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 |
|---|---|---|---|---|---|---|---|---|
[
"48"
] | [
"skywork"
] | b5d827d31950fc5d85b38af5fa8e5ac1bd9d3170448f97bfeb7729a5b6a0cec5 | [
{
"content": "9. On a white checkered board of size $25 \\times 25$ cells, several cells are painted black, with exactly 9 cells painted black in each row and each column. What is the smallest $k$ such that it is always possible to repaint $k$ cells to white in such a way that it is impossible to cut out a blac... | 9. On a white checkered board of size $25 \times 25$ cells, several cells are painted black, with exactly 9 cells painted black in each row and each column. What is the smallest $k$ such that it is always possible to repaint $k$ cells to white in such a way that it is impossible to cut out a black $2 \times 2$ square? ... | "[\"48\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 440, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14472"}] | {
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[
"600"
] | [
"skywork"
] | c15e73cb43b0b993f4573ef1a2d16d56757f3c911e4a72daa51a9b30969272fc | [
{
"content": "Suppose I have 8 shirts, 5 pants, 4 ties, and 2 jackets. If an outfit requires a shirt, pants, and optionally can have a tie and/or a jacket, how many different outfits can I create?",
"role": "user"
}
] | Suppose I have 8 shirts, 5 pants, 4 ties, and 2 jackets. If an outfit requires a shirt, pants, and optionally can have a tie and/or a jacket, how many different outfits can I create? | "[\"600\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 438, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14473"}] | {
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"reference_components": 1,
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} |
[
"n+1"
] | [
"skywork"
] | 3bf6d2139e610518ca50132b1b1f27e123c6cd57cf8c21ad5fd7fb01f6188134 | [
{
"content": "3. Let $a_{n}=\\sqrt{1 \\times 2}+\\sqrt{2 \\times 3}+\\cdots+\\sqrt{n \\times(n+1)}$. Then $\\left[\\frac{2 a_{n}}{n}\\right]=$ $\\qquad$ (where [x] denotes the greatest integer not exceeding the real number $x$).",
"role": "user"
}
] | 3. Let $a_{n}=\sqrt{1 \times 2}+\sqrt{2 \times 3}+\cdots+\sqrt{n \times(n+1)}$. Then $\left[\frac{2 a_{n}}{n}\right]=$ $\qquad$ (where [x] denotes the greatest integer not exceeding the real number $x$). | "[\"n+1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 445, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14474"}] | {
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[
"2001000"
] | [
"skywork"
] | b6ca50f60949d8374fecc00bb99d9e93b43896a6de8749271d51af198227732c | [
{
"content": "17. Let $[x]$ denote the greatest integer not exceeding $x$, for example $[3.15]=3,[3.7]=3,[3]=3$, then $[\\sqrt[3]{1 \\cdot 2 \\cdot 3}]+[\\sqrt[3]{2 \\cdot 3 \\cdot 4}]+[\\sqrt[3]{3 \\cdot 4 \\cdot 5}]+\\cdots+[\\sqrt[3]{2000 \\cdot 2001 \\cdot 2002}]=$ $\\qquad$",
"role": "user"
}
] | 17. Let $[x]$ denote the greatest integer not exceeding $x$, for example $[3.15]=3,[3.7]=3,[3]=3$, then $[\sqrt[3]{1 \cdot 2 \cdot 3}]+[\sqrt[3]{2 \cdot 3 \cdot 4}]+[\sqrt[3]{3 \cdot 4 \cdot 5}]+\cdots+[\sqrt[3]{2000 \cdot 2001 \cdot 2002}]=$ $\qquad$ | "[\"2001000\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 439, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14475"}] | {
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} |
[
"4 \\sqrt{a^{2}+b^{2}}"
] | [
"skywork"
] | 0dddf662c795afb389b69832251fac44dcc0932306308edd553ab8dc7e1c8879 | [
{
"content": "11. (20 points) Given the ellipse $\\Gamma: \\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1$. Find the maximum perimeter of the inscribed parallelogram $A B C D$ in the ellipse.",
"role": "user"
}
] | 11. (20 points) Given the ellipse $\Gamma: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$. Find the maximum perimeter of the inscribed parallelogram $A B C D$ in the ellipse. | "[\"4 \\\\sqrt{a^{2}+b^{2}}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 433, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:14477"}] | {
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"reference_present": true
} |
[
"0.330"
] | [
"skywork"
] | e805bad9ba8ab441b010dd305549656d03de55a165edf844652f2d9fb1a18ca6 | [
{
"content": "9 seeds are divided among three pits, labeled A, B, and C, with each pit containing 3 seeds. Each seed has a 0.5 probability of germinating. If at least one seed in a pit germinates, then that pit does not need to be replanted; if no seeds in a pit germinate, then that pit needs to be replanted. ... | 9 seeds are divided among three pits, labeled A, B, and C, with each pit containing 3 seeds. Each seed has a 0.5 probability of germinating. If at least one seed in a pit germinates, then that pit does not need to be replanted; if no seeds in a pit germinate, then that pit needs to be replanted.
(Ⅰ) Calculate the pro... | "[\"0.330\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 437, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14478"}] | {
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"reference_components": 1,
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} |
[
"0.8"
] | [
"skywork"
] | 36547e53a361b199bb98f13e63d5744597441d83261a411a40e923fb0d559a55 | [
{
"content": "Which of the following is equal to $\\frac{4}{5}$ ?\n(A) 4.5\n(B) 0.8\n(C) 80.0\n(D) 0.08\n(E) 0.45",
"role": "user"
}
] | Which of the following is equal to $\frac{4}{5}$ ?
(A) 4.5
(B) 0.8
(C) 80.0
(D) 0.08
(E) 0.45 | "[\"0.8\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 461, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14479"}] | {
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"reference_components": 1,
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} |
[
"\\frac{3}{10}"
] | [
"skywork"
] | 30cd43aaf5fee1ec088e0557b249b1cc0d68522604fd0d67e939ad7a68602997 | [
{
"content": "On a given circle, six points $A$, $B$, $C$, $D$, $E$, and $F$ are chosen at random, independently and uniformly with respect to arc length. Determine the probability that the two triangles $ABC$ and $DEF$ are disjoint, i.e., have no common points.",
"role": "user"
}
] | On a given circle, six points $A$, $B$, $C$, $D$, $E$, and $F$ are chosen at random, independently and uniformly with respect to arc length. Determine the probability that the two triangles $ABC$ and $DEF$ are disjoint, i.e., have no common points. | "[\"\\\\frac{3}{10}\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 436, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14480"}, {"dataset": "skywork", "extra_i... | {
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} |
[
"2\\cdot36-5\\cdot14"
] | [
"skywork"
] | 4f551091d0bc277684fa67d25d2ec06c768cd92cb6efdea5e5402728ffeeb4d7 | [
{
"content": "732. A grasshopper jumps along a straight line to the left and right, and it can make large jumps of 36 cm and small jumps of 14 cm (to the left or to the right). Can it move 3 cm from its initial position in several jumps? 2 cm? 1234 cm?",
"role": "user"
}
] | 732. A grasshopper jumps along a straight line to the left and right, and it can make large jumps of 36 cm and small jumps of 14 cm (to the left or to the right). Can it move 3 cm from its initial position in several jumps? 2 cm? 1234 cm? | "[\"2\\\\cdot36-5\\\\cdot14\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 441, "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:14482"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"50"
] | [
"skywork"
] | e6a18c628080ea951c1d0e9e3c682624dad20e74a709b5f471799f17b40928df | [
{
"content": "1. (3 points) Calculate: $19 \\times 0.125+281 \\times \\frac{1}{8}+12.5=$",
"role": "user"
}
] | 1. (3 points) Calculate: $19 \times 0.125+281 \times \frac{1}{8}+12.5=$ | "[\"50\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 462, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:14483"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1932"
] | [
"skywork"
] | 4e9d65fd5e508660490d275150d12b985fc727727a0c0520ec5e67d36cbcc350 | [
{
"content": "Find the sum of all the positive integers which have at most three not necessarily distinct prime factors where the primes come from the set $\\{ 2, 3, 5, 7 \\}$ .",
"role": "user"
}
] | Find the sum of all the positive integers which have at most three not necessarily distinct prime factors where the primes come from the set $\{ 2, 3, 5, 7 \}$ . | "[\"1932\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 442, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14484"}, {"dataset": "skywork", "extra_inf... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2016"
] | [
"skywork"
] | fc899b449a204de1668c1502f98351a38f31e6c4f09bdd2f9e2922bf3e5ca0ed | [
{
"content": "7. (10 points) For a natural number $N$, if at least six of the nine natural numbers from $1$ to $9$ can divide $N$, then $N$ is called a \"Six-Union Number\". The smallest \"Six-Union Number\" greater than 2000 is $\\qquad$ .",
"role": "user"
}
] | 7. (10 points) For a natural number $N$, if at least six of the nine natural numbers from $1$ to $9$ can divide $N$, then $N$ is called a "Six-Union Number". The smallest "Six-Union Number" greater than 2000 is $\qquad$ . | "[\"2016\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 458, "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:14485"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"60^\\circ"
] | [
"skywork"
] | 28c85c284785e6c3386c09f99cc9a9c7028d30999b00edcf7c836fcd82815a84 | [
{
"content": "Let $ABCD$ be a convex quadrilateral with side lengths satisfying the equality:\n$$ AB \\cdot CD = AD \\cdot BC = AC \\cdot BD.$$\nDetermine the sum of the acute angles of quadrilateral $ABCD$.\n\n[i]Proposed by Zaza Meliqidze, Georgia[/i]",
"role": "user"
}
] | Let $ABCD$ be a convex quadrilateral with side lengths satisfying the equality:
$$ AB \cdot CD = AD \cdot BC = AC \cdot BD.$$
Determine the sum of the acute angles of quadrilateral $ABCD$.
