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 |
|---|---|---|---|---|---|---|---|---|
[
"36,45"
] | [
"skywork"
] | f9f0cd450f5f0bb8763186a28ffd02db4b2453cbe0fafae27cdbeb393e63a1b7 | [
{
"content": "7.2. Angles $A O B, B O C$ and $C O D$ are equal to each other, while angle $A O D$ is three times smaller than each of them. All rays $\\mathrm{OA}, \\mathrm{OB}, \\mathrm{OC}$, OD are distinct. Find the measure of angle $A O D$ (list all possible options).",
"role": "user"
}
] | 7.2. Angles $A O B, B O C$ and $C O D$ are equal to each other, while angle $A O D$ is three times smaller than each of them. All rays $\mathrm{OA}, \mathrm{OB}, \mathrm{OC}$, OD are distinct. Find the measure of angle $A O D$ (list all possible options). | "[\"36,45\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2037, "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:16015"}] | {
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[
"12"
] | [
"skywork"
] | cefddbbb090b2106a2971c6d8b0c368f2d9ffc914ffbb4aff91cc72d2b09b134 | [
{
"content": "In isosceles triangle $\\triangle ABC$, $CA=CB=6$, $\\angle ACB=120^{\\circ}$, and point $M$ satisfies $\\overrightarrow{BM}=2 \\overrightarrow{MA}$. Determine the value of $\\overrightarrow{CM} \\cdot \\overrightarrow{CB}$.",
"role": "user"
}
] | In isosceles triangle $\triangle ABC$, $CA=CB=6$, $\angle ACB=120^{\circ}$, and point $M$ satisfies $\overrightarrow{BM}=2 \overrightarrow{MA}$. Determine the value of $\overrightarrow{CM} \cdot \overrightarrow{CB}$. | "[\"12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2046, "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:16016"}] | {
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[
"120"
] | [
"skywork"
] | 43da67026f6e5b7638d09f87d9a434fd8998b2a745afbc0e681d40222c4b7a50 | [
{
"content": "Gage skated 1 hr 15 min each day for 5 days and 1 hr 30 min each day for 3 days. How many minutes would he have to skate the ninth day in order to average 85 minutes of skating each day for the entire time?",
"role": "user"
}
] | Gage skated 1 hr 15 min each day for 5 days and 1 hr 30 min each day for 3 days. How many minutes would he have to skate the ninth day in order to average 85 minutes of skating each day for the entire time? | "[\"120\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2056, "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:16017"}] | {
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[
"2086"
] | [
"skywork"
] | 626760aaa205c36058ad340bd674ce4cf399bbb7be154f7c12a57314a8b961ea | [
{
"content": "Let $I, T, E, S$ be distinct positive integers such that the product $ITEST = 2006$. What is the largest possible value of the sum $I + T + E + S + T + 2006$?\n\n$\\textbf{(A) } 2086\\quad\\textbf{(B) } 4012\\quad\\textbf{(C) } 2144$",
"role": "user"
}
] | Let $I, T, E, S$ be distinct positive integers such that the product $ITEST = 2006$. What is the largest possible value of the sum $I + T + E + S + T + 2006$?
$\textbf{(A) } 2086\quad\textbf{(B) } 4012\quad\textbf{(C) } 2144$ | "[\"2086\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2035, "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:16018"}] | {
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[
"38"
] | [
"skywork"
] | 63ef68d885e7aa9e4bd343e727b2ae98e647d8e95c41e8bfb59853c8ae8f9249 | [
{
"content": "1. Ben lives in a large house with his father, mother, sister and brother as well as 2 dogs, 3 cats, 4 parrots and 5 goldfish. How many legs are there in the house?\nA 18\nB 36\nC 38\nD 46\nE 66",
"role": "user"
}
] | 1. Ben lives in a large house with his father, mother, sister and brother as well as 2 dogs, 3 cats, 4 parrots and 5 goldfish. How many legs are there in the house?
A 18
B 36
C 38
D 46
E 66 | "[\"38\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2030, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16019"}] | {
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[
"105^\\circ"
] | [
"skywork"
] | 148ce6dba4d35c02b6c246142b6f05a3f846ead411a3bc1bb3d44d1591677e18 | [
{
"content": "Let $D$ be a point inside the equilateral triangle $\\triangle ABC$ such that $|AD|=\\sqrt{2}, |BD|=3, |CD|=\\sqrt{5}$. $m(\\widehat{ADB}) = ?$\n\n$\\textbf{(A)}\\ 120^{\\circ} \\qquad\\textbf{(B)}\\ 105^{\\circ} \\qquad\\textbf{(C)}\\ 100^{\\circ} \\qquad\\textbf{(D)}\\ 95^{\\circ} \\qquad\\textb... | Let $D$ be a point inside the equilateral triangle $\triangle ABC$ such that $|AD|=\sqrt{2}, |BD|=3, |CD|=\sqrt{5}$. $m(\widehat{ADB}) = ?$
$\textbf{(A)}\ 120^{\circ} \qquad\textbf{(B)}\ 105^{\circ} \qquad\textbf{(C)}\ 100^{\circ} \qquad\textbf{(D)}\ 95^{\circ} \qquad\textbf{(E)}\ 90^{\circ}$ | "[\"105^\\\\circ\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2028, "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:16020"}] | {
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[
"1"
] | [
"skywork"
] | a67e896eec7c9c653c0fc6557c880e8f4dd9b54cbdfc7f920272a117942e5338 | [
{
"content": "What is the least possible value of $(xy-1)^2+(x+y)^2$ for real numbers $x$ and $y$?",
"role": "user"
}
] | What is the least possible value of $(xy-1)^2+(x+y)^2$ for real numbers $x$ and $y$? | "[\"1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2053, "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:16021"}] | {
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} |
[
"31"
] | [
"skywork"
] | 98ae6755ba2d7bed6de2e61f965d6ad6df56109f3183513cae8191df42860a5e | [
{
"content": "Brian writes down four integers $w > x > y > z$ whose sum is $44$. The pairwise positive differences of these numbers are $1,3,4,5,6,$ and $9$. What is the sum of the possible values for $w$?",
"role": "user"
}
] | Brian writes down four integers $w > x > y > z$ whose sum is $44$. The pairwise positive differences of these numbers are $1,3,4,5,6,$ and $9$. What is the sum of the possible values for $w$? | "[\"31\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2051, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16022"}, {"dataset": "skywork", "extra_in... | {
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} |
[
"3p"
] | [
"skywork"
] | 23ec4afbab1e2f156d22eb3173ed7fc07216615f0ddc476439c99e2cfd50c8aa | [
{
"content": "Two rockets are in space in a negligible gravitational field. All observations are made by an observer in a reference frame in which both rockets are initially at rest. The masses of the rockets are $m$ and $9m$. A constant force $F$ acts on the rocket of mass m for a distance $d$. As a result, th... | Two rockets are in space in a negligible gravitational field. All observations are made by an observer in a reference frame in which both rockets are initially at rest. The masses of the rockets are $m$ and $9m$. A constant force $F$ acts on the rocket of mass m for a distance $d$. As a result, the rocket acquires a mo... | "[\"3p\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2011, "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:16023"}] | {
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} |
[
"\\frac{12 \\cdot 10^{11} - 30}{10^{21}}"
] | [
"skywork"
] | 0e37d4f15270e560592b92d3970c75055a28188378a45e71b97fdf144ed575a2 | [
{
"content": "We form a decimal code of $21$ digits. the code may start with $0$. Determine the probability that the fragment $0123456789$ appears in the code.",
"role": "user"
}
] | We form a decimal code of $21$ digits. the code may start with $0$. Determine the probability that the fragment $0123456789$ appears in the code. | "[\" \\\\frac{12 \\\\cdot 10^{11} - 30}{10^{21}} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2049, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:16024"}] | {
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} |
[
"\\left( \\binom{n}{k} \\right)^2"
] | [
"skywork"
] | 7520aee37f6695cd943450b2bb80b7288eda2b1285a106b0f0caa7aed42ada6a | [
{
"content": "Let $n$ be a positive integer and let $k$ be an integer between $1$ and $n$ inclusive. There is a white board of $n \\times n$. We do the following process. We draw $k$ rectangles with integer sides lenghts and sides parallel to the ones of the $n \\times n$ board, and such that each rectangle cov... | Let $n$ be a positive integer and let $k$ be an integer between $1$ and $n$ inclusive. There is a white board of $n \times n$. We do the following process. We draw $k$ rectangles with integer sides lenghts and sides parallel to the ones of the $n \times n$ board, and such that each rectangle covers the top-right corner... | "[\"\\\\left( \\\\binom{n}{k} \\\\right)^2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2039, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16025"}] | {
