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 |
|---|---|---|---|---|---|---|---|---|
[
"24"
] | [
"skywork"
] | e65cda5acdd89e649ad9b083e021d1239bc2842bbd31257a5982863119101cdc | [
{
"content": "Yu Semo and Yu Sejmo have created sequences of symbols $\\mathcal{U} = (\\text{U}_1, \\ldots, \\text{U}_6)$ and $\\mathcal{J} = (\\text{J}_1, \\ldots, \\text{J}_6)$ . These sequences satisfy the following properties.\n\n\n- Each of the twelve symbols must be $\\Sigma$ , $\\#$ , $\\triangle$ ... | Yu Semo and Yu Sejmo have created sequences of symbols $\mathcal{U} = (\text{U}_1, \ldots, \text{U}_6)$ and $\mathcal{J} = (\text{J}_1, \ldots, \text{J}_6)$ . These sequences satisfy the following properties.
- Each of the twelve symbols must be $\Sigma$ , $\#$ , $\triangle$ , or $\mathbb{Z}$ .
- In each of th... | "[\"24\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2777, "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:16738"}] | {
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[
"14"
] | [
"skywork"
] | 948d1455c35bcd4eb9746569187acdf161e14a7d99762c301705405de85fd2b4 | [
{
"content": "8. In an $8 \\times 8$ grid, what is the minimum number of small squares that need to be removed so that it is impossible to cut out a complete \"T-shaped\" pentomino from the remaining grid?\n（Sun Wenxian, problem contributor）\n\nWill the above translation meet your needs?",
"role": "user"
... | 8. In an $8 \times 8$ grid, what is the minimum number of small squares that need to be removed so that it is impossible to cut out a complete "T-shaped" pentomino from the remaining grid?
（Sun Wenxian, problem contributor）
Will the above translation meet your needs? | "[\"14\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2787, "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:16739"}] | {
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[
"70"
] | [
"skywork"
] | a542a024d9a9d852d9efdc147c25a2bc18de93fb64f7b09ba66c12d2ee8d7fd1 | [
{
"content": "We say that a natural number is lucky if all of its digits are equal to 7. For example, 7 and 7777 are lucky, but 767 is not. João wrote on a piece of paper the first twenty lucky numbers starting from 7, and then added them up. What is the remainder of the division of this sum by 1000?",
"rol... | We say that a natural number is lucky if all of its digits are equal to 7. For example, 7 and 7777 are lucky, but 767 is not. João wrote on a piece of paper the first twenty lucky numbers starting from 7, and then added them up. What is the remainder of the division of this sum by 1000? | "[\"70\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2788, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:16740"}] | {
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[
"9"
] | [
"skywork"
] | 6039136b36dc39a8c4c27f34d9b83ddc6efd56fd9334c0fb8bac317272c3d359 | [
{
"content": "11. The function $f(x)$ satisfies $f(3+x)=f(3-x), x \\in \\mathbf{R}$, and the equation $f(x)=0$ has exactly three distinct real roots. The sum of these three real roots is $\\qquad$",
"role": "user"
}
] | 11. The function $f(x)$ satisfies $f(3+x)=f(3-x), x \in \mathbf{R}$, and the equation $f(x)=0$ has exactly three distinct real roots. The sum of these three real roots is $\qquad$ | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2768, "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:16741"}] | {
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[
"2E"
] | [
"skywork"
] | 442e4d4c1e6afa4b37ec13edb6ca8a7ba9d7c45d61b600b77ccffe2ae7af4b01 | [
{
"content": "$\\Phi$ is the union of all triangles that are symmetric of the triangle $ABC$ wrt a point $O$, as point $O$ moves along the triangle's sides. If the area of the triangle is $E$, find the area of $\\Phi$.",
"role": "user"
}
] | $\Phi$ is the union of all triangles that are symmetric of the triangle $ABC$ wrt a point $O$, as point $O$ moves along the triangle's sides. If the area of the triangle is $E$, find the area of $\Phi$. | "[\"2E\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2780, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:16742"}, {"dataset": "skywork", "extra_... | {
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[
"\\frac{4}{11}"
] | [
"skywork"
] | 3af1639f9f0678022fe1489010b8c51635df62dcc7ea9ca348b923f101de6c6e | [
{
"content": "For real numbers \\( x \\) and \\( y \\), simplify the equation \\(\\cfrac{\\frac{1}{x} + \\frac{1}{y}}{\\frac{1}{x} + 2\\frac{1}{y}} = 4\\) and express it as \\(\\frac{x+y}{x+2y}\\).",
"role": "user"
}
] | For real numbers \( x \) and \( y \), simplify the equation \(\cfrac{\frac{1}{x} + \frac{1}{y}}{\frac{1}{x} + 2\frac{1}{y}} = 4\) and express it as \(\frac{x+y}{x+2y}\). | "[\"\\\\frac{4}{11}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2792, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16743"}] | {
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} |
[
"89"
] | [
"skywork"
] | 0e374820e18ce8fcb87155d101b23f1d63d0157bd7871b739a0dd0a5a8b6aa34 | [
{
"content": "Given a convex polygon with 20 vertexes, there are many ways of traingulation it (as 18 triangles). We call the diagram of triangulation, meaning the 20 vertexes, with 37 edges(17 triangluation edges and the original 20 edges), a T-diagram. And the subset of this T-diagram with 10 edges which cove... | Given a convex polygon with 20 vertexes, there are many ways of traingulation it (as 18 triangles). We call the diagram of triangulation, meaning the 20 vertexes, with 37 edges(17 triangluation edges and the original 20 edges), a T-diagram. And the subset of this T-diagram with 10 edges which covers all 20 vertexes(mea... | "[\"89\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2784, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16744"}] | {
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"reference_present": true
} |
[
"11"
] | [
"skywork"
] | 962ebaf79f55bc525e030b3f3950ec3fa7a05f4df74a0e371718539cfc627b14 | [
{
"content": "Meteorological observations. At the weather station, it was noticed that during a certain period of time, if it rained in the morning, then the evening was clear, and if it rained in the evening, then the morning was clear. There were a total of 9 rainy days: 6 times there were clear evenings and ... | Meteorological observations. At the weather station, it was noticed that during a certain period of time, if it rained in the morning, then the evening was clear, and if it rained in the evening, then the morning was clear. There were a total of 9 rainy days: 6 times there were clear evenings and 7 times there were cle... | "[\"11\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2790, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:16745"}] | {
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} |
[
"134"
] | [
"skywork"
] | d986d375811a45e72ce71ea4721058af6bef65ebeb73434e29fc830c01531c0e | [
{
"content": "For $1 \\le n \\le 150$, how many integers are there such that $\\frac{n}{n+1}$ is a repeating decimal?",
"role": "user"
}
] | For $1 \le n \le 150$, how many integers are there such that $\frac{n}{n+1}$ is a repeating decimal? | "[\"134\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2810, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:16746"}] | {
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[
"5"
] | [
"skywork"
] | 2435390a5f9616a41ad8ac6c92d0caa9290933df3ff6ee843538268d8ee6d280 | [
{
"content": "1. Given the set $M=\\{2,0,11\\}$. If $A \\varsubsetneqq M$, and $A$ contains at least one even number, then the number of sets $A$ that satisfy the condition is $\\qquad$ .",
"role": "user"
}
] | 1. Given the set $M=\{2,0,11\}$. If $A \varsubsetneqq M$, and $A$ contains at least one even number, then the number of sets $A$ that satisfy the condition is $\qquad$ . | "[\"5\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2797, "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:16747"}] | {
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} |
[
"13"
] | [
"skywork"
] | bae455a893a70f303393aac18a20baf840010f72be76ca3407ee1f84e8d3bff1 | [
{
"content": "Consider the set $\\{2, 7, 12, 17, 22, 27, 32\\}$. Calculate the number of different integers that can be expressed as the sum of three distinct members of this set.",
"role": "user"
}
] | Consider the set $\{2, 7, 12, 17, 22, 27, 32\}$. Calculate the number of different integers that can be expressed as the sum of three distinct members of this set. | "[\"13\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2813, "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:16748"}] | {
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} |
[
"18.75"
] | [
"skywork"
] | 4db20773c96e2b43b7e42f6ff7c6eae0f91671bb56e4111f1e430f7e30695592 | [
{
"content": "A man bought a number of ping-pong balls where a 16% sales tax is added. If he did not have to pay tax, he could have bought 3 more balls for the same amount of money. If \\( B \\) is the total number of balls that he bought, find \\( B \\).",
"role": "user"
}
] | A man bought a number of ping-pong balls where a 16% sales tax is added. If he did not have to pay tax, he could have bought 3 more balls for the same amount of money. If \( B \) is the total number of balls that he bought, find \( B \). | "[\"18.75\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2795, "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:16749"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"\\frac{2\\pi}{3}"
] | [
"skywork"
] | daa328652c7000de5752a2e9d4cd4b1147ff53b8a066aa548bdd310cc59e232f | [
{
