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 |
|---|---|---|---|---|---|---|---|---|
[
"287"
] | [
"skywork"
] | 86dd85deb42a9637de30a2f22fb88bc8b8876894d6121de0d0fc263283d477fb | [
{
"content": "5. (15 points) The density of a body $\\rho$ is defined as the ratio of the body's mass $m$ to its volume $V$. A unit of mass used in jewelry is the carat (1 carat equals 0.2 grams). A unit of length used in many countries is the inch (1 inch equals 2.54 centimeters). It is known that the density ... | 5. (15 points) The density of a body $\rho$ is defined as the ratio of the body's mass $m$ to its volume $V$. A unit of mass used in jewelry is the carat (1 carat equals 0.2 grams). A unit of length used in many countries is the inch (1 inch equals 2.54 centimeters). It is known that the density of diamond is $\rho=3.5... | "[\"287\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108979, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118879"}] | {
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"reference_components": 1,
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[
"3"
] | [
"skywork"
] | d848e2ea7a9013d0695c7c216ff3dd7911c9d37d412dcb92650dc6940dd7e185 | [
{
"content": "# Task № 1.3\n\n## Condition:\n\nFive friends - Sasha, Yulia, Rita, Alina, and Natasha - meet in the park every day after buying ice cream from the little shop around the corner. One day, the girls had a conversation.\n\nSasha: There were five people in front of me.\n\nAlina: There was no one afte... | # Task № 1.3
## Condition:
Five friends - Sasha, Yulia, Rita, Alina, and Natasha - meet in the park every day after buying ice cream from the little shop around the corner. One day, the girls had a conversation.
Sasha: There were five people in front of me.
Alina: There was no one after me.
Rita: I was the first i... | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108956, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118880"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"23"
] | [
"skywork"
] | 0c8469741edb61f82bfdb7691269030301fe9411bd65a4135a00f8ac577ff7b7 | [
{
"content": "Six bags contain 18, 19, 21, 23, 25, and 34 marbles, respectively. One of the bags contains marbles with cracks, while the remaining five bags contain marbles without cracks. Jenny took three of the bags, and George took two of the other bags, leaving the bag with the cracked marbles. If the numbe... | Six bags contain 18, 19, 21, 23, 25, and 34 marbles, respectively. One of the bags contains marbles with cracks, while the remaining five bags contain marbles without cracks. Jenny took three of the bags, and George took two of the other bags, leaving the bag with the cracked marbles. If the number of marbles Jenny rec... | "[\"23\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108977, "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:118881"}] | {
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[
"65"
] | [
"skywork"
] | d3efa01a50a148d9ac922e8e79a004315884d10bddfa19f1b9af1f497e63776f | [
{
"content": "Out of 10 distinct positive integers, the product of any 5 of them is even, and the sum of all 10 numbers is odd. What is the minimum sum of these 10 positive integers?",
"role": "user"
}
] | Out of 10 distinct positive integers, the product of any 5 of them is even, and the sum of all 10 numbers is odd. What is the minimum sum of these 10 positive integers? | "[\"65\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108975, "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:118882"}] | {
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} |
[
"1024"
] | [
"skywork"
] | 74da7231004d9b6c203ccc0a63d6eb9d25d93c7114fdf806de87d96b1e9379d3 | [
{
"content": "For the set $\\{1, 2, 3, \\ldots, 8\\}$ and each of its non-empty subsets, a unique alternating sum is defined as follows: arrange the numbers in the subset in decreasing order and then, beginning with the largest, alternately add and subtract successive numbers. Calculate the sum of all such alte... | For the set $\{1, 2, 3, \ldots, 8\}$ and each of its non-empty subsets, a unique alternating sum is defined as follows: arrange the numbers in the subset in decreasing order and then, beginning with the largest, alternately add and subtract successive numbers. Calculate the sum of all such alternating sums for $n=8$. | "[\"1024\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108974, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:118884"}] | {
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} |
[
"17.28125"
] | [
"skywork"
] | 5318a20b3b59aa5886cce942dc9847bf95871dddb9d254d43395e49b05e5ba4e | [
{
"content": "Define a new function $\\$N$ such that $\\$N = 0.75N + 2$. Calculate $\\$(\\$(\\$30))$.",
"role": "user"
}
] | Define a new function $\$N$ such that $\$N = 0.75N + 2$. Calculate $\$(\$(\$30))$. | "[\"17.28125\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108987, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118885"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.75"
] | [
"skywork"
] | a0140b07a4a59a8a6e15636404fabd852cfc4bbd9132eb7458b3ebd1e745e9b2 | [
{
"content": "2. Solve the equation $\\sqrt{8 x+5}+2\\{x\\}=2 x+2$. Here $\\{x\\}$ is the fractional part of the number $\\mathrm{x}$, i.e., $\\{x\\}=x-[x]$. In the answer, write the sum of all solutions.",
"role": "user"
}
] | 2. Solve the equation $\sqrt{8 x+5}+2\{x\}=2 x+2$. Here $\{x\}$ is the fractional part of the number $\mathrm{x}$, i.e., $\{x\}=x-[x]$. In the answer, write the sum of all solutions. | "[\"0.75\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108966, "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:118886"}] | {
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"reference_components": 1,
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} |
[
"80"
] | [
"skywork"
] | 76f2889ceb109753211d2d9db35969855678afaf1760c3a2fa9b4319abd007a3 | [
{
"content": "II If one side of the square $A B C D$ lies on the line $y=2 x-17$, and the other two vertices are on the parabola $y=x^{2}$. Then the minimum value of the area of the square is $\\qquad$ .",
"role": "user"
}
] | II If one side of the square $A B C D$ lies on the line $y=2 x-17$, and the other two vertices are on the parabola $y=x^{2}$. Then the minimum value of the area of the square is $\qquad$ . | "[\"80\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108960, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118888"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{20}"
] | [
"skywork"
] | a8a3a2c343d88a584cb34dbfff07f8945df6eecd1b43c54fb9e0b4227056b8b4 | [
{
"content": "1. (2004 College Entrance Examination, Chongqing Paper) In a speech contest held by a senior high school grade, there are 10 students participating, including 3 from Class 1, 2 from Class 2, and 5 from other classes. If the order of their speeches is determined by drawing lots, then the probabilit... | 1. (2004 College Entrance Examination, Chongqing Paper) In a speech contest held by a senior high school grade, there are 10 students participating, including 3 from Class 1, 2 from Class 2, and 5 from other classes. If the order of their speeches is determined by drawing lots, then the probability that the 3 students ... | "[\"\\\\frac{1}{20}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108980, "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:118889"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{7}{10}"
] | [
"skywork"
] | 49ff9dc2b83cb175f9391e68a45a4eba55f08c11d90ee464044838203cf2ca24 | [
{
"content": "$\\frac{1}{1+\\frac{1}{2+\\frac{1}{3}}}$",
"role": "user"
}
] | $\frac{1}{1+\frac{1}{2+\frac{1}{3}}}$ | "[\"\\\\frac{7}{10}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108991, "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:118890"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1989"
] | [
"skywork"
] | f58f9bd3782ad01c994c53c8e5102898b8ac07f92c4bc6d6ade2f95aeef52602 | [
{
"content": "5ـ Let $x_{1}, x_{2}, \\cdots, x_{1990}$ be a permutation of $1,2, \\cdots, 1990$, find the maximum value of $F=|\\cdots| \\mid x_{1}-$ $x_{2}\\left|-x_{3}\\right|-\\cdots\\left|-x_{1990}\\right|$. (24th All-Russian Mathematical Olympiad Problem)",
"role": "user"
}
] | 5ـ Let $x_{1}, x_{2}, \cdots, x_{1990}$ be a permutation of $1,2, \cdots, 1990$, find the maximum value of $F=|\cdots| \mid x_{1}-$ $x_{2}\left|-x_{3}\right|-\cdots\left|-x_{1990}\right|$. (24th All-Russian Mathematical Olympiad Problem) | "[\"1989\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 108981, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:118891"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"995"
] | [
"skywork"
] | 26369014eaf077898000684be2b1692080afc6a7bd16ace8ffddb7bf6d2c85d0 | [
{
"content": "Calculate the total area of a pentagon with sides of lengths 18, 25, 30, 28, and 25 units, assuming it can be divided into a right triangle and a trapezoid.",
"role": "user"
}
] | Calculate the total area of a pentagon with sides of lengths 18, 25, 30, 28, and 25 units, assuming it can be divided into a right triangle and a trapezoid. | "[\"995\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108983, "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:118892"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 42b14baa41fad7319693bb8b0a175875220744ce7e1efd22218a3e1f8972ebc4 | [
{
"content": "How many positive integers $n$ are there such that $n!(2n+1)$ and $221$ are relatively prime?\n\n$ \n\\textbf{(A)}\\ 10\n\\qquad\\textbf{(B)}\\ 11\n\\qquad\\textbf{(C)}\\ 12\n\\qquad\\textbf{(D)}\\ 13\n\\qquad\\textbf{(E)}\\ \\text{None of the above}\n$",
"role": "user"
}
] | How many positive integers $n$ are there such that $n!(2n+1)$ and $221$ are relatively prime?