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} |
[
"90"
] | [
"skywork"
] | 9c45b11dd6dd9e09f73fa391c6b36afe9ebab4283adbee7d11e3faa0a9bf76e0 | [
{
"content": "Circles with centers $O_{1}$ and $O_{2}$ have a common chord $A B, \\angle A O_{1} B=60^{\\circ}$. The ratio of the length of the first circle to the length of the second is $\\sqrt{2}$. Find the angle $A O_{2} B$.",
"role": "user"
}
] | Circles with centers $O_{1}$ and $O_{2}$ have a common chord $A B, \angle A O_{1} B=60^{\circ}$. The ratio of the length of the first circle to the length of the second is $\sqrt{2}$. Find the angle $A O_{2} B$. | "[\"90\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2034, "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:16026"}] | {
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"503"
] | [
"skywork"
] | 4529ac724cfe13f71a9fa0112b5fc3033166f3427262acd34392bb9fca30b7ce | [
{
"content": "The probability that a set of three distinct vertices chosen at random from among the vertices of a regular $n$ -gon determine an obtuse triangle is $\\frac{93}{125}$ . Find the sum of all possible values of $n$ .",
"role": "user"
}
] | The probability that a set of three distinct vertices chosen at random from among the vertices of a regular $n$ -gon determine an obtuse triangle is $\frac{93}{125}$ . Find the sum of all possible values of $n$ . | "[\"503\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 2067, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16027"}, {"dataset": "skywork", "extra_... | {
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} |
[
"174"
] | [
"skywork"
] | b6d176a76b180484f1addf46ca2de8364575421157098ec741f27ea4d18fdf6e | [
{
"content": "In 10 boxes, place ping-pong balls such that the number of balls in each box is at least 11, not equal to 17, not a multiple of 6, and all numbers are distinct. What is the minimum number of ping-pong balls needed?",
"role": "user"
}
] | In 10 boxes, place ping-pong balls such that the number of balls in each box is at least 11, not equal to 17, not a multiple of 6, and all numbers are distinct. What is the minimum number of ping-pong balls needed? | "[\"174\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2055, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:16028"}] | {
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} |
[
"\\lim_{x \\to +\\infty} f(x) = 0"
] | [
"skywork"
] | c6182c858e066260085be44ae32360c2fc0de17313e78755463027baa7ad6bb7 | [
{
"content": "Let $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ be a continuous function with the following property: for all $\\alpha \\in \\mathbb{R}_{>0}$, the sequence $(a_n)_{n \\in \\mathbb{N}}$ defined as $a_n = f(n\\alpha)$ satisfies $\\lim_{n \\to \\infty} a_n = 0$. Is it necessarily true that $\\lim_{x \\... | Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function with the following property: for all $\alpha \in \mathbb{R}_{>0}$, the sequence $(a_n)_{n \in \mathbb{N}}$ defined as $a_n = f(n\alpha)$ satisfies $\lim_{n \to \infty} a_n = 0$. Is it necessarily true that $\lim_{x \to +\infty} f(x) = 0$? | "[\"\\\\lim_{x \\\\to +\\\\infty} f(x) = 0\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2044, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16029"}] | {
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[
"5"
] | [
"skywork"
] | 998e0c5c3323235e95f2f9fe1ec001d51f0a180d7e305eb5b4f0323912f63224 | [
{
"content": "6. (5 points) From point $A$, lying on a circle, chords $A B$, $A C$, and tangent $A D$ are drawn. The angle between the chords is $\\frac{\\pi}{6}$, and the angle between chord $A C$ and tangent $A D$, which does not contain chord $A B$, is $\\frac{5 \\pi}{12}$. Calculate the integer part of the ... | 6. (5 points) From point $A$, lying on a circle, chords $A B$, $A C$, and tangent $A D$ are drawn. The angle between the chords is $\frac{\pi}{6}$, and the angle between chord $A C$ and tangent $A D$, which does not contain chord $A B$, is $\frac{5 \pi}{12}$. Calculate the integer part of the radius of the circle if th... | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2059, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "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:16030"}] | {
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} |
[
"18135"
] | [
"skywork"
] | 65fa6ce5c5cd3a129e8aede9f41584076b17fabd0425624afb0f0c2076242ed7 | [
{
"content": "Problem 3. Determine how many roots of the equation\n\n$$\n4 \\sin 2 x + 3 \\cos 2 x - 2 \\sin x - 4 \\cos x + 1 = 0\n$$\n\nare located on the interval $\\left[10^{2014!} \\pi ; 10^{2014!+2015} \\pi\\right]$. In your answer, write the sum of all digits of the found number.",
"role": "user"
}... | Problem 3. Determine how many roots of the equation
$$
4 \sin 2 x + 3 \cos 2 x - 2 \sin x - 4 \cos x + 1 = 0
$$
are located on the interval $\left[10^{2014!} \pi ; 10^{2014!+2015} \pi\right]$. In your answer, write the sum of all digits of the found number. | "[\"18135\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2060, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16031"}] | {
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} |
[
"51"
] | [
"skywork"
] | 15890aff197e1929484884e4c9f3e5be4d676495d60c8851070cdd23edce04ed | [
{
"content": "15 Given the set $P$ consists of positive integers not exceeding 2012, i.e., $P=$ $\\{1,2,3, \\cdots, 2012\\}$. The set $A$ is a subset of set $P$, and the symbol $|A|$ represents the number of elements in set $A$, while $S(A)$ represents the sum of all elements in set $A$.\n(1) If the difference ... | 15 Given the set $P$ consists of positive integers not exceeding 2012, i.e., $P=$ $\{1,2,3, \cdots, 2012\}$. The set $A$ is a subset of set $P$, and the symbol $|A|$ represents the number of elements in set $A$, while $S(A)$ represents the sum of all elements in set $A$.
(1) If the difference between any two numbers in... | "[\"51\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2048, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:16032"}] | {
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[
"1677"
] | [
"skywork"
] | eb20fe8c06dfb9e402965214dda9b5946017eff2c36b5655a36233224119ee55 | [
{
"content": "Given the set \\( M = \\{1, 2, \\cdots, 2017\\} \\) which consists of the first 2017 positive integers, if one element is removed from \\( M \\) such that the sum of the remaining elements is a perfect square, what is the removed element?",
"role": "user"
}
] | Given the set \( M = \{1, 2, \cdots, 2017\} \) which consists of the first 2017 positive integers, if one element is removed from \( M \) such that the sum of the remaining elements is a perfect square, what is the removed element? | "[\"1677\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2061, "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:16033"}] | {
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[
"\\frac{1}{3}"
] | [
"skywork"
] | e9c322a5f819b87b78a36b7d577c3da44bc015c48122b6436148e081902071df | [
{
"content": "Point P is located on side AB of triangle ABC. What is the probability that the area of triangle PBC is less than or equal to 1/3 of the area of triangle ABC.",
"role": "user"
}
] | Point P is located on side AB of triangle ABC. What is the probability that the area of triangle PBC is less than or equal to 1/3 of the area of triangle ABC. | "[\"\\\\frac{1}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2057, "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:16034"}] | {
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[
"0"
] | [
"skywork"
] | 03f8558e2977c0fb93beada8c0e85a2aedd82be2ef57156adf24321a15eca2e8 | [
{
"content": "For real numbers $a$ and $b$, define $a\\textdollar b = (a - b)^2$. What is $(x - y)^2\\textdollar(y - x)^2$?",
"role": "user"
}
] | For real numbers $a$ and $b$, define $a\textdollar b = (a - b)^2$. What is $(x - y)^2\textdollar(y - x)^2$? | "[\"0\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2058, "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:16035"}] | {
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} |
[
"4(1-e^{-2})"
] | [
"skywork"
] | 9efa93c7bbdef1ab212a8fd29594f4cdccc4aecb98233f7dfa6654ac16978c07 | [
{
"content": "Given the function $f(x)=e^{x}(ax+b)-x^{2}-4x$, the equation of the tangent line to the curve $y=f(x)$ at the point $(0, f(0))$ is $y=4x+4$.\n\n(1) Find the values of $a$ and $b$;\n\n(2) Determine the intervals of monotonicity for $f(x)$ and find the maximum value of $f(x)$.",
"role": "user"
... | Given the function $f(x)=e^{x}(ax+b)-x^{2}-4x$, the equation of the tangent line to the curve $y=f(x)$ at the point $(0, f(0))$ is $y=4x+4$.
