Datasets:
messages listlengths 2 2 | expected_answer stringlengths 1 500 |
|---|---|
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\(a, b, c, d\\) be four positive integers. The integer \\(n\\) is the smallest positive integer such that the sum of every rational number of the form \\(\\frac{1}{a^2 + b^3 + c^8 + d^n}\\) do... | 25 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven that \\( p \\) is a prime number and \\( x \\) and \\( y \\) are natural numbers such that \\(\\frac{p^x - 1}{p-1} = 2^y\\), find the number of divisors of \\( xy \\).",
"reasoning_conten... | 4 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet an integer quadrilateral be a quadrilateral whose sides are all of integer length, whose diagonals form $4$ segments of integer length and whose area is also an integer. Find the area of an int... | 120 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven \\( x, y, z > 0 \\) such that \\( 2x + 4y + 7z = 2xyz \\), find the minimum of \\( S = x + y + z \\).",
"reasoning_content": "",
"role": "user"
},
{
"content": "To minimise \... | \displaystyle \frac{15}{2} |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn triangle \\(ABC\\), the altitude, angle bisector, and median from \\(C\\) divide angle \\(C\\) into four equal angles. Find angle \\(B\\).",
"reasoning_content": "",
"role": "user"
},
... | 22.5^{\circ} |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFor what values of parameter \\( m \\) does the equation \\( x^2 + (m+6)|x| + 2m + 9 = 0 \\) have two distinct solutions?",
"reasoning_content": "",
"role": "user"
},
{
"content": "... | \,m<-\dfrac92\, |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDetermine the minimum value of $\\frac{IA^3+IB^3+IC^3}{AB^3+BC^3+CA^3}$, where $ABC$ is any triangle, and $I$ is the incenter.",
"reasoning_content": "",
"role": "user"
},
{
"conten... | \displaystyle\frac{\sqrt3}{9} |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven hexagon $ABCDEF$ with $AB=FA=14$ and $BC=CD=DE=EF=4$, determine the length of $AD$.",
"reasoning_content": "",
"role": "user"
},
{
"content": "Because the hexagon can be inscr... | 16 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all increasing arithmetic progressions such that each term is the reciprocal of a positive integer and the sum of all terms is $1$.",
"reasoning_content": "",
"role": "user"
},
{
... | \displaystyle \frac16,\;\frac13,\;\frac12 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( A_1A_2\\cdots A_{2002} \\) be a regular 2002-sided polygon. Each vertex \\( A_i \\) is associated with a positive integer \\( a_i \\) such that if \\( j_1, j_2, \\ldots, j_k \\) are positiv... | 287287 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\(ABCD\\) be a parallelogram with points \\(X, Y, Z\\) lying on \\(AD, AB, BC\\) respectively such that \\(AX = CZ\\). Determine if the inequality \\(2(XY + YZ) \\ge AC + BD\\) is true.",
... | \,2\bigl(XY+YZ\bigr)\ge AC+BD\, |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the smallest $ c > 0 $ such that $ \\sum_{i=1}^n \\frac{b_i l_i}{L} - z \\le c $ holds for all possible input data.",
"reasoning_content": "",
"role": "user"
},
{
"content": "T... | 1 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nHow many corner turns are at least necessary to move a rectangular outdoor enclosure, which is 2 meters long and 1 meter wide, by exactly its width (1 meter) in the same direction, such that each c... | 3 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all integers \\( n \\) such that \\( 2^{n-1}n + 1 \\) is a perfect square.",
"reasoning_content": "",
"role": "user"
},
{
"content": "\\[\n\\text{Find all integers }n\\text{ su... | 5 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven a triangle \\(ABC\\) and an interior point \\(P\\), for a natural number \\(n > 2\\), what is the locus of point \\(P\\) that minimizes \\(PA^n + PB^n + PC^n\\)?",
