answers listlengths 1 1 | datasets listlengths 1 1 | id stringlengths 64 64 | messages listlengths 1 1 | prompt stringlengths 10 3.97k | reference_answer_raw stringlengths 9 3.95k | source stringclasses 11
values | source_records stringlengths 283 1.44k | verifiability dict |
|---|---|---|---|---|---|---|---|---|
[
"127"
] | [
"skywork"
] | f533c4fe953019b4c8ca120c2358183e4d6163a70d79ba2681656af4c966d872 | [
{
"content": "If $\\frac{3}{5}=\\frac{M}{45}=\\frac{60}{N}$, what is $M+N$?",
"role": "user"
}
] | If $\frac{3}{5}=\frac{M}{45}=\frac{60}{N}$, what is $M+N$? | "[\"127\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108061, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117996"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | b5a4bae8c43bea4daef1bbb99deebf5f7186022ab28ac1cce5b31e1463ab3cf9 | [
{
"content": "16. $G$ and $H$ are midpoints of two adjacent edges of a cube. A trapezium-shaped cross-section is formed cutting through $G$, $H$ and two further vertices, as shown. The edge-length of the cube is $2 \\sqrt{2}$.\nWhat is the area of the trapezium?\nA 9\nB 8\nC $4 \\sqrt{5}$\nD $4 \\sqrt{3}$\nE $4... | 16. $G$ and $H$ are midpoints of two adjacent edges of a cube. A trapezium-shaped cross-section is formed cutting through $G$, $H$ and two further vertices, as shown. The edge-length of the cube is $2 \sqrt{2}$.
What is the area of the trapezium?
A 9
B 8
C $4 \sqrt{5}$
D $4 \sqrt{3}$
E $4 \sqrt{2}$ | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108041, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117997"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"303369"
] | [
"skywork"
] | cb87e9c7192c726c033c49f572a0c1a8e5cb6e8f729c84622df79cae1292b625 | [
{
"content": "Find the largest six-digit number in which each digit, starting from the third, is the sum of the two preceding digits.",
"role": "user"
}
] | Find the largest six-digit number in which each digit, starting from the third, is the sum of the two preceding digits. | "[\"303369\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108070, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117998"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"25"
] | [
"skywork"
] | dd86c4a7a58c14468205abad48016373fddcf7fb777261670fa21f08df777e8a | [
{
"content": "Let $a,b,c$ be the roots of the cubic $x^3 + 3x^2 + 5x + 7$. Given that $P$ is a cubic polynomial such that $P(a)=b+c$, $P(b) = c+a$, $P(c) = a+b$, and $P(a+b+c) = -16$, find $P(0)$.\n\n[i]Author: Alex Zhu[/i]",
"role": "user"
}
] | Let $a,b,c$ be the roots of the cubic $x^3 + 3x^2 + 5x + 7$. Given that $P$ is a cubic polynomial such that $P(a)=b+c$, $P(b) = c+a$, $P(c) = a+b$, and $P(a+b+c) = -16$, find $P(0)$.
[i]Author: Alex Zhu[/i] | "[\"25\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108051, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117999"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\binom{n}{3}"
] | [
"skywork"
] | e56f25e070f0ad18a97ba3fd3da5ddeb9c2e957f2d6fca0aa82dbd7cce9177eb | [
{
"content": "Set $T\\subset\\{1,2,\\dots,n\\}^3$ has the property that for any two triplets $(a,b,c)$ and $(x,y,z)$ in $T$, we have $a<b<c$, and also, we know that at most one of the equalities $a=x$, $b=y$, $c=z$ holds. Maximize $|T|$.",
"role": "user"
}
] | Set $T\subset\{1,2,\dots,n\}^3$ has the property that for any two triplets $(a,b,c)$ and $(x,y,z)$ in $T$, we have $a<b<c$, and also, we know that at most one of the equalities $a=x$, $b=y$, $c=z$ holds. Maximize $|T|$. | "[\"\\\\binom{n}{3}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108058, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118000"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"0.73r"
] | [
"skywork"
] | 6ebb59d7bdd08457f14cc7f4b0e0d67e9d200f4ed4eb2e6796cd12a87ba2f57f | [
{
"content": "The ratio of the areas of two concentric circles is $1: 3$. If the radius of the smaller is $r$, then the difference between the radii is best approximated by:",
"role": "user"
}
] | The ratio of the areas of two concentric circles is $1: 3$. If the radius of the smaller is $r$, then the difference between the radii is best approximated by: | "[\"0.73r\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108035, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118001"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"[-6,\\frac{25}{4}]"
] | [
"skywork"
] | 057f02c9be9fbc1837c31f2820b7c73607db9f0fcccb8d506a9710962fc83cc1 | [
{
"content": "Example 5 Find the range of the function $y=\\left|x^{2}-4\\right|-3 x(-2 \\leqslant x \\leqslant 5)$.",
"role": "user"
}
] | Example 5 Find the range of the function $y=\left|x^{2}-4\right|-3 x(-2 \leqslant x \leqslant 5)$. | "[\"[-6,\\\\frac{25}{4}]\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108075, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118003"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"401"
] | [
"skywork"
] | a6dcb3921b6c4237afbbd54582ea799f54799c1768db004d9f0116e7dad23ec7 | [
{
"content": "Example 18 (1985 3rd American Invitational Mathematics Examination) The general term of the sequence $101,104,116, \\cdots$ is $a_{n}=100+n^{2}$, where $n=1,2,3, \\cdots$. For each $n$, let $d_{n}$ denote the greatest common divisor of $a_{n}$ and $a_{n+1}$. Find the maximum value of $d_{n}$, wher... | Example 18 (1985 3rd American Invitational Mathematics Examination) The general term of the sequence $101,104,116, \cdots$ is $a_{n}=100+n^{2}$, where $n=1,2,3, \cdots$. For each $n$, let $d_{n}$ denote the greatest common divisor of $a_{n}$ and $a_{n+1}$. Find the maximum value of $d_{n}$, where $n$ takes all positive... | "[\"401\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108068, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118004"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | 337cb535c5870b7408b85b1c06f7a6cc57e63e33b62826706fd82d1531465d0f | [
{
"content": "2. A line with a slope of $\\frac{2}{21} \\sqrt{21}$ passing through the foci of the hyperbola $16 x^{2}-9 y^{2}=144$ intersects the hyperbola. Find the length of the chord intercepted.",
"role": "user"
}
] | 2. A line with a slope of $\frac{2}{21} \sqrt{21}$ passing through the foci of the hyperbola $16 x^{2}-9 y^{2}=144$ intersects the hyperbola. Find the length of the chord intercepted. | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108047, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118005"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"126"
] | [
"skywork"
] | 86486f4b2fb918baf8e90e4d8f765154a4c3ef170fb9764a9ef8c94658cde331 | [
{
"content": "Let $a$ , $b$ , $c$ , and $d$ be positive real numbers such that \n\\[\\begin{array}{c@{\\hspace{3pt}} c@{\\hspace{3pt}} c@{\\hspace{3pt}} c@{\\hspace{3pt}}c}a^2+b^2&=&c^2+d^2&=&2008, ac&=&bd&=&1000.\\end{array}\\]If $S=a+b+c+d$ , compute the value of $\\lfloor S\\rfloor$ .",
"role": "u... | Let $a$ , $b$ , $c$ , and $d$ be positive real numbers such that
\[\begin{array}{c@{\hspace{3pt}} c@{\hspace{3pt}} c@{\hspace{3pt}} c@{\hspace{3pt}}c}a^2+b^2&=&c^2+d^2&=&2008, ac&=&bd&=&1000.\end{array}\]If $S=a+b+c+d$ , compute the value of $\lfloor S\rfloor$ . | "[\"126\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108053, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118006"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 8f571b77eae370c756e4680af7033b545d211779d087538a8d0b49a9cd8c2ef7 | [
{
"content": "9. (16 points) Let the real-coefficient polynomial\n$$\nP_{i}(x)=x^{2}+b_{i} x+c_{i}\\left(b_{i}, c_{i} \\in \\mathbf{R}, i=1,2, \\cdots, n\\right)\n$$\n\nbe distinct, and for any $1 \\leqslant i<j \\leqslant n, P_{i}(x)+$ $P_{j}(x)$ has exactly one real root. Find the maximum value of $n$.",
... | 9. (16 points) Let the real-coefficient polynomial
$$
P_{i}(x)=x^{2}+b_{i} x+c_{i}\left(b_{i}, c_{i} \in \mathbf{R}, i=1,2, \cdots, n\right)
$$
be distinct, and for any $1 \leqslant i<j \leqslant n, P_{i}(x)+$ $P_{j}(x)$ has exactly one real root. Find the maximum value of $n$. | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108062, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118007"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | d36611a2ed86fe73cccdcd00346aaa9579c0acbf806876d25017c12e0acedbf2 | [
{
"content": "## Task 1\n\nAll pioneers compete in good deeds for the Day of the Republic. Class 1a has collected 12 marks worth of recyclables.\n\nClass $1 \\mathrm{~b}$ achieved 5 marks less.\n\nHow many marks did Class $1 \\mathrm{~b}$ donate?",
"role": "user"
}
] | ## Task 1
All pioneers compete in good deeds for the Day of the Republic. Class 1a has collected 12 marks worth of recyclables.
