.453 0–0.9375

There are 5,312 zero-pass examples and no examples with a pass rate of 1.0. These values are empirical results for the profiling setup recorded by the upstream data pipeline; they should not be interpreted as model-independent measures of mathematical difficulty.

Loading the dataset

from datasets import load_dataset

dataset = load_dataset(
    "wflying/nemotron-nano-rl-math-22k",
    split="train",
)

example = dataset[0]
prompt = example["prompt"]
expected_answer = example["metadata"]["expected_answer"]
pass_rate = example["metadata"]["pass_rate"]

Do not train against label, which is empty by design. To remove the two records without a usable reference answer:

dataset = dataset.filter(
    lambda example: bool(example["metadata"]["expected_answer"])
)

For RLVR pipelines, metadata.agent_ref identifies the intended math-with-judge verifier family, while metadata.data_type can be used for source-specific routing or curriculum construction.

Data quality and validation

  • 22,056 of 22,056 lines are valid JSON.
  • Every record contains prompt, label, and metadata.
  • Every prompt contains exactly one user message and a \\boxed{} answer-format instruction.
  • Every profiling tuple satisfies pass_rate == pass_rate_passed / pass_rate_total.
  • Every expected_answer value is a string; 22,054 are non-empty and 2 are empty.
  • All top-level and metadata field types are consistent across the file.
  • The released file's SHA-256 is included above for integrity checking.

The two empty-answer rows have a pass rate of 0 and should normally be filtered before answer-supervised or verifier-based training. Structural validation does not constitute a manual correctness review of every problem or expected answer.

Intended use

This dataset is intended for research and development involving:

  • reinforcement learning with verifiable mathematical rewards;
  • curriculum construction using empirical pass rates;
  • evaluation of answer extraction and mathematical verification;
  • controlled comparisons between DAPO-Math and Skywork math mixtures;
  • mathematical reasoning post-training.

It should not be treated as a standalone benchmark because it contains only a training split and includes repeated question texts.

Limitations

  • label is empty in every record; the reference answer is stored in metadata.expected_answer.
  • Two records also have an empty metadata.expected_answer.
  • The dataset has no validation or test split.
  • The DAPO component contains 3,821 repeated question-text occurrences.
  • Pass rates depend on the upstream model, sampling configuration, prompt template, and verifier; they are not intrinsic difficulty scores.
  • The longest prompt has 2,600 tokens according to metadata.num_tokens.
  • Asymptote diagrams may not render in all training or inspection tools.
  • Source datasets may contain incorrect answers, malformed notation, ambiguous problems, contamination, or other source-specific issues.
  • This compilation has not been independently audited for personal information, harmful content, or overlap with downstream evaluations.

Users should validate reward behavior, answer coverage, deduplication requirements, and train/evaluation separation for their application.

Licensing and attribution

This release uses the ODC Attribution License (odc-by) metadata of the upstream nvidia/Nemotron-3-Nano-RL-Training-Blend.

The DAPO source repository declares Apache-2.0. The Skywork source card does not currently expose a single license identifier in its Hub metadata. Users should review and comply with the NVIDIA blend license and the terms and attribution requirements of each upstream source. This section is informational and is not legal advice.

Citation

Please cite and attribute the upstream dataset releases used by the component(s) in your work:

The DAPO project paper is available as DAPO: An Open-Source LLM Reinforcement Learning System at Scale, and the Skywork-OR1 report is available at arXiv:2505.22312.

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