"reasoning_content": ""... | \text{The sum }PA^{n}+PB^{n}+PC^{n}\text{ is uniquely minimised at the
interior point }P_{n}\text{ satisfying }
PA^{\,n-2}\,\overrightarrow{PA}+PB^{\,n-2}\,\overrightarrow{PB}
+PC^{\,n-2}\,\overrightarrow{PC}=0. |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet $\\triangle ABC$ have $\\angle A=20^{\\circ}$ and $\\angle C=40^{\\circ}$. The angle bisector $AL$ is drawn with $L \\in BC$, and the external angle bisector $CN$ is drawn with $N \\in AB$. Fin... | \,\angle CLN = 80^{\circ}\, |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all $k \\in \\mathbb{R}_{>-2}$ such that the inequality $\\frac{x}{x+y+kz} + \\frac{y}{y+z+kx} + \\frac{z}{z+x+ky} \\ge \\frac{3}{k+2}$ holds for all $x, y, z \\geq 0$.",
"reasoning_conten... | k\ge 1 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nHow many ways are there to cover a $3 \\times n$ grid $(n \\in \\mathbb{Z^{+}})$ using dominoes of size $1 \\times 2$ or $2 \\times 1$?",
"reasoning_content": "",
"role": "user"
},
{
... |
T(n)=
\begin{cases}
0, & n\ \text{odd},\\[4pt]
\displaystyle
\frac12\Bigl((2+\sqrt3)^{\,n/2}+(2-\sqrt3)^{\,n/2}\Bigr)
+\frac{1}{2\sqrt3}\Bigl((2+\sqrt3)^{\,n/2}-(2-\sqrt3)^{\,n/2}\Bigr),
& n\ \text{even}.
\end{cases}
|
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nAn octagon with side lengths 3, 3, 11, 11, 15, 15, 15, 15 cm is inscribed in a circle. What is the area of the octagon in cm²?",
"reasoning_content": "",
"role": "user"
},
{
"conten... | 567 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nTriangle ABC has integer-length sides, and AC = 2007. The internal bisector of angle BAC meets BC at D. Given that AB = CD, determine the lengths of AB and BC.",
"reasoning_content": "",
"r... | AB=1338,\qquad BC=2230 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet $D$ be a point on side $BC$ of $\\triangle ABC$ such that $AB:DC = 1$. If $\\angle B = 80^\\circ$ and $\\angle C = 20^\\circ$, find $\\angle BAD$ and $\\angle CAD$.",
"reasoning_content": "... | \angle BAD = 70^\circ,\qquad \angle CAD = 10^\circ |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nThere are $n$ people in a room, each assigned a unique hat. The hats are placed on a table, and every minute, each person picks a random hat. If a person picks their assigned hat, they leave the ro... | \,n\, |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven an equilateral triangle \\( \\triangle ABC \\) and any point \\( M \\) on the plane, find the maximum value of \n\\[ \\frac{MA + MB + MC}{MA^3 + MB^3 + MC^3}. \\]",
"reasoning_content": "... | 3 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( f(x) = (x^{1999} - 1)^{1999} \\). Find \\( f^{(1999)}(x) \\), the 1999th derivative of \\( f(x) \\).",
"reasoning_content": "",
"role": "user"
},
{
"content": "\\[\nf(x)=\\b... | \,f^{(1999)}(x)=1999!\displaystyle\sum_{j=0}^{1998}
(-1)^{j}\binom{1999}{j+1}\binom{1999(j+1)}{1999}\,x^{1999j}\, |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven three wooden squares with dimensions 2x2 dm, 3x3 dm, and 6x6 dm, how can they be cut into the least number of pieces to form a single square window shade?",
"reasoning_content": "",
"... | 6 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( a_n = 2^n + 3^n + 6^n - 1 \\). Find a natural number \\( m \\) such that \\( \\gcd(a_n, m) = 1 \\) for all \\( n \\in \\mathbb{N}^* \\).",
"reasoning_content": "",
"role": "user"
... | \,m=1\, |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nTwo players, A and B, play a game starting with a positive integer \\( N_0 \\) on the blackboard. A erases \\( N_0 \\) and writes \\( N_1 \\in \\{N_0 - 1, \\lfloor N_0 / 3 \\rfloor\\} \\). B erases... | \text{Player B has a winning strategy.} |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nHow many ways are there to put \\( n \\) balls into 3 buckets given that each bucket can only take a maximum of 6 balls?",
