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 |
|---|---|---|---|---|---|---|---|---|
[
"60"
] | [
"skywork"
] | 01316ed4b6d703f341397ebbe987dade355602d493c1292ef8f34c6ab2006adc | [
{
"content": "132. In a triangle, all sides are equal. Find its angles.",
"role": "user"
}
] | 132. In a triangle, all sides are equal. Find its angles. | "[\"60\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1736, "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:15707"}] | {
"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
} |
[
"0"
] | [
"skywork"
] | 999de164a623364fbeec3be5033e7d3f9f1f701463d2101f73402d62385af18b | [
{
"content": "## 20. Nicolas plays\n\n## with tin soldiers\n\nNicolas has the same number of tin Indians, Arabs, cowboys, and Eskimos. After his cousin Sebastian's visit, he indignantly discovered the disappearance of a third of his soldiers. Suppose the number of Eskimos remaining is the same as the number of ... | ## 20. Nicolas plays
## with tin soldiers
Nicolas has the same number of tin Indians, Arabs, cowboys, and Eskimos. After his cousin Sebastian's visit, he indignantly discovered the disappearance of a third of his soldiers. Suppose the number of Eskimos remaining is the same as the number of cowboys that disappeared, ... | "[\"0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1723, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15708"}] | {
"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
} |
[
"110"
] | [
"skywork"
] | b2d3b917f879e0109d475993e6759a1470d6b6e54bccd8ab52fb8cd3b7683ef7 | [
{
"content": "5*. In rhombus $A B C D$ the measure of angle $B$ is $40^{\\circ}, E-$ is the midpoint of $B C, F$ - is the foot of the perpendicular dropped from $A$ to $D E$. Find the measure of angle $D F C$.",
"role": "user"
}
] | 5*. In rhombus $A B C D$ the measure of angle $B$ is $40^{\circ}, E-$ is the midpoint of $B C, F$ - is the foot of the perpendicular dropped from $A$ to $D E$. Find the measure of angle $D F C$. | "[\"110\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1731, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:15709"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"30"
] | [
"skywork"
] | 5755a1aecd0034be1858fdefebd14e220b32b3a087c6fe8e0af02e9ffe72604c | [
{
"content": "Task B-4.3. Let $A B C A^{\\prime} B^{\\prime} C^{\\prime}$ be a right regular triangular prism. The length of the base edge $A B C$ is $10 \\mathrm{~cm}$, and the height of the prism is $10 \\sqrt{2} \\mathrm{~cm}$. Point $D$ is the midpoint of edge $\\overline{A B}$. Calculate the measure of ang... | Task B-4.3. Let $A B C A^{\prime} B^{\prime} C^{\prime}$ be a right regular triangular prism. The length of the base edge $A B C$ is $10 \mathrm{~cm}$, and the height of the prism is $10 \sqrt{2} \mathrm{~cm}$. Point $D$ is the midpoint of edge $\overline{A B}$. Calculate the measure of angle $D A^{\prime} C$. | "[\"30\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1735, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15710"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | cb72e35845259ebcf585180278c44ad07e19c5ab14c703d830641f4c146a445b | [
{
"content": "Problem 9.3. Find the least number of colors with the following property: the integers $1,2 \\ldots, 2004$ can be colored such that there are no integers $a<b<c$ of the same color for which $a$ divides $b$ and $b$ divides $c$.\n\nAlexander Ivanov",
"role": "user"
}
] | Problem 9.3. Find the least number of colors with the following property: the integers $1,2 \ldots, 2004$ can be colored such that there are no integers $a<b<c$ of the same color for which $a$ divides $b$ and $b$ divides $c$.
Alexander Ivanov | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1729, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15711"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"(2^{\\frac{4}{3}}3^{\\frac{1}{4}},\\frac{1}{2})"
] | [
"skywork"
] | 783be653042bb033c95f353665c00691ed93168121149999e25e90066b40251b | [
{
"content": "10. find all pairs $(\\alpha, \\beta)$ of positive real numbers with the following properties:\n\n(a) For all positive real numbers $x, y, z, w$ applies\n\n$$\nx+y^{2}+z^{3}+w^{6} \\geq \\alpha(x y z w)^{\\beta}\n$$\n\n(b) There is a quadruple $(x, y, z, w)$ of positive real numbers such that equa... | 10. find all pairs $(\alpha, \beta)$ of positive real numbers with the following properties:
(a) For all positive real numbers $x, y, z, w$ applies
$$
x+y^{2}+z^{3}+w^{6} \geq \alpha(x y z w)^{\beta}
$$
(b) There is a quadruple $(x, y, z, w)$ of positive real numbers such that equality holds in (a).
## Solution | "[\"(2^{\\\\frac{4}{3}}3^{\\\\frac{1}{4}},\\\\frac{1}{2})\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1737, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15712"}] | {
"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{e(e - 2)}{e - 1}"
] | [
"skywork"
] | fbe32a03e50c217f9793b9de4c0289f4b5732a06556b4a6a7e91b94b24e43c97 | [
{
"content": "Given the function $f(x) = x^2 - (2t + 1)x + t \\ln x$ where $t \\in \\mathbb{R}$,\n\n(1) If $t = 1$, find the extreme values of $f(x)$.\n\n(2) Let $g(x) = (1 - t)x$, and suppose there exists an $x_0 \\in [1, e]$ such that $f(x_0) \\geq g(x_0)$ holds. Find the maximum value of the real number $t$.... | Given the function $f(x) = x^2 - (2t + 1)x + t \ln x$ where $t \in \mathbb{R}$,
(1) If $t = 1$, find the extreme values of $f(x)$.
(2) Let $g(x) = (1 - t)x$, and suppose there exists an $x_0 \in [1, e]$ such that $f(x_0) \geq g(x_0)$ holds. Find the maximum value of the real number $t$. | "[\"\\\\frac{e(e - 2)}{e - 1}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1730, "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:15713"}] | {
"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"
] | 2d085159c5e4e9d2ba431ae8b725e0089171f1e70923bbe47a42be76a152e5e0 | [
{
"content": "Task No. 1.1\n\n## Condition:\n\nFive friends - Masha, Nastya, Irina, Olya, and Anya - meet in the park every day after buying ice cream from the shop around the corner. One day, the girls had a conversation.\n\nIrina: I was the first in line!\n\nOlya: No one was after me.\n\nAnya: Only one person... | Task No. 1.1
## Condition:
Five friends - Masha, Nastya, Irina, Olya, and Anya - meet in the park every day after buying ice cream from the shop around the corner. One day, the girls had a conversation.
Irina: I was the first in line!
Olya: No one was after me.
Anya: Only one person was after me.
Masha: There wer... | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1708, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15714"}] | {
"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
} |
[
"15-5 \\sqrt {3}"
] | [
"skywork"
] | 6a3c24d0f09a576c01f9288629c6634f88af767a51d3c56a2ac7ce972d9dc8d0 | [
{
"content": "In the rectangular coordinate system xOy, the parametric equation of curve C1 is given by $$\\begin{cases} x=5cos\\alpha \\\\ y=5+5sin\\alpha \\end{cases}$$ (where α is the parameter). Point M is a moving point on curve C1. When the line segment OM is rotated counterclockwise by 90° around point O... | In the rectangular coordinate system xOy, the parametric equation of curve C1 is given by $$\begin{cases} x=5cos\alpha \\ y=5+5sin\alpha \end{cases}$$ (where α is the parameter). Point M is a moving point on curve C1. When the line segment OM is rotated counterclockwise by 90° around point O, line segment ON is obtaine... | "[\"15-5 \\\\sqrt {3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1728, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:15715"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1:3"
] | [
"skywork"
] | c6ea5d995634adce03ac6b6e0b38e02fbca2ceba3984b3984992c834ff4aee5c | [
{
"content": "4. The diagram shows the two squares $B C D E$ and $F G H I$ inside the triangle $A B J$, where $E$ is the midpoint of $A B$ and $C$ is the midpoint of $F G$.\nWhat is the ratio of the area of the square $B C D E$ to the area of the triangle $A B J$ ?",
"role": "user"
}
] | 4. The diagram shows the two squares $B C D E$ and $F G H I$ inside the triangle $A B J$, where $E$ is the midpoint of $A B$ and $C$ is the midpoint of $F G$.
What is the ratio of the area of the square $B C D E$ to the area of the triangle $A B J$ ? | "[\"1:3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1743, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:15716"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{2}"
] | [
"skywork"
] | 31a31662cab4c5b874f6cda36be8da126c628a9488619484d7a7dc34272fbc8a | [
{
"content": "3. In $\\triangle A B C$, it is known that $A B=A C, D$ is the midpoint of side $B C$, $B E \\perp A C$ at point $E, B E$ intersects $A D$ at point $P$. If $B P=3, P E=1$, then $A E=(\\quad)$.\n(A) $\\frac{\\sqrt{6}}{2}$\n(B) $\\sqrt{2}$\n(C) $\\sqrt{3}$\n(D) $\\sqrt{6}$",
"role": "user"
}
] | 3. In $\triangle A B C$, it is known that $A B=A C, D$ is the midpoint of side $B C$, $B E \perp A C$ at point $E, B E$ intersects $A D$ at point $P$. If $B P=3, P E=1$, then $A E=(\quad)$.