(1) Find the values of $a$ and $b$;
(2) Determine the intervals of monotonicity for $f(x)$ and find the maximum value of $f(x)$. | "[\"4(1-e^{-2})\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2050, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16036"}] | {
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} |
[
"14"
] | [
"skywork"
] | b408af4b5bdb572ef3c75ad44d128c4631d5a96676343cc8b4892f8e4602c75e | [
{
"content": "3. Solve the equation\n\n$$\n\\sqrt{\\frac{x-3}{11}}+\\sqrt{\\frac{x-4}{10}}+\\sqrt{\\frac{x-5}{9}}=\\sqrt{\\frac{x-11}{3}}+\\sqrt{\\frac{x-10}{4}}+\\sqrt{\\frac{x-9}{5}}\n$$",
"role": "user"
}
] | 3. Solve the equation
$$
\sqrt{\frac{x-3}{11}}+\sqrt{\frac{x-4}{10}}+\sqrt{\frac{x-5}{9}}=\sqrt{\frac{x-11}{3}}+\sqrt{\frac{x-10}{4}}+\sqrt{\frac{x-9}{5}}
$$ | "[\"14\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2069, "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:16038"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"(2, 2014), (0, -2018), (2018, -2018), (-2016, 2014)"
] | [
"skywork"
] | f77ac58976dbb1fab4b9fb06e86d5416f45d14c86566938f5d76246792e6688e | [
{
"content": "Find all pairs of integers $(a, b)$ such that $$a^2 + ab - b = 2018.$$",
"role": "user"
}
] | Find all pairs of integers $(a, b)$ such that $$a^2 + ab - b = 2018.$$ | "[\" (2, 2014), (0, -2018), (2018, -2018), (-2016, 2014) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2071, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16039"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{2}"
] | [
"skywork"
] | 12b0f247a1be51997cdcca07a4506e79eecdb341539e051819313a9b4f9b5fbf | [
{
"content": "A right triangle has legs $a$ and $b$ and hypotenuse $c.$ Find the largest possible value of\n\\[\\frac{a + b}{c}.\\]",
"role": "user"
}
] | A right triangle has legs $a$ and $b$ and hypotenuse $c.$ Find the largest possible value of
\[\frac{a + b}{c}.\] | "[\"\\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2068, "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:16040"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{4}"
] | [
"skywork"
] | fe0a4a02325cb0c76facdf3cba69d0e900f219f58535570257b250f542d8cf66 | [
{
"content": "A point is chosen at random from within a circular region. What is the probability that the point is closer to the center of the region than it is to the boundary of the region?",
"role": "user"
}
] | A point is chosen at random from within a circular region. What is the probability that the point is closer to the center of the region than it is to the boundary of the region? | "[\"\\\\frac{1}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2064, "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:16041"}] | {
"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
} |
[
"145"
] | [
"skywork"
] | 3d7646d73e8a43e1d53b840b61cfd73dabb0a0472fe559f49722e316881671a7 | [
{
"content": "Find a number such that when it is multiplied by its reverse, the product is 78445.",
"role": "user"
}
] | Find a number such that when it is multiplied by its reverse, the product is 78445. | "[\"145\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2078, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:16042"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"8"
] | [
"skywork"
] | 24bcc92c02ffe5b554b700a1b3db4ef641c8c486e8980083bdded6b36aeaf980 | [
{
"content": "10. (20 points) Draw any line through the fixed point $M(m, 0)$, intersecting the parabola $y^{2}=16 x$ at points $P$ and $Q$. If $\\frac{1}{|P M|^{2}}+\\frac{1}{|Q M|^{2}}$ is a constant, find all possible values of the real number $m$.",
"role": "user"
}
] | 10. (20 points) Draw any line through the fixed point $M(m, 0)$, intersecting the parabola $y^{2}=16 x$ at points $P$ and $Q$. If $\frac{1}{|P M|^{2}}+\frac{1}{|Q M|^{2}}$ is a constant, find all possible values of the real number $m$. | "[\"8\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2065, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16043"}] | {
"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{23}{25}"
] | [
"skywork"
] | 01b7410e57add305e80d025223702bb0cf2fe4e2ae7c223af85b30fc3101b1f7 | [
{
"content": "Given two numbers selected randomly from the interval $[0,1]$, find the probability that the sum of these two numbers is less than $\\frac{8}{5}$.",
"role": "user"
}
] | Given two numbers selected randomly from the interval $[0,1]$, find the probability that the sum of these two numbers is less than $\frac{8}{5}$. | "[\"\\\\frac{23}{25}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2082, "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:16044"}] | {
"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}{4}"
] | [
"skywork"
] | 542537498b1ff4c6ed6910e91c9005ea1a05eab15ff7ced218c7a7a0ba87ba6b | [
{
"content": "What is $\\frac{2^2 \\cdot 2^{-3}}{2^3 \\cdot 2^{-2}}$?",
"role": "user"
}
] | What is $\frac{2^2 \cdot 2^{-3}}{2^3 \cdot 2^{-2}}$? | "[\"\\\\frac{1}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2099, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:16045"}] | {
"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
} |
[
"347"
] | [
"skywork"
] | 929f59418cb0da50ac630c18387ab07f37dd10f298ebb5ed0907fda65d419543 | [
{
"content": "15. (6 points) Given a three-digit number $\\mathrm{abc}$, and $a(b+c)=33, b(a+c)=40$, then this three-digit number is $\\qquad$",
"role": "user"
}
] | 15. (6 points) Given a three-digit number $\mathrm{abc}$, and $a(b+c)=33, b(a+c)=40$, then this three-digit number is $\qquad$ | "[\"347\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2073, "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:16046"}] | {
"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"
] | f1a1ac382e1fa8f9d854798ef8826c903702e317b05b18b3efc7622fa476e955 | [
{
"content": "A right rectangular prism $Q$ has integral side lengths $a, b, c$ with $a \\le b \\le c$. A plane parallel to one of the faces of $Q$ cuts $Q$ into two prisms, one of which is similar to $Q$, with both having nonzero volumes. The middle side length $b = 3969$. Determine the number of ordered tripl... | A right rectangular prism $Q$ has integral side lengths $a, b, c$ with $a \le b \le c$. A plane parallel to one of the faces of $Q$ cuts $Q$ into two prisms, one of which is similar to $Q$, with both having nonzero volumes. The middle side length $b = 3969$. Determine the number of ordered triples $(a, b, c)$ that allo... | "[\"12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2063, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:16047"}] | {
"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
} |
[
"3840"
] | [
"skywork"
] | 7be86f698a6c16a36a9f6a082e4f21541ff78084d875b0a499e22cd855ff2d40 | [
{
"content": "\\( x_{1} = 2001 \\). When \\( n > 1, x_{n} = \\frac{n}{x_{n-1}} \\). Given that \\( x_{1} x_{2} x_{3} \\ldots x_{10} = a \\), find the value of \\( a \\).",
"role": "user"
}
] | \( x_{1} = 2001 \). When \( n > 1, x_{n} = \frac{n}{x_{n-1}} \). Given that \( x_{1} x_{2} x_{3} \ldots x_{10} = a \), find the value of \( a \). | "[\"3840\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2074, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:16048"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"234"
] | [
"skywork"
] | e38961e8ef25b587ae297b1b2b81d8c42662d2f9e0eaac54ddd0c718034bd687 | [
{
"content": "One side of a rectangle has length 18. The area plus the perimeter of the rectangle is 2016. Find the perimeter of the rectangle.",
"role": "user"
}
] | One side of a rectangle has length 18. The area plus the perimeter of the rectangle is 2016. Find the perimeter of the rectangle. | "[\"234\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2095, "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:16049"}, {"dataset": "skywork", "extra_inf... | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{17\\pi}{9}"
] | [
"skywork"
] | 6a023c43f0def916e1cf8147a5c7df3510b8aa1ae375cc9f2f1a7ebaba53d6db | [
{
"content": "2. Find the largest solution of the equation on the interval $(0 ; 2 \\pi)$\n\n$$\n(\\cos 3 x+\\cos 4 x+\\cos 5 x)^{3}=\\cos ^{3} 3 x+\\cos ^{3} 4 x+\\cos ^{3} 5 x\n$$",
"role": "user"
}
] | 2. Find the largest solution of the equation on the interval $(0 ; 2 \pi)$
$$
(\cos 3 x+\cos 4 x+\cos 5 x)^{3}=\cos ^{3} 3 x+\cos ^{3} 4 x+\cos ^{3} 5 x
$$ | "[\"\\\\frac{17\\\\pi}{9}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2076, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:16050"}] | {
"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
} |
[
"3/26"
] | [
"skywork"
] | d270790fa31323e86bcd301d85ffc94b2b1b1d7a91081187d8d54b572db90310 | [
{
"content": "Darryl has a six-sided die with faces $1, 2, 3, 4, 5, 6$ . He knows the die is weighted so that one face\ncomes up with probability $1/2$ and the other five faces have equal probability of coming up. He\nunfortunately does not know which side is weighted, but he knows each face is equally likel... | Darryl has a six-sided die with faces $1, 2, 3, 4, 5, 6$ . He knows the die is weighted so that one face
comes up with probability $1/2$ and the other five faces have equal probability of coming up. He
unfortunately does not know which side is weighted, but he knows each face is equally likely
to be the weighted one... | "[\"3/26\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2085, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:16051"}, {"dataset": "skywork", "extra_in... | {
"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{9 \\sqrt{3}}{4}"
] | [
"skywork"
] | bd6875afa17e62eb3ca31adb608e15a1db24440e7dc2ad678e69597dc43f2c8b | [
{
"content": "9. (14 points) In $\\triangle ABC$, it is known that the sides opposite to $\\angle A$, $\\angle B$, and $\\angle C$ are $a$, $b$, and $c$ respectively, the circumradius of $\\triangle ABC$ is $R=\\sqrt{3}$, and it satisfies\n$\\tan B + \\tan C = \\frac{2 \\sin A}{\\cos C}$.\nFind: (1) $\\angle B$... | 9. (14 points) In $\triangle ABC$, it is known that the sides opposite to $\angle A$, $\angle B$, and $\angle C$ are $a$, $b$, and $c$ respectively, the circumradius of $\triangle ABC$ is $R=\sqrt{3}$, and it satisfies
$\tan B + \tan C = \frac{2 \sin A}{\cos C}$.
Find: (1) $\angle B$, $b$;
(2) the maximum area of $\tri... | "[\"\\\\frac{9 \\\\sqrt{3}}{4}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2081, "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:16052"}] | {
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[
"4320"
] | [
"skywork"
] | 29b521879bf6d00d8c1a6584e96173130ba730d7b1ac6be871a721861b425505 | [
{
"content": "A pet store has 15 puppies, 6 kittens, and 8 hamsters. Alice, Bob, and Charlie each want to buy a pet. For variety, they each want a different kind of pet. How many ways can Alice, Bob, and Charlie buy pets and leave the store satisfied?",
"role": "user"
}
] | A pet store has 15 puppies, 6 kittens, and 8 hamsters. Alice, Bob, and Charlie each want to buy a pet. For variety, they each want a different kind of pet. How many ways can Alice, Bob, and Charlie buy pets and leave the store satisfied? | "[\"4320\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2080, "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:16053"}] | {
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[
"62.8"
] | [
"skywork"
] | 3b23d0ddd91f902802288a57ea4318c2d49f3fd18501ce24e47a4215cbfa8f89 | [
{
"content": "25. The area of a square is 40 square centimeters, then the area of its circumscribed circle is $\\qquad$ square centimeters. ( $\\pi$ is taken as 3.14)",
"role": "user"
}
] | 25. The area of a square is 40 square centimeters, then the area of its circumscribed circle is $\qquad$ square centimeters. ( $\pi$ is taken as 3.14) | "[\"62.8\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2090, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16054"}] | {
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[
"4\\sqrt{3}"
] | [
"skywork"
] | fc0b2559f7a8d9a082352b858e64713be001e0ad200e7fb3c6aa91b9bfbe2afe | [
{
"content": "Given that $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively in $\\triangle ABC$, and $(\\sin A + \\sin B)(a-b) = (\\sin C - \\sin B)c$.\n\n1. Find the measure of angle $A$.\n2. If $a=4$, find the maximum area of $\\triangle ABC$.",
"role": "user"
}
] | Given that $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively in $\triangle ABC$, and $(\sin A + \sin B)(a-b) = (\sin C - \sin B)c$.