$
\textbf{(A)}\ 10
\qquad\textbf{(B)}\ 11
\qquad\textbf{(C)}\ 12
\qquad\textbf{(D)}\ 13
\qquad\textbf{(E)}\ \text{None of the above}
$ | "[\"10\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108976, "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:118893"}] | {
"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"
] | 4c478ca30f4770bf14ba161cc94b7231ca50155decb1d4e78da1285ab7766431 | [
{
"content": "At summer camp, there are $20$ campers in each of the swimming class, the archery class, and the rock climbing class. Each camper is in at least one of these classes. If $4$ campers are in all three classes, and $24$ campers are in exactly one of the classes, how many campers are in exactly two cl... | At summer camp, there are $20$ campers in each of the swimming class, the archery class, and the rock climbing class. Each camper is in at least one of these classes. If $4$ campers are in all three classes, and $24$ campers are in exactly one of the classes, how many campers are in exactly two classes?
$\text{(A) }10... | "[\"12\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108992, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:118894"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"180"
] | [
"skywork"
] | 791bc1428d35a1266f0a5905639707e3702705b39d4c87d3c153effef7d97fc8 | [
{
"content": "13.1.9 ** Let $P(e, \\pi, \\sqrt{5})$ be a point inside a cube whose vertices are the 8 points $(x, y, z)$ (where $x, y, z$ are 0 or 6). Find the volume of the intersection of the polyhedron with the original cube, where the polyhedron's vertices are the 6 symmetric points of $P$ with respect to t... | 13.1.9 ** Let $P(e, \pi, \sqrt{5})$ be a point inside a cube whose vertices are the 8 points $(x, y, z)$ (where $x, y, z$ are 0 or 6). Find the volume of the intersection of the polyhedron with the original cube, where the polyhedron's vertices are the 6 symmetric points of $P$ with respect to the cube's faces. | "[\"180\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108972, "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:118895"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"256"
] | [
"skywork"
] | 2ee36e930cdf83bfdc2bd9c9b1d14e18f71889a9c6e45dac5020937c90ccc9af | [
{
"content": "How many $5$ -digit numbers $N$ (in base $10$ ) contain no digits greater than $3$ and satisfy the equality $\\gcd(N,15)=\\gcd(N,20)=1$ ? (The leading digit of $N$ cannot be zero.)\n\n*Based on a proposal by Yannick Yao*",
"role": "user"
}
] | How many $5$ -digit numbers $N$ (in base $10$ ) contain no digits greater than $3$ and satisfy the equality $\gcd(N,15)=\gcd(N,20)=1$ ? (The leading digit of $N$ cannot be zero.)
*Based on a proposal by Yannick Yao* | "[\"256\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108984, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118896"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{189}{16384}"
] | [
"skywork"
] | a1e50814da5966dfb620ffe4033185ab8e9e7903b153d34a77052c149bac9b16 | [
{
"content": "George flips an unfair coin 7 times. The coin has a $\\frac{1}{4}$ probability of coming up heads and a $\\frac{3}{4}$ probability of coming up tails. What is the probability that he flips exactly 2 tails?",
"role": "user"
}
] | George flips an unfair coin 7 times. The coin has a $\frac{1}{4}$ probability of coming up heads and a $\frac{3}{4}$ probability of coming up tails. What is the probability that he flips exactly 2 tails? | "[\"\\\\frac{189}{16384}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109010, "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:118897"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-2<k<10"
] | [
"skywork"
] | 3753a2aba795c133031758def79f107189d21f87b4d5fd562c7ee17780534977 | [
{
"content": "(3) Given the function $f(x)=\\frac{x^{2}-(k-6) x+16}{x^{2}+k x+25}$ has a domain of $\\mathbf{R}$, and its graph does not intersect the $x$-axis, then the range of values for $k$ is $\\qquad$",
"role": "user"
}
] | (3) Given the function $f(x)=\frac{x^{2}-(k-6) x+16}{x^{2}+k x+25}$ has a domain of $\mathbf{R}$, and its graph does not intersect the $x$-axis, then the range of values for $k$ is $\qquad$ | "[\"-2<k<10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108982, "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:118898"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"2\\csc\\alpha"
] | [
"skywork"
] | 9a6196903cd4cb6879e914ca1bf5c6e8b923c29b8f6c0be20c89cfc93d2b7e12 | [
{
"content": "5. Given $f(x)=\\sqrt{\\frac{1-x}{1+x}}$. If $\\alpha \\in\\left(\\frac{\\pi}{2}, \\pi\\right)$, then $f(\\cos \\alpha)+f(-\\cos \\alpha)$ can be simplified to",
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}
] | 5. Given $f(x)=\sqrt{\frac{1-x}{1+x}}$. If $\alpha \in\left(\frac{\pi}{2}, \pi\right)$, then $f(\cos \alpha)+f(-\cos \alpha)$ can be simplified to | "[\"2\\\\csc\\\\alpha\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108988, "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:118899"}] | {
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[
"\\frac{1}{30}"
] | [
"skywork"
] | 7e1c4b2d9e17395a48f3aa9aa7e79cde17a8d94c2d5af1723bb03a73b2fdcd33 | [
{
"content": "Given the function $f\\left( x \\right)={x}^{2}+{\\left( \\ln 3x \\right)}^{2}-2a(x+3\\ln 3x)+10{{a}^{2}}(a\\in \\mathbf{R})$, determine the value of the real number $a$ for which there exists ${{x}_{0}}$ such that $f\\left( {{x}_{0}} \\right)\\leqslant \\dfrac{1}{10}$.",
"role": "user"
}
] | Given the function $f\left( x \right)={x}^{2}+{\left( \ln 3x \right)}^{2}-2a(x+3\ln 3x)+10{{a}^{2}}(a\in \mathbf{R})$, determine the value of the real number $a$ for which there exists ${{x}_{0}}$ such that $f\left( {{x}_{0}} \right)\leqslant \dfrac{1}{10}$. | "[\"\\\\frac{1}{30}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108985, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118900"}] | {
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[
"16"
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"skywork"
] | a9542ccac054e04194e0925ac8e27267624d38fcd070ca0723bdc95679178809 | [
{
"content": "The base nine numbers $125_9$ and $33_9$ need to be multiplied and the result expressed in base nine. What is the base nine sum of the digits of their product?",
"role": "user"
}
] | The base nine numbers $125_9$ and $33_9$ need to be multiplied and the result expressed in base nine. What is the base nine sum of the digits of their product? | "[\"16\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108997, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118901"}] | {
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[
"2857"
] | [
"skywork"
] | 817b44c0bc83ae817337618ff90629c322772dfb9c603b5384ff5e87edb8a483 | [
{
"content": "How many natural numbers $x$, less than 10000, are there for which $2^{x}-x^{2}$ is divisible by 7?",
"role": "user"
}
] | How many natural numbers $x$, less than 10000, are there for which $2^{x}-x^{2}$ is divisible by 7? | "[\"2857\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109003, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118902"}] | {
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[
"10"
] | [
"skywork"
] | f89ec5988059e3d8b81d688cf141d75e3dafc8b642b4abd790134077d1caaa9b | [
{
"content": "How many points does one have to place on a unit square to guarantee that two of them are strictly less than 1/2 unit apart?",
"role": "user"
}
] | How many points does one have to place on a unit square to guarantee that two of them are strictly less than 1/2 unit apart? | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109001, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118903"}] | {
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[
"2"
] | [
"skywork"
] | c889c1fcbad763b36fdaa4048d4d6b8497d17be3f4388a4b4742b582d1b37a91 | [
{
"content": "As $p$ ranges over the primes greater than $5$, how many different remainders can $p^2$ leave upon division by $120$?",
"role": "user"
}
] | As $p$ ranges over the primes greater than $5$, how many different remainders can $p^2$ leave upon division by $120$? | "[\"2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108993, "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:118904"}] | {
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[
"59"
] | [
"skywork"
] | 86ac7a5af222bf8c500b346ee019d8c475c905b177a703c70ee7725ccc6d1018 | [
{
"content": "Among all the simple fractions where both the numerator and the denominator are two-digit numbers, find the smallest fraction that is greater than $\\frac{3}{5}$. Provide the numerator of this fraction in your answer.",
"role": "user"
}
] | Among all the simple fractions where both the numerator and the denominator are two-digit numbers, find the smallest fraction that is greater than $\frac{3}{5}$. Provide the numerator of this fraction in your answer. | "[\"59\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108996, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118905"}] | {
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[
"60"
] | [
"skywork"
] | d77e646fefa43ecab3b748f6b42e8f57113dbc1938988db0d7c7f7c454723c9e | [
{
"content": "At the beginning of the school year, $50\\%$ of all students in Mr. Well's class answered \"Yes\" to the question \"Do you love math\", and $50\\%$ answered \"No.\" At the end of the school year, $70\\%$ answered \"Yes\" and $30\\%$ answered \"No.\" Altogether, $x\\%$ of the students gave a differ... | At the beginning of the school year, $50\%$ of all students in Mr. Well's class answered "Yes" to the question "Do you love math", and $50\%$ answered "No." At the end of the school year, $70\%$ answered "Yes" and $30\%$ answered "No." Altogether, $x\%$ of the students gave a different answer at the beginning and end o... | "[\"60\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108990, "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:118906"}] | {
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[
"2004"
] | [
"skywork"
] | d7ca6e00eb17ed31f972c4728ed24fea83061da8a1b467d8c804d7d81efb3b06 | [
{
"content": "Let the function \\( f(x) \\) satisfy the following conditions:\n(i) If \\( x > y \\), and \\( f(x) + x \\geq w \\geq f(y) + y \\), then there exists a real number \\( z \\in [y, x] \\), such that \\( f(z) = w - z \\);\n(ii) The equation \\( f(x) = 0 \\) has at least one solution, and among the so... | Let the function \( f(x) \) satisfy the following conditions:
(i) If \( x > y \), and \( f(x) + x \geq w \geq f(y) + y \), then there exists a real number \( z \in [y, x] \), such that \( f(z) = w - z \);
(ii) The equation \( f(x) = 0 \) has at least one solution, and among the solutions of this equation, there exists ... | "[\"2004\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108965, "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:118907"}] | {
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[
"2.1"
] | [
"skywork"
] | 4fe0fe2309ac9e4bd6f0aaed94d89d59654b2d7558e3c8b3c3d354e6f2c46163 | [
{
"content": "Let $(x, y)$ be a solution to the system of equations \n\\[\n\\begin{aligned} \n\\lfloor x \\rfloor - \\{y\\} &= 3.7, \\\\ \n\\{x\\} + \\lfloor y \\rfloor &= 6.2. \n\\end{aligned} \n\\]\nCompute $|x - y|$.",
"role": "user"
}
] | Let $(x, y)$ be a solution to the system of equations
\[
\begin{aligned}
\lfloor x \rfloor - \{y\} &= 3.7, \\
\{x\} + \lfloor y \rfloor &= 6.2.