"content": "6. Let $O$ be the circumcenter of $\\triangle A B C$, and it satisfies\n$$\n\\overrightarrow{O A}+\\overrightarrow{O B}=\\overrightarrow{O C} \\text {. }\n$$\n\nThen $\\angle A C B=$ $\\qquad$",
"role": "user"
}
] | 6. Let $O$ be the circumcenter of $\triangle A B C$, and it satisfies
$$
\overrightarrow{O A}+\overrightarrow{O B}=\overrightarrow{O C} \text {. }
$$
Then $\angle A C B=$ $\qquad$ | "[\"\\\\frac{2\\\\pi}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2811, "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:16750"}] | {
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} |
[
"9"
] | [
"skywork"
] | c2014e5c756569f76c0793f3b6d4e426b54e22514aedb96ecb5e7737d6eda8e1 | [
{
"content": "Let $x$ be a positive real number. Find the minimum value of $4x^5 + 5x^{-4}.$",
"role": "user"
}
] | Let $x$ be a positive real number. Find the minimum value of $4x^5 + 5x^{-4}.$ | "[\"9\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2819, "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:16751"}] | {
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"reference_present": true
} |
[
"\\{3, 7, 13, 17\\}"
] | [
"skywork"
] | d23c62a7454d0110da6c1b0e1814151d2962c7eb21762d297c52c558a03fd21f | [
{
"content": "We have an a sequence such that $a_n = 2 \\cdot 10^{n + 1} + 19$. Determine all the primes $p$, with $p \\le 19$, for which there exists some $n \\ge 1$ such that $p$ divides $a_n$.",
"role": "user"
}
] | We have an a sequence such that $a_n = 2 \cdot 10^{n + 1} + 19$. Determine all the primes $p$, with $p \le 19$, for which there exists some $n \ge 1$ such that $p$ divides $a_n$. | "[\" \\\\{3, 7, 13, 17\\\\} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2796, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16752"}] | {
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"reference_components": 1,
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} |
[
"81"
] | [
"skywork"
] | a4109e9d1edc236a0768f55c305fef49e9125a43552706378f0fab5f19104e7a | [
{
"content": "12. For a positive integer $n \\leqslant 500$, it has the property: when an element $m$ is randomly selected from the set $\\{1,2, \\cdots, 500\\}$, the probability that $m \\mid n$ is $\\frac{1}{100}$. Then the maximum value of $n$ is $\\qquad$",
"role": "user"
}
] | 12. For a positive integer $n \leqslant 500$, it has the property: when an element $m$ is randomly selected from the set $\{1,2, \cdots, 500\}$, the probability that $m \mid n$ is $\frac{1}{100}$. Then the maximum value of $n$ is $\qquad$ | "[\"81\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2809, "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:16753"}] | {
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} |
[
"35"
] | [
"skywork"
] | b895e8ca147980f6fbb63ee66213da3b66c80ef346a3445295935363e380f1cd | [
{
"content": "The sides of the base of a brick are 28 cm and 9 cm, and its height is 6 cm. A snail crawls rectilinearly along the faces of the brick from one vertex of the lower base to the opposite vertex of the upper base. The horizontal and vertical components of its speed $v_{x}$ and $v_{y}$ are related by ... | The sides of the base of a brick are 28 cm and 9 cm, and its height is 6 cm. A snail crawls rectilinearly along the faces of the brick from one vertex of the lower base to the opposite vertex of the upper base. The horizontal and vertical components of its speed $v_{x}$ and $v_{y}$ are related by the equation $v_{x}^{2... | "[\"35\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2800, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16754"}] | {
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} |
[
"-74"
] | [
"skywork"
] | d74f22d4869c378e6edb6b3e6869884a8e174489e8fcfe24567280c6102fca53 | [
{
"content": "The quadratic $x^2-20x+36$ can be written in the form $(x+b)^2+c$, where $b$ and $c$ are constants. What is $b+c$?",
"role": "user"
}
] | The quadratic $x^2-20x+36$ can be written in the form $(x+b)^2+c$, where $b$ and $c$ are constants. What is $b+c$? | "[\"-74\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2824, "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:16755"}] | {
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[
"97"
] | [
"skywork"
] | 4af7b0d64163983614151d080f189e6b681d56c37da68fb8cf2397e15f74dc09 | [
{
"content": "Three, in a $100 \\times 25$ rectangular table, each cell is filled with a non-negative real number, the number filled in the $i$-th row and $j$-th column is $x_{i, j}$ $(i=1,2, \\cdots 100 ; j=1,2, \\cdots 25)$ (as shown in Table 1). Then, the numbers in each column of Table 1 are rearranged in d... | Three, in a $100 \times 25$ rectangular table, each cell is filled with a non-negative real number, the number filled in the $i$-th row and $j$-th column is $x_{i, j}$ $(i=1,2, \cdots 100 ; j=1,2, \cdots 25)$ (as shown in Table 1). Then, the numbers in each column of Table 1 are rearranged in descending order from top ... | "[\"97\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2802, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16756"}] | {
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[
"2"
] | [
"skywork"
] | 8ce3c758762331b31cd58a9a370054465969191e4d40080d3448027dbc7566ac | [
{
"content": "1. Find the value of the expression $2 a-\\left(\\frac{2 a-3}{a+1}-\\frac{a+1}{2-2 a}-\\frac{a^{2}+3}{2 a^{2-2}}\\right) \\cdot \\frac{a^{3}+1}{a^{2}-a}+\\frac{2}{a}$ when $a=1580$.",
"role": "user"
}
] | 1. Find the value of the expression $2 a-\left(\frac{2 a-3}{a+1}-\frac{a+1}{2-2 a}-\frac{a^{2}+3}{2 a^{2-2}}\right) \cdot \frac{a^{3}+1}{a^{2}-a}+\frac{2}{a}$ when $a=1580$. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2822, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16757"}] | {
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[
"90"
] | [
"skywork"
] | dfd209bfd9f860b084aeb5bb9d2e4bbd98355fe9d6fc5d1457f7500125271c09 | [
{
"content": "10. (10 points) A rectangular chessboard composed of unit squares of size $m \\times n$ (where $m, n$ are positive integers not exceeding 10), has a chess piece placed in the unit square at the bottom-left corner. Two players, A and B, take turns moving the piece. The rules are: move up any number... | 10. (10 points) A rectangular chessboard composed of unit squares of size $m \times n$ (where $m, n$ are positive integers not exceeding 10), has a chess piece placed in the unit square at the bottom-left corner. Two players, A and B, take turns moving the piece. The rules are: move up any number of squares, or move ri... | "[\"90\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2791, "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:16758"}] | {
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[
"0 wins, 1 loss, 2 ties"
] | [
"skywork"
] | 8fb3292ccf58a3c4ef922c2c9e349c36176b132481a9faa5b085562cb6697b12 | [
{
"content": "Which combination of outcomes is not possible for a soccer team that played three games, each ending in a win, loss, or tie, if the team scored more goals than were scored against them?",
"role": "user"
}
] | Which combination of outcomes is not possible for a soccer team that played three games, each ending in a win, loss, or tie, if the team scored more goals than were scored against them? | "[\"0 wins, 1 loss, 2 ties\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 2806, "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:16759"}] | {
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[
"20"
] | [
"skywork"
] | 4375ab9c9ec4b424562b12c7b5f8664b512a820f83b4eee6356eed7d31e33b9e | [
{
"content": "Variant 2.\n\nCurrently, mom is 23 years and 8 months old, and her daughter is 9 months old. In how many months will the number of years in mom's age be equal to the number of months in her daughter's age?",
"role": "user"
}
] | Variant 2.
Currently, mom is 23 years and 8 months old, and her daughter is 9 months old. In how many months will the number of years in mom's age be equal to the number of months in her daughter's age? | "[\"20\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2825, "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:16760"}] | {
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[
"11"
] | [
"skywork"
] | 51b575826ae9b65ec510653e70a9017e3363af6619d89e6c4653b039d3e3cc41 | [
{
"content": "23. In a basketball game at a certain middle school, A scored $\\frac{1}{4}$ of the total points, B scored $\\frac{2}{7}$ of the total points, C scored 15 points, and the remaining seven players each scored no more than 2 points. Then the total score of the remaining seven players is ( ).\n(A) 10\... | 23. In a basketball game at a certain middle school, A scored $\frac{1}{4}$ of the total points, B scored $\frac{2}{7}$ of the total points, C scored 15 points, and the remaining seven players each scored no more than 2 points. Then the total score of the remaining seven players is ( ).
(A) 10
(B) 11
(C) 12
(D) 13
(E) ... | "[\"11\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2807, "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:16761"}] | {
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[
"150"
] | [
"skywork"
] | 673ec69ddbc7f529787d028f377b31f5a75c91371e96caa160650fd7ddf64aa0 | [
{
"content": "All sides of the convex pentagon $ ABCDE$ are of equal length, and $ \\angle A \\equal{} \\angle B \\equal{} 90^{\\circ}$. What is the degree measure of $ \\angle E$?\r\n\r\n$ \\textbf{(A)}\\ 90 \\qquad \\textbf{(B)}\\ 108 \\qquad \\textbf{(C)}\\ 120 \\qquad \\textbf{(D)}\\ 144 \\qquad \\textbf{(... | All sides of the convex pentagon $ ABCDE$ are of equal length, and $ \angle A \equal{} \angle B \equal{} 90^{\circ}$. What is the degree measure of $ \angle E$?