[i]Proposed by Zaza Meliqidze, Georgia[/i] | "[\"60^\\\\circ\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 453, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14486"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"A"
] | [
"skywork"
] | d2c823c2d72aab566113ca43e5b2063f65d80de53f9444a88644f54d201dd185 | [
{
"content": "6. The set $M=\\{u \\mid u=12 m+8 n+4 l$, where $m, n, l \\in \\mathbf{Z}\\}$, $N=\\{u \\mid u=20 p+16 q+12 r$, where $p, q, r \\in \\mathbf{Z}\\}$ has the relationship\nA. $M=N$\nB. $M \\nsubseteq N, N \\nsubseteq M$\nC. $M \\varsubsetneqq N$\nD. $M \\supsetneqq N$",
"role": "user"
}
] | 6. The set $M=\{u \mid u=12 m+8 n+4 l$, where $m, n, l \in \mathbf{Z}\}$, $N=\{u \mid u=20 p+16 q+12 r$, where $p, q, r \in \mathbf{Z}\}$ has the relationship
A. $M=N$
B. $M \nsubseteq N, N \nsubseteq M$
C. $M \varsubsetneqq N$
D. $M \supsetneqq N$ | "[\"A\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 451, "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:14487"}] | {
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} |
[
"x_1 \\in \\left(0, \\frac{\\sqrt{3}}{2}\\right)"
] | [
"skywork"
] | cc7b88ff00fb5bb30def5c1c9e5266578e30087c26dda835fc6de164181a794d | [
{
"content": "The sequence $ (x_n)$, $ n\\in\\mathbb{N}^*$ is defined by $ |x_1|<1$, and for all $ n \\ge 1$, \\[ x_{n\\plus{}1} \\equal{}\\frac{\\minus{}x_n \\plus{}\\sqrt{3\\minus{}3x_n^2}}{2}\\] (a) Find the necessary and sufficient condition for $ x_1$ so that each $ x_n > 0$.\r\n(b) Is this sequence period... | The sequence $ (x_n)$, $ n\in\mathbb{N}^*$ is defined by $ |x_1|<1$, and for all $ n \ge 1$, \[ x_{n\plus{}1} \equal{}\frac{\minus{}x_n \plus{}\sqrt{3\minus{}3x_n^2}}{2}\] (a) Find the necessary and sufficient condition for $ x_1$ so that each $ x_n > 0$.
(b) Is this sequence periodic? And why? | "[\" x_1 \\\\in \\\\left(0, \\\\frac{\\\\sqrt{3}}{2}\\\\right) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 444, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14488"}] | {
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} |
[
"(0,2]"
] | [
"skywork"
] | a36f74925a5eeabb548a45d88d63282902499845d6d1748f7eceb7bb06d1fd42 | [
{
"content": "3. If $x \\in(-1,1)$, then\n$$\nf(x)=x^{2}-a x+\\frac{a}{2}\n$$\n\nis always positive, the range of the real number $a$ is $\\qquad$ $ـ$.",
"role": "user"
}
] | 3. If $x \in(-1,1)$, then
$$
f(x)=x^{2}-a x+\frac{a}{2}
$$
is always positive, the range of the real number $a$ is $\qquad$ $ـ$. | "[\"(0,2]\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 452, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14489"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"8362"
] | [
"skywork"
] | 04039bfda7770109ab3288e41bfddf18a4eb58fd2cf4986139d05739bf04fc04 | [
{
"content": "Four. (50 points) Let $M=\\{1,2, \\cdots, 10\\}$. For a partition of $M$ into $A_{1}, A_{2}, A_{3}$ (all $A_{i}$ are non-empty), if there exists a permutation $A_{i 1}, A_{i 2}, A_{i 3}$ of $A_{1}, A_{2}, A_{3}$ such that\n$$\n\\max A_{i k}>\\min A_{i, k+1}\\left(k=1,2,3, A_{i 4}=A_{i 1}\\right) \... | Four. (50 points) Let $M=\{1,2, \cdots, 10\}$. For a partition of $M$ into $A_{1}, A_{2}, A_{3}$ (all $A_{i}$ are non-empty), if there exists a permutation $A_{i 1}, A_{i 2}, A_{i 3}$ of $A_{1}, A_{2}, A_{3}$ such that
$$
\max A_{i k}>\min A_{i, k+1}\left(k=1,2,3, A_{i 4}=A_{i 1}\right) \text {, }
$$
then it is called ... | "[\"8362\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 449, "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:14490"}] | {
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} |
[
"\\frac{3}{4}<a<2"
] | [
"skywork"
] | 4ec5bf856a391c9dbca730b65a51ab58a2138e117f3d4c01e639cf638cfd2a14 | [
{
"content": "9. (16 points) Given the function $f(x)=\\left|x^{2}-a\\right|$, where $a$ is a positive constant. If there are exactly two pairs of solutions $(m, n)$ such that the range of $f(x)$ on the domain $[m, n]$ is also $[m, n]$, find the range of values for $a$.\n\n---\n\nThe translation maintains the o... | 9. (16 points) Given the function $f(x)=\left|x^{2}-a\right|$, where $a$ is a positive constant. If there are exactly two pairs of solutions $(m, n)$ such that the range of $f(x)$ on the domain $[m, n]$ is also $[m, n]$, find the range of values for $a$.