\end{aligned}
\]
Compute $|x - y|$. | "[\"2.1\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108998, "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:118908"}] | {
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} |
[
"6"
] | [
"skywork"
] | a229f01272f20fc76a2b08bd97818b315aeb086d6458a3c1a5a33fa8a66ea82f | [
{
"content": "For what positive value of $t$ is $|{-4+ti}| = 2\\sqrt{13}$?",
"role": "user"
}
] | For what positive value of $t$ is $|{-4+ti}| = 2\sqrt{13}$? | "[\"6\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109018, "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:118909"}] | {
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} |
[
"-\\frac{\\sqrt{10}}{5}"
] | [
"skywork"
] | ac3921f982954ad2d579ce8fe072e998fbbd0258514cab2d8daa8007276c31ea | [
{
"content": "Given that $θ$ is an angle in the second quadrant and $\\tan(\\begin{matrix}θ+ \\frac{π}{4}\\end{matrix}) = \\frac{1}{2}$, find the value of $\\sin(θ) + \\cos(θ)$.",
"role": "user"
}
] | Given that $θ$ is an angle in the second quadrant and $\tan(\begin{matrix}θ+ \frac{π}{4}\end{matrix}) = \frac{1}{2}$, find the value of $\sin(θ) + \cos(θ)$. | "[\"-\\\\frac{\\\\sqrt{10}}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109004, "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:118910"}] | {
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} |
[
"6 \\cdot 4^{n-3}"
] | [
"skywork"
] | d5746735fc49bc6d6a9d58b6e68c56f4f432c9211bc508159ed4b7db3a5607e2 | [
{
"content": "On a bookcase there are $ n \\geq 3$ books side by side by different authors. A librarian considers the first and second book from left and exchanges them iff they are not alphabetically sorted. Then he is doing the same operation with the second and third book from left etc. Using this procedure ... | On a bookcase there are $ n \geq 3$ books side by side by different authors. A librarian considers the first and second book from left and exchanges them iff they are not alphabetically sorted. Then he is doing the same operation with the second and third book from left etc. Using this procedure he iterates through the... | "[\" 6 \\\\cdot 4^{n-3} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108999, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118911"}] | {
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[
"3n - 3"
] | [
"skywork"
] | b001e4e09e6634b6db5a3590698d6ee442d87caa61b97a490f95658e777fe208 | [
{
"content": "Consider $2011^2$ points arranged in the form of a $2011 \\times 2011$ grid. What is the maximum number of points that can be chosen among them so that no four of them form the vertices of either an isosceles trapezium or a rectangle whose parallel sides are parallel to the grid lines?",
"role... | Consider $2011^2$ points arranged in the form of a $2011 \times 2011$ grid. What is the maximum number of points that can be chosen among them so that no four of them form the vertices of either an isosceles trapezium or a rectangle whose parallel sides are parallel to the grid lines? | "[\"3n - 3\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109008, "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:118912"}] | {
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[
"(2n + 1) \\left[ \\binom{n}{m - 1} + \\binom{n + 1}{m - 1} \\right]"
] | [
"skywork"
] | 075327b6284490189624b45a0b69298ed89066c87f67fce315c94d9d9fd8f81e | [
{
"content": "Given two integers $ m,n$ satisfying $ 4 < m < n.$ Let $ A_{1}A_{2}\\cdots A_{2n \\plus{} 1}$ be a regular $ 2n\\plus{}1$ polygon. Denote by $ P$ the set of its vertices. Find the number of convex $ m$ polygon whose vertices belongs to $ P$ and exactly has two acute angles.",
"role": "user"
... | Given two integers $ m,n$ satisfying $ 4 < m < n.$ Let $ A_{1}A_{2}\cdots A_{2n \plus{} 1}$ be a regular $ 2n\plus{}1$ polygon. Denote by $ P$ the set of its vertices. Find the number of convex $ m$ polygon whose vertices belongs to $ P$ and exactly has two acute angles. | "[\"(2n + 1) \\\\left[ \\\\binom{n}{m - 1} + \\\\binom{n + 1}{m - 1} \\\\right]\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108994, "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:118914"}] | {
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} |
[
"7"
] | [
"skywork"
] | 5cdf2f2f1dee039402667d2c083db75d2eed20ca0a43b0cd64b3c2fc58fef686 | [
{
"content": "3. Let the function $f_{0}(x)=|x|, f_{1}(x)=\\left|f_{0}(x)-1\\right|, f_{2}(x)=$ $\\left|f_{1}(x)-2\\right|$, then the area of the closed part of the figure enclosed by the graph of the function $y=f_{2}(x)$ and the $x$-axis is $\\qquad$.",
"role": "user"
}
] | 3. Let the function $f_{0}(x)=|x|, f_{1}(x)=\left|f_{0}(x)-1\right|, f_{2}(x)=$ $\left|f_{1}(x)-2\right|$, then the area of the closed part of the figure enclosed by the graph of the function $y=f_{2}(x)$ and the $x$-axis is $\qquad$. | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108986, "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:118915"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | e300c9cf4e8f478d25510e9f037936f0bbe54cd56a7aead3405ba820813bd8a1 | [
{
"content": "2. Find the greatest possible area of a triangle ABC with medians satisfying $t_{a} \\leqslant 2$, $t_{b} \\leqslant 3, t_{c} \\leqslant 4$.\n\n(Pavel Novotný)",
"role": "user"
}
] | 2. Find the greatest possible area of a triangle ABC with medians satisfying $t_{a} \leqslant 2$, $t_{b} \leqslant 3, t_{c} \leqslant 4$.