1. Find the measure of angle $A$.
2. If $a=4$, find the maximum area of $\triangle ABC$. | "[\"4\\\\sqrt{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2047, "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:16055"}] | {
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[
"90^\\circ"
] | [
"skywork"
] | 70187c85822de2045c25a9c50d2e2baad885055b2639713a9e7e99f5d4669b0e | [
{
"content": "In a right triangle rectangle $ABC$ such that $AB = AC$, $M$ is the midpoint of $BC$. Let $P$ be a point on the perpendicular bisector of $AC$, lying in the semi-plane determined by $BC$ that does not contain $A$. Lines $CP$ and $AM$ intersect at $Q$. Calculate the angles that form the lines $AP... | In a right triangle rectangle $ABC$ such that $AB = AC$, $M$ is the midpoint of $BC$. Let $P$ be a point on the perpendicular bisector of $AC$, lying in the semi-plane determined by $BC$ that does not contain $A$. Lines $CP$ and $AM$ intersect at $Q$. Calculate the angles that form the lines $AP$ and $BQ$. | "[\" 90^\\\\circ \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2079, "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:16056"}] | {
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} |
[
"\\frac{2}{3}"
] | [
"skywork"
] | 55cae01060cf9ae29d4c956bad5214b40d1c2f5dca46072b4729961235a81303 | [
{
"content": "The function $g(x),$ defined for $0 \\le x \\le 1,$ has the following properties:\n\n(i) $g(0) = 0.$\n(ii) If $0 \\le x < y \\le 1,$ then $g(x) \\le g(y).$\n(iii) $g(1 - x) = 1 - g(x)$ for all $0 \\le x \\le 1.$\n(iv) $g\\left( \\frac{2x}{5} \\right) = \\frac{g(x)}{3}$ for $0 \\le x \\le 1.$\n\nFi... | The function $g(x),$ defined for $0 \le x \le 1,$ has the following properties:
(i) $g(0) = 0.$
(ii) If $0 \le x < y \le 1,$ then $g(x) \le g(y).$
(iii) $g(1 - x) = 1 - g(x)$ for all $0 \le x \le 1.$
(iv) $g\left( \frac{2x}{5} \right) = \frac{g(x)}{3}$ for $0 \le x \le 1.$
Find $g\left( \frac{3}{5} \right).$ | "[\"\\\\frac{2}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2091, "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:16057"}] | {
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[
"\\frac{1}{6}"
] | [
"skywork"
] | 22d09f8c279176317f2f1b81817a743b132af3ad9aac45f91e32aec7bd24907c | [
{
"content": "Given the formula $d=\\sqrt[3]{\\frac{16}{9}V}$, where $d$ is the diameter of a sphere and $V$ is its volume, find the volume of a sphere with a radius of $\\frac{1}{3}$.",
"role": "user"
}
] | Given the formula $d=\sqrt[3]{\frac{16}{9}V}$, where $d$ is the diameter of a sphere and $V$ is its volume, find the volume of a sphere with a radius of $\frac{1}{3}$. | "[\"\\\\frac{1}{6}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2084, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16058"}] | {
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} |
[
"\\frac{17}{13}"
] | [
"skywork"
] | 73ce8cc1505a343018287d5cbd80551a8419469f6b5d90826183f818d81350ea | [
{
"content": "Let the hyperbola $C: \\frac{x^2}{a^2} - y^2 = 1$ ($a > 0$) intersect with the line $l: x + y = 1$ at two distinct points $A$ and $B$.\n\n(Ⅰ) Find the range of values for the eccentricity $e$ of the hyperbola $C$.\n\n(Ⅱ) Let the intersection of line $l$ with the y-axis be $P$, and $\\overrightarro... | Let the hyperbola $C: \frac{x^2}{a^2} - y^2 = 1$ ($a > 0$) intersect with the line $l: x + y = 1$ at two distinct points $A$ and $B$.
(Ⅰ) Find the range of values for the eccentricity $e$ of the hyperbola $C$.
(Ⅱ) Let the intersection of line $l$ with the y-axis be $P$, and $\overrightarrow{PA} = \frac{5}{12} \overri... | "[\"\\\\frac{17}{13}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2070, "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:16059"}] | {
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"reference_components": 1,
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} |
[
"200"
] | [
"skywork"
] | e37c04096d251830eec83debeb62bba1694825a39391a5db49f2b35a4a30cd02 | [
{
"content": "Task 4. In a mathematics competition, 300 participants take part. After the competition, some participants play chess. Each pair of participants plays against each other at most once. There are no three participants in this competition who all play against each other. Determine the maximum $n$ for... | Task 4. In a mathematics competition, 300 participants take part. After the competition, some participants play chess. Each pair of participants plays against each other at most once. There are no three participants in this competition who all play against each other. Determine the maximum $n$ for which it is possible ... | "[\"200\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2077, "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:16060"}] | {
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} |
[
"n = 71"
] | [
"skywork"
] | 50dd38d1ebd18f01aa384b8393716ecba8e94d66fa5623398fa177fd66cab605 | [
{
"content": "Find the least non-negative integer $n$ such that exists a non-negative integer $k$ such that the last 2012 decimal digits of $n^k$ are all $1$'s.",
"role": "user"
}
] | Find the least non-negative integer $n$ such that exists a non-negative integer $k$ such that the last 2012 decimal digits of $n^k$ are all $1$'s. | "[\" n = 71 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2097, "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:16061"}] | {
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"reference_present": true
} |
[
"16"
] | [
"skywork"
] | 0c0592cd301426be23bbc8e44d808594aa67fffc2f0cd25e07710b3442a3e561 | [
{
"content": "18. $A, B, C, D$ are four different natural numbers, and their average is 8. By adding them in pairs, we get five different sums: $12, 15, 17, 20, x$. Find $x$.",
"role": "user"
}
] | 18. $A, B, C, D$ are four different natural numbers, and their average is 8. By adding them in pairs, we get five different sums: $12, 15, 17, 20, x$. Find $x$. | "[\"16\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2072, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16062"}] | {
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} |
[
"60^\\circ"
] | [
"skywork"
] | 489b8043e0cc1a5242c56ee8df8550f56e9130c103c4866c8ba37016c23cfa6e | [
{
"content": "$O$ and $I$ are the circumcentre and incentre of $\\vartriangle ABC$ respectively. Suppose $O$ lies in the interior of $\\vartriangle ABC$ and $I$ lies on the circle passing through $B, O$, and $C$. What is the magnitude of $\\angle B AC$ in degrees?",
"role": "user"
}
] | $O$ and $I$ are the circumcentre and incentre of $\vartriangle ABC$ respectively. Suppose $O$ lies in the interior of $\vartriangle ABC$ and $I$ lies on the circle passing through $B, O$, and $C$. What is the magnitude of $\angle B AC$ in degrees? | "[\"60^\\\\circ\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2093, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16063"}, {"dataset": "skywork", "extra_in... | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{8}{3}"
] | [
"skywork"
] | 2ca4c1992ad4c0c9c4f75ea56b25ee260571ac24e5684e3d5752ab854296a955 | [
{
"content": "23. As shown in the figure, the diagonal $BD$ of rectangle $ABCD$ passes through the origin $O$, and the two sides of the rectangle are parallel to the coordinate axes. The graph of the inverse proportion function $y=\\frac{2}{x}$ intersects the rectangle at points $P$ and $Q$. Given that point $A... | 23. As shown in the figure, the diagonal $BD$ of rectangle $ABCD$ passes through the origin $O$, and the two sides of the rectangle are parallel to the coordinate axes. The graph of the inverse proportion function $y=\frac{2}{x}$ intersects the rectangle at points $P$ and $Q$. Given that point $A(-3,-2)$, the area of $... | "[\"\\\\frac{8}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2087, "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:16064"}] | {
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[
"-1"
] | [
"skywork"
] | eae3a70ce96d43cfc89d25a4e2ef9a239416cd8be83b3dedcd09fa5449d9d7f3 | [
{
"content": "When \\( n \\) is a positive integer, the function \\( f \\) satisfies \\( f(n+3)=\\frac{f(n)-1}{f(n)+1} \\), with \\( f(1) \\neq 0 \\) and \\( f(1) \\neq \\pm 1 \\). Find the value of \\( f(8) \\cdot f(2018) \\).",
"role": "user"
}
] | When \( n \) is a positive integer, the function \( f \) satisfies \( f(n+3)=\frac{f(n)-1}{f(n)+1} \), with \( f(1) \neq 0 \) and \( f(1) \neq \pm 1 \). Find the value of \( f(8) \cdot f(2018) \). | "[\"-1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2083, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:16065"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"59"
] | [
"skywork"
] | 0289a106f2f79b948869f38995ef79ac5b2d72cd6530a9ff5fd23281a7e3c661 | [
{
"content": "A prime number $ q $ is called***'Kowai'***number if $ q = p^2 + 10$ where $q$ , $p$ , $p^2-2$ , $p^2-8$ , $p^3+6$ are prime numbers. WE know that, at least one ***'Kowai'*** number can be found. Find the summation of all ***'Kowai'*** numbers.",
"role": "user"
}
] | A prime number $ q $ is called***'Kowai'***number if $ q = p^2 + 10$ where $q$ , $p$ , $p^2-2$ , $p^2-8$ , $p^3+6$ are prime numbers. WE know that, at least one ***'Kowai'*** number can be found. Find the summation of all ***'Kowai'*** numbers. | "[\"59\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2075, "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:16066"}] | {
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{2}"
] | [
"skywork"
] | 4084ea44556d73eb40e540e4f4d9cd054f394854b0c51d67642f6edcca7eeb86 | [
{
"content": "Given that $F_1$ and $F_2$ are the left and right foci of the hyperbola $E: \\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$, and point $M$ is on $E$ with $MF_1$ perpendicular to the x-axis and $\\sin \\angle MF_2F_1 = \\frac{1}{3}$, find the eccentricity of $E$.",
"role": "user"
}
] | Given that $F_1$ and $F_2$ are the left and right foci of the hyperbola $E: \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, and point $M$ is on $E$ with $MF_1$ perpendicular to the x-axis and $\sin \angle MF_2F_1 = \frac{1}{3}$, find the eccentricity of $E$. | "[\"\\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2089, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "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:16067"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"86"
] | [
"skywork"
] | b147f38cedb687aedb3bad5e6d43deab485e3d53ca0f4b9fbd224e1b68563d34 | [
{
"content": "10-7-1. At a large round table, 90 people are feasting, facing the center of the table: 40 barons, 30 counts, and 20 marquises. On a signal, exactly those who have both neighbors—left and right—with the same title should stand up. What is the maximum number of people who can stand up?\n\nFor examp... | 10-7-1. At a large round table, 90 people are feasting, facing the center of the table: 40 barons, 30 counts, and 20 marquises. On a signal, exactly those who have both neighbors—left and right—with the same title should stand up. What is the maximum number of people who can stand up?