---
The translation maintains the original text's formatting an... | "[\"\\\\frac{3}{4}<a<2\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 443, "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:14491"}] | {
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[
"187"
] | [
"skywork"
] | a5826d5f3357ba2b266f966a6bd79647b44cb90436f5f11d6cc58b3ba56e9c3c | [
{
"content": "A standard six-sided fair die is rolled four times. The probability that the product of all four numbers rolled is a perfect square is $\\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.",
"role": "user"
}
] | A standard six-sided fair die is rolled four times. The probability that the product of all four numbers rolled is a perfect square is $\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. | "[\"187\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 467, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14492"}, {"dataset": "skywork", "extra_inf... | {
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[
"\\cos 6 > \\cos 8 > \\cos 2 > \\cos 4"
] | [
"skywork"
] | aa75f46408205435ca94f3947d60e048f52677abfb86ad054b03ee63aaf910c6 | [
{
"content": "Arrange the numbers $\\cos 2, \\cos 4, \\cos 6$ and $\\cos 8$ from the biggest to the smallest where $2,4,6,8$ are given as radians.",
"role": "user"
}
] | Arrange the numbers $\cos 2, \cos 4, \cos 6$ and $\cos 8$ from the biggest to the smallest where $2,4,6,8$ are given as radians. | "[\"\\\\cos 6 > \\\\cos 8 > \\\\cos 2 > \\\\cos 4\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 464, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14493"}] | {
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[
"14"
] | [
"skywork"
] | f711b4303df6ac5d1a972f33cf1b1aadb66fe5dc45cbbad1ef7c5d8b6b5be74d | [
{
"content": "In $\\triangle BAC$, $\\angle BAC=40^\\circ$, $AB=10$, and $AC=6$. Points $D$ and $E$ lie on $\\overline{AB}$ and $\\overline{AC}$ respectively. What is the minimum possible value of $BE+DE+CD$?",
"role": "user"
}
] | In $\triangle BAC$, $\angle BAC=40^\circ$, $AB=10$, and $AC=6$. Points $D$ and $E$ lie on $\overline{AB}$ and $\overline{AC}$ respectively. What is the minimum possible value of $BE+DE+CD$? | "[\"14\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 455, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14494"}] | {
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[
"3025"
] | [
"skywork"
] | 7c28a8a50e601c166691129e3bd78b8471b8d903cca36fcc2c4e62b02cb7a122 | [
{
"content": "Compute the number of functions $f:\\{1,2, \\ldots, 9\\} \\rightarrow\\{1,2, \\ldots, 9\\}$ which satisfy $f(f(f(f(f(x)))))=$ $x$ for each $x \\in\\{1,2, \\ldots, 9\\}$.",
"role": "user"
}
] | Compute the number of functions $f:\{1,2, \ldots, 9\} \rightarrow\{1,2, \ldots, 9\}$ which satisfy $f(f(f(f(f(x)))))=$ $x$ for each $x \in\{1,2, \ldots, 9\}$. | "[\"3025\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 463, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14495"}] | {
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[
"(x-2)(x-11),(x-3)(x-6),x(x+9),(x+4)(x+1)"
] | [
"skywork"
] | 5dbc2bc02434e28093e774d4d7c8332ac02409baf0b334c35905ebc0267b3a28 | [
{
"content": "10.3. Find all quadratic trinomials $P(x)=x^{2}+b x+c$ such that $P(x)$ has integer roots, and the sum of its coefficients (i.e., $1+b+c$) is 10.",
"role": "user"
}
] | 10.3. Find all quadratic trinomials $P(x)=x^{2}+b x+c$ such that $P(x)$ has integer roots, and the sum of its coefficients (i.e., $1+b+c$) is 10. | "[\"(x-2)(x-11),(x-3)(x-6),x(x+9),(x+4)(x+1)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 469, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14496"}] | {
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[
"\\frac{1}{7}+\\frac{1}{8}+\\frac{1}{56}"
] | [
"skywork"
] | fe1f1c0d4810e3d3a2c59cf76128069fc6a897c3894b0d578c7be0a6cb7e6459 | [
{
"content": "3. Represent the number $\\frac{2}{7}$ as the sum of several different common fractions, the numerators of which are equal to one.\n\n#",
"role": "user"
}
] | 3. Represent the number $\frac{2}{7}$ as the sum of several different common fractions, the numerators of which are equal to one.
# | "[\"\\\\frac{1}{7}+\\\\frac{1}{8}+\\\\frac{1}{56}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 471, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14497"}] | {
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[
"f(x) = x^3 + x^2 + x + 1, x^3 + 2x^2 + 2x + 2, 2x^3 + x^2 + 2x + 1, 2x^3 + 2x^2 + x + 2"
] | [
"skywork"
] | d66cb08591cc33b92745f650cc7c576df66816eecfc4f3069d774607d6901a63 | [
{
"content": "Find all $f(x)\\in \\mathbb Z (x)$ that satisfies the following condition, with the lowest degree.\n[b]Condition[/b]: There exists $g(x),h(x)\\in \\mathbb Z (x)$ such that $$f(x)^4+2f(x)+2=(x^4+2x^2+2)g(x)+3h(x)$$.",
"role": "user"
}
] | Find all $f(x)\in \mathbb Z (x)$ that satisfies the following condition, with the lowest degree.
[b]Condition[/b]: There exists $g(x),h(x)\in \mathbb Z (x)$ such that $$f(x)^4+2f(x)+2=(x^4+2x^2+2)g(x)+3h(x)$$. | "[\" f(x) = x^3 + x^2 + x + 1, x^3 + 2x^2 + 2x + 2, 2x^3 + x^2 + 2x + 1, 2x^3 + 2x^2 + x + 2 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 450, "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:14498"}] | {
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} |
[
"\\frac{1}{2}"
] | [
"skywork"
] | 04b7f336f093d9b2d8273221b45705627fbd35eab073f735263f1a3ff469787c | [
{
"content": "23 Let $x_{1}, x_{2}, \\cdots, x_{n}$ and $a_{1}, a_{2}, \\cdots, a_{n}$ be two sets of arbitrary real numbers $(n \\geqslant 2)$ that satisfy the following conditions:\n(1) $x_{1}+x_{2}+\\cdots+x_{n}=0$;\n(2) $\\left|x_{1}\\right|+\\left|x_{2}\\right|+\\cdots+\\left|x_{n}\\right|=1$;\n(3) $a_{1} ... | 23 Let $x_{1}, x_{2}, \cdots, x_{n}$ and $a_{1}, a_{2}, \cdots, a_{n}$ be two sets of arbitrary real numbers $(n \geqslant 2)$ that satisfy the following conditions:
(1) $x_{1}+x_{2}+\cdots+x_{n}=0$;
(2) $\left|x_{1}\right|+\left|x_{2}\right|+\cdots+\left|x_{n}\right|=1$;
(3) $a_{1} \geqslant a_{2} \geqslant \cdots \ge... | "[\"\\\\frac{1}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 448, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:14499"}] | {
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[
"\\text{All positive integers } n \\text{ relatively prime to } 101!"
] | [
"skywork"
] | 19d239f0ede272dbf0af141297d96ed05ce533a266ff42e1d0bbf4736fd30710 | [
{
"content": "Let $\\mathbb{Z}/n\\mathbb{Z}$ denote the set of integers considered modulo $n$ (hence $\\mathbb{Z}/n\\mathbb{Z}$ has $n$ elements). Find all positive integers $n$ for which there exists a bijective function $g: \\mathbb{Z}/n\\mathbb{Z} \\to \\mathbb{Z}/n\\mathbb{Z}$, such that the 101 functions\n... | Let $\mathbb{Z}/n\mathbb{Z}$ denote the set of integers considered modulo $n$ (hence $\mathbb{Z}/n\mathbb{Z}$ has $n$ elements). Find all positive integers $n$ for which there exists a bijective function $g: \mathbb{Z}/n\mathbb{Z} \to \mathbb{Z}/n\mathbb{Z}$, such that the 101 functions
\[g(x), \quad g(x) + x, \quad g(... | "[\"\\\\text{All positive integers } n \\\\text{ relatively prime to } 101!\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 460, "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:14500"}] | {
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[
"\\frac{7\\pi}{10}"
] | [
"skywork"
] | 8a3b6ce9467f3972c7ebf62bdfa8c99cc8d1983e420253f56b61bee9e28d846f | [
{
"content": "8. In the cube $A B C D-A_{1} B_{1} C_{1} D_{1}$, $A A_{1}=1, E, F$ are the midpoints of edges $C C_{1}, D D_{1}$, respectively. Then the area of the section formed by the plane $A E F$ cutting the circumscribed sphere of the cube is $\\qquad$ .",
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}
] | 8. In the cube $A B C D-A_{1} B_{1} C_{1} D_{1}$, $A A_{1}=1, E, F$ are the midpoints of edges $C C_{1}, D D_{1}$, respectively. Then the area of the section formed by the plane $A E F$ cutting the circumscribed sphere of the cube is $\qquad$ . | "[\"\\\\frac{7\\\\pi}{10}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 435, "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:14501"}] | {
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[
"5:1"
] | [
"skywork"
] | ac95ceffd7f29d41e7d6dd37210db45c7a1a44f11c200cccb29250426a8b5da8 | [
{
"content": "5. Let $x$ be the length of the smaller segment. On the upper side of the quadrilateral, which has a length of 1, there are 3 small segments and one large segment. Therefore, the length of the large segment is $(1-3x)$. On the lower side of the quadrilateral, which has a length of 2, there are 3 l... | 5. Let $x$ be the length of the smaller segment. On the upper side of the quadrilateral, which has a length of 1, there are 3 small segments and one large segment. Therefore, the length of the large segment is $(1-3x)$. On the lower side of the quadrilateral, which has a length of 2, there are 3 large segments and one ... | "[\"5:1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 459, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14502"}] | {
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[
"2"
] | [
"skywork"
] | 32556b4c83b21d188dca250ea3026288947e4d16ebec5db2b6b901822d56f475 | [
{
"content": "1. The sum of 5 natural numbers is 1982. What is the greatest value that their greatest common divisor can take?",
"role": "user"
}
] | 1. The sum of 5 natural numbers is 1982. What is the greatest value that their greatest common divisor can take? | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 489, "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:14503"}] | {
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} |
[
"\\frac{1}{\\sqrt{6}}"
] | [
"skywork"
] | c596e898b4e0613350481c91005d3584a293d3c5369439e3c3a45ea50c751931 | [
{
"content": "Suppose that $0^{\\circ}<A<90^{\\circ}$ and $0^{\\circ}<B<90^{\\circ}$ and\n\n$$\n\\left(4+\\tan ^{2} A\\right)\\left(5+\\tan ^{2} B\\right)=\\sqrt{320} \\tan A \\tan B\n$$\n\nDetermine all possible values of $\\cos A \\sin B$.\n\n## PART B\n\nFor each question in Part B, your solution must be wel... | Suppose that $0^{\circ}<A<90^{\circ}$ and $0^{\circ}<B<90^{\circ}$ and
$$
\left(4+\tan ^{2} A\right)\left(5+\tan ^{2} B\right)=\sqrt{320} \tan A \tan B
$$
Determine all possible values of $\cos A \sin B$.