(Pavel Novotný) | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109016, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118916"}] | {
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} |
[
"-8"
] | [
"skywork"
] | ec627e8c4cd31002755e6b626618392a231aa96b296b5477860ee349b224adeb | [
{
"content": "If $3(-2) = \\nabla +2$, then what does $\\nabla$ equal?",
"role": "user"
}
] | If $3(-2) = \nabla +2$, then what does $\nabla$ equal? | "[\"-8\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109023, "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:118917"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{493}{1848}"
] | [
"skywork"
] | 575d3a9d1e99670dbad604b45eb310b5e921362d592679ceb131d6079ef427b4 | [
{
"content": "Find the arithmetic mean of the reciprocals of the first four prime numbers, including the number 7 instead of 5.",
"role": "user"
}
] | Find the arithmetic mean of the reciprocals of the first four prime numbers, including the number 7 instead of 5. | "[\"\\\\frac{493}{1848}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108969, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118918"}] | {
"all_reference_components_parse": true,
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[
"3034"
] | [
"skywork"
] | 50de9118546150727bd47bdfd4a9fa665cfe0352eca33a3469348f4a4356fded | [
{
"content": "For an arithmetic sequence $b_1,$ $b_2,$ $b_3,$ $\\dots,$ let\n\\[P_n = b_1 + b_2 + b_3 + \\dots + b_n,\\]and let\n\\[Q_n = P_1 + P_2 + P_3 + \\dots + P_n.\\]If you are told the value of $P_{2023},$ then you can uniquely determine the value of $Q_n$ for some integer $n.$ What is this integer $n$?... | For an arithmetic sequence $b_1,$ $b_2,$ $b_3,$ $\dots,$ let
\[P_n = b_1 + b_2 + b_3 + \dots + b_n,\]and let
\[Q_n = P_1 + P_2 + P_3 + \dots + P_n.\]If you are told the value of $P_{2023},$ then you can uniquely determine the value of $Q_n$ for some integer $n.$ What is this integer $n$? | "[\"3034\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109011, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:118919"}] | {
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[
"20"
] | [
"skywork"
] | 8413cdb33b41fcb286d1323a0b9157de87530493bc46100d3837e42513cabf38 | [
{
"content": "How many pairs of positive integers \\((x, y)\\) are there such that \\(x < y\\) and \\(\\frac{x^{2}+y^{2}}{x+y}\\) is a divisor of 2835?",
"role": "user"
}
] | How many pairs of positive integers \((x, y)\) are there such that \(x < y\) and \(\frac{x^{2}+y^{2}}{x+y}\) is a divisor of 2835? | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109009, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118920"}] | {
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[
"108"
] | [
"skywork"
] | 67866b28b09aa39b15a65f5dd9ad2d77ae98e9ae7af53c8d22ea3c43be388353 | [
{
"content": "10. As shown in the figure, $ABCD$ is a square piece of paper. The paper is folded along $CE$, with point $D$ folding to point $G$. Then, the paper is folded along $CF$, with point $B$ folding to point $G$. If $DE=18$, $BF=6$, then the area of $\\triangle AEF$ is $\\qquad$ .",
"role": "user"
... | 10. As shown in the figure, $ABCD$ is a square piece of paper. The paper is folded along $CE$, with point $D$ folding to point $G$. Then, the paper is folded along $CF$, with point $B$ folding to point $G$. If $DE=18$, $BF=6$, then the area of $\triangle AEF$ is $\qquad$ . | "[\"108\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109014, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118921"}] | {
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[
"116"
] | [
"skywork"
] | 99e00292d2b4aaba6386ea1f2faeca727576358387b7e6d488606da18b2d6358 | [
{
"content": "Let \\( n \\) be the smallest positive integer with exactly 2015 positive factors. What is the sum of the (not necessarily distinct) prime factors of \\( n \\)? For example, the sum of the prime factors of 72 is \\( 2 + 2 + 2 + 3 + 3 = 14 \\).",
"role": "user"
}
] | Let \( n \) be the smallest positive integer with exactly 2015 positive factors. What is the sum of the (not necessarily distinct) prime factors of \( n \)? For example, the sum of the prime factors of 72 is \( 2 + 2 + 2 + 3 + 3 = 14 \). | "[\"116\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 109012, "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:118922"}] | {
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[
"20"
] | [
"skywork"
] | 33f7dbb1bd7139f925d2518e2572bc0b0ad9a81bf9ee9d538c4944bbaeb3daa0 | [
{
"content": "Example 1 (2002 Shanghai High School Mathematics Competition Question) Let real numbers $a, b, c, d$ satisfy $a^{2}+b^{2}+c^{2}+d^{2}=5$. Then the maximum value of $(a-b)^{2}+$ $(a-c)^{2}+(a-d)^{2}+(b-c)^{2}+(b-d)^{2}+(c-d)^{2}$ is $\\qquad$.",
"role": "user"
}
] | Example 1 (2002 Shanghai High School Mathematics Competition Question) Let real numbers $a, b, c, d$ satisfy $a^{2}+b^{2}+c^{2}+d^{2}=5$. Then the maximum value of $(a-b)^{2}+$ $(a-c)^{2}+(a-d)^{2}+(b-c)^{2}+(b-d)^{2}+(c-d)^{2}$ is $\qquad$. | "[\"20\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109017, "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:118923"}] | {
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[
"(x,y,z)=(4,3,2)or(-6,-5,-4)"
] | [
"skywork"
] | 517a0c884e1e7e0218aad4a98ba4543ddb2db2abdfaf9707c3ec3baecec65f82 | [
{
"content": "3.2. $\\left\\{\\begin{array}{l}x+y+x y=19 \\\\ y+z+y z=11 \\\\ z+x+z x=14 .\\end{array}\\right.$",
"role": "user"
}
] | 3.2. $\left\{\begin{array}{l}x+y+x y=19 \\ y+z+y z=11 \\ z+x+z x=14 .\end{array}\right.$ | "[\"(x,y,z)=(4,3,2)or(-6,-5,-4)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109026, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118924"}] | {
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[
"2"
] | [
"skywork"
] | 4d2a597a1328673258c53a1423291f551c07002f630be450a3dad636f0c1209f | [
{
"content": "$1.53 \\frac{\\sqrt{7+4 \\sqrt{3}} \\cdot \\sqrt{19-8 \\sqrt{3}}}{4-\\sqrt{3}}-\\sqrt{3}=2$.",
"role": "user"
}
] | $1.53 \frac{\sqrt{7+4 \sqrt{3}} \cdot \sqrt{19-8 \sqrt{3}}}{4-\sqrt{3}}-\sqrt{3}=2$. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109020, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "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:118925"}] | {
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[
"2m+n-2"
] | [
"skywork"
] | 23e386910654bd39401d6519bee03dec7a074593493f0fe3d4d69509814df304 | [
{
"content": "Three, take $m$ points randomly inside a convex $n$-sided polygon, and connect these $m+n$ points (the $m$ points taken and the original $n$ vertices) in such a way that no two connecting lines intersect, and all regions in the figure are triangles. How many triangles are there in the figure?",
... | Three, take $m$ points randomly inside a convex $n$-sided polygon, and connect these $m+n$ points (the $m$ points taken and the original $n$ vertices) in such a way that no two connecting lines intersect, and all regions in the figure are triangles. How many triangles are there in the figure? | "[\"2m+n-2\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 109002, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118927"}] | {
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[
"\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1"
] | [
"skywork"
] | 4375584cf7891dacb6e3d710ca6296bf9e7383602c48b42ccc322250c9cab807 | [
{
"content": "14. Let $A_{1}, A_{2}$ be the two vertices on the major axis of the ellipse $\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1(a>b$ $>0)$, and $P_{1} P_{2}$ be a chord perpendicular to the major axis. The intersection point of the lines $A_{1} P_{1}$ and $A_{2} P_{2}$ is $P$. Then the equation of the tr... | 14. Let $A_{1}, A_{2}$ be the two vertices on the major axis of the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b$ $>0)$, and $P_{1} P_{2}$ be a chord perpendicular to the major axis. The intersection point of the lines $A_{1} P_{1}$ and $A_{2} P_{2}$ is $P$. Then the equation of the trajectory of point $P$ is... | "[\"\\\\frac{x^{2}}{a^{2}}-\\\\frac{y^{2}}{b^{2}}=1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 109000, "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:118928"}] | {
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[
"\\frac{(x-\\frac{3}{2})^{2}}{\\frac{21}{4}}+\\frac{(y-2)^{2}}{7}=1"
] | [
"skywork"
] | 5af57fc4fe3ffa5a71ebbd4e2e52b9e492307d58ce98f4f9007311aa4357ddeb | [
{
"content": "Example 3 Let the curve $C_{1}: \\frac{x^{2}}{3}+\\frac{y^{2}}{4}=1$, curve $C_{2}: x+y=1$, and $P$ be a point on $C_{2}$. The ray $O P$ intersects $C_{1}$ at $R$. Also, point $Q$ is on $O P$, and satisfies $|O Q| \\cdot|O P|=|O R|^{2}$. Find the equation of the trajectory of point $Q$ as $P$ move... | Example 3 Let the curve $C_{1}: \frac{x^{2}}{3}+\frac{y^{2}}{4}=1$, curve $C_{2}: x+y=1$, and $P$ be a point on $C_{2}$. The ray $O P$ intersects $C_{1}$ at $R$. Also, point $Q$ is on $O P$, and satisfies $|O Q| \cdot|O P|=|O R|^{2}$. Find the equation of the trajectory of point $Q$ as $P$ moves along the curve $C_{2}$... | "[\"\\\\frac{(x-\\\\frac{3}{2})^{2}}{\\\\frac{21}{4}}+\\\\frac{(y-2)^{2}}{7}=1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109015, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118929"}] | {
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[
"2"
] | [
"skywork"
] | 253e7986746138cce97db704c2ff5ec02f08d2ef57643ddb2fc6a59a9e11728b | [
{
"content": "3.177. Calculate $(1+\\operatorname{ctg} \\alpha)(1+\\operatorname{ctg} \\beta)$, if $\\alpha+\\beta=\\frac{3 \\pi}{4}$.",