For example, for a count to stand... | "[\"86\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2094, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16068"}] | {
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} |
[
"2\\sqrt{130+58\\sqrt{5}}"
] | [
"skywork"
] | a150ab4f89ecd2405ab0e122f0657b1dc5a2e9849ea0f3b01fb0d04059ce1440 | [
{
"content": "4. In triangle $A B C$, the bisector $A D$ is drawn. It is known that the centers of the inscribed circle of triangle $A B D$ and the circumscribed circle of triangle $A B C$ coincide. Find the area of triangle $A B C$, if $C D=4$. The answer should not include trigonometric function notations and... | 4. In triangle $A B C$, the bisector $A D$ is drawn. It is known that the centers of the inscribed circle of triangle $A B D$ and the circumscribed circle of triangle $A B C$ coincide. Find the area of triangle $A B C$, if $C D=4$. The answer should not include trigonometric function notations and their inverses. | "[\"2\\\\sqrt{130+58\\\\sqrt{5}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2086, "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:16069"}] | {
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[
"0"
] | [
"skywork"
] | ca1663b277bda5ca5f3c79c7f617629a2a85d6bfeb5783d2cf891346f224b56b | [
{
"content": "a) Prove that $\\{x+y\\}-\\{y\\}$ can only be equal to $\\{x\\}$ or $\\{x\\}-1$ for any $x,y\\in \\mathbb{R}$.\n\nb) Let $\\alpha\\in \\mathbb{R}\\backslash \\mathbb{Q}$. Denote $a_n=\\{n\\alpha\\}$ for all $n\\in \\mathbb{N}^*$ and define the sequence $(x_n)_{n\\ge 1}$ by\n\n\\[x_n=(a_2-a_1)(a_3-... | a) Prove that $\{x+y\}-\{y\}$ can only be equal to $\{x\}$ or $\{x\}-1$ for any $x,y\in \mathbb{R}$.
b) Let $\alpha\in \mathbb{R}\backslash \mathbb{Q}$. Denote $a_n=\{n\alpha\}$ for all $n\in \mathbb{N}^*$ and define the sequence $(x_n)_{n\ge 1}$ by
\[x_n=(a_2-a_1)(a_3-a_2)\cdot \ldots \cdot (a_{n+1}-a_n)\]
Prove th... | "[\" 0 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2088, "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:16070"}] | {
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[
"12"
] | [
"skywork"
] | 902e0d677452a31a6bc36219522e1b0b61f6c0de606d53280a82d21572459910 | [
{
"content": "3. (7 points) On the radius $A O$ of a circle with center $O$, a point $M$ is chosen. On one side of $A O$ on the circle, points $B$ and $C$ are chosen such that $\\angle A M B = \\angle O M C = \\alpha$. Find the length of $B C$ if the radius of the circle is $15$, and $\\sin \\alpha = \\frac{\\s... | 3. (7 points) On the radius $A O$ of a circle with center $O$, a point $M$ is chosen. On one side of $A O$ on the circle, points $B$ and $C$ are chosen such that $\angle A M B = \angle O M C = \alpha$. Find the length of $B C$ if the radius of the circle is $15$, and $\sin \alpha = \frac{\sqrt{21}}{5}$? | "[\"12\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2096, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16071"}] | {
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[
"0.2"
] | [
"skywork"
] | e40f7e0cfb3e9a24ee58fe599611b04cc922868dc8730533dffafe2dfc00d60a | [
{
"content": "From point \\( A \\), two rays are drawn intersecting a given circle: one at points \\( B \\) and \\( C \\), and the other at points \\( D \\) and \\( E \\). It is known that \\( AB = 7 \\), \\( BC = 7 \\), and \\( AD = 10 \\). Determine \\( DE \\).",
"role": "user"
}
] | From point \( A \), two rays are drawn intersecting a given circle: one at points \( B \) and \( C \), and the other at points \( D \) and \( E \). It is known that \( AB = 7 \), \( BC = 7 \), and \( AD = 10 \). Determine \( DE \). | "[\"0.2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2100, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:16072"}] | {
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[
"0or2"
] | [
"skywork"
] | 5ebacf539121dae17e6efb2b83b8a42888eb40784478e1ace9441b23efcf6110 | [
{
"content": "Problem 3. On an island, there live knights and liars. Knights always tell the truth, while liars always lie. One day, 6 inhabitants of the island gathered together and each said: \"Among the other five, there are exactly four liars!\". How many knights could there be among them?",
"role": "us... | Problem 3. On an island, there live knights and liars. Knights always tell the truth, while liars always lie. One day, 6 inhabitants of the island gathered together and each said: "Among the other five, there are exactly four liars!". How many knights could there be among them? | "[\"0or2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2102, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:16073"}] | {
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} |
[
"-9"
] | [
"skywork"
] | b2e5dc1ea6d83bfe92ecc5b106d2d1e57572bf295ab0c0c7e8d00f8036512ed9 | [
{
"content": "Given that $O$ is the circumcenter of $\\triangle ABC$, $AC \\perp BC$, $AC = 3$, and $\\angle ABC = \\frac{\\pi}{6}$, find the dot product of $\\overrightarrow{OC}$ and $\\overrightarrow{AB}$.",
"role": "user"
}
] | Given that $O$ is the circumcenter of $\triangle ABC$, $AC \perp BC$, $AC = 3$, and $\angle ABC = \frac{\pi}{6}$, find the dot product of $\overrightarrow{OC}$ and $\overrightarrow{AB}$. | "[\"-9\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2109, "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:16074"}] | {
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[
"27"
] | [
"skywork"
] | e172debd866c78875684a0852cac6e65b561c2cacc7d75b29fde96cd644c1b6d | [
{
"content": "The numbers $36,27,42,32,28,31,23,17$ are grouped in pairs so that the sum of each pair is the same. Which number is paired with 32 ?",
"role": "user"
}
] | The numbers $36,27,42,32,28,31,23,17$ are grouped in pairs so that the sum of each pair is the same. Which number is paired with 32 ? | "[\"27\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2110, "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:16075"}] | {
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[
"12.1"
] | [
"skywork"
] | 9ef307ff2d35db079719569e29bdbb062b67389ad6e23a7c22683f45770dc867 | [
{
"content": "A bus line has 12 stops on a straight street. The distance between two consecutive stops is always the same. It is known that the distance between the third and the sixth stops is 3300 meters. What is the distance, in kilometers, between the first and the last stop?\n(a) 8.4\n(b) 12.1\n(c) 9.9\n(d... | A bus line has 12 stops on a straight street. The distance between two consecutive stops is always the same. It is known that the distance between the third and the sixth stops is 3300 meters. What is the distance, in kilometers, between the first and the last stop?