## PART B
For each question in Part B, your solution must be well-organized and contain words of explanation or... | "[\"\\\\frac{1}{\\\\sqrt{6}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 466, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:14504"}] | {
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[
"12"
] | [
"skywork"
] | 9a3f68248ee190a945d899a73397e46dd7d61105012b4ed0e92c828eae090120 | [
{
"content": "23. (USA 4) Find all natural numbers $n$ for which $2^{5}+2^{11}+2^{n}$ is a perfect square.",
"role": "user"
}
] | 23. (USA 4) Find all natural numbers $n$ for which $2^{5}+2^{11}+2^{n}$ is a perfect square. | "[\"12\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 474, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14505"}] | {
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[
"\\frac{\\sqrt{58}}{2}"
] | [
"skywork"
] | 182bc053058b79152ca87aea767ecfcc0d02614eedc6201f91cb9132f2b55aa5 | [
{
"content": "Determine the smallest possible area of triangle $ABC$ with vertices $A = (-1,1,2)$, $B = (1,2,3)$, and $C = (t,s,1)$, where $t$ and $s$ are real numbers.",
"role": "user"
}
] | Determine the smallest possible area of triangle $ABC$ with vertices $A = (-1,1,2)$, $B = (1,2,3)$, and $C = (t,s,1)$, where $t$ and $s$ are real numbers. | "[\"\\\\frac{\\\\sqrt{58}}{2}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 472, "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:14506"}] | {
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} |
[
"40"
] | [
"skywork"
] | 60e715dca346680b344066c2bacd3eac94bdbdd2e815cbd8ebd3583221d0d036 | [
{
"content": "A monkey in Zoo becomes lucky if he eats three different fruits. What is the largest number of monkeys one can make lucky, by having $20$ oranges, $30$ bananas, $40$ peaches and $50$ tangerines? Justify your answer.\n\n(A): $30$ (B): $35$ (C): $40$ (D): $45$ (E): None of the above.",
"role": "... | A monkey in Zoo becomes lucky if he eats three different fruits. What is the largest number of monkeys one can make lucky, by having $20$ oranges, $30$ bananas, $40$ peaches and $50$ tangerines? Justify your answer.
(A): $30$ (B): $35$ (C): $40$ (D): $45$ (E): None of the above. | "[\"40\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 473, "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:14507"}] | {
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} |
[
"8"
] | [
"skywork"
] | 9de7a659e87df9287822ea4df5b977180bccd8c4ea74c6ece87bb46165a0cbbb | [
{
"content": "1. Given the function $f: \\mathbf{N} \\rightarrow \\mathbf{N}$ defined as follows:\n$$\nf(x)=\\left\\{\\begin{array}{ll}\n\\frac{x}{2}, & x \\text { is even; } \\\\\n\\frac{x+7}{2}, & x \\text { is odd. }\n\\end{array}\\right.\n$$\n\nThen the number of elements in the set $A=\\{x \\in \\mathbf{N}... | 1. Given the function $f: \mathbf{N} \rightarrow \mathbf{N}$ defined as follows:
$$
f(x)=\left\{\begin{array}{ll}
\frac{x}{2}, & x \text { is even; } \\
\frac{x+7}{2}, & x \text { is odd. }
\end{array}\right.
$$
Then the number of elements in the set $A=\{x \in \mathbf{N} \mid f(f(f(x)))=x\}$ is . $\qquad$ | "[\"8\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 481, "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:14508"}, {"dataset": "skywork", "extra_i... | {
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[
"362880"
] | [
"skywork"
] | e12a90dc65b9389356aaa4e652571874d6580d84f52b67ce00cd1a32a12bc154 | [
{
"content": "John draws a regular five pointed star in the sand, and at each of the 5 outward-pointing points and 5 inward-pointing points he places one of ten different sea shells. How many ways can he place the shells, if reflections and rotations of an arrangement are considered equivalent?",
"role": "u... | John draws a regular five pointed star in the sand, and at each of the 5 outward-pointing points and 5 inward-pointing points he places one of ten different sea shells. How many ways can he place the shells, if reflections and rotations of an arrangement are considered equivalent? | "[\"362880\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 478, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14509"}] | {
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[
"\\left(\\frac{10}{3}, 0\\right)"
] | [
"skywork"
] | d692010584aaf1db54b0b897334e703502ff7082ebde7d97ae89cd390dbbcf41 | [
{
"content": "12. As shown in Figure 4, let points $A(-\\sqrt{5}, 0)$ and $B(\\sqrt{5}, 0)$, and the incenter of $\\triangle ABC$ moves on the line $x=2$.\n(1) Find the equation of the locus of point $C$;\n(2) If two rays are drawn from point\n$M(2,0)$, intersecting the locus found in (1)\nat points\n$P$ and $Q... | 12. As shown in Figure 4, let points $A(-\sqrt{5}, 0)$ and $B(\sqrt{5}, 0)$, and the incenter of $\triangle ABC$ moves on the line $x=2$.
(1) Find the equation of the locus of point $C$;
(2) If two rays are drawn from point
$M(2,0)$, intersecting the locus found in (1)
at points
$P$ and $Q$, and $\overrightarrow{M P} \... | "[\"\\\\left(\\\\frac{10}{3}, 0\\\\right)\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 468, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14511"}] | {
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[
"4"
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"skywork"
] | 6be2943798788aaafd7812c600f6b348f4cc10d77a6d4036e4d169596871b9f4 | [
{
"content": "9. There are four teacups with their mouths facing up. Now, each time three of them are flipped, and the flipped teacups are allowed to be flipped again. After $n$ flips, all the cup mouths are facing down. Then the minimum value of the positive integer $n$ is $\\qquad$ .",
"role": "user"
}
... | 9. There are four teacups with their mouths facing up. Now, each time three of them are flipped, and the flipped teacups are allowed to be flipped again. After $n$ flips, all the cup mouths are facing down. Then the minimum value of the positive integer $n$ is $\qquad$ . | "[\"4\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 470, "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:14512"}] | {
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[
"\\frac{4}{3}-\\frac{4\\sqrt{3}\\pi}{27}"
] | [
"skywork"
] | cf5f5ace5be1d306ecb9fec756f49099f5ed818c1437b86554dbccd9625e9d2d | [
{
"content": "Sides $\\overline{AB}$ and $\\overline{AC}$ of equilateral triangle $ABC$ are tangent to a circle at points $B$ and $C$ respectively. What fraction of the area of $\\triangle ABC$ lies outside the circle?",
"role": "user"
}
] | Sides $\overline{AB}$ and $\overline{AC}$ of equilateral triangle $ABC$ are tangent to a circle at points $B$ and $C$ respectively. What fraction of the area of $\triangle ABC$ lies outside the circle? | "[\"\\\\frac{4}{3}-\\\\frac{4\\\\sqrt{3}\\\\pi}{27}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 479, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14513"}] | {
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[
"BC"
] | [
"skywork"
] | d6a36b545dac06f2b7122d1ef0fb5e492b8afcfb6932204e32031e1f5648c1c2 | [
{
"content": "An isosceles triangle $ ABC$ with $ AB \\equal{} AC$ is given on the plane. A variable circle $ (O)$ with center $ O$ on the line $ BC$ passes through $ A$ and does not touch either of the lines $ AB$ and $ AC$. Let $ M$ and $ N$ be the second points of intersection of $ (O)$ with lines $ AB$ and ... | An isosceles triangle $ ABC$ with $ AB \equal{} AC$ is given on the plane. A variable circle $ (O)$ with center $ O$ on the line $ BC$ passes through $ A$ and does not touch either of the lines $ AB$ and $ AC$. Let $ M$ and $ N$ be the second points of intersection of $ (O)$ with lines $ AB$ and $ AC$, respectively. Fi... | "[\" BC \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 465, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14514"}] | {
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[
"70"
] | [
"skywork"
] | 9714f326f0039bee9986fbc609f42cabb3aef040da8b1280651776376c802e44 | [
{
"content": "All $20$ diagonals are drawn in a regular octagon. At how many distinct points in the interior of the octagon (not on the boundary) do two or more diagonals intersect?",
"role": "user"
}
] | All $20$ diagonals are drawn in a regular octagon. At how many distinct points in the interior of the octagon (not on the boundary) do two or more diagonals intersect? | "[\"70\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 491, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14515"}] | {
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} |
[
"(2,1)"
] | [
"skywork"
] | 6b6f5765cf22735ef55caeb1f2e755b57f3ce2e94702b70682e2a811c3223b35 | [
{
"content": "Find $A$ and $B$ such that\n\\[\\frac{3x+5}{x^2-x-42}=\\frac{A}{x-7}+\\frac{B}{x+6}.\\]Write your answer in the form $(A,B)$.",
"role": "user"
}
] | Find $A$ and $B$ such that
\[\frac{3x+5}{x^2-x-42}=\frac{A}{x-7}+\frac{B}{x+6}.\]Write your answer in the form $(A,B)$. | "[\"(2,1)\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 483, "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:14516"}] | {
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[
"f(x)=mx \\text{ or } -(m+1)x"
] | [
"skywork"
] | 57c98bc889f9107d15d9e4c39b5c318c88f73b26810e7ac48497b1b653dc3527 | [
{
"content": "Given an integer $n$, find all functions $f: \\mathbf{Z} \\rightarrow \\mathbf{Z}$, such that for any integers $x, y$ we have\n$$\nf(x+y+f(y))=f(x)+n y \\text{. }\n$$\n(2012, China National Training Team Test)\nThe original solution used Cauchy's equation. This article introduces a solution using ... | Given an integer $n$, find all functions $f: \mathbf{Z} \rightarrow \mathbf{Z}$, such that for any integers $x, y$ we have
$$
f(x+y+f(y))=f(x)+n y \text{. }
$$
(2012, China National Training Team Test)
The original solution used Cauchy's equation. This article introduces a solution using pure algebraic manipulation.