Class $1 \mathrm{~b}$ achieved 5 marks less.
How many marks did Class $1 \mathrm{~b}$ donate? | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108073, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118008"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1110_4"
] | [
"skywork"
] | 0e8af2016d2c86ea1ff9a27f85b39c958e73afb7e333e82cb0fa209efbe5a228 | [
{
"content": "Find $120_4\\times13_4\\div2_4$. Express your answer in base 4.",
"role": "user"
}
] | Find $120_4\times13_4\div2_4$. Express your answer in base 4. | "[\"1110_4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108081, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118009"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{25}{4}"
] | [
"skywork"
] | 91f9e74a69a494f17d1cff8bf2ac40c37f4138ff0d37cdfff76567a44237bcf1 | [
{
"content": "Solve for $x$: $x = \\dfrac{35}{6-\\frac{2}{5}}$.",
"role": "user"
}
] | Solve for $x$: $x = \dfrac{35}{6-\frac{2}{5}}$. | "[\"\\\\frac{25}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108092, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118010"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"12"
] | [
"skywork"
] | 6418b1aaa725d59c4b74a482d75dc68d93f2352ade15900f6f82960e5553b13e | [
{
"content": "Sandhya must save 35 files onto disks, each with 1.44 MB space. 5 of the files take up 0.6 MB, 18 of the files take up 0.5 MB, and the rest take up 0.3 MB. Files cannot be split across disks. Calculate the smallest number of disks needed to store all 35 files.",
"role": "user"
}
] | Sandhya must save 35 files onto disks, each with 1.44 MB space. 5 of the files take up 0.6 MB, 18 of the files take up 0.5 MB, and the rest take up 0.3 MB. Files cannot be split across disks. Calculate the smallest number of disks needed to store all 35 files. | "[\"12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108074, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118011"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{34}"
] | [
"skywork"
] | 8802a91436a5e88022b64cf309b827e3933d0116ebd6dcbe604c3bf94eb6271f | [
{
"content": "It is known that the ellipse $C_1$ and the parabola $C_2$ have a common focus $F(1,0)$. The center of $C_1$ and the vertex of $C_2$ are both at the origin. A line $l$ passes through point $M(4,0)$ and intersects the parabola $C_2$ at points $A$ and $B$ (with point $A$ in the fourth quadrant).\n1. ... | It is known that the ellipse $C_1$ and the parabola $C_2$ have a common focus $F(1,0)$. The center of $C_1$ and the vertex of $C_2$ are both at the origin. A line $l$ passes through point $M(4,0)$ and intersects the parabola $C_2$ at points $A$ and $B$ (with point $A$ in the fourth quadrant).
1. If $|MB| = 4|AM|$, find... | "[\"\\\\sqrt{34}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108037, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118012"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"70"
] | [
"skywork"
] | 32162c861b413bc654e5c64fa4cec790f6d6dd97e090753f3cad07141b7da126 | [
{
"content": "Find the smallest positive integer $n$ with the following property: there does not exist an arithmetic progression of $1999$ real numbers containing exactly $n$ integers.",
"role": "user"
}
] | Find the smallest positive integer $n$ with the following property: there does not exist an arithmetic progression of $1999$ real numbers containing exactly $n$ integers. | "[\"70\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108078, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118013"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"12"
] | [
"skywork"
] | 7b8de34c5f8f9e700680e6737a06020c7a8a434a1d8f748673274d9570f8bab3 | [
{
"content": "4. Which number should replace the symbol * in the equation $2 \\times 18 \\times 14=6 \\times * \\times 7$ to make it correct?\nA 8\nB 9\nC 10\nD 12\nE 15",
"role": "user"
}
] | 4. Which number should replace the symbol * in the equation $2 \times 18 \times 14=6 \times * \times 7$ to make it correct?
A 8
B 9
C 10
D 12
E 15 | "[\"12\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108085, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118014"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{5\\sqrt{7}}{14}"
] | [
"skywork"
] | 0fb0ab33756250a4fda9e44472833111bb28058135d9fa22f4a76e443771ec83 | [
{
"content": "Given non-zero vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfying $|\\overrightarrow{a}| = |\\overrightarrow{b}| = |\\overrightarrow{a} + \\overrightarrow{b}|$, the cosine of the angle between $\\overrightarrow{a}$ and $2\\overrightarrow{a} - \\overrightarrow{b}$ is ______.",
"... | Given non-zero vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfying $|\overrightarrow{a}| = |\overrightarrow{b}| = |\overrightarrow{a} + \overrightarrow{b}|$, the cosine of the angle between $\overrightarrow{a}$ and $2\overrightarrow{a} - \overrightarrow{b}$ is ______. | "[\"\\\\frac{5\\\\sqrt{7}}{14}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108071, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118016"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | 027c9b105527bb1d90f32c13838843a2047e42bf806d9014015d21ab82a574d3 | [
{
"content": "4. In my school, $60 \\%$ of the teachers come to school by bicycle. There are 45 teachers who come to school by bicycle. Only $12 \\%$ come to school by car. How many teachers come to school by car?\nA 4\nB 6\nC 9\nD 10\nE 12",
"role": "user"
}
] | 4. In my school, $60 \%$ of the teachers come to school by bicycle. There are 45 teachers who come to school by bicycle. Only $12 \%$ come to school by car. How many teachers come to school by car?
A 4
B 6
C 9
D 10
E 12 | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108091, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118017"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"skywork"
] | 5291547d1477f15cd3fcc6430367d1e0263463b6d044bd7d98ff03f9964b87e4 | [
{
"content": "4. Anton was given a scale, and he started weighing his toys. A car was balanced by a ball and two cubes, and a car with a cube - two balls. How many cubes balance a car? (All of Anton's balls are the same, and the cubes are the same too.)",
"role": "user"
}
] | 4. Anton was given a scale, and he started weighing his toys. A car was balanced by a ball and two cubes, and a car with a cube - two balls. How many cubes balance a car? (All of Anton's balls are the same, and the cubes are the same too.) | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108086, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118018"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"135^{\\circ}"
] | [
"skywork"
] | 05108be371491077864093eee23d0cf5916b09597103ac822cfe1001e13522c4 | [
{
"content": "2. In $\\triangle A B C$, it is known that $\\angle A C B=45^{\\circ}, D$ is any point on side $A B$ other than points $A$ and $B$, and the circumcenters of $\\triangle A B C$, $\\triangle A D C$, and $\\triangle B D C$ are $O$, $O_{1}$, and $O_{2}$, respectively. Then the degree measure of $\\ang... | 2. In $\triangle A B C$, it is known that $\angle A C B=45^{\circ}, D$ is any point on side $A B$ other than points $A$ and $B$, and the circumcenters of $\triangle A B C$, $\triangle A D C$, and $\triangle B D C$ are $O$, $O_{1}$, and $O_{2}$, respectively. Then the degree measure of $\angle O_{1} O O_{2}$ is $\qquad$... | "[\"135^{\\\\circ}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108080, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118019"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"(6,25,29,1),(7,15,20,1),(9,10,17,1),(5,12,13,1),(6,8,10,1),(3,4,5,2)"
] | [
"skywork"
] | fc98955756e724ace32ee1d71764f836a890ff47a0f98cde2d40883c0e0df5cc | [
{
"content": "Find the lengths of the three sides of a triangle that satisfy the following conditions.\n(1) The side lengths are integers;\n(2) The perimeter is an integer multiple of the area.",
"role": "user"
}
] | Find the lengths of the three sides of a triangle that satisfy the following conditions.