(A) $\frac{\sqrt{6}}{2}$
(B) $\sqrt{2}$
(C) $\sqrt{3}$
(D) $\sqrt{6}$ | "[\"\\\\sqrt{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1739, "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:15717"}] | {
"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
} |
[
"C"
] | [
"skywork"
] | fff1e43520aa65cf6037fa0db0217e0fe35e49b643ab373b5b3ea74b799b3da2 | [
{
"content": "Example 6 A class is using an electronic voting system to elect class officer candidates. All $k$ students in the class have the right to vote and be elected, and their numbers are $1,2, \\cdots, k$. The rule is: press “1” for agreement, and press “0” for disagreement (including abstention). Let\n... | Example 6 A class is using an electronic voting system to elect class officer candidates. All $k$ students in the class have the right to vote and be elected, and their numbers are $1,2, \cdots, k$. The rule is: press “1” for agreement, and press “0” for disagreement (including abstention). Let
$$
a_{i j}=\left\{\begin... | "[\"C\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1722, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15718"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"14996"
] | [
"skywork"
] | 42838bb8cacc11bca6d42eca94f0faeeabb4609759c79bf0eae0200090a563d7 | [
{
"content": "229*. Find the integer part of the number\n\n$$\n\\frac{1}{\\sqrt[3]{4}}+\\frac{1}{\\sqrt[3]{5}}+\\frac{1}{\\sqrt[3]{6}}+\\ldots+\\frac{1}{\\sqrt[3]{1000000}}\n$$",
"role": "user"
}
] | 229*. Find the integer part of the number
$$
\frac{1}{\sqrt[3]{4}}+\frac{1}{\sqrt[3]{5}}+\frac{1}{\sqrt[3]{6}}+\ldots+\frac{1}{\sqrt[3]{1000000}}
$$ | "[\"14996\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1749, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15719"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | 04952df4b85bdca67668ea548891e4df489ad790df764f38ea48c06984f73d12 | [
{
"content": "Circle $B$ has its center at $(-6, 2)$ and a radius of $10$ units. What is the sum of the $y$-coordinates of the two points on circle $B$ that are also on the $y$-axis?",
"role": "user"
}
] | Circle $B$ has its center at $(-6, 2)$ and a radius of $10$ units. What is the sum of the $y$-coordinates of the two points on circle $B$ that are also on the $y$-axis? | "[\"4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1750, "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:15720"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2^{997}"
] | [
"skywork"
] | 89eb8ee5491479c37b7dea022ee0a7e89ad940e838e1ea2b1b51e1d480798ac9 | [
{
"content": "Example 13 Let the sequence of positive real numbers $x_{0}, x_{1}, x_{2}, \\cdots, x_{1995}$ satisfy the conditions:\n(1) $x_{0}=x_{1995}$;\n(2) For $i=1,2, \\cdots, 1995$, $x_{i-1}+\\frac{2}{x_{i-1}}=2 x_{i}+\\frac{1}{x_{i}}$, find the maximum value of $x_{0}$.",
"role": "user"
}
] | Example 13 Let the sequence of positive real numbers $x_{0}, x_{1}, x_{2}, \cdots, x_{1995}$ satisfy the conditions:
(1) $x_{0}=x_{1995}$;
(2) For $i=1,2, \cdots, 1995$, $x_{i-1}+\frac{2}{x_{i-1}}=2 x_{i}+\frac{1}{x_{i}}$, find the maximum value of $x_{0}$. | "[\"2^{997}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1738, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15721"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 0e80f4e3a1555daa25e952b35d0709ddce4a6ae5940e8d33d4878706b47e3d69 | [
{
"content": "4. Calculate $\\sqrt{3+\\sqrt{8}}-\\sqrt{3-\\sqrt{8}}$.",
"role": "user"
}
] | 4. Calculate $\sqrt{3+\sqrt{8}}-\sqrt{3-\sqrt{8}}$. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1754, "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:15722"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-1"
] | [
"skywork"
] | 22a57627b020ef472cfdacedb77fa4d5dcf8771355dd0ef44298c71925e97e75 | [
{
"content": "Given \\( a \\in \\mathbb{R} \\), the complex number \\( z = \\frac{(a-i)(1+i)}{i} \\), if \\( \\bar{z} = z \\), then find the value of \\( a \\).",
"role": "user"
}
] | Given \( a \in \mathbb{R} \), the complex number \( z = \frac{(a-i)(1+i)}{i} \), if \( \bar{z} = z \), then find the value of \( a \). | "[\"-1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1740, "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:15723"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"skywork"
] | 9de6535013c80e5e426f1b0a0bc8aa5892071ec2183b7e132fc866849044c8de | [
{
"content": "The product of two positive integers plus their sum equals 119. The integers are relatively prime, and each is less than 25. What is the sum of the two integers?",
"role": "user"
}
] | The product of two positive integers plus their sum equals 119. The integers are relatively prime, and each is less than 25. What is the sum of the two integers? | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1755, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:15724"}] | {
"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
} |
[
"34"
] | [
"skywork"
] | 3ba1f3a258ed410c48b125e116681d09eb2f4aa0a40ebc24e5e3c408f2063184 | [
{
"content": "Given are sheets and the numbers $00, 01, \\ldots, 99$ are written on them. We must put them in boxes $000, 001, \\ldots, 999$ so that the number on the sheet is the number on the box with one digit erased. What is the minimum number of boxes we need in order to put all the sheets?",
"role": "... | Given are sheets and the numbers $00, 01, \ldots, 99$ are written on them. We must put them in boxes $000, 001, \ldots, 999$ so that the number on the sheet is the number on the box with one digit erased. What is the minimum number of boxes we need in order to put all the sheets? | "[\"34\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1727, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15725"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3\\times45\\times28"
] | [
"skywork"
] | b1e3162ea47f4b341f312afe64712023826825cbfc7031f13bd1948b6a58a7a6 | [
{
"content": "4. Find the number of 10 -tuples $\\left(a_{1}, a_{2}, \\ldots, a_{10}\\right)$ of integers such that $\\left|a_{1}\\right| \\leq 1$ and\n\n$$\na_{1}^{2}+a_{2}^{2}+a_{3}^{2}+\\cdots+a_{10}^{2}-a_{1} a_{2}-a_{2} a_{3}-a_{3} a_{4}-\\cdots-a_{9} a_{10}-a_{10} a_{1}=2\n$$",
"role": "user"
}
] | 4. Find the number of 10 -tuples $\left(a_{1}, a_{2}, \ldots, a_{10}\right)$ of integers such that $\left|a_{1}\right| \leq 1$ and
$$
a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+\cdots+a_{10}^{2}-a_{1} a_{2}-a_{2} a_{3}-a_{3} a_{4}-\cdots-a_{9} a_{10}-a_{10} a_{1}=2
$$ | "[\"3\\\\times45\\\\times28\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1725, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15726"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{2}+1"
] | [
"skywork"
] | ae8ba09a9220aea215138cad0f15c7968a5be6eca091465cfeb4f38d163da870 | [
{
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and it is known that $c=a\\cos B+b\\sin A$.\n(1) Find $A$;\n(2) If $a=2$ and $b=c$, find the area of $\\triangle ABC$.",
"role": "user"
}
] | In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and it is known that $c=a\cos B+b\sin A$.
(1) Find $A$;
(2) If $a=2$ and $b=c$, find the area of $\triangle ABC$. | "[\"\\\\sqrt{2}+1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1710, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15727"}] | {
"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
} |
[
"32"
] | [
"skywork"
] | 9696fe92ef3b753f820a6cce676e3c833558a230a5571cc2d18148210a181718 | [
{
"content": "A piece of paper is folded in half, creating two layers of paper. The paper is then folded in half again. This is continued until the paper has been folded in half a total of five times. The total number of layers of paper in the folded sheet is\n(A) 16\n(B) 32\n(C) 25\n(D) 8\n(E) 64",
"role":... | A piece of paper is folded in half, creating two layers of paper. The paper is then folded in half again. This is continued until the paper has been folded in half a total of five times. The total number of layers of paper in the folded sheet is
(A) 16
(B) 32
(C) 25
(D) 8
(E) 64 | "[\"32\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1741, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:15728"}] | {
"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
} |
[
"-z"
] | [
"skywork"
] | 0a14e7d22a902b28b491921f97ff8e49339835d363a906d6778c87cb5efa91e8 | [
{
"content": "20. Let $Q(z), R(z)$ satisfy\n$$\nz^{2021}+1=\\left(z^{2}+z+1\\right) Q(z)+R(z)\n$$\n\nthe unique polynomials, where $\\operatorname{deg} R(z)<2$. Then $R(z)=$ ( ).\n(A) $-z$\n(B) -1\n(C) 2021\n(D) $z+1$\n(E) $2 z+1$",
"role": "user"
}
] | 20. Let $Q(z), R(z)$ satisfy
$$
z^{2021}+1=\left(z^{2}+z+1\right) Q(z)+R(z)
$$
the unique polynomials, where $\operatorname{deg} R(z)<2$. Then $R(z)=$ ( ).