$ \textbf{(A)}\ 90 \qquad \textbf{(B)}\ 108 \qquad \textbf{(C)}\ 120 \qquad \textbf{(D)}\ 144 \qquad \textbf{(E)}\ 150$ | "[\"150\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2823, "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:16762"}] | {
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[
"2+\\sqrt{2}"
] | [
"skywork"
] | 2d03b2d703402716d12c2ccfc9d02b6f48eb88b019324f6ff4d5b05b0857a6e0 | [
{
"content": "Let $ABCD$ be an isosceles trapezoid having parallel bases $\\overline{AB}$ and $\\overline{CD}$ with $AB>CD.$ Line segments from a point inside $ABCD$ to the vertices divide the trapezoid into four triangles whose areas are $2, 3, 4,$ and $5$ starting with the triangle with base $\\overline{CD}$ ... | Let $ABCD$ be an isosceles trapezoid having parallel bases $\overline{AB}$ and $\overline{CD}$ with $AB>CD.$ Line segments from a point inside $ABCD$ to the vertices divide the trapezoid into four triangles whose areas are $2, 3, 4,$ and $5$ starting with the triangle with base $\overline{CD}$ and moving clockwise as s... | "[\"2+\\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2804, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16763"}] | {
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[
"2017"
] | [
"skywork"
] | e363b2e68175dbf0dccaa7744d05ce0eb57542eb87bb59deee0bdf7f18b2352d | [
{
"content": "Marvin had a birthday on Friday, May 27 in the non-leap year 2007. In what year will his birthday next fall on a Thursday?",
"role": "user"
}
] | Marvin had a birthday on Friday, May 27 in the non-leap year 2007. In what year will his birthday next fall on a Thursday? | "[\"2017\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2818, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16764"}] | {
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[
"28"
] | [
"skywork"
] | cea445ebb75f691c36ece481cc6440de4b9668796167a0d96adc63f9278d215f | [
{
"content": "4. On graph paper, a right-angled triangle with legs equal to 7 cells was drawn (see fig.). Then all the grid lines inside the triangle were outlined. What is the maximum number of triangles that can be found in this drawing?\n\n#",
"role": "user"
}
] | 4. On graph paper, a right-angled triangle with legs equal to 7 cells was drawn (see fig.). Then all the grid lines inside the triangle were outlined. What is the maximum number of triangles that can be found in this drawing?
# | "[\"28\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2803, "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:16765"}, {"dataset": "skywork", "extra_... | {
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[
"109368"
] | [
"skywork"
] | 2a6be8cdd6be1408d6edeb0235220cb8ebd37d844285f8ff818f9c0f4fdc2515 | [
{
"content": "In the game of projective set, each card contains some nonempty subset of six distinguishable dots. A projective set deck consists of one card for each of the 63 possible nonempty subsets of dots. How many collections of five cards have an even number of each dot? The order in which the cards appe... | In the game of projective set, each card contains some nonempty subset of six distinguishable dots. A projective set deck consists of one card for each of the 63 possible nonempty subsets of dots. How many collections of five cards have an even number of each dot? The order in which the cards appear does not matter. | "[\"109368\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2812, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16766"}] | {
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} |
[
"3"
] | [
"skywork"
] | 2bb3c307ada24fdf8fc41239231a43cd531b86f35572051ee5fb4f02f7eb8585 | [
{
"content": "14. (25 points) Given the functions\n$$\nf(x)=x-\\ln x-2, \\quad g(x)=x \\ln x+x \\text {. }\n$$\n(1) Prove that $f(x)$ has a zero in the interval $(3,4)$;\n(2) If $k \\in \\mathbf{Z}$, and $g(x)>k(x-1)$ for all $x>1$, find the maximum value of $k$.",
"role": "user"
}
] | 14. (25 points) Given the functions
$$
f(x)=x-\ln x-2, \quad g(x)=x \ln x+x \text {. }
$$
(1) Prove that $f(x)$ has a zero in the interval $(3,4)$;
(2) If $k \in \mathbf{Z}$, and $g(x)>k(x-1)$ for all $x>1$, find the maximum value of $k$. | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2801, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16767"}] | {
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[
"55"
] | [
"skywork"
] | 4651a8e7e48f77616623a44f5e5287248890383cdff16f0109767baf7e0d8626 | [
{
"content": "Stan drove 300 miles in 5 hours, 20 minutes. Next, he drove 360 miles in 6 hours, 40 minutes. What was Stan's average speed in miles per hour for the total trip?",
"role": "user"
}
] | Stan drove 300 miles in 5 hours, 20 minutes. Next, he drove 360 miles in 6 hours, 40 minutes. What was Stan's average speed in miles per hour for the total trip? | "[\"55\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2839, "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:16768"}] | {
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} |
[
"\\frac{\\sqrt{3}}{36}"
] | [
"skywork"
] | 7a3a8c59a6414adbf8675e5966ecfa4bb50987aa7513d2dcc3b1c3b9e017f607 | [
{
"content": "Given a regular triangular prism \\(ABC-A_1B_1C_1\\) with side edges and base edges all equal to 1, find the volume of the common part of the tetrahedra \\(A_1ABC\\), \\(B_1ABC\\), and \\(C_1ABC\\).",
"role": "user"
}
] | Given a regular triangular prism \(ABC-A_1B_1C_1\) with side edges and base edges all equal to 1, find the volume of the common part of the tetrahedra \(A_1ABC\), \(B_1ABC\), and \(C_1ABC\). | "[\"\\\\frac{\\\\sqrt{3}}{36}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2817, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16769"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"338"
] | [
"skywork"
] | e6b9fb8f447167352a734965f6ed67aeb8729ef4adc10dba5fc63567cba233b8 | [
{
"content": "Find the total number of triples of integers $(x,y,n)$ satisfying the equation $\\tfrac 1x+\\tfrac 1y=\\tfrac1{n^2}$, where $n$ is either $2012$ or $2013$.",
"role": "user"
}
] | Find the total number of triples of integers $(x,y,n)$ satisfying the equation $\tfrac 1x+\tfrac 1y=\tfrac1{n^2}$, where $n$ is either $2012$ or $2013$. | "[\"338\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2828, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16771"}, {"dataset": "skywork", "extra_in... | {
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"reference_components": 1,
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} |
[
"23"
] | [
"skywork"
] | 4cdf72e193b919b1ed3728bdda1abee07901c8cdf3d283fb6fe830859f67058f | [
{
"content": "8. Let $S=\\left\\{r_{1}, r_{2}, \\cdots, r_{n}\\right\\} \\subseteq\\{1,2,3, \\cdots, 50\\}$, and any two numbers in $S$ do not sum to a multiple of 7, find the maximum value of $n$.",
"role": "user"
}
] | 8. Let $S=\left\{r_{1}, r_{2}, \cdots, r_{n}\right\} \subseteq\{1,2,3, \cdots, 50\}$, and any two numbers in $S$ do not sum to a multiple of 7, find the maximum value of $n$. | "[\"23\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2831, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:16772"}] | {
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} |
[
"\\frac{57}{20}"
] | [
"skywork"
] | 2d7b72858d98c79250c1ce055169e5b02b0c06ffd58e7968751475e3b7418dc4 | [
{
"content": "Given the sequence $\\left\\{a_{n}\\right\\}$ defined by \\(a_{1}=\\frac{2}{3}\\), \\(a_{n+1}=a_{n}^{2}+a_{n-1}^{2}+\\cdots+a_{1}^{2}\\) (where \\(n \\in \\mathbf{N}^{*}\\)), find the smallest value of \\(M\\) such that for any \\(n \\in \\mathbf{N}^{*}\\), the inequality \\(\\frac{1}{a_{1}+1}+\\f... | Given the sequence $\left\{a_{n}\right\}$ defined by \(a_{1}=\frac{2}{3}\), \(a_{n+1}=a_{n}^{2}+a_{n-1}^{2}+\cdots+a_{1}^{2}\) (where \(n \in \mathbf{N}^{*}\)), find the smallest value of \(M\) such that for any \(n \in \mathbf{N}^{*}\), the inequality \(\frac{1}{a_{1}+1}+\frac{1}{a_{2}+1}+\cdots+\frac{1}{a_{n}+1}<M\) ... | "[\"\\\\frac{57}{20}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2816, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:16773"}] | {
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} |
[
"424"
] | [
"skywork"
] | 57481a9dbab404c022aedd4eaa458c29617f33b0391b6e166336abac10f7818a | [
{
"content": "Find the minimum value of \n\\[(13 - x)(11 - x)(13 + x)(11 + x) + 1000.\\]",
"role": "user"
}
] | Find the minimum value of
\[(13 - x)(11 - x)(13 + x)(11 + x) + 1000.\] | "[\"424\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2837, "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:16774"}] | {
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} |
[
"-5"
] | [
"skywork"
] | 2221842461bdec18edfb2174c32c93bbc224eff7292d730ba1bd46ee83d9256f | [
{
"content": "Given the sequence $\\{a_n\\}$ satisfying $(\\log_3{a_n}+1=\\log_3{a_{n+1}}\\ (n\\in \\mathbb{N}^*)$, and $(a_2+a_4+a_6=9$, find the value of $(\\log_{\\frac{1}{3}}(a_5+a_7+a_9))$.",
"role": "user"
}
] | Given the sequence $\{a_n\}$ satisfying $(\log_3{a_n}+1=\log_3{a_{n+1}}\ (n\in \mathbb{N}^*)$, and $(a_2+a_4+a_6=9$, find the value of $(\log_{\frac{1}{3}}(a_5+a_7+a_9))$. | "[\"-5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2815, "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:16775"}] | {
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[
"-5"
] | [
"skywork"
] | 4fe8f7d5cd3512548e3f2cc629bf8eccf520748f8274bc8144a0c9a0ef5aa877 | [
{
"content": "Three. (Full marks 20 points) Given the equation $x^{2}+m x-m+1=0$ (where $m$ is an integer) has two distinct positive integer roots. Find the value of $m$.\n\n---\n\nThe translation maintains the original format and line breaks as requested.",
"role": "user"
}
] | Three. (Full marks 20 points) Given the equation $x^{2}+m x-m+1=0$ (where $m$ is an integer) has two distinct positive integer roots. Find the value of $m$.