(1) The side lengths are integers;
(2) The perimeter is an integer multiple of the area. | "[\"(6,25,29,1),(7,15,20,1),(9,10,17,1),(5,12,13,1),(6,8,10,1),(3,4,5,2)\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108069, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118020"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"9\\sqrt{3}"
] | [
"skywork"
] | fe2359556ec8eb6b9662e94ade14fc94f762df0ba17055eba43c8dd98a9c61f8 | [
{
"content": "Given triangle $ABC$ where $AB=6$, $\\angle A=30^\\circ$, and $\\angle B=120^\\circ$, find the area of $\\triangle ABC$.",
"role": "user"
}
] | Given triangle $ABC$ where $AB=6$, $\angle A=30^\circ$, and $\angle B=120^\circ$, find the area of $\triangle ABC$. | "[\"9\\\\sqrt{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108094, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118021"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"(8\\sqrt{11}, 71\\sqrt{11}), (-8\\sqrt{11}, -71\\sqrt{11})"
] | [
"skywork"
] | c6e248e863574d239bfd519f9678237db153f703ec2d3b93015c426a399a3cee | [
{
"content": "Let $a$ be a real number such that $\\left(a + \\frac{1}{a}\\right)^2=11$. What possible values can $a^3 + \\frac{1}{a^3}$ and $a^5 + \\frac{1}{a^5}$ take?",
"role": "user"
}
] | Let $a$ be a real number such that $\left(a + \frac{1}{a}\right)^2=11$. What possible values can $a^3 + \frac{1}{a^3}$ and $a^5 + \frac{1}{a^5}$ take? | "[\" (8\\\\sqrt{11}, 71\\\\sqrt{11}), (-8\\\\sqrt{11}, -71\\\\sqrt{11}) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108087, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118022"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3\\sqrt{3}"
] | [
"skywork"
] | 0e8de620058bf747d4708b87f356c100dc57881e3d523474d4b5484a5339b116 | [
{
"content": "The base of the quadrilateral prism $A B C D A_{1} B_{1} C_{1} D_{1}$ is a rhombus $A B C D$, where $B D=3$ and $\\angle A D C=60^{\\circ}$. A sphere passes through the vertices $D, C, B, B_{1}, A_{1}, D_{1}$.\n\na) Find the area of the circle obtained in the cross-section of the sphere by the pla... | The base of the quadrilateral prism $A B C D A_{1} B_{1} C_{1} D_{1}$ is a rhombus $A B C D$, where $B D=3$ and $\angle A D C=60^{\circ}$. A sphere passes through the vertices $D, C, B, B_{1}, A_{1}, D_{1}$.
a) Find the area of the circle obtained in the cross-section of the sphere by the plane passing through the poi... | "[\"3\\\\sqrt{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108057, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118023"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3/7"
] | [
"skywork"
] | 581e89f5b49ce2329dcc065725e61999cc8afd82d9517ab7d02ead09ce6e3248 | [
{
"content": "The sides of triangle \\(ABC\\) are divided by points \\(M, N\\), and \\(P\\) such that \\(AM : MB = BN : NC = CP : PA = 1 : 4\\). Find the ratio of the area of the triangle bounded by lines \\(AN, BP\\), and \\(CM\\) to the area of triangle \\(ABC\\).",
"role": "user"
}
] | The sides of triangle \(ABC\) are divided by points \(M, N\), and \(P\) such that \(AM : MB = BN : NC = CP : PA = 1 : 4\). Find the ratio of the area of the triangle bounded by lines \(AN, BP\), and \(CM\) to the area of triangle \(ABC\). | "[\"3/7\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108077, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118024"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"65"
] | [
"skywork"
] | a8aedf0f1b18e1d3809b312437d484fefff85d593be7c3e425a33ec5ad8cd71d | [
{
"content": "Ann, Bill and Carol each have some tokens. There are four exchanges of tokens that happen in the order below:\n\n- First, Ann gives Bill the number of tokens that Bill has.\n- Next, Ann gives Carol twice the number of tokens that Carol has.\n- Next, Bill gives Ann the number of tokens that Ann has... | Ann, Bill and Carol each have some tokens. There are four exchanges of tokens that happen in the order below:
- First, Ann gives Bill the number of tokens that Bill has.
- Next, Ann gives Carol twice the number of tokens that Carol has.
- Next, Bill gives Ann the number of tokens that Ann has.
- Finally, Bill gives Ca... | "[\"65\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108079, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118025"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 13fc65a4058dd01ae879d8387865fdd05a7e9b8e1d05b9a2082f0ee31cb5d8fe | [
{
"content": "For how many integers \\( n \\) between 1 and 100 is the greatest common divisor (gcd) of 21 and \\( n \\) equal to 7?",
"role": "user"
}
] | For how many integers \( n \) between 1 and 100 is the greatest common divisor (gcd) of 21 and \( n \) equal to 7? | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108099, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118026"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"x_{1}=-\\frac{41}{2},x_{2}=10"
] | [
"skywork"
] | 23b9961b3c4ff5aea3b2bbe41f557dc43269520a5e2db2137966c6252fd6fdbf | [
{
"content": "6.180. $\\left(x^{2}+x+1\\right)+\\left(x^{2}+2 x+3\\right)+\\left(x^{2}+3 x+5\\right)+\\ldots$\n\n$$\n\\ldots+\\left(x^{2}+20 x+39\\right)=4500\n$$",
"role": "user"
}
] | 6.180. $\left(x^{2}+x+1\right)+\left(x^{2}+2 x+3\right)+\left(x^{2}+3 x+5\right)+\ldots$
$$
\ldots+\left(x^{2}+20 x+39\right)=4500
$$ | "[\"x_{1}=-\\\\frac{41}{2},x_{2}=10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108088, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118027"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2010"
] | [
"skywork"
] | 0038998cdddb9386b2798d88d3208361cc5e646c43a6a205648d7554fdd95f37 | [
{
"content": "2011 warehouses are connected by roads in such a way that from any warehouse you can reach any other, possibly passing through several roads. There are $x_{1}, \\ldots, x_{2011}$ kg of cement in the warehouses, respectively. In one trip, an arbitrary amount of cement can be transported from one wa... | 2011 warehouses are connected by roads in such a way that from any warehouse you can reach any other, possibly passing through several roads. There are $x_{1}, \ldots, x_{2011}$ kg of cement in the warehouses, respectively. In one trip, an arbitrary amount of cement can be transported from one warehouse to another alon... | "[\"2010\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108063, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118028"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"skywork"
] | ad38076c2e6328a217d45821d4a0f67d22facff31a7f94e41b874594d33e5af4 | [
{
"content": "In a math test, there are easy and hard questions. The easy questions worth 3 points and the hard questions worth D points.\\\\\nIf all the questions begin to worth 4 points, the total punctuation of the test increases 16 points.\\\\\nInstead, if we exchange the questions scores, scoring D points ... | In a math test, there are easy and hard questions. The easy questions worth 3 points and the hard questions worth D points.\\
If all the questions begin to worth 4 points, the total punctuation of the test increases 16 points.\\
Instead, if we exchange the questions scores, scoring D points for the easy questions and 3... | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108082, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118029"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"a_{n}=\\frac{1}{2^{n}}-\\frac{1}{n(n+1)}"
] | [
"skywork"
] | af9e4d56ee225de8100268ac938b03d49fecec7034b390d02ddcec1391128f46 | [
{
"content": "12. Let the sequence $\\left\\{a_{n}\\right\\}$ have the sum of the first $n$ terms $S_{n}$ satisfying:\n$$\nS_{n}+a_{n}=\\frac{n-1}{n(n+1)}(n=1,2, \\cdots) \\text {. }\n$$\n\nThen the general term $a_{n}=$",
"role": "user"
}
] | 12. Let the sequence $\left\{a_{n}\right\}$ have the sum of the first $n$ terms $S_{n}$ satisfying:
$$
S_{n}+a_{n}=\frac{n-1}{n(n+1)}(n=1,2, \cdots) \text {. }
$$
Then the general term $a_{n}=$ | "[\"a_{n}=\\\\frac{1}{2^{n}}-\\\\frac{1}{n(n+1)}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108065, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118030"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"58"
] | [
"skywork"
] | 171f41265e564cc29365ce2b76639b70da2ebf7c1ef9c8102ca542132fb61697 | [
{
"content": "2. (8 points) Xiaoming's family keeps three hens, the first hen lays one egg per day, the second hen lays one egg every two days, and the third hen lays one egg every three days. It is known that on January 1st, all three hens laid eggs, so in the thirty-one days of January, these three hens laid ... | 2. (8 points) Xiaoming's family keeps three hens, the first hen lays one egg per day, the second hen lays one egg every two days, and the third hen lays one egg every three days. It is known that on January 1st, all three hens laid eggs, so in the thirty-one days of January, these three hens laid $\qquad$ eggs in total... | "[\"58\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108083, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118031"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"26"
] | [
"skywork"
] | fac6a2708d441e12f853cc4137c7011eb43abc357fbccf3355f93bd76f5fc3af | [
{
"content": "Find the sum of all positive integers \\( p \\) such that the expression \\((x-p)(x-13)+4\\) can be expressed in the form \\((x+q)(x+r)\\) for distinct integers \\( q \\) and \\( r \\).",
"role": "user"
}
] | Find the sum of all positive integers \( p \) such that the expression \((x-p)(x-13)+4\) can be expressed in the form \((x+q)(x+r)\) for distinct integers \( q \) and \( r \). | "[\"26\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108090, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118032"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"82"
] | [
"skywork"
] | 83d6c33026f806f1267525f102e75cc2cddac7155838d9e13e3711781e34bf39 | [
{
"content": "In land of Nyemo, the unit of currency is called a [i]quack[/i]. The citizens use coins that are worth $1$, $5$, $25$, and $125$ quacks. How many ways can someone pay off $125$ quacks using these coins?\n\n[i]Proposed by Aaron Lin[/i]",
"role": "user"
}
] | In land of Nyemo, the unit of currency is called a [i]quack[/i]. The citizens use coins that are worth $1$, $5$, $25$, and $125$ quacks. How many ways can someone pay off $125$ quacks using these coins?