(a) 8.4
(b) 12.1
(c) 9.9
(d) 13.2
(e) 9.075 | "[\"12.1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2108, "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:16076"}] | {
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[
"208152"
] | [
"skywork"
] | 9a3618187d24d436b7c086eaf9f84156a1c447e06f220911bf6dc76def57f464 | [
{
"content": "14. (12 points) The six-digit number $20 \\square 15 \\square$ is divisible by 72. What is this six-digit number?",
"role": "user"
}
] | 14. (12 points) The six-digit number $20 \square 15 \square$ is divisible by 72. What is this six-digit number? | "[\"208152\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2106, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16077"}] | {
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} |
[
"91"
] | [
"skywork"
] | bb663d25d3cec70f8210b5656cc06356c5c83fb138b9fc652b1ee34a58536bd4 | [
{
"content": "The increasing geometric sequence $x_{0},x_{1},x_{2},\\ldots$ consists entirely of integral powers of $3.$ Given that\n$\\sum_{n=0}^{7}\\log_{3}(x_{n}) = 308$ and $56 \\leq \\log_{3}\\left ( \\sum_{n=0}^{7}x_{n}\\right ) \\leq 57,$\n find $\\log_{3}(x_{14}).$",
"role": "user"
}
] | The increasing geometric sequence $x_{0},x_{1},x_{2},\ldots$ consists entirely of integral powers of $3.$ Given that
$\sum_{n=0}^{7}\log_{3}(x_{n}) = 308$ and $56 \leq \log_{3}\left ( \sum_{n=0}^{7}x_{n}\right ) \leq 57,$
find $\log_{3}(x_{14}).$ | "[\"91\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2107, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16078"}, {"dataset": "skywork", "extra_in... | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"50"
] | [
"skywork"
] | 53091b2ae769a53535c48fd412f0b70e61b6184657ccb19c85a345ae7a2772ed | [
{
"content": "In a certain country, there are 100 cities. The Ministry of Aviation requires that each pair of cities be connected by a bidirectional flight operated by exactly one airline, and that for each airline, it must be possible to travel from any city to any other city (possibly with transfers). What is... | In a certain country, there are 100 cities. The Ministry of Aviation requires that each pair of cities be connected by a bidirectional flight operated by exactly one airline, and that for each airline, it must be possible to travel from any city to any other city (possibly with transfers). What is the maximum number of... | "[\"50\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2111, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:16079"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"\\frac{11}{12}"
] | [
"skywork"
] | 5c8b68d33cd99a0255b5cf7a297d08bb766e9a177f3e8a08b7b1d150e2f43d40 | [
{
"content": "3. In triangle $A B C$, the angle bisectors $A A_{1}, B B_{1}, C C_{1}$ are drawn, $L$ is the intersection point of segments $B_{1} C_{1}$ and $A A_{1}$, $K$ is the intersection point of segments $B_{1} A_{1}$ and $C C_{1}$. Find the ratio $L M: M K$, if $M$ is the intersection point of the angle ... | 3. In triangle $A B C$, the angle bisectors $A A_{1}, B B_{1}, C C_{1}$ are drawn, $L$ is the intersection point of segments $B_{1} C_{1}$ and $A A_{1}$, $K$ is the intersection point of segments $B_{1} A_{1}$ and $C C_{1}$. Find the ratio $L M: M K$, if $M$ is the intersection point of the angle bisector $B B_{1}$ wit... | "[\"\\\\frac{11}{12}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2112, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16080"}] | {
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[
"\\frac{5^9}{2 \\cdot 3^9}"
] | [
"skywork"
] | 9eaf9b4adc426b10494f224e3911d95f544550e2002ed7aa77e4db8a55c25c48 | [
{
"content": "Given $x = \\frac{2}{3}$ and $y = \\frac{5}{2}$, find the value of $\\frac{1}{3}x^8y^9$.",
"role": "user"
}
] | Given $x = \frac{2}{3}$ and $y = \frac{5}{2}$, find the value of $\frac{1}{3}x^8y^9$. | "[\"\\\\frac{5^9}{2 \\\\cdot 3^9}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2131, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16081"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 422dc8df0fa77d34c443a4b0efd1baf676c3060519b897ded5b5b15e9f615b78 | [
{
"content": "4. Let the line $y=k x+m$ passing through any point $P$ on the ellipse $\\frac{x^{2}}{4}+y^{2}=1$ intersect the ellipse $\\frac{x^{2}}{16}+\\frac{y^{2}}{4}=1$ at points $A$ and $B$, and let the ray $P O$ intersect the ellipse $\\frac{x^{2}}{16}+\\frac{y^{2}}{4}=1$ at point $Q$. Then the value of $... | 4. Let the line $y=k x+m$ passing through any point $P$ on the ellipse $\frac{x^{2}}{4}+y^{2}=1$ intersect the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{4}=1$ at points $A$ and $B$, and let the ray $P O$ intersect the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{4}=1$ at point $Q$. Then the value of $S_{\triangle A B Q}: S_{\tr... | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2092, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16082"}] | {
"all_reference_components_parse": true,
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[
"\\frac{2}{3}"
] | [
"skywork"
] | d55359d952066c8a11df2ae039a09af0749d81dc8041691c5d15296dd159e8c2 | [
{
"content": "In the triangles \\( \\triangle ABC \\) and \\( \\triangle AEF \\), \\( B \\) is the midpoint of \\( EF \\). Given that \\( AB = EF = 1 \\), \\( BC = 6 \\), \\( CA = \\sqrt{33} \\), and \\( \\overrightarrow{AB} \\cdot \\overrightarrow{AE} + \\overrightarrow{AC} \\cdot \\overrightarrow{AF} = 2 \\),... | In the triangles \( \triangle ABC \) and \( \triangle AEF \), \( B \) is the midpoint of \( EF \). Given that \( AB = EF = 1 \), \( BC = 6 \), \( CA = \sqrt{33} \), and \( \overrightarrow{AB} \cdot \overrightarrow{AE} + \overrightarrow{AC} \cdot \overrightarrow{AF} = 2 \), find the cosine of the angle between \( \overr... | "[\"\\\\frac{2}{3}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2104, "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:16083"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"100"
] | [
"skywork"
] | 2bca9313fe6bd31bb9abfd1371917e1dd2e9f9dd37b35811c4a94af9239544f7 | [
{
"content": "In trapezoid $ABCD$, sides $AB$ and $CD$ are parallel, and diagonal $BD$ and side $AD$ have equal length. If $m\\angle DCB=110^\\circ$ and $m\\angle CBD=30^\\circ$, then $m\\angle ADB=$\n$\\textbf{(A)}\\ 80^\\circ\\qquad\\textbf{(B)}\\ 90^\\circ\\qquad\\textbf{(C)}\\ 100^\\circ\\qquad\\textbf{(D)}... | In trapezoid $ABCD$, sides $AB$ and $CD$ are parallel, and diagonal $BD$ and side $AD$ have equal length. If $m\angle DCB=110^\circ$ and $m\angle CBD=30^\circ$, then $m\angle ADB=$
$\textbf{(A)}\ 80^\circ\qquad\textbf{(B)}\ 90^\circ\qquad\textbf{(C)}\ 100^\circ\qquad\textbf{(D)}\ 110^\circ\qquad\textbf{(E)}\ 120^\circ$ | "[\"100\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 2114, "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:16085"}] | {
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} |
[
"200"
] | [
"skywork"
] | 4ff8d22deb6fe5f2dc82e6294b209f0eebec86512968e39346e65b6721f7c2dc | [
{
"content": "Find the number of ordered triples $(a,b,c)$ where $a$ , $b$ , and $c$ are positive integers , $a$ is a factor of $b$ , $a$ is a factor of $c$ , and $a+b+c=100$ .",
"role": "user"
}
] | Find the number of ordered triples $(a,b,c)$ where $a$ , $b$ , and $c$ are positive integers , $a$ is a factor of $b$ , $a$ is a factor of $c$ , and $a+b+c=100$ . | "[\"200\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 2124, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "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:16086"}, {"dataset": "skywork", "extra_inf... | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.87"
] | [
"skywork"
] | 70da76a9ac1edd73cdc06b49af80a5ce08b7f9c8b5a8732f115b522565926972 | [
{
"content": "The number \\( x \\) is such that \\( \\log _{2}\\left(\\log _{4} x\\right) + \\log _{4}\\left(\\log _{8} x\\right) + \\log _{8}\\left(\\log _{2} x\\right) = 1 \\). Find the value of the expression \\( \\log _{4}\\left(\\log _{2} x\\right) + \\log _{8}\\left(\\log _{4} x\\right) + \\log _{2}\\left... | The number \( x \) is such that \( \log _{2}\left(\log _{4} x\right) + \log _{4}\left(\log _{8} x\right) + \log _{8}\left(\log _{2} x\right) = 1 \). Find the value of the expression \( \log _{4}\left(\log _{2} x\right) + \log _{8}\left(\log _{4} x\right) + \log _{2}\left(\log _{8} x\right) \). If necessary, round your ... | "[\"0.87\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2101, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:16087"}] | {
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[
"99"
] | [
"skywork"
] | d5710785309ff16544ed0a4b678ca6c40cc98660fb66d86d3aa7969437fe6b6e | [
{
"content": "There are 100 positive integers written on a board. At each step, Alex composes 50 fractions using each number written on the board exactly once, brings these fractions to their irreducible form, and then replaces the 100 numbers on the board with the new numerators and denominators to create 100 ... | There are 100 positive integers written on a board. At each step, Alex composes 50 fractions using each number written on the board exactly once, brings these fractions to their irreducible form, and then replaces the 100 numbers on the board with the new numerators and denominators to create 100 new numbers.
Find th... | "[\"99\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2098, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16088"}, {"dataset": "skywork", "extra_... | {
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[
"91"
] | [
"skywork"
] | cfa68ca0d0716d6213c93ffa277db8f48f0c072ae2260beae81d3e564f0a933e | [
{
"content": "Given that socks cost $4 per pair and a T-shirt costs $5 more than a pair of socks, and each member needs one pair of socks and a shirt for home games and another pair of socks and a shirt for away games, with a total cost of $2366, determine the number of members in the League.",
"role": "use... | Given that socks cost $4 per pair and a T-shirt costs $5 more than a pair of socks, and each member needs one pair of socks and a shirt for home games and another pair of socks and a shirt for away games, with a total cost of $2366, determine the number of members in the League. | "[\"91\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2121, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "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:16090"}] | {
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[
"C"
] | [
"skywork"
] | 432da24c0a6879c76f6a45d90f0defc0f4aefcb2f162dfd6ceb1e870c6bd8f1a | [
{
"content": "12・20 Assume $z=a+b i$ is a solution to the polynomial equation\n$$\nc_{4} z^{4}+i c_{3} z^{3}+c_{2} z^{2}+i c_{1} z+c_{0}=0\n$$\n\nwhere $c_{0}, c_{1}, c_{2}, c_{3}, a$ and $b$ are real constants, and $i^{2}=-1$. Then which of the following numbers is also a solution to the equation?\n(A) $-a-b i... | 12・20 Assume $z=a+b i$ is a solution to the polynomial equation
$$
c_{4} z^{4}+i c_{3} z^{3}+c_{2} z^{2}+i c_{1} z+c_{0}=0
$$
where $c_{0}, c_{1}, c_{2}, c_{3}, a$ and $b$ are real constants, and $i^{2}=-1$. Then which of the following numbers is also a solution to the equation?