---
The translation maintains the original format and line breaks as requested. | "[\"-5\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2826, "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:16776"}] | {
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} |
[
"S_{1}=S_{2}"
] | [
"skywork"
] | 964a4cbc622f3b6bfb5d75c699574118059bbc3f4b8d097e7c038fd229b63d62 | [
{
"content": "1. As shown in the figure: In $\\triangle A B C$, the angle bisector of $\\angle A$ intersects $B C$ at $D$, and intersects the circumcircle of $\\triangle A B C$ at $P$. A circle is drawn with $A D$ as a chord, intersecting $A B$ at $M$ and the extension of $A C$ at $N$. $P M$ intersects $B C$ at... | 1. As shown in the figure: In $\triangle A B C$, the angle bisector of $\angle A$ intersects $B C$ at $D$, and intersects the circumcircle of $\triangle A B C$ at $P$. A circle is drawn with $A D$ as a chord, intersecting $A B$ at $M$ and the extension of $A C$ at $N$. $P M$ intersects $B C$ at $G$. If the area of $\tr... | "[\"S_{1}=S_{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2808, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:16777"}] | {
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[
"\\frac{\\sqrt{2}+1}{2}"
] | [
"skywork"
] | bf1aab2c576766bf9c8eecc4fe47a78f26b73831d8cb9cd890debbf59ce6f0e3 | [
{
"content": "Find the least upper bound for the set of values \\((x_1 x_2 + 2x_2 x_3 + x_3 x_4) / (x_1^2 + x_2^2 + x_3^2 + x_4^2)\\), where \\(x_i\\) are real numbers, not all zero.",
"role": "user"
}
] | Find the least upper bound for the set of values \((x_1 x_2 + 2x_2 x_3 + x_3 x_4) / (x_1^2 + x_2^2 + x_3^2 + x_4^2)\), where \(x_i\) are real numbers, not all zero. | "[\"\\\\frac{\\\\sqrt{2}+1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2830, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:16778"}] | {
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} |
[
"6-3\\sqrt{3}"
] | [
"skywork"
] | 77d4550ced5ea737d75769f328a286d19803fa940ffc46616c91e42bca122e65 | [
{
"content": "The larger root minus the smaller root of the equation $(7+4\\sqrt{3})x^2+(2+\\sqrt{3})x-2=0$ is",
"role": "user"
}
] | The larger root minus the smaller root of the equation $(7+4\sqrt{3})x^2+(2+\sqrt{3})x-2=0$ is | "[\"6-3\\\\sqrt{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2835, "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:16779"}] | {
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[
"37"
] | [
"skywork"
] | e31f7090eb9e281a832fe6f4d47ecaafbb57e6ca4349a7fa73a8358d6c754af9 | [
{
"content": "Let $S$ be the set of triples $(a,b,c)$ of non-negative integers with $a+b+c$ even. The value of the sum\n \\[\\sum_{(a,b,c)\\in S}\\frac{1}{2^a3^b5^c}\\]\n can be expressed as $\\frac{m}{n}$ for relative prime positive integers $m$ and $n$. Compute $m+n$.\n\n[i]Proposed by Nathan Xiong[/i]"... | Let $S$ be the set of triples $(a,b,c)$ of non-negative integers with $a+b+c$ even. The value of the sum
\[\sum_{(a,b,c)\in S}\frac{1}{2^a3^b5^c}\]
can be expressed as $\frac{m}{n}$ for relative prime positive integers $m$ and $n$. Compute $m+n$.
[i]Proposed by Nathan Xiong[/i] | "[\"37\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2827, "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:16780"}] | {
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[
"127"
] | [
"skywork"
] | 295c0a71154afcaa36a1965cf204baa5b06f089ea1b1005d8b907cda62ebbaac | [
{
"content": "There are $5$ vertices labelled $1,2,3,4,5$. For any two pairs of vertices $u, v$, the edge $uv$\nis drawn with probability $1/2$. If the probability that the resulting graph is a tree is given by $\\dfrac{p}{q}$ where $p, q$ are coprime, then find the value of $q^{1/10} + p$.",
"role": "user"... | There are $5$ vertices labelled $1,2,3,4,5$. For any two pairs of vertices $u, v$, the edge $uv$
is drawn with probability $1/2$. If the probability that the resulting graph is a tree is given by $\dfrac{p}{q}$ where $p, q$ are coprime, then find the value of $q^{1/10} + p$. | "[\"127\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2834, "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:16781"}] | {
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[
"100\\pi"
] | [
"skywork"
] | 2805dbfbab284e2e7c778ac10c88b05104450f4bfeecab900e4663943ee544c0 | [
{
"content": "The slant height of a cone is 13 cm, and the height from the vertex to the center of the base is 12 cm. What is the number of cubic centimeters in the volume of the cone? Express your answer in terms of $\\pi$.",
"role": "user"
}
] | The slant height of a cone is 13 cm, and the height from the vertex to the center of the base is 12 cm. What is the number of cubic centimeters in the volume of the cone? Express your answer in terms of $\pi$. | "[\"100\\\\pi\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2820, "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:16782"}] | {
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} |
[
"8"
] | [
"skywork"
] | b906bbd2225c4604387f3b2c15c44595f0de294a550feeeed5fa2acd239db69c | [
{
"content": "5. Let $S=\\{1,2,3,4\\}$, and the sequence $a_{1}, a_{2}, \\cdots, a_{n}$ has the following property: for any non-empty subset $B$ of $S$, there are consecutive $|B|$ terms in the sequence that exactly form the set $B$. Find the minimum value of $n$.\n(1997, Shanghai High School Mathematics Compet... | 5. Let $S=\{1,2,3,4\}$, and the sequence $a_{1}, a_{2}, \cdots, a_{n}$ has the following property: for any non-empty subset $B$ of $S$, there are consecutive $|B|$ terms in the sequence that exactly form the set $B$. Find the minimum value of $n$.
(1997, Shanghai High School Mathematics Competition) | "[\"8\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2844, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16783"}] | {
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} |
[
"70000000"
] | [
"skywork"
] | e30274ccd2112adbb68522064111aa1f307c94f553114eab4ed24daed97062ca | [
{
"content": "2. (5 points) Two different natural numbers end with 7 zeros and have exactly 72 divisors. Find their sum.",
"role": "user"
}
] | 2. (5 points) Two different natural numbers end with 7 zeros and have exactly 72 divisors. Find their sum. | "[\"70000000\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2833, "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:16784"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 66ff37db1efaa5229c47bc8caf86ba8a119c4c4b882c2144eb0ff979a4bd58e6 | [
{
"content": "The value of $\\sqrt{\\frac{\\sqrt{81}+\\sqrt{81}}{2}}$ is\n(A) 3\n(B) 18\n(C) 27\n(D) 81\n(E) 162",
"role": "user"
}
] | The value of $\sqrt{\frac{\sqrt{81}+\sqrt{81}}{2}}$ is
(A) 3
(B) 18
(C) 27
(D) 81
(E) 162 | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2852, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16785"}] | {
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} |
[
"(a_{n},a_{n+1})"
] | [
"skywork"
] | 38e3c43a6288fa3b41a064c0a196e657941b69bb4ca255ef496027d0fb39271e | [
{
"content": "6) Find all pairs of coprime positive integers $(x, y)$ such that: $x \\mid y^{2}+210$, $y \\mid x^{2}+210$.",
"role": "user"
}
] | 6) Find all pairs of coprime positive integers $(x, y)$ such that: $x \mid y^{2}+210$, $y \mid x^{2}+210$. | "[\"(a_{n},a_{n+1})\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2843, "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:16786"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"13\\times13=169,31\\times31=961"
] | [
"skywork"
] | 79bb3ba9ee7f78d095036866107de854d80d26b5017d633c8d2fa14049e5a98c | [
{
"content": "[ Rebus $]$\n\nRebus system. Decode the numerical rebus - system\n\n$\\left\\{\\begin{array}{c}M A \\cdot M A=M H P \\\\ A M \\cdot A M=P h M\\end{array}\\right.$\n\n(different letters correspond to different digits, and the same 一 the same).\n\n#",
"role": "user"
}
] | [ Rebus $]$
Rebus system. Decode the numerical rebus - system
$\left\{\begin{array}{c}M A \cdot M A=M H P \\ A M \cdot A M=P h M\end{array}\right.$
(different letters correspond to different digits, and the same 一 the same).
# | "[\"13\\\\times13=169,31\\\\times31=961\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2821, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16787"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"23"
] | [
"skywork"
] | ecda48191611f4495d32117713c5d21031957dab0ef24b55366e00671bde1c71 | [
{
"content": "If $f(x)$ is a monic quartic polynomial such that $f(-1)=-1, f(2)=-4, f(-3)=-9$, and $f(4)=-16$, find $f(1)$.",
"role": "user"
}
] | If $f(x)$ is a monic quartic polynomial such that $f(-1)=-1, f(2)=-4, f(-3)=-9$, and $f(4)=-16$, find $f(1)$. | "[\"23\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2838, "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:16788"}, {"dataset": "skywork", "extra_inf... | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"77"
] | [
"skywork"
] | 48dab2d19b4bb2dcbd7cfb4b26a0f5bc64e081f82a10e5290c11d26012b122d2 | [
{
"content": "What is the sum of the prime factors of $2010$?",
"role": "user"
}
] | What is the sum of the prime factors of $2010$? | "[\"77\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2860, "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:16789"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2\\sqrt{5}"
] | [
"skywork"
] | 2e7264c4fbc39bb73b5fd8bb9d33a568ea908cf8a6c364bf0a58497e25c24392 | [
{
"content": "Given $a, b, c > 0$ and $(a+b)bc = 5$, find the minimum value of $2a+b+c$.",
"role": "user"
}
] | Given $a, b, c > 0$ and $(a+b)bc = 5$, find the minimum value of $2a+b+c$. | "[\"2\\\\sqrt{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2857, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:16790"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 6d9d1a0f676db149216c68d327aaf3e839667759139ee04cc567df8d7389ee87 | [
{
"content": "7.055. $\\log _{3}\\left(3^{x}-8\\right)=2-x$.\n\nTranslate the above text into English, please keep the original text's line breaks and format, and output the translation result directly.\n\n7.055. $\\log _{3}\\left(3^{x}-8\\right)=2-x$.",
"role": "user"
}
] | 7.055. $\log _{3}\left(3^{x}-8\right)=2-x$.