(A) $-z$
(B) -1
(C) 2021
(D) $z+1$
(E) $2 z+1$ | "[\"-z\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1761, "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:15729"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"9-\\sqrt{3}"
] | [
"skywork"
] | 4fc0237b2b364b9a5574bf04082dd4bca07ab7c49d63265f5e8669bf71071fd4 | [
{
"content": "4. In an isosceles trapezoid $A B C D (B C \\| A D)$, angles $A B D$ and $D B C$ are $135^{\\circ}$ and $15^{\\circ}$ respectively, and $B D=\\sqrt{6}$. Find the perimeter of the trapezoid.",
"role": "user"
}
] | 4. In an isosceles trapezoid $A B C D (B C \| A D)$, angles $A B D$ and $D B C$ are $135^{\circ}$ and $15^{\circ}$ respectively, and $B D=\sqrt{6}$. Find the perimeter of the trapezoid. | "[\"9-\\\\sqrt{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1751, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15730"}] | {
"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
} |
[
"11"
] | [
"skywork"
] | facefb23787ade790a3b4e9a6d2df269e7f0ef3816972026202233e73b146c07 | [
{
"content": "Four players stand at distinct vertices of a square. They each independently choose a vertex of the square (which might be the vertex they are standing on). Then, they each, at the same time, begin running in a straight line to their chosen vertex at 10 mph, stopping when they reach the vertex. If... | Four players stand at distinct vertices of a square. They each independently choose a vertex of the square (which might be the vertex they are standing on). Then, they each, at the same time, begin running in a straight line to their chosen vertex at 10 mph, stopping when they reach the vertex. If at any time two playe... | "[\"11\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1726, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15732"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"12"
] | [
"skywork"
] | 24fe5e98ec8d73a92eff9299c1782eac2f0f5146fa8f47071cf74536f2031c30 | [
{
"content": "Calculate the length of the arc of the astroid given by \\(x=\\cos^{3} t\\), \\(y=\\sin^{3} t\\), where \\(0 \\leq t \\leq 2\\pi\\).",
"role": "user"
}
] | Calculate the length of the arc of the astroid given by \(x=\cos^{3} t\), \(y=\sin^{3} t\), where \(0 \leq t \leq 2\pi\). | "[\"12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1767, "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:15733"}] | {
"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{\\sqrt{63}}{8}"
] | [
"skywork"
] | f82f5358a8b809b6651638da3e86917e67d65f7ecbf9efb949b5f5fe332a0d2c | [
{
"content": "Example 4 As shown in Figure 7, in the quadrilateral pyramid $P-ABCD$, $PA \\perp$ base $ABCD$, $BC=CD=2$, $AC=4$, $\\angle ACB=\\angle ACD=\\frac{\\pi}{3}$, $F$ is the midpoint of $PC$, and $AF \\perp PB$.\nFigure 7\nFind (1) the length of $PA$;\n(2) the sine value of the dihedral angle $B-AF-D$.... | Example 4 As shown in Figure 7, in the quadrilateral pyramid $P-ABCD$, $PA \perp$ base $ABCD$, $BC=CD=2$, $AC=4$, $\angle ACB=\angle ACD=\frac{\pi}{3}$, $F$ is the midpoint of $PC$, and $AF \perp PB$.
Figure 7
Find (1) the length of $PA$;
(2) the sine value of the dihedral angle $B-AF-D$. ${ }^{[4]}$ | "[\"\\\\frac{\\\\sqrt{63}}{8}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1747, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15734"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-6\\pi + \\frac{7\\pi}{4}"
] | [
"skywork"
] | 0c006e85365e070122c1f1ae0fdbb60b083b4a8af37a80b7be50fc8bb9d8ee03 | [
{
"content": "Given $-765^\\circ$, convert this angle into the form $2k\\pi + \\alpha$ ($0 \\leq \\alpha < 2\\pi$), where $k \\in \\mathbb{Z}$.",
"role": "user"
}
] | Given $-765^\circ$, convert this angle into the form $2k\pi + \alpha$ ($0 \leq \alpha < 2\pi$), where $k \in \mathbb{Z}$. | "[\"-6\\\\pi + \\\\frac{7\\\\pi}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1760, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15735"}] | {
"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\\mathrm{~}"
] | [
"skywork"
] | 997a43eaa043c2487c1cddf9c6f95626b08afbf3e73a909ced7c3ab3c73d6983 | [
{
"content": "A water fountain flows at a steady rate of $500 \\mathrm{~mL}$ every 6 seconds. At this rate, how long will it take to fill a $250 \\mathrm{~mL}$ bottle?\n(A) $2 \\mathrm{~s}$\n(B) $9 \\mathrm{~s}$\n(C) $3 \\mathrm{~s}$\n(D) $6 \\mathrm{~s}$\n(E) $1 \\mathrm{~s}$",
"role": "user"
}
] | A water fountain flows at a steady rate of $500 \mathrm{~mL}$ every 6 seconds. At this rate, how long will it take to fill a $250 \mathrm{~mL}$ bottle?
(A) $2 \mathrm{~s}$
(B) $9 \mathrm{~s}$
(C) $3 \mathrm{~s}$
(D) $6 \mathrm{~s}$
(E) $1 \mathrm{~s}$ | "[\"3\\\\mathrm{~}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1773, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15736"}] | {
"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
} |
[
"840"
] | [
"skywork"
] | 307b02db88928502ba52994516edc6a08772f5ea3d532d91e9aee8e0df1954cd | [
{
"content": "Between 1000 and 9999, the number of four-digit integers with distinct digits where the absolute difference between the first and last digit is 2.",
"role": "user"
}
] | Between 1000 and 9999, the number of four-digit integers with distinct digits where the absolute difference between the first and last digit is 2. | "[\"840\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1762, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "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:15737"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{5}{27}"
] | [
"skywork"
] | 91c3232329d94b35b7f01fb77b608be6fad22b08fb99373651a88fdbe5c2991c | [
{
"content": "7. Given real numbers $a, b, c$ satisfy $a+b+c=1, a^{2}+b^{2}+c^{2}=3$. Then the maximum value of $a b c$ is $\\qquad$ .",
"role": "user"
}
] | 7. Given real numbers $a, b, c$ satisfy $a+b+c=1, a^{2}+b^{2}+c^{2}=3$. Then the maximum value of $a b c$ is $\qquad$ . | "[\"\\\\frac{5}{27}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1753, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15739"}] | {
"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{1}{3}"
] | [
"skywork"
] | db4cb9eca6014984b62fabbbc40e5d70c6d1397ed22e5c87e68b6519875853a6 | [
{
"content": "2. During the transportation of a box containing 21 standard and 10 non-standard parts, one part was lost, and it is unknown which one. A part randomly extracted from the box (after transportation) turned out to be standard. Find the probability that the lost part was: a) a standard part; b) a non... | 2. During the transportation of a box containing 21 standard and 10 non-standard parts, one part was lost, and it is unknown which one. A part randomly extracted from the box (after transportation) turned out to be standard. Find the probability that the lost part was: a) a standard part; b) a non-standard part. | "[\"\\\\frac{1}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1744, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:15740"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"72"
] | [
"skywork"
] | 2c294e3b460cfab5892d461df38e4b8d16d92dc94d9712bda51f477525d3a5f2 | [
{
"content": "44. Given that the time it takes for a mouse to run 5 steps is the same as the time it takes for a cat to run 4 steps, and the distance a mouse runs in 9 steps is the same as the distance a cat runs in 7 steps. Now, the mouse and the cat are 2 meters apart. The cat starts to chase the mouse, the c... | 44. Given that the time it takes for a mouse to run 5 steps is the same as the time it takes for a cat to run 4 steps, and the distance a mouse runs in 9 steps is the same as the distance a cat runs in 7 steps. Now, the mouse and the cat are 2 meters apart. The cat starts to chase the mouse, the cat needs to run $\qqua... | "[\"72\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1732, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15741"}] | {
"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
} |
[
"4760"
] | [
"skywork"
] | d01a647292177053313de94a0c80b16d070ee3cffcbda1cddb362f98c710c9bd | [
{
"content": "3. Find the number of distinct reduced quadratic trinomials (i.e., with the leading coefficient equal to 1) with integer coefficients such that they have at least one root, all their roots are powers of the number 7 with integer non-negative exponents, and their coefficients in absolute value do n... | 3. Find the number of distinct reduced quadratic trinomials (i.e., with the leading coefficient equal to 1) with integer coefficients such that they have at least one root, all their roots are powers of the number 7 with integer non-negative exponents, and their coefficients in absolute value do not exceed \(49^{68}\). | "[\"4760\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1759, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15742"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"n + 1 + r"
] | [
"skywork"
] | db26031e885b52cb45ef7c8bbda49f0d473a29a26f90bea45fcc9e6051d5fd9f | [
{
"content": "Let $M$ be the set of the integer numbers from the range $[-n, n]$. The subset $P$ of $M$ is called a [i]base subset[/i] if every number from $M$ can be expressed as a sum of some different numbers from $P$. Find the smallest natural number $k$ such that every $k$ numbers that belongs to $M$ form ... | Let $M$ be the set of the integer numbers from the range $[-n, n]$. The subset $P$ of $M$ is called a [i]base subset[/i] if every number from $M$ can be expressed as a sum of some different numbers from $P$. Find the smallest natural number $k$ such that every $k$ numbers that belongs to $M$ form a base subset. | "[\" n + 1 + r \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1756, "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:15743"}] | {
"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
} |
[
"14.6"
] | [
"skywork"
] | 9d13982a89f63ee6431c6221bf9a4975606fc47e73108093117833c16c041bd7 | [
{
"content": "Given that the odometer initially showed 35,400 miles and the driver filled the gas tank with 8 gallons of gasoline, and later filled the tank again with 15 gallons when the odometer showed 35,680 miles, and finally filled the tank with 18 gallons of gasoline when the odometer read 36,000 miles, c... | Given that the odometer initially showed 35,400 miles and the driver filled the gas tank with 8 gallons of gasoline, and later filled the tank again with 15 gallons when the odometer showed 35,680 miles, and finally filled the tank with 18 gallons of gasoline when the odometer read 36,000 miles, calculate the car's ave... | "[\"14.6\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1777, "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:15744"}] | {
"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
} |
[
"512"
] | [
"skywork"
] | c6579a622bd7c65f15b5a4b5066ee9d225bef8f98a3b81be918d91df8a0568f2 | [
{
"content": "C1. Sara has 10 blocks numbered $1 \\mathrm{t} / \\mathrm{m}$ 10. She wants to stack all the blocks into a tower. A block can only be placed on top of a block with a higher number, or on a block with a number that is exactly one lower. An example is, from top to bottom: 2, 1, 5, 4, 3, 6, 7, 9, 8, ... | C1. Sara has 10 blocks numbered $1 \mathrm{t} / \mathrm{m}$ 10. She wants to stack all the blocks into a tower. A block can only be placed on top of a block with a higher number, or on a block with a number that is exactly one lower. An example is, from top to bottom: 2, 1, 5, 4, 3, 6, 7, 9, 8, 10. How many different t... | "[\"512\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1757, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15745"}] | {
"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{2}{3}"
] | [
"skywork"
] | dd21606cc32b1119d2351acb5d2de5c1011850ebc451a9f458d410448d6779da | [
{
"content": "Yan is between his home and the library. To get to the library, he can either walk directly to the library or walk home and then ride his bicycle to the library. He rides 5 times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yan's distance from his hom... | Yan is between his home and the library. To get to the library, he can either walk directly to the library or walk home and then ride his bicycle to the library. He rides 5 times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yan's distance from his home to his distance from... | "[\"\\\\frac{2}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1765, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15746"}] | {
"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
} |
[
"49894"
] | [
"skywork"
] | 5f74496154b74ecde92c6661e5fc25e123475e831468af3b0e6841e4b692d1f3 | [
{
"content": "4. A palindrome is a positive integer which is the same when reading from the right hand side or from the left hand side, e.g. 2002. Find the largest five-digit palindrome which is divisible by 101 .\n(1 mark)\n若某正整數不論從左面或右面讀起皆相同（例如：2002），則該數稱為「回文數」。求可被 101 整除的最大五位回文數。",
"role": "user"
}
] | 4. A palindrome is a positive integer which is the same when reading from the right hand side or from the left hand side, e.g. 2002. Find the largest five-digit palindrome which is divisible by 101 .