T... | "[\"f(x)=mx \\\\text{ or } -(m+1)x\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 493, "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:14517"}] | {
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[
"40"
] | [
"skywork"
] | 6fbadc1bd9fe730c11e122d7ef6f812c7adcac04ba36a2ef3dd99cafa39a5905 | [
{
"content": "I2.4 In the figure, $A B$ is a diameter of the circle. $A P Q$ and $R B Q$ are straight lines.\nIf $\\angle P A B=35^{\\circ}, \\angle P Q B=y^{\\circ}$ and $\\angle R P B=p^{\\circ}$, find $p$.",
"role": "user"
}
] | I2.4 In the figure, $A B$ is a diameter of the circle. $A P Q$ and $R B Q$ are straight lines.
If $\angle P A B=35^{\circ}, \angle P Q B=y^{\circ}$ and $\angle R P B=p^{\circ}$, find $p$. | "[\"40\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 485, "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:14518"}] | {
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[
"1.0452"
] | [
"skywork"
] | 60eeaf3abf1d9d81343013d32c4b1140475c30fe1851315ade899ea5cfbb879b | [
{
"content": "7. Given that the line $y=x$ intersects the cosine curve $y=\\cos x$ at point $A$. Then the distance from the origin $O$ to point $A$, $|O A|=$ (accurate to $10^{-4}$ ).",
"role": "user"
}
] | 7. Given that the line $y=x$ intersects the cosine curve $y=\cos x$ at point $A$. Then the distance from the origin $O$ to point $A$, $|O A|=$ (accurate to $10^{-4}$ ). | "[\"1.0452\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 482, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14519"}] | {
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[
"50"
] | [
"skywork"
] | 86e83c2bcb6a8ef382bc1ee087916a6cf5f5d4b6e0477b7fdd911e737c324754 | [
{
"content": "Example 6 Given that $O$ is the circumcenter of $\\triangle ABC$, and $X, Y$ are points on $AC, AB$ respectively, such that $BX$ and $CY$ intersect at $O$, and $\\angle BAC = \\angle AYX = \\angle XYC$. Find the size of $\\angle BAC$.\n\n---\n\nThe translation maintains the original text's formatt... | Example 6 Given that $O$ is the circumcenter of $\triangle ABC$, and $X, Y$ are points on $AC, AB$ respectively, such that $BX$ and $CY$ intersect at $O$, and $\angle BAC = \angle AYX = \angle XYC$. Find the size of $\angle BAC$.
---
The translation maintains the original text's formatting and line breaks. | "[\"50\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 476, "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:14520"}] | {
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[
"45"
] | [
"skywork"
] | 3005c1f72dad667f0ae7396eca3cefe8f1565fca375f39820784f9170a1f8b17 | [
{
"content": "Given a 3x3 matrix where each row and each column forms an arithmetic sequence, and the middle element $a_{22} = 5$, find the sum of all nine elements.",
"role": "user"
}
] | Given a 3x3 matrix where each row and each column forms an arithmetic sequence, and the middle element $a_{22} = 5$, find the sum of all nine elements. | "[\"45\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 494, "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:14521"}] | {
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} |
[
"\\frac{3}{10}"
] | [
"skywork"
] | 367a08727f5fda189c87e8eec7a87de4c9b372f91f5163eddddf21533c3fcd58 | [
{
"content": "In a bag, there are 2 black balls labeled $1$ and $2$, and 3 white balls labeled $3$, $4$, and $5$. These 5 balls are identical except for their labels and colors. \n$(1)$ If two balls are randomly drawn from the bag with replacement, one at a time, what is the probability of drawing a black ball... | In a bag, there are 2 black balls labeled $1$ and $2$, and 3 white balls labeled $3$, $4$, and $5$. These 5 balls are identical except for their labels and colors.
$(1)$ If two balls are randomly drawn from the bag with replacement, one at a time, what is the probability of drawing a black ball first and then a white... | "[\"\\\\frac{3}{10}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 484, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14522"}] | {
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[
"\\frac{1}{3}"
] | [
"skywork"
] | 6d679694fac35417f33f96e8931d60c83b25046639a0d1229126d481d0f3957f | [
{
"content": "The digits 2, 2, 3, and 5 are randomly arranged to form a four digit number. What is the probability that the sum of the first and last digits is even?\n(A) $\\frac{1}{4}$\n(B) $\\frac{1}{3}$\n(C) $\\frac{1}{6}$\n(D) $\\frac{1}{2}$\n(E) $\\frac{2}{3}$",
"role": "user"
}
] | The digits 2, 2, 3, and 5 are randomly arranged to form a four digit number. What is the probability that the sum of the first and last digits is even?
(A) $\frac{1}{4}$
(B) $\frac{1}{3}$
(C) $\frac{1}{6}$
(D) $\frac{1}{2}$
(E) $\frac{2}{3}$ | "[\"\\\\frac{1}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 500, "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:14523"}] | {
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"reference_components": 1,
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} |
[
"\\frac{1}{10}"
] | [
"skywork"
] | dc2347a17a416eacb22d41ebd6fda04f4bf3bf1db1b827433c49d910a7a103b8 | [
{
"content": "3. Arrange $1,2,3,4,5,6$ randomly in a row, denoted as $a, b, c, d, e, f$, then the probability that $a b c+\\operatorname{def}$ is an odd number is $\\qquad$.",
"role": "user"
}
] | 3. Arrange $1,2,3,4,5,6$ randomly in a row, denoted as $a, b, c, d, e, f$, then the probability that $a b c+\operatorname{def}$ is an odd number is $\qquad$. | "[\"\\\\frac{1}{10}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 475, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14524"}] | {
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[
"55n + \\binom{n+1}{3}"
] | [
"skywork"
] | b30b3076e6003e0f038353d7e9220cd8374ace7d1056d18e021fd960ab6dfc4a | [
{
"content": "Archipelago consists of $ n$ islands : $ I_1,I_2,...,I_n$ and $ a_1,a_2,...,a_n$ - number of the roads on each island. $ a_1 \\equal{} 55$, $ a_k \\equal{} a_{k \\minus{} 1} \\plus{} (k \\minus{} 1)$, ($ k \\equal{} 2,3,...,n$)\r\na) Does there exist an island with 2008 roads?\r\nb) Calculate $ a... | Archipelago consists of $ n$ islands : $ I_1,I_2,...,I_n$ and $ a_1,a_2,...,a_n$ - number of the roads on each island. $ a_1 \equal{} 55$, $ a_k \equal{} a_{k \minus{} 1} \plus{} (k \minus{} 1)$, ($ k \equal{} 2,3,...,n$)
a) Does there exist an island with 2008 roads?