(A) $-a-b i$.
(B) $a-b i$.
(C) $-a+b i$... | "[\"C\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2128, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16091"}] | {
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[
"177"
] | [
"skywork"
] | c398a9461aef204efcbe8df144e2a389b27a527daec8b1d8b6616a86d1c35d1c | [
{
"content": "There are 6 rectangular prisms with edge lengths of \\(3 \\text{ cm}\\), \\(4 \\text{ cm}\\), and \\(5 \\text{ cm}\\). The faces of these prisms are painted red in such a way that one prism has only one face painted, another has exactly two faces painted, a third prism has exactly three faces pain... | There are 6 rectangular prisms with edge lengths of \(3 \text{ cm}\), \(4 \text{ cm}\), and \(5 \text{ cm}\). The faces of these prisms are painted red in such a way that one prism has only one face painted, another has exactly two faces painted, a third prism has exactly three faces painted, a fourth prism has exactly... | "[\"177\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2116, "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:16092"}] | {
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[
"11"
] | [
"skywork"
] | f0ec07b77ea699734f55ac245611cf853b72297fa4f634d147fa862faa91d548 | [
{
"content": "Which of the following numbers divide exactly into $(15+\\sqrt{49})$ ?\n(A) 3\n(B) 4\n(C) 5\n(D) 7\n(E) 11",
"role": "user"
}
] | Which of the following numbers divide exactly into $(15+\sqrt{49})$ ?
(A) 3
(B) 4
(C) 5
(D) 7
(E) 11 | "[\"11\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2132, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16093"}] | {
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[
"130"
] | [
"skywork"
] | c82bb6ddbdb8236bab334d66f7ffd54e29a6c7cf4922d7a486cb80ca5834dee5 | [
{
"content": "14. Person A departs from location A to location B, while persons B and C depart from location B to location A. After person A has traveled 50 kilometers, persons B and C start from B simultaneously. As a result, person A meets person B at location C, and person A meets person C at location D. It ... | 14. Person A departs from location A to location B, while persons B and C depart from location B to location A. After person A has traveled 50 kilometers, persons B and C start from B simultaneously. As a result, person A meets person B at location C, and person A meets person C at location D. It is known that person A... | "[\"130\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2113, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:16094"}] | {
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[
"70"
] | [
"skywork"
] | 437878a6133f05357bc8df5dc5d7a7785431c286186b9cd2ec312d3495cf5882 | [
{
"content": "7.1. In a football tournament, 20 teams participated. Each team played one match against each other. A team receives 3 points for a win, 1 point for a draw, and 0 points for a loss. After the tournament, Vasya calculated the total points scored by the teams. It turned out to be 500. How many match... | 7.1. In a football tournament, 20 teams participated. Each team played one match against each other. A team receives 3 points for a win, 1 point for a draw, and 0 points for a loss. After the tournament, Vasya calculated the total points scored by the teams. It turned out to be 500. How many matches ended in a draw? | "[\"70\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2123, "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:16095"}] | {
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} |
[
"-\\frac{1}{2}"
] | [
"skywork"
] | 780f6053c775d607a93bbf0680437a9f99574980debe317e5e60dede16f7d184 | [
{
"content": "Given: $A=2a^{2}-5ab+3b$, $B=4a^{2}+6ab+8a$. \n$(1)$ Simplify: $2A-B$; \n$(2)$ If $a=-2$, $b=1$, find the value of $2A-B$; \n$(3)$ If the value of the algebraic expression $2A-B$ is independent of $a$, find the value of $b$.",
"role": "user"
}
] | Given: $A=2a^{2}-5ab+3b$, $B=4a^{2}+6ab+8a$.
$(1)$ Simplify: $2A-B$;
$(2)$ If $a=-2$, $b=1$, find the value of $2A-B$;
$(3)$ If the value of the algebraic expression $2A-B$ is independent of $a$, find the value of $b$. | "[\"-\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2134, "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:16096"}] | {
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[
"15"
] | [
"skywork"
] | 62e08f40d229c8dba68838037c7fc4339139137d2f2833e373071cf699db38bb | [
{
"content": "Mary typed a six-digit number, but the two $1$ s she typed didn't show. What appeared was $2002$ . How many different six-digit numbers could she have typed?",
"role": "user"
}
] | Mary typed a six-digit number, but the two $1$ s she typed didn't show. What appeared was $2002$ . How many different six-digit numbers could she have typed? | "[\"15\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2137, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16097"}] | {
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} |
[
"(x,y,z)=(0,0,0)"
] | [
"skywork"
] | 411170458d7a6d5b5637ede9e31bc38896f448ac035cdcf37c4f6447ec614fdc | [
{
"content": "Find all integer solutions of the equation:\n\n$$\nx^{2}+y^{2}=3 z^{2}\n$$",
"role": "user"
}
] | Find all integer solutions of the equation:
$$
x^{2}+y^{2}=3 z^{2}
$$ | "[\"(x,y,z)=(0,0,0)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2120, "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:16098"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"8"
] | [
"skywork"
] | bee16a21cb3bd355fdd5503e7ae9b4b4bd7e4eb0700de3808d6fc67b4eda944c | [
{
"content": "9. Let $f(x)=a x^{4}+b x^{3}+c x^{2}+d x+e$, for any $x \\in[-1,1]$, we have $f(x) \\in[-1,1]$, find the maximum value of $|c|$.",
"role": "user"
}
] | 9. Let $f(x)=a x^{4}+b x^{3}+c x^{2}+d x+e$, for any $x \in[-1,1]$, we have $f(x) \in[-1,1]$, find the maximum value of $|c|$. | "[\"8\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2127, "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:16099"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\sqrt{6}}{6}"
] | [
"skywork"
] | cdb35ecc14d74dcde504f80ce50ea259056ee8230a790d66313c8eae8303cfb9 | [
{
"content": "Elective 4-4: Coordinate System and Parametric Equations\n\nIn the Cartesian coordinate system $xOy$, with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. If the polar equation of curve $C$ is $\\rho\\cos^2\\theta-4\\sin\\th... | Elective 4-4: Coordinate System and Parametric Equations
In the Cartesian coordinate system $xOy$, with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. If the polar equation of curve $C$ is $\rho\cos^2\theta-4\sin\theta=0$, and the polar coordin... | "[\"\\\\frac{\\\\sqrt{6}}{6}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2126, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "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:16100"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"123"
] | [
"skywork"
] | 8e405905ee3b2dfed8bb4f9b68437c2753b925d51cccb78448f104d12a34f278 | [
{
"content": "Given the real numbers \\( x \\) and \\( y \\) that satisfy\n\n\\[ x + y = 3 \\]\n\\[ \\frac{1}{x + y^2} + \\frac{1}{x^2 + y} = \\frac{1}{2} \\]\n\nfind the value of \\( x^5 + y^5 \\).",
"role": "user"
}
] | Given the real numbers \( x \) and \( y \) that satisfy
\[ x + y = 3 \]
\[ \frac{1}{x + y^2} + \frac{1}{x^2 + y} = \frac{1}{2} \]
find the value of \( x^5 + y^5 \). | "[\"123\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2125, "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:16101"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"81"
] | [
"skywork"
] | 29a16e561dcafb7f049d8b02b002017dd347198180863c30b3141a281398aab8 | [
{
"content": "For a positive integer $n$ and a nonzero digit $d$, let $f(n, d)$ be the smallest positive integer $k$, such that $kn$ starts with $d$. What is the maximal value of $f(n, d)$, over all positive integers $n$ and nonzero digits $d$?",
"role": "user"
}
] | For a positive integer $n$ and a nonzero digit $d$, let $f(n, d)$ be the smallest positive integer $k$, such that $kn$ starts with $d$. What is the maximal value of $f(n, d)$, over all positive integers $n$ and nonzero digits $d$? | "[\" 81 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2143, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16102"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"12"
] | [
"skywork"
] | 36407e52592895e0d9f35ab75afa22673b48d6cab4f43f36f67dab5b552b0f94 | [
{
"content": "Nadia bought a compass and after opening its package realized that the length of the needle leg is $10$ centimeters whereas the length of the pencil leg is $16$ centimeters! Assume that in order to draw a circle with this compass, the angle between the pencil leg and the paper must be at least $30... | Nadia bought a compass and after opening its package realized that the length of the needle leg is $10$ centimeters whereas the length of the pencil leg is $16$ centimeters! Assume that in order to draw a circle with this compass, the angle between the pencil leg and the paper must be at least $30$ degrees but the need... | "[\"12\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2135, "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:16103"}] | {
"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,\\frac{3}{4}]"
] | [
"skywork"
] | 48f1afd17b619d9f1950c1ec02340135b0f501c6a04d39c0ca7fea233d84c6a2 | [
{
"content": "4. Given the function $f(x)=4 \\sin x \\cdot \\sin ^{2}$ $\\left(\\frac{\\pi}{4}+\\frac{x}{2}\\right)+\\cos 2 x$, if the constant $w>0, y=f(w x)$ is an increasing function on the interval $\\left[-\\frac{\\pi}{2}, \\frac{2 \\pi}{3}\\right]$, then the range of $w$ is_ _. $\\qquad$",
"role": "us... | 4. Given the function $f(x)=4 \sin x \cdot \sin ^{2}$ $\left(\frac{\pi}{4}+\frac{x}{2}\right)+\cos 2 x$, if the constant $w>0, y=f(w x)$ is an increasing function on the interval $\left[-\frac{\pi}{2}, \frac{2 \pi}{3}\right]$, then the range of $w$ is_ _. $\qquad$ | "[\"(0,\\\\frac{3}{4}]\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2122, "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:16104"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 9fb69c19fbb2b95fb4cd6381c57dff31f1a74518e4e6c205c5df0d9c8cbb8c19 | [