(1 mark)
若某正整數不論從左面或右面讀起皆相同（例如：2002），則該數稱為「回文數」。求可被 101 整除的最大五位回文數。 | "[\"49894\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1772, "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:15747"}] | {
"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
} |
[
"50"
] | [
"skywork"
] | d037c79da7a5a343da738ef5456d1eddebb2c275ef6197fc2d391fa14583cce7 | [
{
"content": "There is a tram with a starting station A and an ending station B. A tram departs from station A every 5 minutes towards station B, completing the journey in 15 minutes. A person starts cycling along the tram route from station B towards station A just as a tram arrives at station B. On his way, h... | There is a tram with a starting station A and an ending station B. A tram departs from station A every 5 minutes towards station B, completing the journey in 15 minutes. A person starts cycling along the tram route from station B towards station A just as a tram arrives at station B. On his way, he encounters 10 trams ... | "[\"50\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1752, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15748"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-1"
] | [
"skywork"
] | 9b33f1d6ad3c68da5285af468c3461194ca2f1ed16934f0f98ddd4ebe3857d29 | [
{
"content": "3. What is the value of $1-(2-(3-4-(5-6)))$ ?\nA -2\nB -1\nC 0\nD 1\nE 2",
"role": "user"
}
] | 3. What is the value of $1-(2-(3-4-(5-6)))$ ?
A -2
B -1
C 0
D 1
E 2 | "[\"-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1779, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15749"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"30"
] | [
"skywork"
] | bd76c4979a8f949096b38788d0cabc0108b78cfa99ed6b5c459b64007d3c6581 | [
{
"content": "3. The positive integers are written into rows so that Row $n$ includes every integer $m$ with the following properties:\n(i) $m$ is a multiple of $n$,\n(ii) $m \\leq n^{2}$, and\n(iii) $m$ is not in an earlier row.\nThe table below shows the first six rows.\n(a) Determine the smallest integer in ... | 3. The positive integers are written into rows so that Row $n$ includes every integer $m$ with the following properties:
(i) $m$ is a multiple of $n$,
(ii) $m \leq n^{2}$, and
(iii) $m$ is not in an earlier row.
The table below shows the first six rows.
(a) Determine the smallest integer in Row 10.
(b) Show that, for a... | "[\"30\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1745, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15750"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2^{2005}"
] | [
"skywork"
] | 6f88c28c7733164730a3212aef3251ac6936ce0bff067e39674a8007c0a24f68 | [
{
"content": "Let $p_{1}, p_{2}, \\ldots, p_{2005}$ be different prime numbers. Let $\\mathrm{S}$ be a set of natural numbers which elements have the property that their simple divisors are some of the numbers $p_{1}, p_{2}, \\ldots, p_{2005}$ and product of any two elements from $\\mathrm{S}$ is not a perfect ... | Let $p_{1}, p_{2}, \ldots, p_{2005}$ be different prime numbers. Let $\mathrm{S}$ be a set of natural numbers which elements have the property that their simple divisors are some of the numbers $p_{1}, p_{2}, \ldots, p_{2005}$ and product of any two elements from $\mathrm{S}$ is not a perfect square.
What is the maxim... | "[\"2^{2005}\"]" | train-math-numinamath1.5_olympiads_ref | [{"dataset": "skywork", "extra_info": {"index": 1746, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15751"}] | {
"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
} |
[
"\\left(-\\infty, \\frac{9}{4}\\right]"
] | [
"skywork"
] | fa78197a1b9d364564b29af7eba854f9b5db67fdec14f7e4b63b192025d795e3 | [
{
"content": "29. Given two positive numbers $x, y$ satisfying $x+y=4$, the range of real number $m$ that makes the inequality $\\frac{1}{x}+\\frac{4}{y} \\geqslant m$ always true is $\\qquad$.",
"role": "user"
}
] | 29. Given two positive numbers $x, y$ satisfying $x+y=4$, the range of real number $m$ that makes the inequality $\frac{1}{x}+\frac{4}{y} \geqslant m$ always true is $\qquad$. | "[\"\\\\left(-\\\\infty, \\\\frac{9}{4}\\\\right]\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 1748, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15752"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1-2x"
] | [
"skywork"
] | 70c81324c9e452fa2ac8b5045d3cbd6296d9dc386c85a3ccc01c9090bc426c55 | [
{
"content": "If $x<0$, then $|x-\\sqrt{(x-1)^2}|$ equals",
"role": "user"
}
] | If $x<0$, then $|x-\sqrt{(x-1)^2}|$ equals | "[\"1-2x\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1758, "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:15753"}] | {
"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
} |
[
"61"
] | [
"skywork"
] | 0c6c3efabc9208cc39b2f8a873fe70ee9068f665488bf16f5876fe533817d16b | [
{
"content": "Find the smallest prime number that can be represented as the sum of two, three, four, five, and six distinct prime numbers.",
"role": "user"
}
] | Find the smallest prime number that can be represented as the sum of two, three, four, five, and six distinct prime numbers. | "[\"61\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1769, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15754"}] | {
"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
} |
[
"296"
] | [
"skywork"
] | 608fd69f24db468497b82d4382a3dc99c44ddffaa0efec833163f26c1ad45e30 | [
{
"content": "How many of the 512 smallest positive integers written in base 8 use 5 or 6 (or both) as a digit?",
"role": "user"
}
] | How many of the 512 smallest positive integers written in base 8 use 5 or 6 (or both) as a digit? | "[\"296\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1778, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:15755"}] | {
"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
} |
[
"24200"
] | [
"skywork"
] | ccefdc4bb1ddb90a20c01a49a0b8eeea64424bd8a87f65030c59b956c1adbaa0 | [
{
"content": "8. Two circles with radii 71 and 100 are externally tangent. Compute the largest possible area of a right triangle whose vertices are each on at least one of the circles.",
"role": "user"
}
] | 8. Two circles with radii 71 and 100 are externally tangent. Compute the largest possible area of a right triangle whose vertices are each on at least one of the circles. | "[\"24200\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1785, "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:15756"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | 244257f043b5d9ee066829de36f39b55ef05b67d8aeb6d31d79a9e01647d721c | [
{
"content": "17. (18 points) Among 200 small balls numbered $1, 2, \\cdots, 200$, any $k$ balls are drawn such that there must be two balls with numbers $m$ and $n$ satisfying\n$$\n\\frac{2}{5} \\leqslant \\frac{n}{m} \\leqslant \\frac{5}{2} \\text {. }\n$$\n\nDetermine the minimum value of $k$ and explain the... | 17. (18 points) Among 200 small balls numbered $1, 2, \cdots, 200$, any $k$ balls are drawn such that there must be two balls with numbers $m$ and $n$ satisfying
$$
\frac{2}{5} \leqslant \frac{n}{m} \leqslant \frac{5}{2} \text {. }
$$
Determine the minimum value of $k$ and explain the reasoning. | "[\"7\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1766, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15757"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2^n"
] | [
"skywork"
] | 64a1e9d2efd3e2563a08af837b47c8abb6209a569778516373cbc06ce3cc153f | [
{
"content": "Two people $A$ and $B$ play the following game: They take from $\\{0, 1, 2, 3,..., 1024\\}$ alternately $512$, $256$, $128$, $64$, $32$, $16$, $8$, $4$, $2$, $1$, numbers away where $A$ first removes $512$ numbers, $B$ removes $256$ numbers etc. Two numbers $a, b$ remain ($a < b$). $B$ pays $A$ t... | Two people $A$ and $B$ play the following game: They take from $\{0, 1, 2, 3,..., 1024\}$ alternately $512$, $256$, $128$, $64$, $32$, $16$, $8$, $4$, $2$, $1$, numbers away where $A$ first removes $512$ numbers, $B$ removes $256$ numbers etc. Two numbers $a, b$ remain ($a < b$). $B$ pays $A$ the amount $b - a$. $A$ w... | "[\"2^n\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1775, "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:15758"}] | {
"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
} |
[
"3943"
] | [
"skywork"
] | 52a8cc5d84afc802a2044bb9502b7be53296333c14f8240afda91d29282f60f6 | [
{
"content": "6. In the sequence of positive integers, starting from 1, certain numbers are painted red according to the following rules. First, paint 1, then paint 2 even numbers $2, 4$; then paint the 3 nearest consecutive odd numbers after 4, which are $5, 7, 9$; then paint the 4 nearest consecutive even num... | 6. In the sequence of positive integers, starting from 1, certain numbers are painted red according to the following rules. First, paint 1, then paint 2 even numbers $2, 4$; then paint the 3 nearest consecutive odd numbers after 4, which are $5, 7, 9$; then paint the 4 nearest consecutive even numbers after 9, which ar... | "[\"3943\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1780, "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:15759"}, {"dataset": "skywork", "extra_... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{2} + 1"
] | [
"skywork"
] | d9d0f589096557ed1e08ca5a46999c5015c007ca31a350777e6efced7ed25660 | [
{
"content": "Let \\( x, y, z \\in [0, 1] \\). The maximum value of \\( M = \\sqrt{|x-y|} + \\sqrt{|y-z|} + \\sqrt{|z-x|} \\) is ______",
"role": "user"
}
] | Let \( x, y, z \in [0, 1] \). The maximum value of \( M = \sqrt{|x-y|} + \sqrt{|y-z|} + \sqrt{|z-x|} \) is ______ | "[\"\\\\sqrt{2} + 1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1763, "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:15760"}] | {
"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{n!(n-1)!}{2^{n-1}}"
] | [
"skywork"
] | f2bad3a815012a731138d8fa5acc21ec4b0f0348499bc873a23762b446319a2d | [
{
"content": "Example 3 Let $P_{m}=\\left\\{A_{1}, A_{2}, \\cdots, A_{m}\\right\\}$ be a partition of an $n$-element set $X$ (i.e., $A_{1}, A_{2}, \\cdots, A_{m}$ is a partition of $X$). If one of the $A_{i}$ is further divided into two sets, this results in a partition $P_{m+1}$ of $X$, which consists of $m+1$... | Example 3 Let $P_{m}=\left\{A_{1}, A_{2}, \cdots, A_{m}\right\}$ be a partition of an $n$-element set $X$ (i.e., $A_{1}, A_{2}, \cdots, A_{m}$ is a partition of $X$). If one of the $A_{i}$ is further divided into two sets, this results in a partition $P_{m+1}$ of $X$, which consists of $m+1$ sets. $P_{m+1}$ is called a... | "[\"\\\\frac{n!(n-1)!}{2^{n-1}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1770, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15761"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-2\\cosx+C"
] | [
"skywork"
] | 58903148b57cf8783007df3135fdae9b4fb6df760cc3a42fa95512e076cbffcf | [
{
"content": "77. $\\int \\frac{\\sin 2 x}{\\cos x} d x$.\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.\n\n77. $\\int \\frac{\\sin 2 x}{\\cos x} d x$.",
"role": "user"
}
] | 77. $\int \frac{\sin 2 x}{\cos x} d x$.
Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.
77. $\int \frac{\sin 2 x}{\cos x} d x$. | "[\"-2\\\\cosx+C\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1793, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15762"}] | {
"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{8}{35}"
] | [
"skywork"
] | 1cacfc672e045951712b23d24a205fd41e8bb1dec728aa2a8b9d029838735221 | [
{
"content": "Imagine a box containing seven sticks with lengths 2, 4, 6, 8, 12, 14, and 18 inches. If one is to randomly pick three sticks, what is the probability that those three sticks could be joined to form a triangle? Return your answer as a fraction.",
"role": "user"
}
] | Imagine a box containing seven sticks with lengths 2, 4, 6, 8, 12, 14, and 18 inches. If one is to randomly pick three sticks, what is the probability that those three sticks could be joined to form a triangle? Return your answer as a fraction. | "[\"\\\\frac{8}{35}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1782, "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:15763"}] | {
"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
} |
[
"88:45"
] | [
"skywork"
] | 36326f5282207d3feccba19c79954192367219b3a928c94abe1faa0837d78d36 | [
{
"content": "5. In an acute triangle $A B C$, let $D$ be the foot of the altitude from vertex $C$ and $P, Q$ be the feet of the perpendiculars from point $D$ to sides $A C$ and $B C$. The areas of triangles $A D P, D C P, D B Q, C D Q$ are denoted by $S_{1}, S_{2}, S_{3}, S_{4}$, respectively. Calculate $S_{1}... | 5. In an acute triangle $A B C$, let $D$ be the foot of the altitude from vertex $C$ and $P, Q$ be the feet of the perpendiculars from point $D$ to sides $A C$ and $B C$. The areas of triangles $A D P, D C P, D B Q, C D Q$ are denoted by $S_{1}, S_{2}, S_{3}, S_{4}$, respectively. Calculate $S_{1}: S_{3}$, given that $... | "[\"88:45\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1774, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15764"}] | {
"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{11}{10}"
] | [
"skywork"
] | bf415e87f7bcda6830918f4ea950f1c1f4205a495e8f18bbd38fe9fa996c0c58 | [
{
"content": "In a right triangle $A B C$ with legs $A B=3$ and $B C=4$, a circle is drawn through the midpoints of sides $A B$ and $A C$, touching the leg $B C$. Find the length of the segment of the hypotenuse $A C$ that lies inside this circle.",
"role": "user"
}
] | In a right triangle $A B C$ with legs $A B=3$ and $B C=4$, a circle is drawn through the midpoints of sides $A B$ and $A C$, touching the leg $B C$. Find the length of the segment of the hypotenuse $A C$ that lies inside this circle. | "[\"\\\\frac{11}{10}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1784, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:15765"}] | {
"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
} |
[
"1006"
] | [
"skywork"
] | 59c76b1cbab2e8bba95a86565a17c83aa5eed83e262484f10d6332ca027b3910 | [
{
"content": "2. Let the function $f(x)$ be defined on $\\mathbb{R}$, and for any $x$, the condition $f(x+2) + f(x) = x$ holds. It is also known that $f(x) = x^3$ on the interval $(-2; 0]$. Find $f(2012)$.",
"role": "user"
}
] | 2. Let the function $f(x)$ be defined on $\mathbb{R}$, and for any $x$, the condition $f(x+2) + f(x) = x$ holds. It is also known that $f(x) = x^3$ on the interval $(-2; 0]$. Find $f(2012)$. | "[\"1006\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1771, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15766"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | 655d783a3df74c88104696cd633d124ef80301afde777fcc5cb692e5743eb180 | [
{
"content": "## Task 3 - 040613\n\nA 6th grade class made various paper triangles. The students wanted to store these triangles in a cabinet in their school's mathematics room, which had nine compartments. The students had designated three compartments for the equilateral triangles, three for the isosceles tri... | ## Task 3 - 040613
A 6th grade class made various paper triangles. The students wanted to store these triangles in a cabinet in their school's mathematics room, which had nine compartments. The students had designated three compartments for the equilateral triangles, three for the isosceles triangles (i.e., those that... | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1764, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15767"}] | {
"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
} |
[
"D"
] | [
"skywork"
] | de11ce9a7e8692cd1710b2ac51e48989300c0cf19b855ba11baccbeb3d5cbfbd | [
{
"content": "17-126 $D$ is a point on the base $BC$ of an isosceles acute $\\triangle ABC$, then $AD, BD$, $CD$ satisfy the relation\n(A) $A D^{2}=B D^{2}+C D^{2}$.\n(B) $A D^{2}>B D^{2}+C D^{2}$.\n(C) $2 A D^{2}=B D^{2}+C D^{2}$.\n(D) $2 A D^{2}>B D^{2}+C D^{2}$.\n(2nd \"Hope Cup\" National Mathematics Invita... | 17-126 $D$ is a point on the base $BC$ of an isosceles acute $\triangle ABC$, then $AD, BD$, $CD$ satisfy the relation
(A) $A D^{2}=B D^{2}+C D^{2}$.
(B) $A D^{2}>B D^{2}+C D^{2}$.
(C) $2 A D^{2}=B D^{2}+C D^{2}$.
(D) $2 A D^{2}>B D^{2}+C D^{2}$.