[i]Proposed by Aaron Lin[/i] | "[\"82\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108100, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118034"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"96"
] | [
"skywork"
] | a7b7cf7a2eb4f5c3b221ed3b8ad3cd42105964a15a58c370b53e110f84f70dbd | [
{
"content": "Suppose $a,b$ are nonzero integers such that two roots of $x^3+ax^2+bx+9a$ coincide, and all three roots are integers. Find $|ab|$.",
"role": "user"
}
] | Suppose $a,b$ are nonzero integers such that two roots of $x^3+ax^2+bx+9a$ coincide, and all three roots are integers. Find $|ab|$. | "[\"96\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108101, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118035"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 83374f16b09a0da1d43f012e1c189069b0a1083c60f0fe37dbac2cbe9f57ecdd | [
{
"content": "Exercise 6. Let $n \\geqslant 1$ be an integer. Morgane initially has $n$ piles, each containing one coin. She then allows herself operations of the following form: she chooses two piles, takes as many coins from the first pile as from the second, and forms a new pile with the coins she has taken.... | Exercise 6. Let $n \geqslant 1$ be an integer. Morgane initially has $n$ piles, each containing one coin. She then allows herself operations of the following form: she chooses two piles, takes as many coins from the first pile as from the second, and forms a new pile with the coins she has taken.
Determine, as a funct... | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108096, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118036"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\binom{n+k-1}{n-1}"
] | [
"skywork"
] | 93bc661f190c26d984e224b81202fa3f37bf233077dd05cc5aef540b906ce2a2 | [
{
"content": "How many ways are there to distribute $k+n$ identical photocopies to $n$ students so that each student receives at least one?",
"role": "user"
}
] | How many ways are there to distribute $k+n$ identical photocopies to $n$ students so that each student receives at least one? | "[\"\\\\binom{n+k-1}{n-1}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108102, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118037"}, {"dataset": "skywork", "extra_... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | 015053d0373d9ec5dc19ef125a65c8ee6332603418e5c7ad86986a9be957acaf | [
{
"content": "10. For $i=2,3, \\cdots, k$, the remainder when the positive integer $n$ is divided by $i$ is $i-1$. If the smallest value of $n$, $n_{0}$, satisfies $2000<n_{0}<3000$, then the smallest value of the positive integer $k$ is",
"role": "user"
}
] | 10. For $i=2,3, \cdots, k$, the remainder when the positive integer $n$ is divided by $i$ is $i-1$. If the smallest value of $n$, $n_{0}$, satisfies $2000<n_{0}<3000$, then the smallest value of the positive integer $k$ is | "[\"9\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108093, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118038"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{2011}{2009}"
] | [
"skywork"
] | 433de96bb312d787490a7484a8727af14ded063220636d7ecddbdb23853cd5ad | [
{
"content": "1. Let $\\left\\{a_{n}\\right\\}$ be an arithmetic sequence with the sum of the first $n$ terms denoted as $S_{n}$. If $S_{2010}-S_{1}=1$, then $S_{2011}=$",
"role": "user"
}
] | 1. Let $\left\{a_{n}\right\}$ be an arithmetic sequence with the sum of the first $n$ terms denoted as $S_{n}$. If $S_{2010}-S_{1}=1$, then $S_{2011}=$ | "[\"\\\\frac{2011}{2009}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108097, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118039"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"73"
] | [
"skywork"
] | bbc97374cccc9942191ac70d0a31e45758be24964c0907733b46d1a5fb4bd3bb | [
{
"content": "Given that $x^2 + y^2 = 14x + 6y + 6,$ find the largest possible value of $3x + 4y.$",
"role": "user"
}
] | Given that $x^2 + y^2 = 14x + 6y + 6,$ find the largest possible value of $3x + 4y.$ | "[\"73\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108128, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118040"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"488"
] | [
"skywork"
] | 4d06752cf2982c9a985b8434e79e60614edb218510f6295af6d67b4eaded34de | [
{
"content": "Bob rolls a fair eight-sided die each morning. The die sides are numbered from 1 to 8. If Bob rolls a composite number (4, 6, 8), he eats sweetened cereal. If he rolls a prime number (2, 3, 5, 7), he eats unsweetened cereal. If he rolls a 1 or an 8, then he rolls again. In a leap year (366 days), ... | Bob rolls a fair eight-sided die each morning. The die sides are numbered from 1 to 8. If Bob rolls a composite number (4, 6, 8), he eats sweetened cereal. If he rolls a prime number (2, 3, 5, 7), he eats unsweetened cereal. If he rolls a 1 or an 8, then he rolls again. In a leap year (366 days), what is the expected n... | "[\"488\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108089, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118041"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"14\\pi"
] | [
"skywork"
] | e80b1ff886265bf3205bec4aadd5a789d3c8ea3fa237d0896558b22da3fcfe1a | [
{
"content": "There are \\(2n\\) complex numbers satisfying \\(z^{28} - z^8 - 1 = 0\\). They have the form \\(z_{m} = \\cos \\theta_{m} + i \\sin \\theta_{m}\\), \\(m = 1, 2, \\cdots, 2n\\), where \\(0 \\leqslant \\theta_{1} < \\theta_{2} < \\cdots < \\theta_{2n} < 2\\pi\\). Find the value of \\(\\theta_{1} + \... | There are \(2n\) complex numbers satisfying \(z^{28} - z^8 - 1 = 0\). They have the form \(z_{m} = \cos \theta_{m} + i \sin \theta_{m}\), \(m = 1, 2, \cdots, 2n\), where \(0 \leqslant \theta_{1} < \theta_{2} < \cdots < \theta_{2n} < 2\pi\). Find the value of \(\theta_{1} + \theta_{2} + \cdots + \theta_{2n}\). | "[\"14\\\\pi\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108084, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118042"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | 36d2c131fe148ee6c4ffbb80ec9e6752c61b0bd852f103dca42c1a26e2bb6ba1 | [
{
"content": "Find the minimum value of\n\\[(\\sin x + \\csc x)^2 + (\\cos x + \\sec x)^2\\]for $0 < x < \\frac{\\pi}{2}.$",
"role": "user"
}
] | Find the minimum value of
\[(\sin x + \csc x)^2 + (\cos x + \sec x)^2\]for $0 < x < \frac{\pi}{2}.$ | "[\"9\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108111, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118043"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"25"
] | [
"skywork"
] | 57caeada26ab309ab8ddebf3000584fe43b820b997963bf818b396ff1946a851 | [
{
"content": "Given that Fox wants to ensure he has 20 coins left after crossing the bridge four times, and paying a $50$-coin toll each time, determine the number of coins that Fox had at the beginning.",
"role": "user"
}
] | Given that Fox wants to ensure he has 20 coins left after crossing the bridge four times, and paying a $50$-coin toll each time, determine the number of coins that Fox had at the beginning. | "[\"25\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108109, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118044"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2 \\sqrt{5}"
] | [
"skywork"
] | 35b9469c091cb43ea77c71699697f0de6718d9d50e1b764c85d90a164be743b7 | [
{
"content": "A particle moves so that it is at $(2t + 7, 4t - 13)$ at time $t.$ Find the speed of the particle, measured in unit of distance per unit of time.",
"role": "user"
}
] | A particle moves so that it is at $(2t + 7, 4t - 13)$ at time $t.$ Find the speed of the particle, measured in unit of distance per unit of time. | "[\"2 \\\\sqrt{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108118, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118045"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4022"
] | [
"skywork"
] | ad68fc38c6fa2c4d344fc350964027542be013ceec2d211a8b0c6f17d8d98b28 | [
{
"content": "20. Suppose $x_{1}, x_{2}, \\ldots, x_{2011}$ are positive integers satisfying\n$$\nx_{1}+x_{2}+\\cdots+x_{2011}=x_{1} x_{2} \\cdots x_{2011}\n$$\n\nFind the maximum value of $x_{1}+x_{2}+\\cdots+x_{2011}$.",
"role": "user"
}
] | 20. Suppose $x_{1}, x_{2}, \ldots, x_{2011}$ are positive integers satisfying
$$
x_{1}+x_{2}+\cdots+x_{2011}=x_{1} x_{2} \cdots x_{2011}
$$
Find the maximum value of $x_{1}+x_{2}+\cdots+x_{2011}$. | "[\"4022\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108105, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118046"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"8"
] | [
"skywork"
] | 806328d244996f8046dd73ae0a9eb814d846d51a000a196bb375ae22a0c96513 | [
{
"content": "【Question 11】\nXiao Ling is reading an interesting storybook. Every day she reads twice the number of pages she has read in the previous days, and on the sixth day, she read $\\frac{1}{9}$ of the book. On which day did Xiao Ling finish reading the book?",
"role": "user"
}
] | 【Question 11】
Xiao Ling is reading an interesting storybook. Every day she reads twice the number of pages she has read in the previous days, and on the sixth day, she read $\frac{1}{9}$ of the book. On which day did Xiao Ling finish reading the book? | "[\"8\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108107, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118047"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\left(2^{2014}-4\\right) / 3"
] | [
"skywork"
] | 5e5e2bec777954143771cb6b5ccee461cb59e8dc4358184eeb73b82a96d12b1c | [
{
"content": "You are repeatedly flipping a fair coin. What is the expected number of flips until the first time that your previous 2012 flips are 'HTHT...HT'?",
"role": "user"
}
] | You are repeatedly flipping a fair coin. What is the expected number of flips until the first time that your previous 2012 flips are 'HTHT...HT'? | "[\"\\\\left(2^{2014}-4\\\\right) / 3\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 108108, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118049"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"73"
] | [
"skywork"
] | db40cec71db29e1976c636725a61dcca428e07b4fa5a05219e7e6bde25b0079f | [
{
"content": "The average age of grandpa, grandma, and their five grandchildren is 26 years. The average age of the grandchildren themselves is 7 years. Grandma is one year younger than grandpa.\n\nHow old is grandma?\n\n(L. Hozová)\n\nHint. How old are all the grandchildren together?",
"role": "user"
}
] | The average age of grandpa, grandma, and their five grandchildren is 26 years. The average age of the grandchildren themselves is 7 years. Grandma is one year younger than grandpa.