"role": "user"
}
] | 3.177. Calculate $(1+\operatorname{ctg} \alpha)(1+\operatorname{ctg} \beta)$, if $\alpha+\beta=\frac{3 \pi}{4}$. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109021, "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:118930"}] | {
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[
"-1"
] | [
"skywork"
] | bc8e120f079e7c375b347569b6d214020f50b658f640dcfc0fc9c7db70ce9722 | [
{
"content": "Given the line $y=x+\\sqrt{6}$, the circle $(O)$: $x^2+y^2=5$, and the ellipse $(E)$: $\\frac{y^2}{a^2}+\\frac{x^2}{b^2}=1$ $(b > 0)$ with an eccentricity of $e=\\frac{\\sqrt{3}}{3}$. The length of the chord intercepted by line $(l)$ on circle $(O)$ is equal to the length of the major axis of the ... | Given the line $y=x+\sqrt{6}$, the circle $(O)$: $x^2+y^2=5$, and the ellipse $(E)$: $\frac{y^2}{a^2}+\frac{x^2}{b^2}=1$ $(b > 0)$ with an eccentricity of $e=\frac{\sqrt{3}}{3}$. The length of the chord intercepted by line $(l)$ on circle $(O)$ is equal to the length of the major axis of the ellipse. Find the product o... | "[\"-1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108995, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118931"}] | {
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[
"[\\frac{1}{2}+\\sqrt{2n+\\frac{1}{4}}]"
] | [
"skywork"
] | cc53cbbcfa760d97ee7a8703421923d3855a9393387ab054f36dabc44e879234 | [
{
"content": "In a city with $n$ inhabitants, clubs are organized in such a way that any two clubs have, and any three clubs do not have, a common member. What is the maximum number of clubs that can be organized this way?",
"role": "user"
}
] | In a city with $n$ inhabitants, clubs are organized in such a way that any two clubs have, and any three clubs do not have, a common member. What is the maximum number of clubs that can be organized this way? | "[\"[\\\\frac{1}{2}+\\\\sqrt{2n+\\\\frac{1}{4}}]\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109022, "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:118932"}] | {
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} |
[
"\\frac{1}{4}"
] | [
"skywork"
] | cd578af2898e0ad5c43eb970c28dac626b294f8f8b826ae09159716dbfb25c84 | [
{
"content": "Given square $ABCD$, points $E$ and $F$ lie on $\\overline{AB}$ so that $\\overline{ED}$ and $\\overline{FD}$ bisect $\\angle ADC$. Calculate the ratio of the area of $\\triangle DEF$ to the area of square $ABCD$.",
"role": "user"
}
] | Given square $ABCD$, points $E$ and $F$ lie on $\overline{AB}$ so that $\overline{ED}$ and $\overline{FD}$ bisect $\angle ADC$. Calculate the ratio of the area of $\triangle DEF$ to the area of square $ABCD$. | "[\"\\\\frac{1}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109025, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118935"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | ab600b6850b0fcae4621cf83f2229bf2dcb0eaec147199f394961e8da8a18198 | [
{
"content": "The roots of the equation $x^2+kx+5 = 0$ differ by $\\sqrt{61}$. Find the greatest possible value of $k$.",
"role": "user"
}
] | The roots of the equation $x^2+kx+5 = 0$ differ by $\sqrt{61}$. Find the greatest possible value of $k$. | "[\"9\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109028, "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:118936"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{199}{100}"
] | [
"skywork"
] | 549ada92df4fa8b7e000e40d2e9fdea70e145bc09e082e67ddf407b82b1431b1 | [
{
"content": "Observing the equations:<br/>$1\\times 3+1=4=2^{2}$;<br/>$2\\times 4+1=9=3^{2}$;<br/>$3\\times 5+1=16=4^{2}$;<br/>$4\\times 6+1=25=5^{2}$;<br/>$\\ldots $<br/>$(1)7\\times 9+1=( $______)$^{2}$;<br/>$(2)$ Using the pattern you discovered, calculate: $(1+\\frac{1}{1×3})×(1+\\frac{1}{2×4})×(1+\\frac{1... | Observing the equations:<br/>$1\times 3+1=4=2^{2}$;<br/>$2\times 4+1=9=3^{2}$;<br/>$3\times 5+1=16=4^{2}$;<br/>$4\times 6+1=25=5^{2}$;<br/>$\ldots $<br/>$(1)7\times 9+1=( $______)$^{2}$;<br/>$(2)$ Using the pattern you discovered, calculate: $(1+\frac{1}{1×3})×(1+\frac{1}{2×4})×(1+\frac{1}{3×5})×⋅⋅⋅×(1+\frac{1}{198×200... | "[\"\\\\frac{199}{100}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109013, "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:118937"}] | {
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"reference_present": true
} |
[
"125"
] | [
"skywork"
] | 01fedbbab4cf00d7db260aaaccd7d4f253016ecbc9ffa2b3c2359623007886d8 | [
{
"content": "179. Find $N=p^{3}$, if $\\varphi(N)=100$.\n\nTranslate the text above into English, please keep the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | 179. Find $N=p^{3}$, if $\varphi(N)=100$.
Translate the text above into English, please keep the original text's line breaks and format, and output the translation result directly. | "[\"125\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109027, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118938"}] | {
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} |
[
"2"
] | [
"skywork"
] | 90e73ac1b803e4e5125abeca651b033823365227bfb8d0a59e0a28b9d241b646 | [
{
"content": "Harriet ran a 1000 m course in 380 seconds. She ran the first 720 m of the course at a constant speed of 3 m/s. What was her speed for the remaining part of the course?",
"role": "user"
}
] | Harriet ran a 1000 m course in 380 seconds. She ran the first 720 m of the course at a constant speed of 3 m/s. What was her speed for the remaining part of the course? | "[\"2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109032, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "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:118939"}] | {
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} |
[
"\\text{True}"
] | [
"skywork"
] | ee338d1cf5649b13a1d2a0eeef36e156f15e2adae5c8190d790c44ce628e6a32 | [
{
"content": "A grasshopper is sitting at an integer point in the Euclidean plane. Each second it jumps to another integer point in such a way that the jump vector is constant. A hunter that knows neither the starting point of the grasshopper nor the jump vector (but knows that the jump vector for each second i... | A grasshopper is sitting at an integer point in the Euclidean plane. Each second it jumps to another integer point in such a way that the jump vector is constant. A hunter that knows neither the starting point of the grasshopper nor the jump vector (but knows that the jump vector for each second is constant) wants to c... | "[\"\\\\text{True}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109019, "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:118940"}] | {
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[
"a_{n}=\\frac{n(n-1)}{2}"
] | [
"skywork"
] | 95dc2404922e1a4a1fe1e2e5aa3fff3ca4816697e61396767ba0bd6beccc3927 | [
{
"content": "186. The sequence $\\left(a_{n}\\right)$ is defined by the conditions:\n\n$$\na_{1}=0, \\quad a_{n+1}=a_{n}+n\n$$\n\nFind the formula for the general term of the sequence.",
"role": "user"
}
] | 186. The sequence $\left(a_{n}\right)$ is defined by the conditions:
$$
a_{1}=0, \quad a_{n+1}=a_{n}+n
$$
Find the formula for the general term of the sequence. | "[\"a_{n}=\\\\frac{n(n-1)}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109031, "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:118943"}] | {
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[
"23"
] | [
"skywork"
] | 0d6cc8ab94f31542916334c0a23391222cdb61c84dc9eef3c3ee6e0ce82782f0 | [
{
"content": "4. Xiaoli put a plate of cat food in front of the big cat QiQi and the small cat TianTian. Later, Xiaoli felt that she had given too much to QiQi, so she transferred 7 pieces of cat food from QiQi's plate to TianTian's. As a result, QiQi still had 9 more pieces of cat food than TianTian. Initially... | 4. Xiaoli put a plate of cat food in front of the big cat QiQi and the small cat TianTian. Later, Xiaoli felt that she had given too much to QiQi, so she transferred 7 pieces of cat food from QiQi's plate to TianTian's. As a result, QiQi still had 9 more pieces of cat food than TianTian. Initially, QiQi had $\qquad$ mo... | "[\"23\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109030, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:118944"}] | {
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[
"205"
] | [
"skywork"
] | 541b92729c0e2f9ec04426e14f3ad86509d8159807601a3c668a8e36ff6e40a5 | [
{
"content": "The difference between two perfect squares is 133. What is the smallest possible sum of the two perfect squares?",
"role": "user"
}
] | The difference between two perfect squares is 133. What is the smallest possible sum of the two perfect squares? | "[\"205\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109038, "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:118945"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"10,20,11,30,21,12,31,22,13"
] | [
"skywork"
] | 9c95f1e012732ce9992c26d1ab228bc55a44433329862912f08ab6fa2ec3c676 | [
{
"content": "8.3. The square of the sum of the digits of the number $A$ is equal to the sum of the digits of the number $A^{2}$. Find all such two-digit numbers $A$ and explain why there are no others.",
"role": "user"
}
] | 8.3. The square of the sum of the digits of the number $A$ is equal to the sum of the digits of the number $A^{2}$. Find all such two-digit numbers $A$ and explain why there are no others. | "[\"10,20,11,30,21,12,31,22,13\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109036, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:118948"}] | {