(2nd "Hope Cup" National Mathematics Invitational Competition, 1991) | "[\"D\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1781, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:15768"}] | {
"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{\\sqrt{3}}{3}"
] | [
"skywork"
] | e0f33ff89b9223660f7a3160cfe7bb02d9daf5c5d9a0e7d1efa7e88764d5b7f8 | [
{
"content": "Example 1 Find the maximum value of the function $y=\\frac{\\sin x}{2+\\cos x}(0<x<\\pi)$.",
"role": "user"
}
] | Example 1 Find the maximum value of the function $y=\frac{\sin x}{2+\cos x}(0<x<\pi)$. | "[\"\\\\frac{\\\\sqrt{3}}{3}\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 1799, "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:15769"}] | {
"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
} |
[
"4044"
] | [
"skywork"
] | f50d4d0b54d7e613cc44a58c5cedef3f54a6653f18f61aa98218f4940aa68d55 | [
{
"content": "Given that the sequence \\( a_1, a_2, \\cdots, a_n, \\cdots \\) satisfies \\( a_1 = a_2 = 1 \\) and \\( a_3 = 2 \\), and for any \\( n \\in \\mathbf{N}^{*} \\), it holds that \\( a_n \\cdot a_{n+1} \\cdot a_{n+2} \\cdot a_{n+3} = a_n + a_{n+1} + a_{n+2} + a_{n+3} \\). Find the value of \\( \\sum_{... | Given that the sequence \( a_1, a_2, \cdots, a_n, \cdots \) satisfies \( a_1 = a_2 = 1 \) and \( a_3 = 2 \), and for any \( n \in \mathbf{N}^{*} \), it holds that \( a_n \cdot a_{n+1} \cdot a_{n+2} \cdot a_{n+3} = a_n + a_{n+1} + a_{n+2} + a_{n+3} \). Find the value of \( \sum_{i=1}^{2023} a_i \). | "[\"4044\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1776, "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:15770"}] | {
"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
} |
[
"210"
] | [
"skywork"
] | a83fb9a8a35e61adc5d4694c680e78a292615844dfc00cb08f1ae781569e2e77 | [
{
"content": "Determine the smallest positive integer $n$ such that $n^2$ is divisible by 50 and $n^3$ is divisible by 294.",
"role": "user"
}
] | Determine the smallest positive integer $n$ such that $n^2$ is divisible by 50 and $n^3$ is divisible by 294. | "[\"210\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1789, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15771"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2 + 3\\sqrt{2}"
] | [
"skywork"
] | 62b5e50db17ab273c2ff5a704837d0373a2185c9ad23e27ee4a944ad87529214 | [
{
"content": "Let \\(a, b, c\\) be the side lengths of a right triangle, with \\(a \\leqslant b < c\\). Determine the maximum constant \\(k\\) such that the inequality \\(a^{2}(b+c) + b^{2}(c+a) + c^{2}(a+b) \\geqslant k a b c\\) holds for all right triangles, and specify when equality occurs.",
"role": "us... | Let \(a, b, c\) be the side lengths of a right triangle, with \(a \leqslant b < c\). Determine the maximum constant \(k\) such that the inequality \(a^{2}(b+c) + b^{2}(c+a) + c^{2}(a+b) \geqslant k a b c\) holds for all right triangles, and specify when equality occurs. | "[\"2 + 3\\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1786, "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:15772"}] | {
"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
} |
[
"60"
] | [
"skywork"
] | 48e225f7cf3ec11de213f095ec3eb55c10cc4b16767025f75f325e411d8a1fe3 | [
{
"content": "Let $x$ and $y$ be real numbers such that $x+y=10$ and $x^{3}+y^{3}=400$, determine the value of $x^{2}+y^{2}$.",
"role": "user"
}
] | Let $x$ and $y$ be real numbers such that $x+y=10$ and $x^{3}+y^{3}=400$, determine the value of $x^{2}+y^{2}$. | "[\"60\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1800, "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:15773"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-1"
] | [
"skywork"
] | ed76930004c5a520fa2bda49a47af5c64d51aa8df8b5470455635b9c86588efe | [
{
"content": "2. If $a^{2}+a+1=0$, determine the value of the expression\n\n$$\na^{1987}+\\frac{1}{a^{1987}}\n$$",
"role": "user"
}
] | 2. If $a^{2}+a+1=0$, determine the value of the expression
$$
a^{1987}+\frac{1}{a^{1987}}
$$ | "[\"-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1787, "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:15774"}] | {
"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
} |
[
"3456"
] | [
"skywork"
] | ceac0c390bcacd05635a56930ae3691c2a8c52f532cbcca01bc5aac84f4cb2f2 | [
{
"content": "1.35 A four-digit number is composed of four consecutive digits in sequence. If the first two digits from the left are swapped, the resulting number is a perfect square. Find the four-digit number.\n\n保留源文本的换行和格式，直接输出翻译结果。",
"role": "user"
}
] | 1.35 A four-digit number is composed of four consecutive digits in sequence. If the first two digits from the left are swapped, the resulting number is a perfect square. Find the four-digit number.
保留源文本的换行和格式，直接输出翻译结果。 | "[\"3456\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 1790, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15775"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2^{8/3}"
] | [
"skywork"
] | 10929b5e133ed47103b983a40a30ff9b195833d615fa71ee3bc65748779b1ae0 | [
{
"content": "Determine the value of $x$ that satisfies $\\sqrt[4]{x\\sqrt{x^4}}=4$.",
"role": "user"
}
] | Determine the value of $x$ that satisfies $\sqrt[4]{x\sqrt{x^4}}=4$. | "[\"2^{8/3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1801, "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:15776"}] | {
"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
} |
[
"364"
] | [
"skywork"
] | 45f759ba1a1c0de5b3159736e65b8cf201ab22ba002d309ad0c8b6e2798e9735 | [
{
"content": "Compute $\\dbinom{14}{11}$.",
"role": "user"
}
] | Compute $\dbinom{14}{11}$. | "[\"364\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1810, "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:15777"}] | {
"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
} |
[
"777"
] | [
"skywork"
] | 36fd55923553f183d67abf1e925677ef17c64cd71925cdb0b2f5d7f1f1a31165 | [
{
"content": "In convex quadrilateral $ABCD, \\angle A \\cong \\angle C, AB = CD = 180,$ and $AD \\neq BC.$ The perimeter of $ABCD$ is $640$. Find $\\lfloor 1000 \\cos A \\rfloor.$ (The notation $\\lfloor x \\rfloor$ means the greatest integer that is less than or equal to $x.$)",
"role": "user"
}
] | In convex quadrilateral $ABCD, \angle A \cong \angle C, AB = CD = 180,$ and $AD \neq BC.$ The perimeter of $ABCD$ is $640$. Find $\lfloor 1000 \cos A \rfloor.$ (The notation $\lfloor x \rfloor$ means the greatest integer that is less than or equal to $x.$) | "[\"777\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1795, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15779"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3^{2^{2019}} - 1"
] | [
"skywork"
] | bb70fef104521e37c5fdd6cfb161f1a28dcbef1fb8e9ebe5d207f70207d3edae | [
{
"content": "Given the function f(x) = x^2 + 2x (x > 0), if f1(x) = f(x), f(n+1)(x) = f(f(n)(x)), n ∈ N*, determine the maximum value of f2019(x) on [1, 2].",
"role": "user"
}
] | Given the function f(x) = x^2 + 2x (x > 0), if f1(x) = f(x), f(n+1)(x) = f(f(n)(x)), n ∈ N*, determine the maximum value of f2019(x) on [1, 2]. | "[\"3^{2^{2019}} - 1\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1791, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15780"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"(1, 10, 3, 12, 5), (10, 3, 12, 5, 1), (3, 12, 5, 1, 10), (12, 5, 1, 10, 3), (5, 1, 10, 3, 12)"
] | [
"skywork"
] | a6342ed23862d0bf69add2c23aac7e813f88913b4861e5315adc843da8767992 | [
{
"content": "A circle is divided into $13$ segments, numbered consecutively from $1$ to $13$. Five fleas called $A,B,C,D$ and $E$ are sitting in the segments $1,2,3,4$ and $5$. A flea is allowed to jump to an empty segment five positions away in either direction around the circle. Only one flea jumps at the sa... | A circle is divided into $13$ segments, numbered consecutively from $1$ to $13$. Five fleas called $A,B,C,D$ and $E$ are sitting in the segments $1,2,3,4$ and $5$. A flea is allowed to jump to an empty segment five positions away in either direction around the circle. Only one flea jumps at the same time, and two fleas... | "[\" (1, 10, 3, 12, 5), (10, 3, 12, 5, 1), (3, 12, 5, 1, 10), (12, 5, 1, 10, 3), (5, 1, 10, 3, 12) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1797, "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:15781"}] | {
"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
} |
[
"857500"
] | [
"skywork"
] | 610c90da40638be42ec5056f14d063103e00f9bb2b7ab6c6753a0c057952fd61 | [
{
"content": "The number \\( N \\) is of the form \\( p^{\\alpha} q^{\\beta} r^{\\gamma} \\), where \\( p, q, r \\) are prime numbers, and \\( p q - r = 3, p r - q = 9 \\). Additionally, the numbers \\( \\frac{N}{p}, \\frac{N}{q}, \\frac{N}{r} \\) respectively have 20, 12, and 15 fewer divisors than the number ... | The number \( N \) is of the form \( p^{\alpha} q^{\beta} r^{\gamma} \), where \( p, q, r \) are prime numbers, and \( p q - r = 3, p r - q = 9 \). Additionally, the numbers \( \frac{N}{p}, \frac{N}{q}, \frac{N}{r} \) respectively have 20, 12, and 15 fewer divisors than the number \( N \). Find the number \( N \). | "[\"857500\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1792, "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:15782"}] | {
"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
} |
[
"40"
] | [
"skywork"
] | 31d48470bf715d90fc9b12a0a58c426865d8662d144e29910ea2fa94ff631384 | [
{
"content": "A trainee cook took two buckets of unpeeled potatoes and peeled everything in an hour. Meanwhile, $25\\%$ of the potatoes went into peels. How much time did it take for him to collect exactly one bucket of peeled potatoes?",
"role": "user"
}
] | A trainee cook took two buckets of unpeeled potatoes and peeled everything in an hour. Meanwhile, $25\%$ of the potatoes went into peels. How much time did it take for him to collect exactly one bucket of peeled potatoes? | "[\"40\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1806, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:15783"}] | {
"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
} |
[
"4107"
] | [
"skywork"
] | 38c84576a195309d65e3b68e0d30ae1cf9d612afc676b43a6cc408dd78ab9c06 | [
{
"content": "For positive integer $n,$ let $s(n)$ be the sum of the digits of n when n is expressed in base ten. For example, $s(2022) = 2 + 0 + 2 + 2 = 6.$ Find the sum of the two solutions to the equation $n - 3s(n) = 2022.$",
"role": "user"
}
] | For positive integer $n,$ let $s(n)$ be the sum of the digits of n when n is expressed in base ten. For example, $s(2022) = 2 + 0 + 2 + 2 = 6.$ Find the sum of the two solutions to the equation $n - 3s(n) = 2022.$ | "[\"4107\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1804, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15784"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"a_{n}=\\frac{(-\\omega)^{n-1}}{\\omega-\\omega^{2}}[(\\omega^{n-1}-1)\\cdot493-(\\omega^{n-1}-\\omega)\\cdot\\omega\\cdot999]"