How old is grandma?
(L. Hozová)
Hint. How old are all the grandchildren together? | "[\"73\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108116, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118050"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"x^4"
] | [
"skywork"
] | d43a6555d35f5202345e989b542f3f739deda125a724427fdd4244bb827dea10 | [
{
"content": "Let $S=(x-1)^4+4(x-1)^3+6(x-1)^2+4(x-1)+1$. Then $S$ equals:",
"role": "user"
}
] | Let $S=(x-1)^4+4(x-1)^3+6(x-1)^2+4(x-1)+1$. Then $S$ equals: | "[\"x^4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108127, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118051"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | cb51a34d5908546a8c0fea3d468921ef2563e1fb584b4f477a7a3e467795e8ee | [
{
"content": "Let $n$ be a positive integer and $d$ be the greatest common divisor of $n^2+1$ and $(n + 1)^2 + 1$. Find all the possible values of $d$. Justify your answer.",
"role": "user"
}
] | Let $n$ be a positive integer and $d$ be the greatest common divisor of $n^2+1$ and $(n + 1)^2 + 1$. Find all the possible values of $d$. Justify your answer. | "[\"1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108120, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118052"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"Yes, $A_1 \\le A_2$."
] | [
"skywork"
] | 604c012429c4990591ab6005353cf108c8a3de5c33b324f018742193ef49d0ee | [
{
"content": "For $i = 1,2$ let $T_i$ be a triangle with side lengths $a_i, b_i, c_i$, and area $A_i$. Suppose that $a_1 \\le a_2, b_1 \\le b_2, c_1 \\le c_2$, and that $T_2$ is an acute triangle. Does it follow that $A_1 \\le A_2$?",
"role": "user"
}
] | For $i = 1,2$ let $T_i$ be a triangle with side lengths $a_i, b_i, c_i$, and area $A_i$. Suppose that $a_1 \le a_2, b_1 \le b_2, c_1 \le c_2$, and that $T_2$ is an acute triangle. Does it follow that $A_1 \le A_2$? | "[\"Yes, $A_1 \\\\le A_2$.\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 108110, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118053"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"464"
] | [
"skywork"
] | 00ec2f9a63d656d1ffc52dc60b7528a21c21910497f96a21e6fa3c71ed6c377b | [
{
"content": "Let $S$ be the sum of all positive integers $n$ such that $n^2+12n-2007$ is a perfect square. Find the remainder when $S$ is divided by $1000.$",
"role": "user"
}
] | Let $S$ be the sum of all positive integers $n$ such that $n^2+12n-2007$ is a perfect square. Find the remainder when $S$ is divided by $1000.$ | "[\"464\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108115, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118054"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2008"
] | [
"skywork"
] | 96c6b4a23862024cdfd47359be2bac9a17ed389bb6e62ffec1b48a3ff21181e5 | [
{
"content": "Three. (25 points) Let $a$ be a prime number, $b$ and $c$ be positive integers, and satisfy\n$$\n\\left\\{\\begin{array}{l}\n9(2 a+2 b-c)^{2}=509(4 a+1022 b-511 c), \\\\\nb-c=2 .\n\\end{array}\\right.\n$$\n\nFind the value of $a(b+c)$.",
"role": "user"
}
] | Three. (25 points) Let $a$ be a prime number, $b$ and $c$ be positive integers, and satisfy
$$
\left\{\begin{array}{l}
9(2 a+2 b-c)^{2}=509(4 a+1022 b-511 c), \\
b-c=2 .
\end{array}\right.
$$
Find the value of $a(b+c)$. | "[\"2008\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108117, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118055"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2626"
] | [
"skywork"
] | 3865c95f716345a33f44d8b1a0e2c6acc9f6a0386d18b014f1f1ff2178d449e4 | [
{
"content": "A school has between 150 and 250 students enrolled. Each day, all the students split into eight different sections for a special workshop. If two students are absent, each section can contain an equal number of students. Find the sum of all possible values of student enrollment at the school.",
... | A school has between 150 and 250 students enrolled. Each day, all the students split into eight different sections for a special workshop. If two students are absent, each section can contain an equal number of students. Find the sum of all possible values of student enrollment at the school. | "[\"2626\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108106, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118056"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"36"
] | [
"skywork"
] | e0e315eb1d271e5b6733fd649b4eaf14e975aa6a193e2f17229f1a25b7b89470 | [
{
"content": "Task 1. (5 points) Find $\\frac{a^{12}-4096}{64 a^{6}}$, if $\\frac{a^{2}}{4}-\\frac{4}{a^{2}}=3$.",
"role": "user"
}
] | Task 1. (5 points) Find $\frac{a^{12}-4096}{64 a^{6}}$, if $\frac{a^{2}}{4}-\frac{4}{a^{2}}=3$. | "[\"36\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108125, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118057"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2\\sqrt{2}"
] | [
"skywork"
] | d1105f14a8786f2089700fcf8543fc774ff7ccff9be6865c694cdfc90357f678 | [
{
"content": "Given \\(x\\) and \\(y\\) are real numbers, and:\n\\[\nz_1 = x + (y + 2)i,\n\\]\n\\[\nz_2 = (x - 2) + yi,\n\\]\nwith the condition \\(\\left|z_1\\right| + \\left|z_2\\right| = 4\\),\n\nFind the maximum value of \\(|x + y|\\).",
"role": "user"
}
] | Given \(x\) and \(y\) are real numbers, and:
\[
z_1 = x + (y + 2)i,
\]
\[
z_2 = (x - 2) + yi,
\]
with the condition \(\left|z_1\right| + \left|z_2\right| = 4\),
Find the maximum value of \(|x + y|\). | "[\"2\\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108112, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118058"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\pi}{3}"
] | [
"skywork"
] | ee172af6bab4caf09cda7bd276c2c1c698fa6693845d22256159b54f516bb694 | [
{
"content": "Given vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfy $|\\overrightarrow{a}|=1$, $|\\overrightarrow{b}|=2$ and $|2\\overrightarrow{a}+\\overrightarrow{b}|=2\\sqrt{3}$, find the angle between vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$.",
"role": "user"
}
] | Given vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfy $|\overrightarrow{a}|=1$, $|\overrightarrow{b}|=2$ and $|2\overrightarrow{a}+\overrightarrow{b}|=2\sqrt{3}$, find the angle between vectors $\overrightarrow{a}$ and $\overrightarrow{b}$. | "[\"\\\\frac{\\\\pi}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108126, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118059"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2: 3"
] | [
"skywork"
] | 3fc2ca428b4bac28b25e970b9ba1a413cd450a0249a97e7789dc013c273a9ae1 | [
{
"content": "3. If the circumference of the top base of a frustum is $4 \\pi$, and the circumference of the bottom base is $9 \\pi$, and the circumference of a section parallel to the bases is the geometric mean of the circumferences of the top and bottom bases, then the ratio of the two segments of the height... | 3. If the circumference of the top base of a frustum is $4 \pi$, and the circumference of the bottom base is $9 \pi$, and the circumference of a section parallel to the bases is the geometric mean of the circumferences of the top and bottom bases, then the ratio of the two segments of the height of the frustum divided ... | "[\"2: 3\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108113, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118060"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 7818747fa926eebfe4dd011871375381243ead6080c876b6adcb8da640040451 | [
{