{
"content": "Find the smallest positive number $\\lambda $ , such that for any complex numbers ${z_1},{z_2},{z_3}\\in\\{z\\in C\\big| |z|<1\\}$ ,if $z_1+z_2+z_3=0$, then $$\\left|z_1z_2 +z_2z_3+z_3z_1\\right|^2+\\left|z_1z_2z_3\\right|^2 <\\lambda .$$",
"role": "user"
}
] | Find the smallest positive number $\lambda $ , such that for any complex numbers ${z_1},{z_2},{z_3}\in\{z\in C\big| |z|<1\}$ ,if $z_1+z_2+z_3=0$, then $$\left|z_1z_2 +z_2z_3+z_3z_1\right|^2+\left|z_1z_2z_3\right|^2 <\lambda .$$ | "[\"1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2130, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16105"}] | {
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} |
[
"a<\\frac{3}{5}"
] | [
"skywork"
] | 532b22620f19b30316b4d803029e55133b7d8c7c07371e422ad11f4a69cf12d6 | [
{
"content": "1. If $x=3-5a$ is a solution to the inequality $\\frac{1}{3}(x-2)$ $<x-\\frac{1}{3}$, then the range of values for $a$ is",
"role": "user"
}
] | 1. If $x=3-5a$ is a solution to the inequality $\frac{1}{3}(x-2)$ $<x-\frac{1}{3}$, then the range of values for $a$ is | "[\"a<\\\\frac{3}{5}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2136, "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:16106"}] | {
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} |
[
"0"
] | [
"skywork"
] | a2c19da52bb9e2c350d95a83c3be0ae1fc94c2b9e7ead548f43535bb7e8a9b1c | [
{
"content": "Let $ABCDE$ be an equiangular convex pentagon of perimeter $1$. The pairwise intersections of the lines that extend the sides of the pentagon determine a five-pointed star polygon. Let $s$ be the perimeter of this star. What is the difference between the maximum and the minimum possible values of ... | Let $ABCDE$ be an equiangular convex pentagon of perimeter $1$. The pairwise intersections of the lines that extend the sides of the pentagon determine a five-pointed star polygon. Let $s$ be the perimeter of this star. What is the difference between the maximum and the minimum possible values of $s$? | "[\"0\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2118, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16107"}] | {
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} |
[
"10989"
] | [
"skywork"
] | 3374943ebe30a1158d480cd7d702b8ceed656c65165584cf71562588b060f3d5 | [
{
"content": "Find a five-digit number that has the following property: when multiplied by 9, the result is a number represented by the same digits but in reverse order.",
"role": "user"
}
] | Find a five-digit number that has the following property: when multiplied by 9, the result is a number represented by the same digits but in reverse order. | "[\"10989\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2147, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16108"}] | {
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} |
[
"25"
] | [
"skywork"
] | e84119f06adc18c0ab7178baf977d7f201efbfcd506f4753caecd4a94ed07690 | [
{
"content": "51. (SWE 4) A subset \\( S \\) of the set of integers \\( 0, \\ldots, 99 \\) is said to have property A if it is impossible to fill a crossword puzzle with 2 rows and 2 columns with numbers in \\( S \\) (0 is written as 00, 1 as 01, and so on). Determine the maximal number of elements in sets \\( ... | 51. (SWE 4) A subset \( S \) of the set of integers \( 0, \ldots, 99 \) is said to have property A if it is impossible to fill a crossword puzzle with 2 rows and 2 columns with numbers in \( S \) (0 is written as 00, 1 as 01, and so on). Determine the maximal number of elements in sets \( S \) with property A. | "[\"25\"]" | train-math-numinamath1.5_olympiads_ref | [{"dataset": "skywork", "extra_info": {"index": 2139, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16109"}] | {
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} |
[
"146"
] | [
"skywork"
] | 54f736f3b8d7f165f6d348567898dfb74d49490c7f343c9ede0939cda0b29a1e | [
{
"content": "If $g(x) = 3x + 7$ and $f(x) = 5x - 9$, what is the value of $f(g(8))$?",
"role": "user"
}
] | If $g(x) = 3x + 7$ and $f(x) = 5x - 9$, what is the value of $f(g(8))$? | "[\"146\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2156, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:16110"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\left(-\\frac{1}{2}, 4\\right)"
] | [
"skywork"
] | 9914251e306b72286843ec9f59c8be1dcd1dacae7793c9db4caf745300490d84 | [
{
"content": "4. Let $f(x)=\\frac{x^{4}+k x^{2}+1}{x^{4}+x^{2}+1}(x \\in R)$, for any three real numbers $a, b, c$, it is known that there exists a triangle with side lengths $f(a), f(b), f(c)$, then all real numbers $k$ that satisfy the above condition are $\\qquad$ .",
"role": "user"
}
] | 4. Let $f(x)=\frac{x^{4}+k x^{2}+1}{x^{4}+x^{2}+1}(x \in R)$, for any three real numbers $a, b, c$, it is known that there exists a triangle with side lengths $f(a), f(b), f(c)$, then all real numbers $k$ that satisfy the above condition are $\qquad$ . | "[\"\\\\left(-\\\\frac{1}{2}, 4\\\\right)\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2133, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16111"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{2\\sqrt{10}-5}{5}r"
] | [
"skywork"
] | 3f5d7af4e54583054caedd7e30a419deb00704fd09b33de3e862245fa48dfee5 | [
{
"content": "For a triangle inscribed in a circle of radius $r$, we know that\n\n$$\n\\operatorname{tg} \\alpha=\\frac{1}{3}, \\quad \\sin \\alpha \\sin \\gamma=\\frac{1}{\\sqrt{10}}\n$$\n\nExpress the radius of the inscribed circle (@) as a function of $r$.",
"role": "user"
}
] | For a triangle inscribed in a circle of radius $r$, we know that
$$
\operatorname{tg} \alpha=\frac{1}{3}, \quad \sin \alpha \sin \gamma=\frac{1}{\sqrt{10}}
$$
Express the radius of the inscribed circle (@) as a function of $r$. | "[\"\\\\frac{2\\\\sqrt{10}-5}{5}r\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2138, "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:16112"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"40"
] | [
"skywork"
] | 14adcd3691135022cf8631af6213e97cbe34bc24572b5609a245da92fdf1944f | [
{
"content": "13.310. There is scrap steel of two grades with nickel content of 5 and $40 \\%$. How much of each of these grades of metal is needed to obtain 140 tons of steel with a $30 \\%$ nickel content?",
"role": "user"
}
] | 13.310. There is scrap steel of two grades with nickel content of 5 and $40 \%$. How much of each of these grades of metal is needed to obtain 140 tons of steel with a $30 \%$ nickel content? | "[\"40\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2150, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:16114"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1/12"
] | [
"skywork"
] | c35d8109a7eefe6b0304c81ff321e417a6c40c3b5f768f7a5b5ff471abe04ec9 | [
{
"content": "Katrine has a bag containing 4 buttons with distinct letters M, P, F, G on them (one letter per button). She picks buttons randomly, one at a time, without replacement, until she picks the button with letter G. What is the probability that she has at least three picks and her third pick is the b... | Katrine has a bag containing 4 buttons with distinct letters M, P, F, G on them (one letter per button). She picks buttons randomly, one at a time, without replacement, until she picks the button with letter G. What is the probability that she has at least three picks and her third pick is the button with letter M? | "[\"1/12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2155, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16115"}] | {
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} |
[
"1"
] | [
"skywork"
] | ae3bd975ba35e7eef43d79212b209f73e31686ed05e533cc9aa5fb23c33b4e71 | [
{
"content": "【Question 7】\nIn a certain mathematics competition, there are a total of 6 questions, each worth 7 points (the final score for each question is an integer, with a minimum of 0 points and a maximum of 7 points). Each contestant's total score is the product of the scores of the 6 questions. If two c... | 【Question 7】
In a certain mathematics competition, there are a total of 6 questions, each worth 7 points (the final score for each question is an integer, with a minimum of 0 points and a maximum of 7 points). Each contestant's total score is the product of the scores of the 6 questions. If two contestants have the sam... | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2144, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16116"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 539c9427e21719a248b1fcdb09e5e52a2c5f4b0af0927cb5c0705fab446a2593 | [
{
"content": "What is the smallest value that the sum of the digits of the number $3n^2+n+1,$ $n\\in\\mathbb{N}$ can take?",
"role": "user"
}
] | What is the smallest value that the sum of the digits of the number $3n^2+n+1,$ $n\in\mathbb{N}$ can take? | "[\"3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2153, "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:16117"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"22"
] | [
"skywork"
] | d117d4c06504185de651fd224223b51ad47e34c8e7c1128c9af992a4bf15a3a4 | [
{
"content": "10. In a certain archery competition, the rules are as follows: hitting area 1 scores 4 points; hitting area 2 scores 3 points; hitting other areas scores 1 point. Xiao Hu has 50 arrows. When he still has 7 arrows left to shoot, his score exceeds 150 points. At this point, Xiao Hu has at least $\\... | 10. In a certain archery competition, the rules are as follows: hitting area 1 scores 4 points; hitting area 2 scores 3 points; hitting other areas scores 1 point. Xiao Hu has 50 arrows. When he still has 7 arrows left to shoot, his score exceeds 150 points. At this point, Xiao Hu has at least $\qquad$ arrows hitting a... | "[\"22\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2142, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16118"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
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