b) Calculate $ a_1 \plus{} a_2 \plus{} ... \plus... | "[\" 55n + \\\\binom{n+1}{3} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 456, "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:14525"}] | {
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} |
[
"669^3"
] | [
"skywork"
] | 8b8ca45575c2685733352f793f7981665aa22b30f85a4173ccee82fa727d04a4 | [
{
"content": "(given to Juliette Fournier). What is the maximum number of subsequences of the form $n, n+1, n+2$ that a sequence of 2007 natural numbers can have? For example, the sequence $1,2,2,3,3$ has 4 subsequences of this nature.",
"role": "user"
}
] | (given to Juliette Fournier). What is the maximum number of subsequences of the form $n, n+1, n+2$ that a sequence of 2007 natural numbers can have? For example, the sequence $1,2,2,3,3$ has 4 subsequences of this nature. | "[\"669^3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 497, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:14526"}] | {
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[
"9"
] | [
"skywork"
] | 61b6044528147033ec503009036cca0b88272efec57d05ee13959ebaf64099a1 | [
{
"content": "2. A square sheet of checkered paper $8 \\times 8$ was folded several times along the grid lines so that a $1 \\times 1$ square was obtained. It was then cut along a segment connecting the midpoints of two opposite sides of the square. Into how many pieces could the square have split as a result?"... | 2. A square sheet of checkered paper $8 \times 8$ was folded several times along the grid lines so that a $1 \times 1$ square was obtained. It was then cut along a segment connecting the midpoints of two opposite sides of the square. Into how many pieces could the square have split as a result? | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 498, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14527"}] | {
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[
"1337"
] | [
"skywork"
] | 165c29bc9089d1e13c78b5c05f87870c38a7be42f4e27ee0c06e536b0aa262e6 | [
{
"content": "The number 8 is the sum and product of the numbers in the collection of four positive integers $\\{1,1,2,4\\}$, since $1+1+2+4=8$ and $1 \\times 1 \\times 2 \\times 4=8$. The number 2007 can be made up from a collection of $n$ positive integers that multiply to 2007 and add to 2007 . What is the s... | The number 8 is the sum and product of the numbers in the collection of four positive integers $\{1,1,2,4\}$, since $1+1+2+4=8$ and $1 \times 1 \times 2 \times 4=8$. The number 2007 can be made up from a collection of $n$ positive integers that multiply to 2007 and add to 2007 . What is the smallest value of $n$ with $... | "[\"1337\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 480, "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:14528"}] | {
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[
"15"
] | [
"skywork"
] | 8af0b6ae0dd52dc08580f838f3e826c784a178e61bdbe823ac7902497df56431 | [
{
"content": "Triangle $ABC$ has $AB=27$, $AC=26$, and $BC=25$. Let $I$ be the intersection of the internal angle bisectors of $\\triangle ABC$. What is $BI$?",
"role": "user"
}
] | Triangle $ABC$ has $AB=27$, $AC=26$, and $BC=25$. Let $I$ be the intersection of the internal angle bisectors of $\triangle ABC$. What is $BI$? | "[\"15\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 515, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:14529"}] | {
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[
"16"
] | [
"skywork"
] | dff0a9f12e786efd8b6b79ef433374b3ebca70d52c50efe29183ab4bcbed1313 | [
{
"content": "$24.3 .7 \\star$ Place the numbers $1, 2, 3, 4, 5, 6, 7, 8$ at the eight vertices of a cube, such that the sum of any three numbers on each face is not less than 10. Find the minimum value of the sum of the four numbers on each face.",
"role": "user"
}
] | $24.3 .7 \star$ Place the numbers $1, 2, 3, 4, 5, 6, 7, 8$ at the eight vertices of a cube, such that the sum of any three numbers on each face is not less than 10. Find the minimum value of the sum of the four numbers on each face. | "[\"16\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 487, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14530"}] | {
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[
"4"
] | [
"skywork"
] | 7472a267cb2d9364356760512e5e0b2515030348e7c20001f8e66e3ba2facc68 | [
{
"content": "4. Let $P$ be any point on the ellipse $\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1(a>b>0)$, with foci at $F_{1}(-c, 0), F_{2}(c, 0)$. $P F_{1}$ and $P F_{2}$ intersect the ellipse at points $A$ and $B$, respectively. If $a^{2}$, $b^{2}$, and $c^{2}$ form an arithmetic sequence, then $\\frac{\\lef... | 4. Let $P$ be any point on the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)$, with foci at $F_{1}(-c, 0), F_{2}(c, 0)$. $P F_{1}$ and $P F_{2}$ intersect the ellipse at points $A$ and $B$, respectively. If $a^{2}$, $b^{2}$, and $c^{2}$ form an arithmetic sequence, then $\frac{\left|P F_{1}\right|}{\left|A ... | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 490, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:14531"}] | {
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[
"3\\pi"
] | [
"skywork"
] | 7ed9b24a5fa3c37f6b99c1af8d0eca7527db48dca0a2f595c8967bf293dca3fa | [
{
"content": "A tetrahedron with each edge length equal to $\\sqrt{2}$ has all its vertices on the same sphere. Calculate the surface area of this sphere.",
"role": "user"
}
] | A tetrahedron with each edge length equal to $\sqrt{2}$ has all its vertices on the same sphere. Calculate the surface area of this sphere. | "[\"3\\\\pi\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 499, "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:14532"}] | {
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[
"26"
] | [
"skywork"
] | f59f051169b78cf60c4eec9f79d572257aa140ab1107099822f50c1b09fe84be | [
{
"content": "24) I have at my disposal five digits equal to 1 and one digit equal to 2. Using all or some of these digits, how many different numbers can I construct?\n(A) 15\n(B) 21\n(C) 24\n(D) 26\n(E) 27.",
"role": "user"
}
] | 24) I have at my disposal five digits equal to 1 and one digit equal to 2. Using all or some of these digits, how many different numbers can I construct?
(A) 15
(B) 21
(C) 24
(D) 26
(E) 27. | "[\"26\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 519, "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:14533"}] | {
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[
"9744=100^{2}-16^{2}"
] | [
"skywork"
] | d007280819261758b01b9ef87ec3875beb67c2a7af474e06a80291b8a64003ae | [
{
"content": "10.4. In each cell of a $100 \\times 100$ square, a certain natural number is written. A rectangle, whose sides lie along the grid lines, is called good if the sum of the numbers in all its cells is divisible by 17. It is allowed to simultaneously color all the cells in some good rectangle. It is ... | 10.4. In each cell of a $100 \times 100$ square, a certain natural number is written. A rectangle, whose sides lie along the grid lines, is called good if the sum of the numbers in all its cells is divisible by 17. It is allowed to simultaneously color all the cells in some good rectangle. It is forbidden to color a ce... | "[\"9744=100^{2}-16^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 501, "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:14534"}] | {
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[
"2"
] | [
"skywork"
] | 74dba853c4162fdbe8188a6f24d1d65c2fc91061c7667cef4a8833cfd506bc48 | [
{
"content": "G3.1 Find the smallest prime factor of $101^{303}+301^{101}$.",
"role": "user"
}
] | G3.1 Find the smallest prime factor of $101^{303}+301^{101}$. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 526, "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:14535"}] | {
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[
"5"
] | [
"skywork"
] | 6d272b8f75e364b0ff8bc66f2bc0f189510f015ba1c9f5993dd72124cb5e1fb6 | [
{
"content": "Shapovalov A.V.\n\nThe plan of the palace of the Shah is a $6 \\times 6$ square, divided into rooms of size $1 \\times 1$. In the middle of each wall between the rooms, there is a door. The Shah said to his architect: \"Knock down some of the walls so that all rooms become $2 \\times 1$, no new do... | Shapovalov A.V.