Translate the above text into English, please keep the original text's line breaks and format, and output the translation result directly.
7.055. $\log _{3}\left(3^{x}-8\right)=2-x$. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2863, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16791"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{5\\pi}{6}"
] | [
"skywork"
] | 49eee7dfa7b1b5cd110535e8765db501360ed4b9a0807e47a6ea334b43d0dea9 | [
{
"content": "Given vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfy $|\\overrightarrow{a}|=1$, $|\\overrightarrow{b}|=2$, and $\\overrightarrow{a} \\cdot \\overrightarrow{b} = -\\sqrt{3}$, calculate the angle between $\\overrightarrow{a}$ and $\\overrightarrow{b}$.",
"role": "user"
}
] | Given vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfy $|\overrightarrow{a}|=1$, $|\overrightarrow{b}|=2$, and $\overrightarrow{a} \cdot \overrightarrow{b} = -\sqrt{3}$, calculate the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$. | "[\"\\\\frac{5\\\\pi}{6}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2851, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16792"}] | {
"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{40}{9}"
] | [
"skywork"
] | 217c80db9b5e20c76f359c7af6155cb45a503cf78564ef2c1919996964e02ded | [
{
"content": "A noodle shop offers classic specialty noodles to customers, who can either dine in at the shop (referred to as \"dine-in\" noodles) or purchase packaged fresh noodles with condiments (referred to as \"fresh\" noodles). It is known that the total price of 3 portions of \"dine-in\" noodles and 2 po... | A noodle shop offers classic specialty noodles to customers, who can either dine in at the shop (referred to as "dine-in" noodles) or purchase packaged fresh noodles with condiments (referred to as "fresh" noodles). It is known that the total price of 3 portions of "dine-in" noodles and 2 portions of "fresh" noodles is... | "[\"\\\\frac{40}{9}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2841, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16793"}] | {
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} |
[
"17"
] | [
"skywork"
] | e452b35ab50d9ed49c1fe1ca1b01297922b39c6f76dc4b8c91fde5da9f0ba38b | [
{
"content": "An architect is building a structure that will place vertical pillars at the vertices of regular hexagon $ABCDEF$, which is lying horizontally on the ground. The six pillars will hold up a flat solar panel that will not be parallel to the ground. The heights of pillars at $A$, $B$, and $C$ are $12... | An architect is building a structure that will place vertical pillars at the vertices of regular hexagon $ABCDEF$, which is lying horizontally on the ground. The six pillars will hold up a flat solar panel that will not be parallel to the ground. The heights of pillars at $A$, $B$, and $C$ are $12$, $9$, and $10$ meter... | "[\"17\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2829, "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:16794"}] | {
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[
"2006"
] | [
"skywork"
] | fbe7a25a7ec5c681ed8e71dcb295b2b34e2ee4586499eb5cbc56c978f950c8f7 | [
{
"content": "Let $f(x)$ be the function such that $f(x)>0$ at $x\\geq 0$ and $\\{f(x)\\}^{2006}=\\int_{0}^{x}f(t) dt+1.$ \r\n\r\nFind the value of $\\{f(2006)\\}^{2005}.$",
"role": "user"
}
] | Let $f(x)$ be the function such that $f(x)>0$ at $x\geq 0$ and $\{f(x)\}^{2006}=\int_{0}^{x}f(t) dt+1.$
Find the value of $\{f(2006)\}^{2005}.$ | "[\"2006\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2842, "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:16795"}, {"dataset": "skywork", "extra_inf... | {
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[
"490"
] | [
"skywork"
] | 7aa10b580f9545931b7579471aeca554307190f66272aab5fb2e6278a831beda | [
{
"content": "There are $8$ balls of the same size, including $4$ different black balls, $2$ different red balls, and $2$ different yellow balls.<br/>$(1)$ Arrange these $8$ balls in a line, with the black balls together, the 2 red balls adjacent, and the 2 yellow balls not adjacent. Find the number of ways to ... | There are $8$ balls of the same size, including $4$ different black balls, $2$ different red balls, and $2$ different yellow balls.<br/>$(1)$ Arrange these $8$ balls in a line, with the black balls together, the 2 red balls adjacent, and the 2 yellow balls not adjacent. Find the number of ways to arrange them;<br/>$(2)... | "[\"490\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2836, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16796"}] | {
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[
"1240"
] | [
"skywork"
] | 26d331f3155982d6e5a0cec9f06a24eb9927f2264fd759e0fd682cdcb4f55a41 | [
{
"content": "If \\(\\frac{5+6+7+8}{4} = \\frac{2014+2015+2016+2017}{N}\\), calculate the value of \\(N\\).",
"role": "user"
}
] | If \(\frac{5+6+7+8}{4} = \frac{2014+2015+2016+2017}{N}\), calculate the value of \(N\). | "[\"1240\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2854, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16797"}] | {
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[
"1"
] | [
"skywork"
] | 9bff009dc9e9f2804156561e69e234bbd76488b06d238c830f29c239e91797e8 | [
{
"content": "Three. (25 points) If the pair of positive integers $(a, x)$ satisfies\n$$\n\\sqrt{\\frac{a-x}{1+x}}=\\frac{a-x^{2}}{1+x^{2}} \\neq x \\text {, }\n$$\n\nfind all positive integers $a$ that meet the requirement.",
"role": "user"
}
] | Three. (25 points) If the pair of positive integers $(a, x)$ satisfies
$$
\sqrt{\frac{a-x}{1+x}}=\frac{a-x^{2}}{1+x^{2}} \neq x \text {, }
$$
find all positive integers $a$ that meet the requirement. | "[\"1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2848, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:16798"}] | {
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[
"20"
] | [
"skywork"
] | 5ace24b387e921488cd24ff672bb1c62d11776b7905d9a6398a44f037d2f1b6b | [
{
"content": "Example 4 A store sells goods that cost 10 yuan each at 18 yuan each, and can sell 60 of them per day. After conducting a market survey, the store manager found that if the selling price of the goods (based on 18 yuan each) is increased by 1 yuan, the daily sales volume will decrease by 5; if the ... | Example 4 A store sells goods that cost 10 yuan each at 18 yuan each, and can sell 60 of them per day. After conducting a market survey, the store manager found that if the selling price of the goods (based on 18 yuan each) is increased by 1 yuan, the daily sales volume will decrease by 5; if the selling price of the g... | "[\"20\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2832, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:16799"}] | {
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[
"15 \\, \\text{cm}^2"
] | [
"skywork"
] | a2b24430306ca4362cfbec421cfaf42aff9a6ea0840be8c1ef53ebfac420591a | [
{
"content": "Let be given a triangle $ABC$ and points $D,M,N$ belong to $BC,AB,AC$, respectively. Suppose that $MD$ is parallel to $AC$ and $ND$ is parallel to $AB$. If $S_{\\vartriangle BMD} = 9$ cm $^2, S_{\\vartriangle DNC} = 25$ cm$^2$, compute $S_{\\vartriangle AMN}$?",
"role": "user"
}
] | Let be given a triangle $ABC$ and points $D,M,N$ belong to $BC,AB,AC$, respectively. Suppose that $MD$ is parallel to $AC$ and $ND$ is parallel to $AB$. If $S_{\vartriangle BMD} = 9$ cm $^2, S_{\vartriangle DNC} = 25$ cm$^2$, compute $S_{\vartriangle AMN}$? | "[\"15 \\\\, \\\\text{cm}^2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2840, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:16800"}] | {
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} |
[
"2"
] | [
"skywork"
] | d2e29721a35e2ee4e7825140cc1077697d0859fd0e66a0acc0ff076c4f2c55f7 | [
{
"content": "Let $f(x)=x^2+bx+1,$ where $b$ is a real number. Find the number of integer solutions to the inequality $f(f(x)+x)<0.$",
"role": "user"
}
] | Let $f(x)=x^2+bx+1,$ where $b$ is a real number. Find the number of integer solutions to the inequality $f(f(x)+x)<0.$ | "[\"2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2849, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16801"}] | {
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"reference_components": 1,
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} |
[
"715"
] | [
"skywork"
] | 8d0a2f3c43e75a87a378593a4fad5efe91441a91f8cb324ded7cf49f5b2ebab9 | [
{
"content": "Triangle $ABC$ has side lengths $AB=120,BC=220$, and $AC=180$. Lines $\\ell_A,\\ell_B$, and $\\ell_C$ are drawn parallel to $\\overline{BC},\\overline{AC}$, and $\\overline{AB}$, respectively, such that the intersections of $\\ell_A,\\ell_B$, and $\\ell_C$ with the interior of $\\triangle ABC$ are... | Triangle $ABC$ has side lengths $AB=120,BC=220$, and $AC=180$. Lines $\ell_A,\ell_B$, and $\ell_C$ are drawn parallel to $\overline{BC},\overline{AC}$, and $\overline{AB}$, respectively, such that the intersections of $\ell_A,\ell_B$, and $\ell_C$ with the interior of $\triangle ABC$ are segments of lengths $55,45$, an... | "[\"715\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 2859, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:16802"}, {"dataset": "skywork", "extra_... | {
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[
"3033"
] | [
"skywork"
] | 9b3f1a4750c9dfc7db2555472aad27059d628131343d5daa441c431ed2db59f8 | [
{
"content": "Task 4. (20 points) In a sequence of natural numbers, each subsequent number, starting from the third, is equal to the absolute difference of the two preceding ones. Determine the maximum number of elements such a sequence can contain if the value of each of them does not exceed 2021.\n\n#",
"... | Task 4. (20 points) In a sequence of natural numbers, each subsequent number, starting from the third, is equal to the absolute difference of the two preceding ones. Determine the maximum number of elements such a sequence can contain if the value of each of them does not exceed 2021.