"content": "Problem 5. On the edge $A A^{\\prime}$ of the cube $A B C D A^{\\prime} B^{\\prime} C^{\\prime} D^{\\prime}$ with edge length 2, a point $K$ is marked. In space, a point $T$ is marked such that $T B=\\sqrt{11}$ and $T C=\\sqrt{15}$. Find the length of the height of the tetrahedron $T B C K$, dropp... | Problem 5. On the edge $A A^{\prime}$ of the cube $A B C D A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ with edge length 2, a point $K$ is marked. In space, a point $T$ is marked such that $T B=\sqrt{11}$ and $T C=\sqrt{15}$. Find the length of the height of the tetrahedron $T B C K$, dropped from vertex $C$. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108119, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118061"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 568dbdf05f99b0e161ac9011f0569937ccab510e07cce8280481c2c68d663856 | [
{
"content": "I3.2 Two bags $U_{1}$ and $U_{2}$ contain identical red and white balls. $U_{1}$ contains $A$ red balls and 2 white balls. $U_{2}$ contains 2 red balls and $B$ white balls. Take two balls out of each bag. If the probability of all four balls are red is $\\frac{1}{60}$, find the value of $B$.",
... | I3.2 Two bags $U_{1}$ and $U_{2}$ contain identical red and white balls. $U_{1}$ contains $A$ red balls and 2 white balls. $U_{2}$ contains 2 red balls and $B$ white balls. Take two balls out of each bag. If the probability of all four balls are red is $\frac{1}{60}$, find the value of $B$. | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108104, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118062"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2551"
] | [
"skywork"
] | a01b48fc1323e0d6e44edbeb94dba82c9e01b8de91812bdfcf7f0e8591f7b05c | [
{
"content": "4. In the Cartesian coordinate plane, the number of integer points that satisfy the system of inequalities $\\left\\{\\begin{array}{l}y \\leqslant 3 x \\\\ y \\geqslant \\frac{x}{3} \\\\ x+y \\leqslant 100\\end{array}\\right.$ is",
"role": "user"
}
] | 4. In the Cartesian coordinate plane, the number of integer points that satisfy the system of inequalities $\left\{\begin{array}{l}y \leqslant 3 x \\ y \geqslant \frac{x}{3} \\ x+y \leqslant 100\end{array}\right.$ is | "[\"2551\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108130, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118063"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | f880d437964bbdfe0c7674571464a3ae08d201acb6624f849a9f0f9944c60a57 | [
{
"content": "8. (7 points) Arrange even numbers as shown in the figure below. Ask: 2008 is in the $\\qquad$ column.\n\\begin{tabular}{lllc}\n2 & 4 & 6 & 8 \\\\\n16 & 14 & 12 & 10 \\\\\n18 & 20 & 22 & 24 \\\\\n32 & 30 & 28 & 26 \\\\\n$\\ldots$ & & &\n\\end{tabular}",
"role": "user"
}
] | 8. (7 points) Arrange even numbers as shown in the figure below. Ask: 2008 is in the $\qquad$ column.
\begin{tabular}{lllc}
2 & 4 & 6 & 8 \\
16 & 14 & 12 & 10 \\
18 & 20 & 22 & 24 \\
32 & 30 & 28 & 26 \\
$\ldots$ & & &
\end{tabular} | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108114, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118064"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"30"
] | [
"skywork"
] | a95f09354e450cc3b2e0558d031485726b422a876e832ee328f10f2cc6d83237 | [
{
"content": "Captain Billy the Pirate looted 1010 gold doubloons and set sail on his ship to a deserted island to bury his treasure. Each evening of their voyage, he paid each of his pirates one doubloon. On the eighth day of sailing, the pirates plundered a Spanish caravel, doubling Billy's treasure and halvi... | Captain Billy the Pirate looted 1010 gold doubloons and set sail on his ship to a deserted island to bury his treasure. Each evening of their voyage, he paid each of his pirates one doubloon. On the eighth day of sailing, the pirates plundered a Spanish caravel, doubling Billy's treasure and halving the number of pirat... | "[\"30\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108122, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118065"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"90"
] | [
"skywork"
] | c63a0776b97b23058dbc395df7d66ce0d33ad4cb8cbca9db6cfad8d5c38e71d1 | [
{
"content": "On a circular track with a perimeter of 360 meters, three individuals A, B, and C start from the same point: A starts first, running counterclockwise. Before A completes one lap, B and C start simultaneously, running clockwise. When A and B meet for the first time, C is exactly halfway between the... | On a circular track with a perimeter of 360 meters, three individuals A, B, and C start from the same point: A starts first, running counterclockwise. Before A completes one lap, B and C start simultaneously, running clockwise. When A and B meet for the first time, C is exactly halfway between them. After some time, wh... | "[\"90\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108121, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118066"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\dfrac{2}{11}"
] | [
"skywork"
] | bc281b2915532c4817c4d6725bde97e447666ad7624531a4ed17c962941bd5f0 | [
{
"content": "A box contains 5 white balls and 6 black balls. Two balls are drawn out of the box at random. What is the probability that they both are white?",
"role": "user"
}
] | A box contains 5 white balls and 6 black balls. Two balls are drawn out of the box at random. What is the probability that they both are white? | "[\"\\\\dfrac{2}{11}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108144, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118067"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{k^{3}+3k^{2}}{3k+1}"
] | [
"skywork"
] | dd3579b47c4fa6d69e03aaa4a6d0272e2f82c17d7d3b8dfd168a25d7911e6e5a | [
{
"content": "3. (CZS) A tetrahedron $A B C D$ is given. The lengths of the edges $A B$ and $C D$ are $a$ and $b$, respectively, the distance between the lines $A B$ and $C D$ is $d$, and the angle between them is equal to $w$. The tetrahedron is divided into two parts by the plane $\\pi$ parallel to the lines ... | 3. (CZS) A tetrahedron $A B C D$ is given. The lengths of the edges $A B$ and $C D$ are $a$ and $b$, respectively, the distance between the lines $A B$ and $C D$ is $d$, and the angle between them is equal to $w$. The tetrahedron is divided into two parts by the plane $\pi$ parallel to the lines $A B$ and $C D$. Calcul... | "[\"\\\\frac{k^{3}+3k^{2}}{3k+1}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108095, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118068"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | b9b93e11a53099af3084c979bd6f3405ad2397dff6258c7338c27d17c88782e6 | [
{
"content": "Let's determine all cyclic quadrilaterals whose sides are integers, and the numerical value of their area is equal to the numerical value of their perimeter.",
"role": "user"
}
] | Let's determine all cyclic quadrilaterals whose sides are integers, and the numerical value of their area is equal to the numerical value of their perimeter. | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108133, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118069"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"33"
] | [
"skywork"
] | 44d5063a1d7f8603dab845c6d85a03a099faa7a6348e215e9cf65a929f34e516 | [
{
"content": "Example 2. Find the smallest positive integer $n$, such that in any 9-vertex and $n$-edge graph with edges colored in two colors, there must exist a monochromatic triangle.\n\n untranslated portion: \n(There is no additional text to translate, as the provided text has been fully translated.)",
... | Example 2. Find the smallest positive integer $n$, such that in any 9-vertex and $n$-edge graph with edges colored in two colors, there must exist a monochromatic triangle.