The plan of the palace of the Shah is a $6 \times 6$ square, divided into rooms of size $1 \times 1$. In the middle of each wall between the rooms, there is a door. The Shah said to his architect: "Knock down some of the walls so that all rooms become $2 \times 1$, no new doors appear, and the path bet... | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 502, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14536"}] | {
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[
"\\frac{28}{5}\\sqrt{69}"
] | [
"skywork"
] | 6d12d33b628258903de1b44a1306400f766c5f196f90f3a728c22c21ea9dfdd5 | [
{
"content": "In cyclic quadrilateral $ABCD$ with $AB = AD = 49$ and $AC = 73$, let $I$ and $J$ denote the incenters of triangles $ABD$ and $CBD$. If diagonal $\\overline{BD}$ bisects $\\overline{IJ}$, find the length of $IJ$.",
"role": "user"
}
] | In cyclic quadrilateral $ABCD$ with $AB = AD = 49$ and $AC = 73$, let $I$ and $J$ denote the incenters of triangles $ABD$ and $CBD$. If diagonal $\overline{BD}$ bisects $\overline{IJ}$, find the length of $IJ$. | "[\"\\\\frac{28}{5}\\\\sqrt{69}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 510, "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:14537"}] | {
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[
"103"
] | [
"skywork"
] | d13303b4b45eb9c62145447d75a2aaf9c7a2f3397638e1196f74d34fa9c54cea | [
{
"content": "In a sequence of positive integers starting from 1, some numbers are colored red according to the following rules: first color 1 red, then color the next 2 even numbers 2 and 4 red; next, color the 4 closest consecutive odd numbers after 4, which are 5, 7, 9, red; then color the 4 closest consecut... | In a sequence of positive integers starting from 1, some numbers are colored red according to the following rules: first color 1 red, then color the next 2 even numbers 2 and 4 red; next, color the 4 closest consecutive odd numbers after 4, which are 5, 7, 9, red; then color the 4 closest consecutive even numbers after... | "[\"103\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 488, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14538"}] | {
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[
"1"
] | [
"skywork"
] | ae2932a612222ea17e04c4828f6952b5f95e9c82a5d71ef482dbb55e2ae93793 | [
{
"content": "Marcus has two numbers, $a$ and $b$. When he divides $a$ by 45 he gets a remainder of 37. When he divides $b$ by 30 he gets a remainder of $9$. What remainder does he get when he divides $a+b$ by 15?",
"role": "user"
}
] | Marcus has two numbers, $a$ and $b$. When he divides $a$ by 45 he gets a remainder of 37. When he divides $b$ by 30 he gets a remainder of $9$. What remainder does he get when he divides $a+b$ by 15? | "[\"1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 507, "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:14539"}] | {
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} |
[
"50"
] | [
"skywork"
] | 84358d0bd65ba7f10819e31d2d7586c92789da75ea086145b9fd5339e5052724 | [
{
"content": "An ellipse has foci at $(5, 10)$ and $(35, 40)$ in the $xy$-plane and is tangent to the $y$-axis. What is the length of its major axis?",
"role": "user"
}
] | An ellipse has foci at $(5, 10)$ and $(35, 40)$ in the $xy$-plane and is tangent to the $y$-axis. What is the length of its major axis? | "[\"50\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 525, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:14540"}] | {
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[
"\\$675"
] | [
"skywork"
] | 88c04d9adddd89c3d5d8cda04b6373867f04ee31db60198900a63929cf41396e | [
{
"content": "A two-inch cube ($2\\times2\\times2$) of silver weighs 3 pounds and is worth $\\$200$. How much is a three-inch cube of silver worth? Round your answer to the nearest dollar.",
"role": "user"
}
] | A two-inch cube ($2\times2\times2$) of silver weighs 3 pounds and is worth $\$200$. How much is a three-inch cube of silver worth? Round your answer to the nearest dollar. | "[\"\\\\$675\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 508, "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:14541"}] | {
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} |
[
"4x-3y-1=0"
] | [
"skywork"
] | 69f2a9c422de281afab075c8ed95f61415395e4176809e5a44afae8398ea12bf | [
{
"content": "Example 2. Form the equation of the line passing through the intersection point of the lines $x+y-2=0$ and $3x+2y-5=0$ and perpendicular to the line $3x+4y-12=0$.",
"role": "user"
}
] | Example 2. Form the equation of the line passing through the intersection point of the lines $x+y-2=0$ and $3x+2y-5=0$ and perpendicular to the line $3x+4y-12=0$. | "[\"4x-3y-1=0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 521, "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:14542"}] | {
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} |
[
"\\frac{4}{3}"
] | [
"skywork"
] | 63dff04e14a44a43109aa6a38f272db42bae427157ad5e46936ec6c59ac6a79f | [
{
"content": "7. A cone and a cylinder, with their bottom faces on the same plane, have a common inscribed sphere. Let the volume of the cone be $V_{1}$, and the volume of the cylinder be $V_{2}$, and $V_{1}=k V_{2}$, then $k_{\\text {min }}=$ $\\qquad$",
"role": "user"
}
] | 7. A cone and a cylinder, with their bottom faces on the same plane, have a common inscribed sphere. Let the volume of the cone be $V_{1}$, and the volume of the cylinder be $V_{2}$, and $V_{1}=k V_{2}$, then $k_{\text {min }}=$ $\qquad$ | "[\"\\\\frac{4}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 496, "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:14543"}] | {
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[
"768"
] | [
"skywork"
] | b2163a357f0831fce43427edb14212907cfd6e91debd10595089dbddb06acce5 | [
{
"content": "20. Carl wrote a list of 10 distinct positive integers on a board. Each integer in the list, apart from the first, is a multiple of the previous integer. The last of the 10 integers is between 600 and 1000 . What is this last integer?\nA 640\nB 729\nС 768\nD 840\nE 990",
"role": "user"
}
] | 20. Carl wrote a list of 10 distinct positive integers on a board. Each integer in the list, apart from the first, is a multiple of the previous integer. The last of the 10 integers is between 600 and 1000 . What is this last integer?
A 640
B 729
С 768
D 840
E 990 | "[\"768\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 512, "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:14546"}] | {
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[
"387"
] | [
"skywork"
] | a6d840846df3ed7f7d2411d4f03104c71d768d96935bf0d26b4b3d0498fd805c | [
{
"content": "Find the remainder when $3^{3^{3^3}}$ is divided by 1000.",
"role": "user"
}
] | Find the remainder when $3^{3^{3^3}}$ is divided by 1000. | "[\"387\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 529, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:14547"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 51d2c17e8b68034ebb25a28fa3e97eb6d8f6c6ccfe06d000ccc9ff8d1f79ea39 | [
{
"content": "6. Let the sum of the digits of a positive integer $a$ be $b$, the sum of the digits of $b$ be $c$, and so on. Eventually, a single-digit number will be obtained, denoted as $f(a)$ (for example: $a=1996, b=1+9+9+6=25, c=2+5=7$, thus $f(a)=7$). Now, let $x>3$ and both $x$ and $x+2$ be prime numbers... | 6. Let the sum of the digits of a positive integer $a$ be $b$, the sum of the digits of $b$ be $c$, and so on. Eventually, a single-digit number will be obtained, denoted as $f(a)$ (for example: $a=1996, b=1+9+9+6=25, c=2+5=7$, thus $f(a)=7$). Now, let $x>3$ and both $x$ and $x+2$ be prime numbers, $A=1996 x(x+2)$, the... | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 503, "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:14548"}] | {
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} |
[
"11111111"
] | [
"skywork"
] | bfbb38fc021f1cc12e8ef9c4e0441e74faf23ea46ab70f9edb5ecda407de83a2 | [
{
"content": "Let \\( c_{n}=11 \\ldots 1 \\) be a number in which the decimal representation contains \\( n \\) ones. Then \\( c_{n+1}=10 \\cdot c_{n}+1 \\). Therefore:\n\n\\[ c_{n+1}^{2}=100 \\cdot c_{n}^{2} + 22 \\ldots 2 \\cdot 10 + 1 \\]\n\nFor example,\n\n\\( c_{2}^{2}=11^{2}=(10 \\cdot 1+1)^{2}=100+2 \\cd... | Let \( c_{n}=11 \ldots 1 \) be a number in which the decimal representation contains \( n \) ones. Then \( c_{n+1}=10 \cdot c_{n}+1 \). Therefore:
\[ c_{n+1}^{2}=100 \cdot c_{n}^{2} + 22 \ldots 2 \cdot 10 + 1 \]
For example,
\( c_{2}^{2}=11^{2}=(10 \cdot 1+1)^{2}=100+2 \cdot 10+1=121 \),
\( c_{3}^{2} = 111^{2} = 10... | "[\"11111111\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 486, "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:14550"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{-605}{119}"
] | [
"skywork"
] | 9208cfae8a5a8b32585680fe880c826b620916e16f3b0ec2044fc03bf4c50292 | [
{
"content": "Suppose \n\\[\n3 + \\frac{1}{1 + \\frac{1}{3 + \\frac{3}{4+y}}} = \\frac{169}{53}.\n\\]\nSolve for the value of $y$.",
"role": "user"
}
] | Suppose
\[
3 + \frac{1}{1 + \frac{1}{3 + \frac{3}{4+y}}} = \frac{169}{53}.