# | "[\"3033\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2850, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16804"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"512"
] | [
"skywork"
] | f09dd40a2eac442d98693cb91cd52e5593fc5fca3bfe128b0e63e31b06817c9e | [
{
"content": "Subject (4). For each non-empty subset $A=\\left\\{a_{1}, a_{2}, \\ldots, a_{k}\\right\\}$ of the set $\\{1,2, \\ldots, 10\\}, k=1,2, \\ldots, 10$, consider the sum\n\n$$\nS(A)=a_{1}-a_{1} a_{2}+a_{1} a_{2} a_{3}-\\cdots-(-1)^{k} a_{1} a_{2} \\cdots a_{k}\n$$\n\nwhere $a_{1}<a_{2}<\\cdots<a_{k}$. ... | Subject (4). For each non-empty subset $A=\left\{a_{1}, a_{2}, \ldots, a_{k}\right\}$ of the set $\{1,2, \ldots, 10\}, k=1,2, \ldots, 10$, consider the sum
$$
S(A)=a_{1}-a_{1} a_{2}+a_{1} a_{2} a_{3}-\cdots-(-1)^{k} a_{1} a_{2} \cdots a_{k}
$$
where $a_{1}<a_{2}<\cdots<a_{k}$. Determine the sum of all these sums. | "[\"512\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2853, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16805"}] | {
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[
"3"
] | [
"skywork"
] | d53a2b3fcf4ec99ebace38fc5e66541c82d101a67aca8fadee4aeb66662e6323 | [
{
"content": "Let $\\sigma(n)$ be the sum of the prime divisors of $n$ (counted without multiplicity). Find all $n$ such that:\n\n$$\n\\sigma\\left(2^{n}+1\\right)=\\sigma(n)\n$$",
"role": "user"
}
] | Let $\sigma(n)$ be the sum of the prime divisors of $n$ (counted without multiplicity). Find all $n$ such that:
$$
\sigma\left(2^{n}+1\right)=\sigma(n)
$$ | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2861, "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:16806"}] | {
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"reference_present": true
} |
[
"\\frac{1152}{125}\\pi\\mathrm{}^{3}"
] | [
"skywork"
] | 45ecb4fbe1ee74fe57645d1dc2982ea9dac1b83ef54519d044a8553368d58b16 | [
{
"content": "11.082. The height of the cone and its slant height are 4 and 5 cm, respectively. Find the volume of a hemisphere inscribed in the cone, with its base lying on the base of the cone.",
"role": "user"
}
] | 11.082. The height of the cone and its slant height are 4 and 5 cm, respectively. Find the volume of a hemisphere inscribed in the cone, with its base lying on the base of the cone. | "[\"\\\\frac{1152}{125}\\\\pi\\\\mathrm{}^{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2856, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16807"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"108"
] | [
"skywork"
] | 01dc6ea4d81e9cc7c1911323168bdebc6e7b0c043a93d86017a4236472017298 | [
{
"content": "Find the smallest positive integer $b$ for which $x^2 + bx + 1760$ factors into a product of two polynomials, each having integer coefficients.",
"role": "user"
}
] | Find the smallest positive integer $b$ for which $x^2 + bx + 1760$ factors into a product of two polynomials, each having integer coefficients. | "[\"108\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2876, "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:16808"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{2}"
] | [
"skywork"
] | 8f575564a36bfa75065a25db32622ad650479c38083cfab9f424d2f211558b79 | [
{
"content": "8. Given that $A B C D-A_{1} B_{1} C_{1} D_{1}$ is a unit cube, two ants, one black and one white, start from point $A$ and crawl along the edges. Each time they complete an edge, it is called “completing a segment”. The white ant’s crawling route is $A A_{1} \\rightarrow A_{1} D_{1} \\rightarrow ... | 8. Given that $A B C D-A_{1} B_{1} C_{1} D_{1}$ is a unit cube, two ants, one black and one white, start from point $A$ and crawl along the edges. Each time they complete an edge, it is called “completing a segment”. The white ant’s crawling route is $A A_{1} \rightarrow A_{1} D_{1} \rightarrow \cdots$, and the black a... | "[\"\\\\sqrt{2}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2847, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16809"}] | {
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} |
[
"16"
] | [
"skywork"
] | 6f76d9c8ad25d1da706e55ee79cf4ee8e6f81926dba4d0c84a20f954b6032db3 | [
{
"content": "[Tournaments and tournament tables]\n\nA school table tennis championship was held according to the Olympic system. The winner won six matches. How many participants in the tournament won more games than they lost? (In a tournament according to the Olympic system, participants are divided into pai... | [Tournaments and tournament tables]
A school table tennis championship was held according to the Olympic system. The winner won six matches. How many participants in the tournament won more games than they lost? (In a tournament according to the Olympic system, participants are divided into pairs. Those who lost a gam... | "[\"16\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2846, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16810"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"AB"
] | [
"skywork"
] | 50c20ab29fc79ff180a9af7c4892131bde59462e2c1a228a2bb3c2521120da5a | [
{
"content": "Let a semicircle $AB$ be given and let $X$ be an inner point of the arc. Consider a point $Y$ on ray $XA$ such that $XY=XB$. Find the locus of all points $Y$ when $X$ moves on the arc $AB$ (excluding the endpoints).",
"role": "user"
}
] | Let a semicircle $AB$ be given and let $X$ be an inner point of the arc. Consider a point $Y$ on ray $XA$ such that $XY=XB$. Find the locus of all points $Y$ when $X$ moves on the arc $AB$ (excluding the endpoints). | "[\" AB \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2867, "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:16811"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"70"
] | [
"skywork"
] | a36f02a1ef164a36dd8d9c9dc4f0e234c78b87623e1ffc8cb0735ddada7c72b1 | [
{
"content": "10. (10 points) The area of rectangle $A B C D$ is 70 square centimeters. The vertex $F$ of trapezoid $A F G E$ is on $B C$, and $D$ is the midpoint of the non-parallel side $E G$. Find the area of trapezoid $A F G E$.",
"role": "user"
}
] | 10. (10 points) The area of rectangle $A B C D$ is 70 square centimeters. The vertex $F$ of trapezoid $A F G E$ is on $B C$, and $D$ is the midpoint of the non-parallel side $E G$. Find the area of trapezoid $A F G E$. | "[\"70\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2858, "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:16812"}] | {
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[
"288"
] | [
"skywork"
] | 22bbff3f757210edf4f3c2b901ae331e73190c490575750d5094d9c50e8be8b8 | [
{
"content": "Two teachers are taking a photo with 3 male students and 3 female students lined up in a row. The teachers can only stand at the ends, and the male students cannot be adjacent. How many different ways are there to arrange the photo?",
"role": "user"
}
] | Two teachers are taking a photo with 3 male students and 3 female students lined up in a row. The teachers can only stand at the ends, and the male students cannot be adjacent. How many different ways are there to arrange the photo? | "[\"288\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2866, "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:16813"}] | {
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[
"110^\\circ"
] | [
"skywork"
] | c6e53cfc7ffe2d8e2f1665e4c39582f0cdf882ac5382be0ffd409eb1a070ed4e | [
{
"content": "The number of degrees in the measures of the interior angles of a convex pentagon are five consecutive integers. What is the number of degrees in the largest angle?",
"role": "user"
}
] | The number of degrees in the measures of the interior angles of a convex pentagon are five consecutive integers. What is the number of degrees in the largest angle? | "[\"110^\\\\circ\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2887, "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:16814"}] | {
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[
"5"
] | [
"skywork"
] | 439e31900fb0b5e83abf7bab1e97d121c5c99e519330e475e48402a5b737a2d8 | [
{
"content": "4. The maximum weight allowed in a service lift is satisfied exactly by 12 identical large packages or by 20 identical small packages. What is the greatest number of small packages that the lift can carry alongside nine large packages?\nA 3\nB 4\nC 5\nD 6\nE 8",
"role": "user"
}
] | 4. The maximum weight allowed in a service lift is satisfied exactly by 12 identical large packages or by 20 identical small packages. What is the greatest number of small packages that the lift can carry alongside nine large packages?
A 3
B 4
C 5
D 6
E 8 | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2862, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16815"}] | {
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[
"\\frac{(115-62\\sqrt{3})\\pi}{12}+10-5\\sqrt{3}"
] | [
"skywork"
] | 6edcf57b2bb5b346d88e37535454b8de06f87ce8cea73ac601e976626b4394d9 | [
{
"content": "## Zadatak A-3.5.\n\nKocka $A B C D A^{\\prime} B^{\\prime} C^{\\prime} D^{\\prime}$ stranice duljine 1 presječena je sferom. Središte sfere je točka $S$ na dužini $\\overline{A D}$ takva da je $|A S|=\\sqrt{3}-1$. Sfera prolazi točkama $C$ i $D^{\\prime}$, te siječe bridove $\\overline{A B}$ i $\... | ## Zadatak A-3.5.
Kocka $A B C D A^{\prime} B^{\prime} C^{\prime} D^{\prime}$ stranice duljine 1 presječena je sferom. Središte sfere je točka $S$ na dužini $\overline{A D}$ takva da je $|A S|=\sqrt{3}-1$. Sfera prolazi točkama $C$ i $D^{\prime}$, te siječe bridove $\overline{A B}$ i $\overline{A A^{\prime}}$.