"reasoning_content": "",
"role": "user"
},
{
"content": "L... | \displaystyle
a_n=\sum_{k=0}^{\lfloor n/7\rfloor}(-1)^{k}\binom{3}{k}\binom{n-7k+2}{2}
|
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the number of positive integers \\( n < 3^8 \\) such that the number of positive integers \\( k \\) (where \\( 1 \\leq k \\leq \\frac{n}{3} \\)) for which \\( \\frac{n!}{(n-3k)! \\cdot k! \\cd... | 0 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn a $1000 \\times 1000$ array filled with integers between $1$ and $1000$ inclusive, with each integer appearing $1000$ times, what is the maximum value of $n$ such that there necessarily exists a... | 32 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the number of solutions of the equation $x^n - y^n = 2^{2000}$ in $\\mathbb{N}$.",
"reasoning_content": "",
"role": "user"
},
{
"content": "\\[\nx^{n}-y^{n}=2^{2000},\\qquad x,... | 999 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all non-negative integer solutions \\((a, b)\\) of the equation \\(a^3 = a(3b + 1) + 3T(b)\\), where \\(T(n)\\) is the \\(n\\)-th triangular number.",
"reasoning_content": "",
"role": ... | (a,b)=(0,0),\;(1,0),\;(5,5),\;(6,7) |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind a 3-tuple of positive numbers such that the sum of any two numbers in the tuple is a perfect square.",
"reasoning_content": "",
"role": "user"
},
{
"content": "Let \n\n\\[\na+... | (6,\;19,\;30) |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all positive integers \\( n \\) for which the equation \\( a + b + c + d = n\\sqrt{abcd} \\) has a solution in positive integers.",
"reasoning_content": "",
"role": "user"
},
{
... | \,1,\;2,\;3,\;4\, |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDetermine how many integers \\( a \\) in the range \\( 1 \\) to \\( 3^{2000} \\) satisfy \\( P(a) \\) being divisible by \\( 3^{2000} \\), where \\( P(x) = x^3 + 153x^2 - 111x + 38 \\).",
"reas... | 9 |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIf the incentre of $\\triangle ABC$ is the midpoint of the median $AD$, find $\\cos A$.",
"reasoning_content": "",
"role": "user"
},
{
"content": "\\[\n\\boxed{-1}\n\\]",
"reaso... | -1 |
End of preview. Expand in Data Studio
Polaris-Filtered Nemotron Easy Math (Verifiable)
A filtered subset of nvidia/Nemotron-Math-v2 (low / easy split), retaining only non-TIR samples with verifiable boxed answers.
Filtering Pipeline
- Remove TIR / tool-use samples — drop any sample that contains Python code blocks (
\``python,<|python_start|>,) or has a non-emptytools/tool` field. - Polaris decontamination — remove samples whose user prompt shares any 15-gram overlap with problems in POLARIS-Project/Polaris-Dataset-53K.
- Answer verification — keep only samples where the
\boxed{}answer in the assistant response matches theexpected_answerfield (verified via math-verify).
Dataset Statistics
| Metric | Value |
|---|---|
| Total samples | 268,631 |
| Min tokens | 99 |
| Max tokens | 31,802 |
| Mean tokens | 1,561.8 |
| Median tokens | 1,416.0 |
| P25 | 972 |
| P75 | 1,975 |
| P90 | 2,647 |
| P95 | 3,118 |
| P99 | 4,186 |
Token counts measured with Qwen/Qwen2.5-7B-Instruct (full conversation including reasoning + content).
Sequence Length Distribution
| Bucket | Count | Percentage |
|---|---|---|
| <2k | 203,591 | 75.8% |
| 2k-4k | 61,494 | 22.9% |
| 4k-6k | 3,281 | 1.2% |
| 6k-8k | 229 | 0.1% |
| 8k-10k | 30 | 0.0% |
| 10k-12k | 5 | 0.0% |
| 12k-14k | 0 | 0.0% |
| 14k-16k | 0 | 0.0% |
| 16k-18k | 0 | 0.0% |
| >18k | 1 | 0.0% |
Usage
from datasets import load_dataset
ds = load_dataset("devvrit/polaris_filtered_nemotron_easy_math_verifiable", split="train")
Source
- Base dataset: nvidia/Nemotron-Math-v2 —
data/low.jsonl - Decontamination reference: POLARIS-Project/Polaris-Dataset-53K
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