untranslated portion:
(There is no additional text to translate, as the provided text has been fully translated.) | "[\"33\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108134, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118070"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2C_{2024}^{4}"
] | [
"skywork"
] | f8cefaea22147fdb26c83c162a50409de6dbf24677068a737217251d4843968c | [
{
"content": "8. The number of non-negative integer solutions satisfying $x_{1}{ }^{2}+x_{2}{ }^{2}+\\cdots+x_{2023}{ }^{2}=2+x_{1} x_{2}+x_{2} x_{3}+\\cdots+x_{2022} x_{2023}$ is $\\qquad$ groups\n(You can use binomial coefficients to represent the result)",
"role": "user"
}
] | 8. The number of non-negative integer solutions satisfying $x_{1}{ }^{2}+x_{2}{ }^{2}+\cdots+x_{2023}{ }^{2}=2+x_{1} x_{2}+x_{2} x_{3}+\cdots+x_{2022} x_{2023}$ is $\qquad$ groups
(You can use binomial coefficients to represent the result) | "[\"2C_{2024}^{4}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108131, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118071"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"72\\sqrt{3}"
] | [
"skywork"
] | 9fbc3d4bec989a9ed2b0d11bcf885c9e760d0972028488a78fc02ff6171694ba | [
{
"content": "12. A small ball with a radius of 1 can move freely in all directions inside a regular tetrahedron container with an internal edge length of $4 \\sqrt{6}$. The area of the container's inner wall that the ball can never touch is $\\qquad$.",
"role": "user"
}
] | 12. A small ball with a radius of 1 can move freely in all directions inside a regular tetrahedron container with an internal edge length of $4 \sqrt{6}$. The area of the container's inner wall that the ball can never touch is $\qquad$. | "[\"72\\\\sqrt{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108129, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118072"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"84"
] | [
"skywork"
] | 9810e85a09df62753bf57320ec365873177edbb3e09a86f07d99c200a51df22b | [
{
"content": "【Question 10】\nA total of 100 students from grades three, four, and five participated in a tree planting activity, planting a total of 566 trees. It is known that the number of students in grades three and four is equal, with third-grade students planting an average of 4 trees per person, fourth-g... | 【Question 10】
A total of 100 students from grades three, four, and five participated in a tree planting activity, planting a total of 566 trees. It is known that the number of students in grades three and four is equal, with third-grade students planting an average of 4 trees per person, fourth-grade students planting ... | "[\"84\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108124, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118073"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | f4a3d452cb43ced9ca4e19797b29c1d93d6ad71f6f40e8e3365c51035feafc48 | [
{
"content": "What is the value of $\\sqrt{36+64}-\\sqrt{25-16}$?",
"role": "user"
}
] | What is the value of $\sqrt{36+64}-\sqrt{25-16}$? | "[\"7\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108147, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118074"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"n = 1342"
] | [
"skywork"
] | e06a6947aeca6fa3f89989cc0405d1997aad857a773f5b8010ca28f6090b39fd | [
{
"content": "Find all natural numbers $n> 1$ for which the following applies:\nThe sum of the number $n$ and its second largest divisor is $2013$.\n\n(R. Henner, Vienna)",
"role": "user"
}
] | Find all natural numbers $n> 1$ for which the following applies:
The sum of the number $n$ and its second largest divisor is $2013$.
(R. Henner, Vienna) | "[\" n = 1342 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108138, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118075"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"981"
] | [
"skywork"
] | f6462659c2c237a77da97b2f3ae45b81d261c1a4aedcc5ee0d0f33fd12814a37 | [
{
"content": "Example 5 (4th American Invitational Mathematics Examination) The increasing sequence $1,3,4,9,10,12,13, \\cdots$ consists of some positive integers, which are either powers of 3 or sums of several different powers of 3. Find the 100th term of this sequence.",
"role": "user"
}
] | Example 5 (4th American Invitational Mathematics Examination) The increasing sequence $1,3,4,9,10,12,13, \cdots$ consists of some positive integers, which are either powers of 3 or sums of several different powers of 3. Find the 100th term of this sequence. | "[\"981\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108132, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118076"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"skywork"
] | b201278f5e5eadd4ec3b79bc075f7206f92675191b95beda0a0600151695929a | [
{
"content": "2. (3 points) Calculate: $99 \\times \\frac{5}{8}-0.625 \\times 68+6.25 \\times 0.1=$ $\\qquad$",
"role": "user"
}
] | 2. (3 points) Calculate: $99 \times \frac{5}{8}-0.625 \times 68+6.25 \times 0.1=$ $\qquad$ | "[\"20\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108137, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118077"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"77"
] | [
"skywork"
] | 6c4614a8a5c71b14f9c86fe19d26202d3d8b22c8f020b8fb0c46c26e6a803c4a | [
{
"content": "Engineer Sergei received a research object with a volume of approximately 200 monoliths (a container designed for 200 monoliths, which was almost completely filled). Each monolith has a specific designation (either \"sand loam\" or \"clay loam\") and genesis (either \"marine\" or \"lake-glacial\" ... | Engineer Sergei received a research object with a volume of approximately 200 monoliths (a container designed for 200 monoliths, which was almost completely filled). Each monolith has a specific designation (either "sand loam" or "clay loam") and genesis (either "marine" or "lake-glacial" deposits). The relative freque... | "[\"77\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108135, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118078"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"17"
] | [
"skywork"
] | c63e44f600955e98b1eb9d72e542900c27069a571740fe1fe170a2c5352f1367 | [
{
"content": "Lazim rolls two $24$-sided dice. From the two rolls, Lazim selects the die with the highest number. $N$ is an integer not greater than $24$. What is the largest possible value for $N$ such that there is a more than $50$% chance that the die Lazim selects is larger than or equal to $N$?",
"role... | Lazim rolls two $24$-sided dice. From the two rolls, Lazim selects the die with the highest number. $N$ is an integer not greater than $24$. What is the largest possible value for $N$ such that there is a more than $50$% chance that the die Lazim selects is larger than or equal to $N$? | "[\"17\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108146, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118079"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2\\sqrt{2}"
] | [
"skywork"
] | 1b33ed876bea33426f6c3d4c1a715ece75f4855f80c2cce7fce7ddd53f60b8fe | [
{
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively, and it is given that $c=2$, $b=\\sqrt{2}a$. The maximum area of $\\triangle ABC$ is ______.",
"role": "user"
}
] | In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively, and it is given that $c=2$, $b=\sqrt{2}a$. The maximum area of $\triangle ABC$ is ______. | "[\"2\\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108141, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118080"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"x + 3"
] | [
"skywork"
] | c54fa882cc10b917b3570386cca8f631bf2393f710e386e0e330c11e6a906c1a | [
{
"content": "Let $f(x) : \\mathbb{R} \\to \\mathbb{R}$ be a function such that\n\\[\\frac{f(x) f(y) - f(xy)}{3} = x + y + 2\\]for all $x,$ $y \\in \\mathbb{R}.$ Find $f(x).$",
"role": "user"
}
] | Let $f(x) : \mathbb{R} \to \mathbb{R}$ be a function such that
\[\frac{f(x) f(y) - f(xy)}{3} = x + y + 2\]for all $x,$ $y \in \mathbb{R}.$ Find $f(x).$ | "[\"x + 3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108140, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118081"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3}{4}"
] | [
"skywork"
] | e25762c099be583b264633eeecfaff6704328977c36e8dda3311ed38787a1c5b | [
{
"content": "6. Given real numbers $x, y, z$ satisfy $x+y+z=1$. Then the maximum value of $M=xy+2yz+3xz$ is ( ).\n(A) $\\frac{1}{2}$\n(B) $\\frac{2}{3}$\n(C) $\\frac{3}{4}$\n(D) 1",
"role": "user"
}
] | 6. Given real numbers $x, y, z$ satisfy $x+y+z=1$. Then the maximum value of $M=xy+2yz+3xz$ is ( ).
(A) $\frac{1}{2}$
(B) $\frac{2}{3}$
(C) $\frac{3}{4}$
(D) 1 | "[\"\\\\frac{3}{4}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108148, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118082"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-\\sqrt{\\frac{72}{11}}"
] | [
"skywork"
] | e032e640b0eb7a1729fe2d16fb4c1f9322771b76425d863030793b981bf2a81a | [
{
"content": "Find the smallest constant $D$ so that\n\\[ 2x^2 + 3y^2 + z^2 + 3 \\ge D(x + y + z) \\]\nfor all real numbers $x$, $y$, and $z$.",
"role": "user"
}
] | Find the smallest constant $D$ so that
\[ 2x^2 + 3y^2 + z^2 + 3 \ge D(x + y + z) \]
for all real numbers $x$, $y$, and $z$. | "[\"-\\\\sqrt{\\\\frac{72}{11}}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108153, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118084"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"105"
] | [
"skywork"
] | d042d93f7cd2380d686e04639d45dded8534f3066f083a322291851f0c238905 | [
{
"content": "Choose six out of the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to fill in the blanks below, so that the equation is true. Each blank is filled with a single digit, and no two digits are the same. \n\n$\\square + \\square \\square = \\square \\square \\square$. \n\nWhat is the largest possible three... | Choose six out of the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to fill in the blanks below, so that the equation is true. Each blank is filled with a single digit, and no two digits are the same.
$\square + \square \square = \square \square \square$.
What is the largest possible three-digit number in the equation? | "[\"105\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108143, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118085"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | bb94129db8e533ac921941e946254b03df2f4ff4eea8f4e56337e33cf4292be7 | [
{
"content": "## Task B-3.1.\n\nSolve the equation $5 \\cdot 0.16^{x}+8 \\cdot 0.4^{x}=4$.",
"role": "user"
}
] | ## Task B-3.1.