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} |
[
"74"
] | [
"skywork"
] | a537c2ae80ae11b9034020b37578b634b00b6c45349d83047ac18cc60a60007e | [
{
"content": "5. A $20 \\times 19$ rectangle is plotted on the Cartesian plane with one corner at the origin and with sides parallel to the coordinate axes. How many unit squares do the two diagonals of this rectangle pass through?",
"role": "user"
}
] | 5. A $20 \times 19$ rectangle is plotted on the Cartesian plane with one corner at the origin and with sides parallel to the coordinate axes. How many unit squares do the two diagonals of this rectangle pass through? | "[\"74\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109042, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118949"}] | {
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} |
[
"3\\sqrt{2}"
] | [
"skywork"
] | 2c5ca3b7fdcf428326ea0505c1a7cb366fe375e5937530005ac05da6e06b54f5 | [
{
"content": "In the Cartesian coordinate system $xOy$, line $l_{1}$: $kx-y+2=0$ intersects with line $l_{2}$: $x+ky-2=0$ at point $P$. When the real number $k$ varies, the maximum distance from point $P$ to the line $x-y-4=0$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | In the Cartesian coordinate system $xOy$, line $l_{1}$: $kx-y+2=0$ intersects with line $l_{2}$: $x+ky-2=0$ at point $P$. When the real number $k$ varies, the maximum distance from point $P$ to the line $x-y-4=0$ is \_\_\_\_\_\_. | "[\"3\\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109041, "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:118950"}] | {
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[
"(1, 1, 1)"
] | [
"skywork"
] | 927d3de1e9ad5ccf785c5c07696d449e26d37923598a6dd26a1fc5b060f51f46 | [
{
"content": "Find all real solutions $(x,y,z)$ of the system of equations\n$$\\begin{cases} x^3 = 2y-1 \\\\y^3 = 2z-1\\\\ z^3 = 2x-1\\end{cases}$$",
"role": "user"
}
] | Find all real solutions $(x,y,z)$ of the system of equations
$$\begin{cases} x^3 = 2y-1 \\y^3 = 2z-1\\ z^3 = 2x-1\end{cases}$$ | "[\" (1, 1, 1) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109052, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118951"}] | {
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"reference_components": 1,
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} |
[
"\\{(5,12),(6,8)\\}"
] | [
"skywork"
] | c8deff616a495de9b04a8e946d69d8b357dd7003d5994a698bd56623a4e87e03 | [
{
"content": "Consider a rectangular tiled room with dimensions $m\\times n$, where the tiles are $1\\times1$ in size. Compute all ordered pairs $(m,n)$ with $m\\leq n$ such that the number of tiles on the perimeter is equal to the number of tiles in the interior (i.e. not on the perimeter).",
"role": "user... | Consider a rectangular tiled room with dimensions $m\times n$, where the tiles are $1\times1$ in size. Compute all ordered pairs $(m,n)$ with $m\leq n$ such that the number of tiles on the perimeter is equal to the number of tiles in the interior (i.e. not on the perimeter). | "[\" \\\\{(5,12),(6,8)\\\\} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109039, "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:118952"}] | {
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[
"\\arccos\\frac{2-\\sqrt{2}}{4};\\arccos\\frac{2\\sqrt{2}+1}{4}"
] | [
"skywork"
] | 5be8f4dd53bfa816ae1139257296e5a15b6a2f261ef83ecc8e0d681e3adb10f7 | [
{
"content": "12.154. In an acute isosceles triangle, the radius of the inscribed circle is 4 times smaller than the radius of the circumscribed circle. Find the angles of the triangle.",
"role": "user"
}
] | 12.154. In an acute isosceles triangle, the radius of the inscribed circle is 4 times smaller than the radius of the circumscribed circle. Find the angles of the triangle. | "[\"\\\\arccos\\\\frac{2-\\\\sqrt{2}}{4};\\\\arccos\\\\frac{2\\\\sqrt{2}+1}{4}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109040, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118953"}] | {
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} |
[
"\\frac{2\\alpha\\cos^{4}(\\frac{\\pi}{4}-\\frac{\\alpha}{4})}{\\pi\\sin^{2}\\frac{\\alpha}{2}}"
] | [
"skywork"
] | 7f2632735f52bda553debee204333fa3e9c708acc6a7e2da9792c2fa7de5c2e6 | [
{
"content": "12.135. Find the ratio of the area of a sector with a given central angle $\\alpha$ radians to the area of the circle inscribed in it.",
"role": "user"
}
] | 12.135. Find the ratio of the area of a sector with a given central angle $\alpha$ radians to the area of the circle inscribed in it. | "[\"\\\\frac{2\\\\alpha\\\\cos^{4}(\\\\frac{\\\\pi}{4}-\\\\frac{\\\\alpha}{4})}{\\\\pi\\\\sin^{2}\\\\frac{\\\\alpha}{2}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109048, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118954"}] | {
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"plain_numeric_reference": false,
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} |
[
"2x^{4}-4x^{3}+3x^{2}-x+C"
] | [
"skywork"
] | e8b167c9996d8b61c4feb0a5c957e21a08b08b61d78dcd99dfb9e520409352fc | [
{
"content": "42. $\\int(2 x-1)^{3} d x$.\n\nThe integral of $(2x-1)^3$ with respect to $x$.",
"role": "user"
}
] | 42. $\int(2 x-1)^{3} d x$.
The integral of $(2x-1)^3$ with respect to $x$. | "[\"2x^{4}-4x^{3}+3x^{2}-x+C\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109045, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118955"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"24"
] | [
"skywork"
] | afb9db440902aaea5b97e2ff6863e5c15519a15ee6f2e07f1897d47a53718efb | [
{
"content": "Let $M$ be the number of positive integers that are less than or equal to $2048$ and whose base-$2$ representation has more $1$'s than $0$'s. Find the remainder when $M$ is divided by $1000$.",
"role": "user"
}
] | Let $M$ be the number of positive integers that are less than or equal to $2048$ and whose base-$2$ representation has more $1$'s than $0$'s. Find the remainder when $M$ is divided by $1000$. | "[\"24\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109047, "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:118956"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2}"
] | [
"skywork"
] | 9f464865ecbe16dd21b042419f0ccba3ab344205554533db20d8df7623f4b1bb | [
{
"content": "Given circle $C$: $(x-2)^2 + y^2 = 4$, and line $l$: $x - \\sqrt{3}y = 0$, the probability that the distance from point $A$ on circle $C$ to line $l$ is not greater than $1$ is $\\_\\_\\_\\_\\_\\_\\_.$",
"role": "user"
}
] | Given circle $C$: $(x-2)^2 + y^2 = 4$, and line $l$: $x - \sqrt{3}y = 0$, the probability that the distance from point $A$ on circle $C$ to line $l$ is not greater than $1$ is $\_\_\_\_\_\_\_.$ | "[\"\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109043, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118957"}] | {
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} |
[
"2"
] | [
"skywork"
] | a5dc0710c0c0ce14cef419dd5ddaa1b0329b0b9b0d3de8945493674712fa33c9 | [
{
"content": "11. Let $a \\in \\mathbf{R}$, the equation ||$x-a|-a|=2$ has exactly three distinct roots, then $a=$",
"role": "user"
}
] | 11. Let $a \in \mathbf{R}$, the equation ||$x-a|-a|=2$ has exactly three distinct roots, then $a=$ | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109056, "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:118958"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1/2"
] | [
"skywork"
] | 97ef9e9c92c152c796fcc7bb11787d4913556985454cd853ee967c5b66215ee1 | [
{
"content": "Two hunters, $A$ and $B$, went duck hunting. Assume that each of them hits a duck as often as they miss it. Hunter $A$ encountered 50 ducks during the hunt, while hunter $B$ encountered 51 ducks. What is the probability that hunter $B$'s catch exceeds hunter $A$'s catch?",
"role": "user"
}
] | Two hunters, $A$ and $B$, went duck hunting. Assume that each of them hits a duck as often as they miss it. Hunter $A$ encountered 50 ducks during the hunt, while hunter $B$ encountered 51 ducks. What is the probability that hunter $B$'s catch exceeds hunter $A$'s catch? | "[\"1/2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109049, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:118959"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-3"
] | [
"skywork"
] | 2b0f6c18fb54a3c9402c4a20a8cf1ca17a7b7b08c50b54f944ec6322741bb106 | [
{
"content": "3. Two numbers \\(x\\) and \\(y\\) satisfy the equation \\(26 x^{2} + 23 x y - 3 y^{2} - 19 = 0\\) and are the sixth and eleventh terms, respectively, of a decreasing arithmetic progression consisting of integers. Find the common difference of this progression.",
"role": "user"
}
] | 3. Two numbers \(x\) and \(y\) satisfy the equation \(26 x^{2} + 23 x y - 3 y^{2} - 19 = 0\) and are the sixth and eleventh terms, respectively, of a decreasing arithmetic progression consisting of integers. Find the common difference of this progression. | "[\"-3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109046, "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:118960"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | 51d34b68d76cecf3d8c27c6d88c248855857bd7783cbf74b5e6cf798f3800366 | [
{
"content": "## Task 30/67\n\nThe sum is sought\n\n$$\n\\sum_{k=1}^{\\infty} a_{k}=a_{1}+a_{2}+a_{3}+\\ldots+a_{n}+\\ldots\n$$\n\nof which the following is known:\n\n1. The terms of the series form a monotonic sequence.\n2. It is $a_{1}=1, a_{n}>0$ for every $n$.\n3. It is $\\prod_{k=1}^{\\infty} a_{2 k-1}=\\p... | ## Task 30/67
The sum is sought
$$
\sum_{k=1}^{\infty} a_{k}=a_{1}+a_{2}+a_{3}+\ldots+a_{n}+\ldots
$$
of which the following is known:
1. The terms of the series form a monotonic sequence.
2. It is $a_{1}=1, a_{n}>0$ for every $n$.
3. It is $\prod_{k=1}^{\infty} a_{2 k-1}=\prod_{k=1}^{\infty} a_{2 k}$.
4. It is $a_... | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109050, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118961"}] | {
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[
"21"
] | [
"skywork"
] | 6cb9a89b7345c8596b5b09a692c5322e812c5cdc25e618bacda29675f59d3030 | [
{
"content": "12. (5 points) $A, B, C, D$ four people are carrying a flashlight and need to cross a dark tunnel that only allows 2 people to walk at a time. Each time, 2 people take the flashlight to cross, then one person returns with the flashlight, and again 2 people take the flashlight to cross $\\cdots$, i... | 12. (5 points) $A, B, C, D$ four people are carrying a flashlight and need to cross a dark tunnel that only allows 2 people to walk at a time. Each time, 2 people take the flashlight to cross, then one person returns with the flashlight, and again 2 people take the flashlight to cross $\cdots$, if $A, B, C, D$ four peo... | "[\"21\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109044, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:118962"}] | {
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[
"10"
] | [
"skywork"
] | d62c0ada6c56d8345add8a815739d7483636dd69e6d007904e70be45cd599185 | [
{
"content": "If $b$ is an even multiple of $7786$, find the greatest common divisor of $8b^2 + 85b + 200$ and $2b + 10$.",
"role": "user"
}
] | If $b$ is an even multiple of $7786$, find the greatest common divisor of $8b^2 + 85b + 200$ and $2b + 10$. | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109053, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118963"}] | {
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[
"4"
] | [
"skywork"
] | 67236d99b50821f693c6a1efcdd344e9f53389db00d7d9cf1baeebcb00c2d98a | [
{
"content": "14. In space, there are five points, no four of which are coplanar. If several line segments are drawn such that no tetrahedron exists in the graph, then the maximum number of triangles in the graph is $\\qquad$.",
"role": "user"
}
] | 14. In space, there are five points, no four of which are coplanar. If several line segments are drawn such that no tetrahedron exists in the graph, then the maximum number of triangles in the graph is $\qquad$. | "[\"4\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 109051, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118965"}] | {
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[
"1,1,1"
] | [
"skywork"
] | 7f4837c50d07d6d47197fbbbae95139990344ca12ec4195914e811156ad71253 | [
{
"content": "11-1. Given three numbers. If each of them is decreased by 1, then their product also decreases by 1. If all the original numbers are decreased by 2, then their product also decreases by 2.\n\na) By how much will the product decrease if all the original numbers are decreased by 3?\n\nb) Provide an... | 11-1. Given three numbers. If each of them is decreased by 1, then their product also decreases by 1. If all the original numbers are decreased by 2, then their product also decreases by 2.
a) By how much will the product decrease if all the original numbers are decreased by 3?
b) Provide any three numbers that satis... | "[\"1,1,1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109060, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "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:118966"}] | {
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[
"\\sqrt{5}"
] | [
"skywork"
] | ad65523d35b37e875a2ad26699f8a95e9336073f43505c8b17a429e2d2fe3880 | [
{
"content": "Let $ABCD$ be a square with side length $5$, and let $E$ be the midpoint of $CD$. Let $F$ be the point on $AE$ such that $CF=5$. Compute $AF$.",
"role": "user"
}
] | Let $ABCD$ be a square with side length $5$, and let $E$ be the midpoint of $CD$. Let $F$ be the point on $AE$ such that $CF=5$. Compute $AF$. | "[\"\\\\sqrt{5}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109058, "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:118967"}] | {
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[
"\\sqrt{4027}"
] | [
"skywork"
] | 9eb832933c7bcb29c2b4cf429899cbc4b7748024cd40540f8e8ee558c1d45915 | [
{
"content": "14. [8] Let $A B C D$ be a trapezoid with $A B \\| C D$ and $\\angle D=90^{\\circ}$. Suppose that there is a point $E$ on $C D$ such that $A E=B E$ and that triangles $A E D$ and $C E B$ are similar, but not congruent. Given that $\\frac{C D}{A B}=2014$, find $\\frac{B C}{A D}$.",
"role": "use... | 14. [8] Let $A B C D$ be a trapezoid with $A B \| C D$ and $\angle D=90^{\circ}$. Suppose that there is a point $E$ on $C D$ such that $A E=B E$ and that triangles $A E D$ and $C E B$ are similar, but not congruent. Given that $\frac{C D}{A B}=2014$, find $\frac{B C}{A D}$. | "[\"\\\\sqrt{4027}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109054, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118968"}] | {
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} |
[
"16 \\pi"
] | [
"skywork"
] | 6469d0c38839c609293414e8cbc0f6eb75a5c262f4dc4361b3c820e73f3b5326 | [
{
"content": "Let $A B C$ be a triangle with $C A=C B=5$ and $A B=8$. A circle $\\omega$ is drawn such that the interior of triangle $A B C$ is completely contained in the interior of $\\omega$. Find the smallest possible area of $\\omega$.",
"role": "user"
}
] | Let $A B C$ be a triangle with $C A=C B=5$ and $A B=8$. A circle $\omega$ is drawn such that the interior of triangle $A B C$ is completely contained in the interior of $\omega$. Find the smallest possible area of $\omega$. | "[\"16 \\\\pi\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109055, "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:118969"}] | {
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[
"135"
] | [
"skywork"
] | 89e44a683237c8b4bd5b0dd017f57ff5c5bea52bfe4da1cfd9d7571dbd020ff8 | [
{
"content": "16. Line $a$ is parallel to line $b$, and there are 5 points and 6 points on lines $a$ and $b$ respectively. Using these points as vertices, $\\qquad$ different triangles can be drawn.",
"role": "user"
}
] | 16. Line $a$ is parallel to line $b$, and there are 5 points and 6 points on lines $a$ and $b$ respectively. Using these points as vertices, $\qquad$ different triangles can be drawn. | "[\"135\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109062, "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:118970"}] | {
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[
"5238.85"
] | [
"skywork"
] | 561c353576c85c8ecf4b130e12c0572dbcd27b8511c6c5e6b9d4ec86fb2956d2 | [
{
"content": "A rectangle with sides of $15 \\mathrm{~cm}$ and $20 \\mathrm{~cm}$ is rotated about one of its diagonals. What is the volume of the resulting solid of revolution?",
"role": "user"
}
] | A rectangle with sides of $15 \mathrm{~cm}$ and $20 \mathrm{~cm}$ is rotated about one of its diagonals. What is the volume of the resulting solid of revolution? | "[\"5238.85\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109072, "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:118971"}] | {
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[
"x=1 \\pm \\frac{5 \\sqrt{3}}{2}"
] | [
"skywork"
] | 9188ffdf93ccb1d5fb9e1795f3c17bbd6ff66b007b6dafce01e35b43ca5f2dba | [
{
"content": "Example 1. Solve the equation\n$$\n\\sqrt{x^{2}+4 x+8}+\\sqrt{x^{2}-8 x+20}=10 \\text {. }\n$$",
"role": "user"
}
] | Example 1. Solve the equation
$$
\sqrt{x^{2}+4 x+8}+\sqrt{x^{2}-8 x+20}=10 \text {. }
$$ | "[\"x=1 \\\\pm \\\\frac{5 \\\\sqrt{3}}{2}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 109083, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "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:118972"}] | {
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} |
[
"3^{n}"
] | [
"skywork"
] | b4340e179f27bb491b105a7383d31e40700ffb294a08e1b77fd50400ab1a42aa | [
{
"content": "10. Given that $n$ is a natural number, the polynomial $P(x)=\\sum_{h=0}^{n} \\mathrm{C}_{n}^{h} x^{n-h} \\cdot(x-1)^{h}$ can be expanded into an ascending power series of $x$ as $a_{0}+a_{1} x+a_{2} x^{2}+$ $\\cdots+a_{n} x^{n}$. Then $\\left|a_{0}\\right|+\\left|a_{1}\\right|+\\left|a_{2}\\right... | 10. Given that $n$ is a natural number, the polynomial $P(x)=\sum_{h=0}^{n} \mathrm{C}_{n}^{h} x^{n-h} \cdot(x-1)^{h}$ can be expanded into an ascending power series of $x$ as $a_{0}+a_{1} x+a_{2} x^{2}+$ $\cdots+a_{n} x^{n}$. Then $\left|a_{0}\right|+\left|a_{1}\right|+\left|a_{2}\right|+\cdots+\left|a_{n}\right|=$ $\... | "[\"3^{n}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 109066, "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:118973"}] | {
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} |
[
"2;2\\sqrt{65}"
] | [
"skywork"
] | 4f5cbbde6fb511debf8567e010506e57e2bc17a64b0781d7214894c79122ada5 | [
{
"content": "# Problem 4.\n\nIn the Oxy plane, find the smallest and largest distances between two points $(x ; y)$, the coordinates of which are integers and satisfy the equation $y^{2}=4 x^{2}-15$.",
"role": "user"
}
] | # Problem 4.
In the Oxy plane, find the smallest and largest distances between two points $(x ; y)$, the coordinates of which are integers and satisfy the equation $y^{2}=4 x^{2}-15$. | "[\"2;2\\\\sqrt{65}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109084, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118974"}] | {
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[
"85"
] | [
"skywork"
] | d8c0b90e008150d6e1029b7c52c50949bd0292ce5089ae39bb67fdb7b6786996 | [
{
"content": "Quadrilateral $ABCD$ has $AB = BC = CD$, $m\\angle ABC = 70^\\circ$ and $m\\angle BCD = 170^\\circ$. What is the degree measure of $\\angle BAD$?",
"role": "user"
}
] | Quadrilateral $ABCD$ has $AB = BC = CD$, $m\angle ABC = 70^\circ$ and $m\angle BCD = 170^\circ$. What is the degree measure of $\angle BAD$? | "[\"85\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109100, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118975"}] | {
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[
"0"
] | [
"skywork"
] | ae5e787489504ea344ba88ad01494baf3ef2111ccc7e2c41be373ad7b474a598 | [
{
"content": "What is $(-1)^{1} + (-1)^{2} + ... + (-1)^{2006}$ ?\n$\\textbf{(A)} -2006\\qquad \\textbf{(B)} -1\\qquad \\textbf{(C) } 0\\qquad \\textbf{(D) } 1\\qquad \\textbf{(E) } 2006$",
"role": "user"
}
] | What is $(-1)^{1} + (-1)^{2} + ... + (-1)^{2006}$ ?