] | [
"skywork"
] | 3ba764681d4945264eb649984e43107ab3e8bdf8fe5b05aca8c9116d5a253cf8 | [
{
"content": "5. Select a sequence of integers $a_{1}, a_{2}, a_{3}, \\cdots$, such that for each $n \\geqslant 3$, there is $a_{n}=a_{n-1}-a_{n-2}$. If the sum of the first 1492 terms is 1985, and the sum of the first 1985 terms is 1492, find the general term of the sequence.",
"role": "user"
}
] | 5. Select a sequence of integers $a_{1}, a_{2}, a_{3}, \cdots$, such that for each $n \geqslant 3$, there is $a_{n}=a_{n-1}-a_{n-2}$. If the sum of the first 1492 terms is 1985, and the sum of the first 1985 terms is 1492, find the general term of the sequence. | "[\"a_{n}=\\\\frac{(-\\\\omega)^{n-1}}{\\\\omega-\\\\omega^{2}}[(\\\\omega^{n-1}-1)\\\\cdot493-(\\\\omega^{n-1}-\\\\omega)\\\\cdot\\\\omega\\\\cdot999]\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1788, "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:15785"}] | {
"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
} |
[
"f(n)=n+1"
] | [
"skywork"
] | 5ee94b8892a0e0d679b36bdaa537f064b65f0172023ee28ff4c6c49fe8a5dc31 | [
{
"content": ". Find all increasing functions $f: \\mathbb{N} \\rightarrow \\mathbb{N}$ such that\n\n$$\n\\left(2^{m}+1\\right) f(n) f\\left(2^{m} n\\right)=2^{m} f(n)^{2}+f\\left(2^{m} n\\right)^{2}+\\left(2^{m}-1\\right)^{2} n\n$$\n\nfor all integers $n$ and $m$.",
"role": "user"
}
] | . Find all increasing functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that
$$
\left(2^{m}+1\right) f(n) f\left(2^{m} n\right)=2^{m} f(n)^{2}+f\left(2^{m} n\right)^{2}+\left(2^{m}-1\right)^{2} n
$$
for all integers $n$ and $m$. | "[\"f(n)=n+1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1805, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:15786"}] | {
"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
} |
[
"11"
] | [
"skywork"
] | ccb74db3ed327978cdac508086d4299e20719f10be895a19d7e5c31c714c736e | [
{
"content": "For how many positive integers $n$ does $\\frac{1}{n}$ yield a terminating decimal with a non-zero hundredths digit?",
"role": "user"
}
] | For how many positive integers $n$ does $\frac{1}{n}$ yield a terminating decimal with a non-zero hundredths digit? | "[\"11\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1816, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15787"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 600728909be63ca3722ed5296ac91d3169391c2d6437375508fbc540783c1c4f | [
{
"content": "Let $n$ be the answer to this problem. The polynomial $x^{n}+ax^{2}+bx+c$ has real coefficients and exactly $k$ real roots. Find the sum of the possible values of $k$.",
"role": "user"
}
] | Let $n$ be the answer to this problem. The polynomial $x^{n}+ax^{2}+bx+c$ has real coefficients and exactly $k$ real roots. Find the sum of the possible values of $k$. | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1796, "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:15788"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | d648a79ee46a8a0dadd97fbcd351e50d12c1114ca9588bca65b5da24778b3e3a | [
{
"content": "25. The diagram shows a quadrilateral divided into four smaller quadrilaterals with a common vertex $K$. The other labelled points divide the sides of the large quadrilateral into three equal parts. The numbers indicate the areas of the corresponding small quadrilaterals. What is the area of the s... | 25. The diagram shows a quadrilateral divided into four smaller quadrilaterals with a common vertex $K$. The other labelled points divide the sides of the large quadrilateral into three equal parts. The numbers indicate the areas of the corresponding small quadrilaterals. What is the area of the shaded quadrilateral?
A... | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1817, "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:15789"}] | {
"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
} |
[
"42"
] | [
"skywork"
] | 73c4990c69ac01cab8ae81591b86e3d7999125984988b9eeda6e7074606aa0f6 | [
{
"content": "The smallest three positive proper divisors of an integer n are $d_1 < d_2 < d_3$ and they satisfy $d_1 + d_2 + d_3 = 57$ . Find the sum of the possible values of $d_2$ .",
"role": "user"
}
] | The smallest three positive proper divisors of an integer n are $d_1 < d_2 < d_3$ and they satisfy $d_1 + d_2 + d_3 = 57$ . Find the sum of the possible values of $d_2$ . | "[\"42\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1794, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15790"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20\\%"
] | [
"skywork"
] | caaf7472b25ab5a72de971811f3c903753e191c77ee41244cbc670477fc344a3 | [
{
"content": "Carlos took $70\\%$ of a whole pie. Maria took one third of the remainder. What portion of the whole pie was left?",
"role": "user"
}
] | Carlos took $70\%$ of a whole pie. Maria took one third of the remainder. What portion of the whole pie was left? | "[\"20\\\\%\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1829, "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:15791"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | 50de33ce0c37d14fb4d8c2266581fc98335146cf7faffc32d663a755d5c1c432 | [
{
"content": "2. What is the sum of all the solutions of the equation $6 x=\\frac{150}{x}$ ?\nA 0\nB 5\nC 6\nD 25\nE 156",
"role": "user"
}
] | 2. What is the sum of all the solutions of the equation $6 x=\frac{150}{x}$ ?
A 0
B 5
C 6
D 25
E 156 | "[\"0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1822, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15792"}] | {
"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
} |
[
"\\mathrm{C}_{1950}^{9}"
] | [
"skywork"
] | 4a12d17e820a8575999cbcccc4abb901d1deec4a6ac6856df6d5c2d304b87972 | [
{
"content": "Example 3 Put 1996 identical balls into 10 different boxes, so that the $i$-th box contains at least $i$ balls. How many different ways are there to do this?",
"role": "user"
}
] | Example 3 Put 1996 identical balls into 10 different boxes, so that the $i$-th box contains at least $i$ balls. How many different ways are there to do this? | "[\"\\\\mathrm{C}_{1950}^{9}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1808, "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:15793"}] | {
"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
} |
[
"245"
] | [
"skywork"
] | 7a9f0a1e183715c40fea0a51e40df92b8fccb454c9f35562bc8a6a0d3c2339e1 | [
{
"content": "Evaluate $$\\lceil\\sqrt{5}\\rceil + \\lceil\\sqrt{6}\\rceil + \\lceil\\sqrt{7}\\rceil + \\cdots + \\lceil\\sqrt{49}\\rceil$$Note: For a real number $x,$ $\\lceil x \\rceil$ denotes the smallest integer that is greater than or equal to $x.$",
"role": "user"
}
] | Evaluate $$\lceil\sqrt{5}\rceil + \lceil\sqrt{6}\rceil + \lceil\sqrt{7}\rceil + \cdots + \lceil\sqrt{49}\rceil$$Note: For a real number $x,$ $\lceil x \rceil$ denotes the smallest integer that is greater than or equal to $x.$ | "[\"245\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1813, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15794"}] | {
"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
} |
[
"2001"
] | [
"skywork"
] | fc2a23bba9ba31e7fcc05ac0e2e0869cbbfd1e0519e0c70efc8ed586bfbc2f5b | [
{
"content": "[ [Decimal numeral system ]\n\nThe numbers $2^{2000}$ and $5^{2000}$ are written in sequence. How many digits are written in total?\n\n#",
"role": "user"
}
] | [ [Decimal numeral system ]
The numbers $2^{2000}$ and $5^{2000}$ are written in sequence. How many digits are written in total?
# | "[\"2001\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1819, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15795"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-1,-3,0,1,3"
] | [
"skywork"
] | 528026a8982913afe69e5e01eeb64a468c02f233dc42bf11001b68aacf95e2a9 | [
{
"content": "Example 31 (2002 Australian National Mathematics Olympiad) Given the polynomial $p(n)=n^{3}-n^{2}-5 n+2$, find all integers $n$ such that $p^{2}(n)$ is the square of a prime number.",
"role": "user"
}
] | Example 31 (2002 Australian National Mathematics Olympiad) Given the polynomial $p(n)=n^{3}-n^{2}-5 n+2$, find all integers $n$ such that $p^{2}(n)$ is the square of a prime number. | "[\"-1,-3,0,1,3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1809, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:15796"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3}{4}"
] | [
"skywork"
] | c141eaa12d511a536ec0b2220566951bc32fd20626d799bfc0401bbbf90db1b8 | [
{
"content": "Let $\\{a_{n}\\}$ be a sequence with the sum of its first $n$ terms denoted as $S_{n}$, and ${S}_{n}=2{a}_{n}-{2}^{n+1}$. The sequence $\\{b_{n}\\}$ satisfies ${b}_{n}=log_{2}\\frac{{a}_{n}}{n+1}$, where $n\\in N^{*}$. Find the maximum real number $m$ such that the inequality $(1+\\frac{1}{{b}_{2}... | Let $\{a_{n}\}$ be a sequence with the sum of its first $n$ terms denoted as $S_{n}$, and ${S}_{n}=2{a}_{n}-{2}^{n+1}$. The sequence $\{b_{n}\}$ satisfies ${b}_{n}=log_{2}\frac{{a}_{n}}{n+1}$, where $n\in N^{*}$. Find the maximum real number $m$ such that the inequality $(1+\frac{1}{{b}_{2}})•(1+\frac{1}{{b}_{4}})•⋯•(1... | "[\"\\\\frac{3}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1811, "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:15797"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"(0,0,0,0)"
] | [
"skywork"
] | 87da3989012c2217bb758bf0eed71ac34544489bd2647bd705feea9d489fa688 | [
{
"content": "Find all real solutions of the equation with 4 unknowns: $x^{2}+y^{2}+z^{2}+t^{2}=x(y+z+t)$.",
"role": "user"
}
] | Find all real solutions of the equation with 4 unknowns: $x^{2}+y^{2}+z^{2}+t^{2}=x(y+z+t)$. | "[\"(0,0,0,0)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1825, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15798"}] | {
"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
} |
[
"186"
] | [
"skywork"
] | 10bc2161f0a58e0f5bdd42ea269cae692b50ddc3420a774a16f2d1608f3c3885 | [
{
"content": "A student, Theo, needs to earn a total of 30 homework points. For the first six homework points, he has to do one assignment each; for the next six points, he needs to do two assignments each; and so on, such that for every subsequent set of six points, the number of assignments he needs to comple... | A student, Theo, needs to earn a total of 30 homework points. For the first six homework points, he has to do one assignment each; for the next six points, he needs to do two assignments each; and so on, such that for every subsequent set of six points, the number of assignments he needs to complete doubles the previou... | "[\"186\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1827, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15799"}] | {
"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
} |
[
"Existence of \\(\\beta_{c}\\) and limits as described in the solution."