Solve the equation $5 \cdot 0.16^{x}+8 \cdot 0.4^{x}=4$. | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108158, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118086"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"127"
] | [
"skywork"
] | f04868591eae17657b7a90586ea1ed2bea2244224c0beba695afeb07624a6184 | [
{
"content": "A Mersenne prime is defined to be a prime number of the form $2^n - 1$, where $n$ must itself be a prime. For example, since $2^3 - 1 = 7$, and 3 is a prime number, 7 is a Mersenne prime. What is the largest Mersenne prime less than 200?",
"role": "user"
}
] | A Mersenne prime is defined to be a prime number of the form $2^n - 1$, where $n$ must itself be a prime. For example, since $2^3 - 1 = 7$, and 3 is a prime number, 7 is a Mersenne prime. What is the largest Mersenne prime less than 200? | "[\"127\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108154, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118087"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"544"
] | [
"skywork"
] | 0c00f18c6297979d8134265d8bb9a4d59bada943fe46d3079c2794ba3c9c8802 | [
{
"content": "What three-digit number with units digit 4 and hundreds digit 5 is divisible by 8 and has an even tens digit?",
"role": "user"
}
] | What three-digit number with units digit 4 and hundreds digit 5 is divisible by 8 and has an even tens digit? | "[\"544\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108161, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118088"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1008"
] | [
"skywork"
] | b0dd5c541148cf61760f408e0eebd643f158754d58b9468ae17af8460fa2ff22 | [
{
"content": "At a conference, the 2016 participants were registered from P1 to P2016. Each participant from P1 to P2015 shook hands with exactly the same number of participants as the number on their registration form. How many hands did the 2016th participant shake?",
"role": "user"
}
] | At a conference, the 2016 participants were registered from P1 to P2016. Each participant from P1 to P2015 shook hands with exactly the same number of participants as the number on their registration form. How many hands did the 2016th participant shake? | "[\"1008\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108159, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118090"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{8}{3}"
] | [
"skywork"
] | 6cc40b02b4a9815551b470f00ed953e68e140e4d35f3ffdafd0e7af76253bac5 | [
{
"content": "A ladder is $2 \\frac{2}{3}$ m shorter than the height of the wall. If we lean it against the wall so that the foot of the ladder is at a distance of $\\frac{3}{5}$ of the ladder's length from the wall, then the upper part of the ladder reaches $\\frac{2}{5}$ of the wall's height. How long is the ... | A ladder is $2 \frac{2}{3}$ m shorter than the height of the wall. If we lean it against the wall so that the foot of the ladder is at a distance of $\frac{3}{5}$ of the ladder's length from the wall, then the upper part of the ladder reaches $\frac{2}{5}$ of the wall's height. How long is the ladder? | "[\"\\\\frac{8}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108152, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118091"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | b1975b5f22d66b066a0c67e407bba2f19ea2b53b9ce5fe6cf2a96aaffdd443c4 | [
{
"content": "7. If $a_{1}=a_{2}=1, a_{n}=4 a_{n-1}-a_{n-2}$, then $a_{n} a_{n-2}-a_{n-1}^{2}=$",
"role": "user"
}
] | 7. If $a_{1}=a_{2}=1, a_{n}=4 a_{n-1}-a_{n-2}$, then $a_{n} a_{n-2}-a_{n-1}^{2}=$ | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108149, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118092"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt {2}"
] | [
"skywork"
] | e64e2a292da30f2efe3e622cd14ce868d44383fbb9fe66dc739e97f0f0469def | [
{
"content": "Evaluate the expression: \\\\( \\frac {\\cos 40 ^{\\circ} +\\sin 50 ^{\\circ} (1+ \\sqrt {3}\\tan 10 ^{\\circ} )}{\\sin 70 ^{\\circ} \\sqrt {1+\\cos 40 ^{\\circ} }}\\\\)",
"role": "user"
}
] | Evaluate the expression: \\( \frac {\cos 40 ^{\circ} +\sin 50 ^{\circ} (1+ \sqrt {3}\tan 10 ^{\circ} )}{\sin 70 ^{\circ} \sqrt {1+\cos 40 ^{\circ} }}\\) | "[\"\\\\sqrt {2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108157, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118093"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"82"
] | [
"skywork"
] | 77b516a9f439178d1e81a554522eb135b4e4b6f02e8ee78d82a6bd87ca56916d | [
{
"content": "Given the two functions $f(x)=x^2+1$ and $g(x)=2x-1$, find $f(g(5))$.",
"role": "user"
}
] | Given the two functions $f(x)=x^2+1$ and $g(x)=2x-1$, find $f(g(5))$. | "[\"82\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108173, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118094"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-3"
] | [
"skywork"
] | a5cb3b78d8ca02b0f5a9b3bb671dba40679e1f85f81cc5277ae42ccb72d3257b | [
{
"content": "There are three real numbers $x$ that are not in the domain of $$ f(x) = \\frac{1}{1+\\frac{1}{1+\\frac{2}{x}}}.$$ What is the sum of those three numbers?",
"role": "user"
}
] | There are three real numbers $x$ that are not in the domain of $$ f(x) = \frac{1}{1+\frac{1}{1+\frac{2}{x}}}.$$ What is the sum of those three numbers? | "[\"-3\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108164, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118095"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2004"
] | [
"skywork"
] | e04d08ef68e0a5a7b2300b6e458a15084ff244f3dec789c7f27451a990392997 | [
{
"content": "How many of the integers \\(1, 2, \\ldots, 2004\\) can be represented as \\(\\frac{mn+1}{m+n}\\) for positive integers \\(m\\) and \\(n\\)?",
"role": "user"
}
] | How many of the integers \(1, 2, \ldots, 2004\) can be represented as \(\frac{mn+1}{m+n}\) for positive integers \(m\) and \(n\)? | "[\"2004\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108162, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118096"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"8044"
] | [
"skywork"
] | 86b0288ba9f6bf24a186d2abf83ba613f73e7ba83982cec09395d52b40e3f978 | [
{
"content": "Two positive integers $x$ and $y$ are such that:\n\n$$\n\\frac{2010}{2011}<\\frac{x}{y}<\\frac{2011}{2012}\n$$\n\nFind the smallest possible value for the sum $x+y$.\n\n#",
"role": "user"
}
] | Two positive integers $x$ and $y$ are such that:
$$
\frac{2010}{2011}<\frac{x}{y}<\frac{2011}{2012}
$$
Find the smallest possible value for the sum $x+y$.
# | "[\"8044\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108163, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118097"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"21"
] | [
"skywork"
] | 9e82c4132a2ff05763298eeb61b18a60a9e00f2e887d9092b779f3fc001a1a09 | [
{
"content": "Given that Ron has eight sticks with integer lengths, and he is unable to form a triangle using any three of these sticks as side lengths, determine the shortest possible length of the longest of the eight sticks.",
"role": "user"
}
] | Given that Ron has eight sticks with integer lengths, and he is unable to form a triangle using any three of these sticks as side lengths, determine the shortest possible length of the longest of the eight sticks. | "[\"21\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108165, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118098"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{7}"
] | [
"skywork"
] | 12b3f1313f5bfe2a1e8f74bf1dd37564077f92243ec057375e85c39e7751a444 | [
{
"content": "Given a triangle $\\triangle ABC$ with angles $A$, $B$, $C$ and their respective opposite sides $a$, $b$, $c$, such that $b^2 + c^2 - a^2 = \\sqrt{3}bc$.\n\n(1) If $\\tan B = \\frac{\\sqrt{6}}{12}$, find $\\frac{b}{a}$;\n\n(2) If $B = \\frac{2\\pi}{3}$ and $b = 2\\sqrt{3}$, find the length of the ... | Given a triangle $\triangle ABC$ with angles $A$, $B$, $C$ and their respective opposite sides $a$, $b$, $c$, such that $b^2 + c^2 - a^2 = \sqrt{3}bc$.
(1) If $\tan B = \frac{\sqrt{6}}{12}$, find $\frac{b}{a}$;
(2) If $B = \frac{2\pi}{3}$ and $b = 2\sqrt{3}$, find the length of the median on side $BC$. | "[\"\\\\sqrt{7}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108150, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118099"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\text{No}"
] | [
"skywork"
] | 24b20b716df23ffc59dc9bc7b743643a4f9a373af7d4cea6aff6646de5ad4174 | [
{
"content": "Does there exist a set $S$ of $100$ points in a plane such that the center of mass of any $10$ points in $S$ is also a point in $S$?",
"role": "user"
}
] | Does there exist a set $S$ of $100$ points in a plane such that the center of mass of any $10$ points in $S$ is also a point in $S$? | "[\"\\\\text{No}\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 108168, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118100"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{42}{47}"
] | [
"skywork"
] | 0639b6a1ad0a8bfd3b2ef6875a18f173259109bb955c1447dd4baf48d92c69fc | [
{
"content": "Three, let $x<0$ and $x-\\frac{1}{x}=\\sqrt{5}$. Find the value of the rational expression $\\frac{x^{10}+x^{0}+x^{4}+1}{x^{16}+x^{8}+x^{2}+1}$.",
"role": "user"
}
] | Three, let $x<0$ and $x-\frac{1}{x}=\sqrt{5}$. Find the value of the rational expression $\frac{x^{10}+x^{0}+x^{4}+1}{x^{16}+x^{8}+x^{2}+1}$. | "[\"\\\\frac{42}{47}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108169, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118101"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.