Odredi... | "[\"\\\\frac{(115-62\\\\sqrt{3})\\\\pi}{12}+10-5\\\\sqrt{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2871, "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:16816"}] | {
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} |
[
"-\\frac{2}{3}"
] | [
"skywork"
] | 185ded97f000634d7508296a512e2307ae0d34debcfb7f1a962e7f3fd84287ea | [
{
"content": "The operation $\\otimes$ is defined for all nonzero numbers by $a \\otimes b = \\frac{a^{2}}{b}$. Determine $[(1 \\otimes 2) \\otimes 3] - [1 \\otimes (2 \\otimes 3)]$.",
"role": "user"
}
] | The operation $\otimes$ is defined for all nonzero numbers by $a \otimes b = \frac{a^{2}}{b}$. Determine $[(1 \otimes 2) \otimes 3] - [1 \otimes (2 \otimes 3)]$. | "[\"-\\\\frac{2}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2872, "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:16817"}] | {
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[
"58"
] | [
"skywork"
] | 0c31b434007e0637b0981a165d93d23ff76bdde88cb94b4b4ec1ef2d4802ef25 | [
{
"content": "Find all solutions to the equation $\\displaystyle\\sqrt[3]{2 - \\frac{x}{2}} = -3$.",
"role": "user"
}
] | Find all solutions to the equation $\displaystyle\sqrt[3]{2 - \frac{x}{2}} = -3$. | "[\"58\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2880, "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:16818"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | 4800bfbf29899ae2c68e23d5879ce82bd8a0fd09ceec7b7e76ef18d4e2fa3806 | [
{
"content": "I4.1 If $\\frac{6 \\sqrt{3}}{3 \\sqrt{2}+2 \\sqrt{3}}=3 \\sqrt{\\alpha}-6$, determine the value of $\\alpha$.",
"role": "user"
}
] | I4.1 If $\frac{6 \sqrt{3}}{3 \sqrt{2}+2 \sqrt{3}}=3 \sqrt{\alpha}-6$, determine the value of $\alpha$. | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2891, "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:16819"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"\\frac{5}{14}"
] | [
"skywork"
] | 995b4a8d47017a6174d7991dbff0f16de08de298e3cbc278e7fe257f5a15e6d6 | [
{
"content": "12. Buses. (From 8th grade, 2 points) At the stop near the Absent-Minded Scholar's house, buses of two routes stop: No. 152 and No. 251. Both of them head to the metro station. The interval between buses No. 152 is exactly 5 minutes, and the interval between buses of route No. 251 is exactly 7 min... | 12. Buses. (From 8th grade, 2 points) At the stop near the Absent-Minded Scholar's house, buses of two routes stop: No. 152 and No. 251. Both of them head to the metro station. The interval between buses No. 152 is exactly 5 minutes, and the interval between buses of route No. 251 is exactly 7 minutes. The intervals ar... | "[\"\\\\frac{5}{14}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2864, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16820"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"\\frac{3}{2}"
] | [
"skywork"
] | b134f667dcde0f163f19aa87201be5d88a99779a54c72c1f44d0968783b77620 | [
{
"content": "Example 12 Find the largest constant $M>0$, such that for any positive integer $n$, there exist positive real number sequences $a_{1}, a_{2}, \\cdots, a_{n}$ and $b_{1}, b_{2}, \\cdots, b_{n}$, satisfying:\n(1) $\\sum_{k=1}^{n} b_{k}=1, 2 b_{k} \\geqslant b_{k-1}+b_{k+1}, k=2,3, \\cdots, n-1$;\n(2... | Example 12 Find the largest constant $M>0$, such that for any positive integer $n$, there exist positive real number sequences $a_{1}, a_{2}, \cdots, a_{n}$ and $b_{1}, b_{2}, \cdots, b_{n}$, satisfying:
(1) $\sum_{k=1}^{n} b_{k}=1, 2 b_{k} \geqslant b_{k-1}+b_{k+1}, k=2,3, \cdots, n-1$;
(2) $a_{k}^{2} \leqslant 1+\sum... | "[\"\\\\frac{3}{2}\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 2869, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16821"}] | {
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[
"\\frac{3\\sqrt{3}}{2}"
] | [
"skywork"
] | c3287a910a4ec3d3ba851592cc633e0755d8f7515522e37b8abfcb0d88eb0946 | [
{
"content": "Real numbers \\(a\\), \\(b\\), and \\(c\\) and positive number \\(\\lambda\\) make \\(f(x) = x^3 + ax^2 + b x + c\\) have three real roots \\(x_1\\), \\(x_2\\), \\(x_3\\), such that:\n(1) \\(x_2 - x_1 = \\lambda\\);\n(2) \\(x_3 > \\frac{1}{2}(x_1 + x_2)\\).\nFind the maximum value of \\(\\frac{2 a... | Real numbers \(a\), \(b\), and \(c\) and positive number \(\lambda\) make \(f(x) = x^3 + ax^2 + b x + c\) have three real roots \(x_1\), \(x_2\), \(x_3\), such that:
(1) \(x_2 - x_1 = \lambda\);
(2) \(x_3 > \frac{1}{2}(x_1 + x_2)\).
Find the maximum value of \(\frac{2 a^3 + 27 c - 9 a b}{\lambda^3}\). | "[\"\\\\frac{3\\\\sqrt{3}}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2845, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16822"}] | {
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[
"269"
] | [
"skywork"
] | 2897813205a57fba25768dbf8671a692120f33ad08a82bc9a07e1aad96b6af75 | [
{
"content": "7. $\\left(10\\right.$ points) An arc, with a central angle of $\\alpha=60^{\\circ}$, is cut from a circle with radius $R=40 \\mathrm{~cm}$. A charge $q=5$ μC is uniformly distributed along the arc. Determine the electric field strength $E$ at the center of curvature of this arc.",
"role": "us... | 7. $\left(10\right.$ points) An arc, with a central angle of $\alpha=60^{\circ}$, is cut from a circle with radius $R=40 \mathrm{~cm}$. A charge $q=5$ μC is uniformly distributed along the arc. Determine the electric field strength $E$ at the center of curvature of this arc. | "[\"269\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2879, "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:16823"}] | {
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[
"25"
] | [
"skywork"
] | fb5537c4963ccb96bc3b98d92e87f11acba01af156479098def1d71c438cc8cd | [
{
"content": "Determine the smallest odd integer $n \\ge 3$, for which there exist $n$ rational numbers $x_1 , x_2 , . . . , x_n$ with the following properties:\n\n$(a)$ \\[\\sum_{i=1}^{n} x_i =0 , \\ \\sum_{i=1}^{n} x_i^2 = 1.\\]\n\n$(b)$ \\[x_i \\cdot x_j \\ge - \\frac 1n \\ \\forall \\ 1 \\le i,j \\le n.\\]... | Determine the smallest odd integer $n \ge 3$, for which there exist $n$ rational numbers $x_1 , x_2 , . . . , x_n$ with the following properties:
$(a)$ \[\sum_{i=1}^{n} x_i =0 , \ \sum_{i=1}^{n} x_i^2 = 1.\]
$(b)$ \[x_i \cdot x_j \ge - \frac 1n \ \forall \ 1 \le i,j \le n.\] | "[\"25\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2877, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16824"}] | {
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} |
[
"\\frac{2}{3}"
] | [
"skywork"
] | 19bef024072985ff92ff4348e01ecfeb00b02df162609eadc237e4e984aa66db | [
{
"content": "Let $\\triangle ABC$ be a triangle with a right angle $\\angle ABC$. Let $D$ be the midpoint of $\\overline{BC}$, let $E$ be the midpoint of $\\overline{AC}$, and let $F$ be the midpoint of $\\overline{AB}$. Let $G$ be the midpoint of $\\overline{EC}$. One of the angles of $\\triangle DFG$ is a... | Let $\triangle ABC$ be a triangle with a right angle $\angle ABC$. Let $D$ be the midpoint of $\overline{BC}$, let $E$ be the midpoint of $\overline{AC}$, and let $F$ be the midpoint of $\overline{AB}$. Let $G$ be the midpoint of $\overline{EC}$. One of the angles of $\triangle DFG$ is a right angle. What is the le... | "[\"\\\\frac{2}{3}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2868, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:16825"}, {"dataset": "skywork", "extra_inf... | {
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[
"20.6\\%"
] | [
"skywork"
] | 73bf95080fcb4c539de7083da3fd8c610b4e5347d432cee67fc977a0f6f40f5b | [
{
"content": "Given Elmer’s new car provides a 70% better fuel efficiency and uses a type of fuel that is 35% more expensive per liter, calculate the percentage by which Elmer will save money on fuel costs if he uses his new car for his journey.",
"role": "user"
}
] | Given Elmer’s new car provides a 70% better fuel efficiency and uses a type of fuel that is 35% more expensive per liter, calculate the percentage by which Elmer will save money on fuel costs if he uses his new car for his journey. | "[\"20.6\\\\%\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2873, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16826"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"76"
] | [
"skywork"
] | 8449b1a89137c0d0bc0a2a8452d9560113ddb0e38583324d2ba7429f3da5fde3 | [
{
"content": "8. Find the last two digits of $2^{100}$.",
"role": "user"
}
] | 8. Find the last two digits of $2^{100}$. | "[\"76\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2898, "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:16827"}] | {
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} |
[
"64"
] | [
"skywork"
] | a765f03ec0efc75811b30f0b022fcb5ded7f1a9d71cc9d14842445ddd015a62b | [
{
"content": "There are $n\\leq 99$ people around a circular table. At every moment everyone can either be truthful (always says the truth) or a liar (always lies). Initially some of people (possibly none) are truthful and the rest are liars. At every minute everyone answers at the same time the question \"Is y... | There are $n\leq 99$ people around a circular table. At every moment everyone can either be truthful (always says the truth) or a liar (always lies). Initially some of people (possibly none) are truthful and the rest are liars. At every minute everyone answers at the same time the question "Is your left neighbour truth... | "[\"64\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2865, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16828"}, {"dataset": "skywork", "extra_in... | {