] | [
"skywork"
] | 3c8f18c600fb3c5dca2d7809f4b5706795c383ef2d655823d9118b5a5eb3eae3 | [
{
"content": "A binary tree is a tree in which each node has exactly two descendants. Suppose that each node of the tree is coloured black with probability \\(p\\), and white otherwise, independently of all other nodes. For any path \\(\\pi\\) containing \\(n\\) nodes beginning at the root of the tree, let \\(B... | A binary tree is a tree in which each node has exactly two descendants. Suppose that each node of the tree is coloured black with probability \(p\), and white otherwise, independently of all other nodes. For any path \(\pi\) containing \(n\) nodes beginning at the root of the tree, let \(B(\pi)\) be the number of black... | "[\"Existence of \\\\(\\\\beta_{c}\\\\) and limits as described in the solution.\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 1783, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15800"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | b47f1ac1281640a3a66460846109fc9d97b3d8f7ae35ee74cc03bbde49bba8bc | [
{
"content": "Example 1: $n$ teams are to hold a home-and-away double round-robin match (each pair of teams plays two matches, each having one home match), and each team can play multiple away matches within a week (from Sunday to Saturday). However, if a team has a home match in a certain week, no away matches... | Example 1: $n$ teams are to hold a home-and-away double round-robin match (each pair of teams plays two matches, each having one home match), and each team can play multiple away matches within a week (from Sunday to Saturday). However, if a team has a home match in a certain week, no away matches for that team can be ... | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1814, "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:15801"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | c44ad1431282e0728ffa90857579001f5addb38fab4d8db3544707aa10ac3af5 | [
{
"content": "4. Given the sequence $\\left\\{a_{n}\\right\\}$ with the sum of the first $n$ terms as $S_{n}$, and\n$$\na_{1}=3, S_{n}=2 a_{n}+\\frac{3}{2}\\left((-1)^{n}-1\\right) \\text {. }\n$$\n\nIf $\\left\\{a_{n}\\right\\}$ contains three terms $a_{1} 、 a_{p} 、 a_{q}(p 、 q \\in$ $\\left.\\mathbf{Z}_{+}, 1... | 4. Given the sequence $\left\{a_{n}\right\}$ with the sum of the first $n$ terms as $S_{n}$, and
$$
a_{1}=3, S_{n}=2 a_{n}+\frac{3}{2}\left((-1)^{n}-1\right) \text {. }
$$
If $\left\{a_{n}\right\}$ contains three terms $a_{1} 、 a_{p} 、 a_{q}(p 、 q \in$ $\left.\mathbf{Z}_{+}, 1<p<q\right)$ that form an arithmetic seque... | "[\"1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1807, "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:15802"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"12.1"
] | [
"skywork"
] | 7d53047e59cf5b8385d47e6607fe367c81f40d5966ab84e5342b7a96838964ee | [
{
"content": "A right cylindrical oil tank is $15$ feet tall and its circular bases have diameters of $4$ feet each. When the tank is lying flat on its side (not on one of the circular ends), the oil inside is $3$ feet deep. How deep, in feet, would the oil have been if the tank had been standing upright on one... | A right cylindrical oil tank is $15$ feet tall and its circular bases have diameters of $4$ feet each. When the tank is lying flat on its side (not on one of the circular ends), the oil inside is $3$ feet deep. How deep, in feet, would the oil have been if the tank had been standing upright on one of its bases? Express... | "[\"12.1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1828, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15803"}] | {
"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
} |
[
"16"
] | [
"skywork"
] | 5438a75d2526a3e75a48cba3029b898e213416d172233565a671910f4cbcc111 | [
{
"content": "Let $S = \\{1, 2, \\ldots, 2005\\}$. If any set of $n$ pairwise coprime numbers from $S$ always contains at least one prime number, find the smallest value of $n$.",
"role": "user"
}
] | Let $S = \{1, 2, \ldots, 2005\}$. If any set of $n$ pairwise coprime numbers from $S$ always contains at least one prime number, find the smallest value of $n$. | "[\"16\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1823, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15804"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"(-9, 72)"
] | [
"skywork"
] | 9dddc4fa2b159e8ba774cfda0aaf0bc3f84e211d3a7612595bd8a30d00198502 | [
{
"content": "The triangle $ABC$ lies on the coordinate plane. The midpoint of $\\overline{AB}$ has coordinates $(-16, -63)$, the midpoint of $\\overline{AC}$ has coordinates $(13, 50)$, and the midpoint of $\\overline{BC}$ has coordinates $(6, -85)$. What are the coordinates of point $A$?",
"role": "user... | The triangle $ABC$ lies on the coordinate plane. The midpoint of $\overline{AB}$ has coordinates $(-16, -63)$, the midpoint of $\overline{AC}$ has coordinates $(13, 50)$, and the midpoint of $\overline{BC}$ has coordinates $(6, -85)$. What are the coordinates of point $A$? | "[\"(-9, 72)\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1820, "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:15805"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | c3fc255700708de7e524715fe5434207e463344c0b0c67e2d99ce97936595454 | [
{
"content": "Lil Wayne, the rain god, determines the weather. If Lil Wayne makes it rain on any given day, the probability that he makes it rain the next day is $75 \\%$. If Lil Wayne doesn't make it rain on one day, the probability that he makes it rain the next day is $25 \\%$. He decides not to make it rain... | Lil Wayne, the rain god, determines the weather. If Lil Wayne makes it rain on any given day, the probability that he makes it rain the next day is $75 \%$. If Lil Wayne doesn't make it rain on one day, the probability that he makes it rain the next day is $25 \%$. He decides not to make it rain today. Find the smalles... | "[\"9\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1798, "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:15806"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"65"
] | [
"skywork"
] | c9276ed3c3fbd056f0b0e300439473c2ff59aa1edeaccf105a9b0092638c507e | [
{
"content": "14. In $\\triangle A B C$, it is known that $A B=\\sqrt{30}, A C=$ $\\sqrt{6}, B C=\\sqrt{15}$, point $D$ makes $A D$ bisect $B C$, and $\\angle A D B=90^{\\circ}$, the ratio $\\frac{S_{\\triangle A D B}}{S_{\\triangle A B C}}$ can be written in the form $\\frac{m}{n}$, where $m, n$ are coprime po... | 14. In $\triangle A B C$, it is known that $A B=\sqrt{30}, A C=$ $\sqrt{6}, B C=\sqrt{15}$, point $D$ makes $A D$ bisect $B C$, and $\angle A D B=90^{\circ}$, the ratio $\frac{S_{\triangle A D B}}{S_{\triangle A B C}}$ can be written in the form $\frac{m}{n}$, where $m, n$ are coprime positive integers. Then $m+n=$ | "[\"65\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1830, "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:15807"}] | {
"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
} |
[
"31 \\text{ and } 32"
] | [
"skywork"
] | 61ba926e63760783020657f7f2153107bbde1f347f6af2787c320d5d1fcee90d | [
{
"content": "Point $B$ is due east of point $A$. Point $C$ is due north of point $B$. The distance between points $A$ and $C$ is $10\\sqrt 2$, and $\\angle BAC = 45^\\circ$. Point $D$ is $20$ meters due north of point $C$. The distance $AD$ is between which two integers?",
"role": "user"
}
] | Point $B$ is due east of point $A$. Point $C$ is due north of point $B$. The distance between points $A$ and $C$ is $10\sqrt 2$, and $\angle BAC = 45^\circ$. Point $D$ is $20$ meters due north of point $C$. The distance $AD$ is between which two integers? | "[\"31 \\\\text{ and } 32\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1815, "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:15808"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1-2p^{5}+(2p-1)^{5}"
] | [
"skywork"
] | ed3d5783cb0a2bd4c9621cb2642c07a6f1c141833448a309d619fdc6eec4742e | [
{
"content": "When a Brilliant Idea comes to the Scattered Scholar, he writes it down on a piece of paper, but immediately realizes that the idea is not brilliant, crumples the paper, and throws it under the table, where there are two wastebaskets. The Scholar misses the first wastebasket with a probability of ... | When a Brilliant Idea comes to the Scattered Scholar, he writes it down on a piece of paper, but immediately realizes that the idea is not brilliant, crumples the paper, and throws it under the table, where there are two wastebaskets. The Scholar misses the first wastebasket with a probability of $p>0.5$, and with the ... | "[\"1-2p^{5}+(2p-1)^{5}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1821, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15809"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.