$\textbf{(A)} -2006\qquad \textbf{(B)} -1\qquad \textbf{(C) } 0\qquad \textbf{(D) } 1\qquad \textbf{(E) } 2006$ | "[\"0\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 109076, "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:118976"}] | {
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[
"SXY"
] | [
"skywork"
] | 11318913d56846b22bc895d533d929a264c32b17bdea89ea2cfa963b53158510 | [
{
"content": "Let $ABCD$ be a regular tetrahedron. To an arbitrary point $M$ on one edge, say $CD$, corresponds the point $P = P(M)$ which is the intersection of two lines $AH$ and $BK$, drawn from $A$ orthogonally to $BM$ and from $B$ orthogonally to $AM$. What is the locus of $P$ when $M$ varies ?",
"role... | Let $ABCD$ be a regular tetrahedron. To an arbitrary point $M$ on one edge, say $CD$, corresponds the point $P = P(M)$ which is the intersection of two lines $AH$ and $BK$, drawn from $A$ orthogonally to $BM$ and from $B$ orthogonally to $AM$. What is the locus of $P$ when $M$ varies ? | "[\" SXY \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109064, "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:118977"}] | {
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[
"10"
] | [
"skywork"
] | b711e54059a20b3ab1b159819a29a54ade4ddd5379ce368014aa45420b5b07f4 | [
{
"content": "4. (13 points) Sixteen people are standing in a circle: each of them is either a truth-teller (he always tells the truth) or a liar (he always lies). Everyone said that both of their neighbors are liars. What is the maximum number of liars that can be in this circle?",
"role": "user"
}
] | 4. (13 points) Sixteen people are standing in a circle: each of them is either a truth-teller (he always tells the truth) or a liar (he always lies). Everyone said that both of their neighbors are liars. What is the maximum number of liars that can be in this circle? | "[\"10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109068, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118978"}] | {
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"reference_present": true
} |
[
"3"
] | [
"skywork"
] | ebcaf3dfa353d72bfe0f54d24162aefb09316df5199f489415537cef6973f6ee | [
{
"content": "What value of $x$ will give the minimum value of $2x^2 - 12x + 3$?",
"role": "user"
}
] | What value of $x$ will give the minimum value of $2x^2 - 12x + 3$? | "[\"3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109108, "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:118979"}] | {
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} |
[
"98"
] | [
"skywork"
] | cd854bfb32c28ea7b8b5d40152940ebd7cda52f90c0973b4d82ffc7080076833 | [
{
"content": "The sum of seven consecutive even numbers is 686. What is the smallest of these seven numbers? Additionally, calculate the median and mean of this sequence.",
"role": "user"
}
] | The sum of seven consecutive even numbers is 686. What is the smallest of these seven numbers? Additionally, calculate the median and mean of this sequence. | "[\"98\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109080, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118980"}] | {
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} |
[
"\\frac{6102}{256}"
] | [
"skywork"
] | ccffd8e4fc610e4e2a83c78008e07d94767d3ad35af6d7f823cc9761d94dd62b | [
{
"content": "Three. (20 points) Let the general term of the sequence $\\left\\{a_{n}\\right\\}$ be\n$$\na_{n}=n+\\frac{2006}{n^{2}}(n=1,2, \\cdots) \\text {. }\n$$\n\nFind the minimum term of the sequence $\\left\\{a_{n}\\right\\}$.",
"role": "user"
}
] | Three. (20 points) Let the general term of the sequence $\left\{a_{n}\right\}$ be
$$
a_{n}=n+\frac{2006}{n^{2}}(n=1,2, \cdots) \text {. }
$$
Find the minimum term of the sequence $\left\{a_{n}\right\}$. | "[\"\\\\frac{6102}{256}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 109075, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:118981"}] | {
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} |
[
"49"
] | [
"skywork"
] | 04b791c1a9a6f72dbf27a8b2e181a946142172fc0b39c3bdd8a774dd31bc43c7 | [
{
"content": "The positive integer divisors of 294, except 1, are arranged around a circle so that every pair of adjacent integers has a common factor greater than 1. What is the sum of the two integers adjacent to 21?",
"role": "user"
}
] | The positive integer divisors of 294, except 1, are arranged around a circle so that every pair of adjacent integers has a common factor greater than 1. What is the sum of the two integers adjacent to 21? | "[\"49\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109088, "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:118982"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | cc7ce577318c22b50b7d5ea9ef35758f5d51a18c381db74ecac9eb4ed6a93d21 | [
{
"content": "A4. The arithmetic mean of the numbers $2,4,5,8, x, 15,20$ is $x$. The value of $x$ is:\n(A) -9\n(B) 9\n(C) 10\n(D) 12\n(E) 13",
"role": "user"
}
] | A4. The arithmetic mean of the numbers $2,4,5,8, x, 15,20$ is $x$. The value of $x$ is:
(A) -9
(B) 9
(C) 10
(D) 12
(E) 13 | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109079, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118983"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"(x, y, z) = (7, 5, 2)"
] | [
"skywork"
] | 7400877dafe9b459114e0168a38cc6d6b8ec1d86a47299a54f7c286067ebd8bd | [
{
"content": "Find all triples $(x, y, z)$ such that $x, y, z, x - y, y - z, x - z$ are all prime positive integers.",
"role": "user"
}
] | Find all triples $(x, y, z)$ such that $x, y, z, x - y, y - z, x - z$ are all prime positive integers. | "[\"(x, y, z) = (7, 5, 2)\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109070, "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:118984"}] | {
"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
} |
[
"22"
] | [
"skywork"
] | 042c4ca2fd2ae5ecdaa25ddf889af1c61b1726fe78e87780543fda34827ae101 | [
{
"content": "Suppose that at the end of any year, a unit of money has lost $10\\%$ of the value it had at the beginning of that year. Find the smallest integer $n$ such that after $n$ years, the money will have lost at least $90\\%$ of its value. (To the nearest thousandth $\\log_{10}3=.477$.)\r\n\r\n$\\text{(... | Suppose that at the end of any year, a unit of money has lost $10\%$ of the value it had at the beginning of that year. Find the smallest integer $n$ such that after $n$ years, the money will have lost at least $90\%$ of its value. (To the nearest thousandth $\log_{10}3=.477$.)
$\text{(A)}\ 14 \qquad \text{(B)}\ 16 ... | "[\"22\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109078, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118986"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"n+1"
] | [
"skywork"
] | bf40a1fa90c0293bfd2d68c15a51bd86ad9f8c1530369b37bc766ffa23a52c13 | [
{
"content": "4. Let there be $n(n \\geqslant 4)$ points $V_{1}, V_{2}, \\cdots, V_{n}$ in a plane, with no three points collinear. Some of these points are connected by line segments. Place $n$ chess pieces, labeled $1, 2, \\cdots, n$, on these $n$ points, with exactly one piece on each point. Now perform the ... | 4. Let there be $n(n \geqslant 4)$ points $V_{1}, V_{2}, \cdots, V_{n}$ in a plane, with no three points collinear. Some of these points are connected by line segments. Place $n$ chess pieces, labeled $1, 2, \cdots, n$, on these $n$ points, with exactly one piece on each point. Now perform the following operation on th... | "[\"n+1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 109059, "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:118988"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"0.375"
] | [
"skywork"
] | d203c1916f7e8a7d1bb7f6f8ca375ce39c6b5b050748e8ea1cbb085107b1858e | [
{
"content": "1571. A regular coin was tossed 4 times. What is the probability of the coat of arms landing twice?",
"role": "user"
}
] | 1571. A regular coin was tossed 4 times. What is the probability of the coat of arms landing twice? | "[\"0.375\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109098, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "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:118989"}] | {
"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
} |
[
"1716"
] | [
"skywork"
] | a83d9772ca47e6adf2d608c9819516f125a284b14550bff89bdb3edf1c763ab9 | [
{
"content": "In a cultural performance, there are already 10 programs arranged in the program list. Now, 3 more programs are to be added, with the requirement that the relative order of the originally scheduled 10 programs remains unchanged. How many different arrangements are there for the program list? (Answ... | In a cultural performance, there are already 10 programs arranged in the program list. Now, 3 more programs are to be added, with the requirement that the relative order of the originally scheduled 10 programs remains unchanged. How many different arrangements are there for the program list? (Answer with a number). | "[\"1716\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109093, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:118990"}] | {
"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
} |
[
"1332"
] | [
"skywork"
] | a532b43c3dfb58800d4b0a445e06721d49d733813aff3ea6ec279ad7b8571373 | [
{
"content": "1. Find the sum of all three-digit numbers that can be written using the digits $1,2,3$ such that all digits in each number are different.",
"role": "user"
}
] | 1. Find the sum of all three-digit numbers that can be written using the digits $1,2,3$ such that all digits in each number are different. | "[\"1332\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109104, "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:118991"}] | {
"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
} |
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