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"reference_components": 1,
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} |
[
"\\frac{1}{3}"
] | [
"skywork"
] | 60c1d79c8c40e651a1948e0db7930e2d08b51b8a697e33f31991a68942dbbcd4 | [
{
"content": "XXXVI OM - II - Problem 3\n\nLet $ L $ be the set of all broken lines $ ABCDA $, where $ A, B, C, D $ are distinct vertices of a fixed regular 1985-gon. A broken line is randomly chosen from the set $ L $. Calculate the probability that it is the boundary of a convex quadrilateral.",
"role": "... | XXXVI OM - II - Problem 3
Let $ L $ be the set of all broken lines $ ABCDA $, where $ A, B, C, D $ are distinct vertices of a fixed regular 1985-gon. A broken line is randomly chosen from the set $ L $. Calculate the probability that it is the boundary of a convex quadrilateral. | "[\"\\\\frac{1}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2875, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16829"}] | {
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[
"10"
] | [
"skywork"
] | 1603a6208837afb31f4762cc9822652c9c9a2d7fb4d9a1cd4fde1af31c9da454 | [
{
"content": "2. Find all values of $n, n \\in N$, for which the sum of the first terms of the sequence $a_{k}=3 k^{2}-3 k+1, \\quad k \\in N$, is equal to the sum of the first $n$ terms of the sequence $b_{k}=2 k+89, k \\in N . \\quad(12$ points)",
"role": "user"
}
] | 2. Find all values of $n, n \in N$, for which the sum of the first terms of the sequence $a_{k}=3 k^{2}-3 k+1, \quad k \in N$, is equal to the sum of the first $n$ terms of the sequence $b_{k}=2 k+89, k \in N . \quad(12$ points) | "[\"10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2874, "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:16830"}] | {
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} |
[
"\\frac{n!\\cdot(n-r)!}{(n-2r)!}"
] | [
"skywork"
] | 5f2f7d2e88c0adc63703d01000e468ee83b5a34c23c23a30b271033261582a18 | [
{
"content": "【Example 5】 There are $n$ young people and $r$ elderly people, $n>2r$, to be arranged in a row. It is required that each elderly person has a young person on both sides to support them (but each pair of young people only supports one elderly person). How many different arrangements are there?",
... | 【Example 5】 There are $n$ young people and $r$ elderly people, $n>2r$, to be arranged in a row. It is required that each elderly person has a young person on both sides to support them (but each pair of young people only supports one elderly person). How many different arrangements are there? | "[\"\\\\frac{n!\\\\cdot(n-r)!}{(n-2r)!}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2878, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16831"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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[
"19"
] | [
"skywork"
] | 401f1f1766a21daa7fb44345ab7f6a506fa21b61a6e7286038056f3894456a2d | [
{
"content": "Let $A_1A_2A_3\\ldots A_{12}$ be a dodecagon ($12$-gon). Three frogs initially sit at $A_4,A_8,$ and $A_{12}$. At the end of each minute, simultaneously, each of the three frogs jumps to one of the two vertices adjacent to its current position, chosen randomly and independently with both choices b... | Let $A_1A_2A_3\ldots A_{12}$ be a dodecagon ($12$-gon). Three frogs initially sit at $A_4,A_8,$ and $A_{12}$. At the end of each minute, simultaneously, each of the three frogs jumps to one of the two vertices adjacent to its current position, chosen randomly and independently with both choices being equally likely. Al... | "[\"19\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2870, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16832"}, {"dataset": "skywork", "extra_... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{3^{8}}"
] | [
"skywork"
] | 636571f10c169e9410bb896243feb63402e47665230ba538bcb708038b3aee34 | [
{
"content": "A6. The first term of a geometric sequence with only positive terms is 27, and the seventh term is $\\frac{1}{27}$. The twelfth term is equal to:\n(A) $\\frac{1}{3^{8}}$\n(B) $\\pm \\frac{1}{3^{9}}$\n(C) $-\\frac{1}{6561}$\n(D) 1\n(E) 10\n\n## II. PART",
"role": "user"
}
] | A6. The first term of a geometric sequence with only positive terms is 27, and the seventh term is $\frac{1}{27}$. The twelfth term is equal to:
(A) $\frac{1}{3^{8}}$
(B) $\pm \frac{1}{3^{9}}$
(C) $-\frac{1}{6561}$
(D) 1
(E) 10
## II. PART | "[\"\\\\frac{1}{3^{8}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2882, "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:16833"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | b4b0500f3c4fb2214f4ed9f1f714968279fa3507357da6029f3b50c553cf2826 | [
{
"content": "5. In a football tournament where each team played against each other once, teams $A$, B, V, G, D, and E participated. Teams received 3 points for a win, 1 point for a draw, and 0 points for a loss. In the end, it turned out that teams $A$, B, V, G, and D each scored 7 points. What is the maximum ... | 5. In a football tournament where each team played against each other once, teams $A$, B, V, G, D, and E participated. Teams received 3 points for a win, 1 point for a draw, and 0 points for a loss. In the end, it turned out that teams $A$, B, V, G, and D each scored 7 points. What is the maximum number of points that ... | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2889, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16834"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{4}{5}"
] | [
"skywork"
] | 98d1b57716a97ddb974b21caaabc8dfa4cba9d88d2802c2eaad0395bfa3517d8 | [
{
"content": "Given that $\\cos(\\alpha+\\pi)= \\frac {3}{5}$ and $\\pi \\leq \\alpha < 2\\pi$, calculate the value of $\\sin(-\\alpha-2\\pi)$.",
"role": "user"
}
] | Given that $\cos(\alpha+\pi)= \frac {3}{5}$ and $\pi \leq \alpha < 2\pi$, calculate the value of $\sin(-\alpha-2\pi)$. | "[\"\\\\frac{4}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2892, "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:16835"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{6}, \\frac{25}{6}"
] | [
"skywork"
] | df7768d2e5a907412d7f3163c3435df8165e53553e71c9bb42848d28cf3a9fdb | [
{
"content": "1. If $a, b, c$ satisfy the conditions $a+b+c=1, a^{2}$ $+b^{2}+c^{2}=2, a^{3}+b^{3}+c^{3}=3$, then $a b c=$ $\\qquad$ $a^{4}+b^{4}+c^{4}=$ $\\qquad$",
"role": "user"
}
] | 1. If $a, b, c$ satisfy the conditions $a+b+c=1, a^{2}$ $+b^{2}+c^{2}=2, a^{3}+b^{3}+c^{3}=3$, then $a b c=$ $\qquad$ $a^{4}+b^{4}+c^{4}=$ $\qquad$ | "[\"\\\\frac{1}{6}, \\\\frac{25}{6}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2886, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16836"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"5\\sqrt{2}"
] | [
"skywork"
] | 9ae069c3a74783f620344bf3362b410ede0061d59738755bd3db0cfcc173c09d | [
{
"content": "6. Through the midpoints of sides $A B$ and $A D$ of the base of a regular quadrilateral pyramid $S A B C D$, a plane is drawn parallel to the median of the lateral face $S D C$, drawn from vertex $D$. Find the area of the section of the pyramid by this plane, if the side of the base of the pyrami... | 6. Through the midpoints of sides $A B$ and $A D$ of the base of a regular quadrilateral pyramid $S A B C D$, a plane is drawn parallel to the median of the lateral face $S D C$, drawn from vertex $D$. Find the area of the section of the pyramid by this plane, if the side of the base of the pyramid is 2, and the latera... | "[\"5\\\\sqrt{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2895, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16837"}] | {
"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"
] | [
"skywork"
] | f648ad5431371d4aab6a70abee9ee3cdbc5395516c11b9e4fe511fed8ea7253d | [
{
"content": "7. (4 points) With the number written on the board, one of the following operations is allowed:\n1) If there is a digit in the original number that is not 9 and has two neighboring digits greater than 0, you can increase this digit by 1, and decrease the neighboring digits by 1.\n2) Subtract 1 fro... | 7. (4 points) With the number written on the board, one of the following operations is allowed:
1) If there is a digit in the original number that is not 9 and has two neighboring digits greater than 0, you can increase this digit by 1, and decrease the neighboring digits by 1.
2) Subtract 1 from any non-zero digit exc... | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2890, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16838"}] | {
"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{3136}{81} \\pi"
] | [
"skywork"
] | f30e1b42bee8a3c0192c78faf3dbdd9107fc60f259c179b0f22e38a87705dd74 | [
{
"content": "A circle with its center on side $AB$ of triangle $ABC$ touches the other two sides. Find the area of the circle if $a = 13$ cm, $b = 14$ cm, and $c = 15$ cm, where $a$, $b$, and $c$ are the lengths of the sides of the triangle.",
"role": "user"
}
] | A circle with its center on side $AB$ of triangle $ABC$ touches the other two sides. Find the area of the circle if $a = 13$ cm, $b = 14$ cm, and $c = 15$ cm, where $a$, $b$, and $c$ are the lengths of the sides of the triangle. | "[\"\\\\frac{3136}{81} \\\\pi\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2897, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16839"}] | {
"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
} |
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