\]
Solve for the value of $y$. | "[\"\\\\frac{-605}{119}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 530, "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:14551"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3750"
] | [
"skywork"
] | f318cefa7b4bc733e60f1824d7532c2976dab55b59036425b4bb1e12a174dd59 | [
{
"content": "For a pair $ A \\equal{} (x_1, y_1)$ and $ B \\equal{} (x_2, y_2)$ of points on the coordinate plane, let $ d(A,B) \\equal{} |x_1 \\minus{} x_2| \\plus{} |y_1 \\minus{} y_2|$. We call a pair $ (A,B)$ of (unordered) points [i]harmonic[/i] if $ 1 < d(A,B) \\leq 2$. Determine the maximum number of ha... | For a pair $ A \equal{} (x_1, y_1)$ and $ B \equal{} (x_2, y_2)$ of points on the coordinate plane, let $ d(A,B) \equal{} |x_1 \minus{} x_2| \plus{} |y_1 \minus{} y_2|$. We call a pair $ (A,B)$ of (unordered) points [i]harmonic[/i] if $ 1 < d(A,B) \leq 2$. Determine the maximum number of harmonic pairs among 100 points... | "[\"3750\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 513, "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:14552"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | 54a44ba749bf8bd0a3e8753e64f26ae775028803b24bab4b10b81a5e47707dc0 | [
{
"content": "Example 12. Calculate the circulation of the vector field given in cylindrical coordinates: $2=\\rho \\sin \\varphi \\mathrm{e}_{\\rho}+\\rho z \\mathrm{e}_{\\varphi}+\\rho^{3} \\mathrm{e}_{z}$, along the curve L: $\\{\\rho=\\sin \\varphi, z=0,0 \\leqslant \\varphi \\leqslant \\pi\\}$ directly and... | Example 12. Calculate the circulation of the vector field given in cylindrical coordinates: $2=\rho \sin \varphi \mathrm{e}_{\rho}+\rho z \mathrm{e}_{\varphi}+\rho^{3} \mathrm{e}_{z}$, along the curve L: $\{\rho=\sin \varphi, z=0,0 \leqslant \varphi \leqslant \pi\}$ directly and using Stokes' theorem. | "[\"0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 511, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:14553"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{1993}"
] | [
"skywork"
] | 12aa026a0527dadc7a7685f8effb0283e7f2b9cae145e580110f1cba97fc6d69 | [
{
"content": "[ Induction (other). ] [ Pascal's Triangle and the Binomial Theorem ]\n\n$$\n\\begin{array}{lccccc}\n1 & \\frac{1}{2} & \\frac{1}{3} & \\frac{1}{4} & \\ldots & \\frac{1}{1993} \\\\\n\\frac{1}{2} & \\frac{1}{6} & \\frac{1}{12} & \\cdots & \\frac{1}{1992 \\cdot 1993} \\\\\n\\frac{1}{3} & \\frac{1}{1... | [ Induction (other). ] [ Pascal's Triangle and the Binomial Theorem ]
$$
\begin{array}{lccccc}
1 & \frac{1}{2} & \frac{1}{3} & \frac{1}{4} & \ldots & \frac{1}{1993} \\
\frac{1}{2} & \frac{1}{6} & \frac{1}{12} & \cdots & \frac{1}{1992 \cdot 1993} \\
\frac{1}{3} & \frac{1}{12} & \ldots &
\end{array}
$$
(The first row i... | "[\"\\\\frac{1}{1993}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 509, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:14554"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"43"
] | [
"skywork"
] | 029de4098d966141081fd59eac95fcee1b0895ddbb531286196ad49fc79d94c2 | [
{
"content": "2. In Donald Duck's Happy Swimming Pool, the number of boys is 1 more than 6 times the number of girls, and 6 less than 7 times the number of girls. The number of boys in the swimming pool is $\\qquad$ people.",
"role": "user"
}
] | 2. In Donald Duck's Happy Swimming Pool, the number of boys is 1 more than 6 times the number of girls, and 6 less than 7 times the number of girls. The number of boys in the swimming pool is $\qquad$ people. | "[\"43\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 514, "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:14555"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"23514"
] | [
"skywork"
] | f4fe2569cede972a1bb9c4921ab7ac22f00d4de6506cdaca40717f15a79d7bfb | [
{
"content": "9. (12 points) Five students, Jia, Yi, Bing, Ding, and Wu, ranked in the top 5 (no ties) in a math competition and stood in a row for a photo. They each said the following:\n\nJia said: The two students next to me have ranks that are both behind mine;\nYi said: The two students next to me have ran... | 9. (12 points) Five students, Jia, Yi, Bing, Ding, and Wu, ranked in the top 5 (no ties) in a math competition and stood in a row for a photo. They each said the following:
Jia said: The two students next to me have ranks that are both behind mine;
Yi said: The two students next to me have ranks that are adjacent to m... | "[\"23514\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 518, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14556"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"11"
] | [
"skywork"
] | 6aad42e3116ddd7ad720f56f3e7a9f328ec815a138f3a822b45838467586817d | [
{
"content": "Alice needs to paint 10 cylindrical columns, including the top faces but not the bottom faces. Each column has a height of 14 feet and a diameter of 8 feet. One gallon of paint covers 400 square feet. How many gallons of paint does Alice need to buy if paint is sold only in full gallons?",
"ro... | Alice needs to paint 10 cylindrical columns, including the top faces but not the bottom faces. Each column has a height of 14 feet and a diameter of 8 feet. One gallon of paint covers 400 square feet. How many gallons of paint does Alice need to buy if paint is sold only in full gallons? | "[\"11\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 531, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:14557"}] | {
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"reference_present": true
} |
[
"$(-1030, -990)$"
] | [
"skywork"
] | be5466a951431df9caa36ae33673cd078078fc0a914587d021c0815e1ecafe89 | [
{
"content": "Andy the Ant lives on a coordinate plane and is currently at $(-20, 20)$ facing east (that is, in the positive $x$-direction). Andy moves $1$ unit and then turns $90^{\\circ}$ left. From there, Andy moves $2$ units (north) and then turns $90^{\\circ}$ left. He then moves $3$ units (west) and again... | Andy the Ant lives on a coordinate plane and is currently at $(-20, 20)$ facing east (that is, in the positive $x$-direction). Andy moves $1$ unit and then turns $90^{\circ}$ left. From there, Andy moves $2$ units (north) and then turns $90^{\circ}$ left. He then moves $3$ units (west) and again turns $90^{\circ}$ left... | "[\"$(-1030, -990)$\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 523, "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:14558"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"22"
] | [
"skywork"
] | a9846962e8db6b979903fe146b904cab4d463ea7a7b8bf293d9948941e41da59 | [
{
"content": "$3, 7$ different positive integers arranged in ascending order form an arithmetic sequence. It is known that the average of the first three numbers is 20, and the average of the last three numbers is 24. Then, the average of the middle three numbers is $\\qquad$ -",
"role": "user"
}
] | $3, 7$ different positive integers arranged in ascending order form an arithmetic sequence. It is known that the average of the first three numbers is 20, and the average of the last three numbers is 24. Then, the average of the middle three numbers is $\qquad$ - | "[\"22\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 504, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14559"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{31\\pi}{60}"
] | [
"skywork"
] | 3fdf431e9053c121a64f71ddee7b0a5f2627232eb8abb1d069b2182bd84c1c68 | [
{
"content": "Calculate the value of the following expression and find angle $\\theta$ if the number can be expressed as $r e^{i \\theta}$, where $0 \\le \\theta < 2\\pi$:\n\\[ e^{11\\pi i/60} + e^{21\\pi i/60} + e^{31 \\pi i/60} + e^{41\\pi i /60} + e^{51 \\pi i /60} \\]",
"role": "user"
}
] | Calculate the value of the following expression and find angle $\theta$ if the number can be expressed as $r e^{i \theta}$, where $0 \le \theta < 2\pi$:
\[ e^{11\pi i/60} + e^{21\pi i/60} + e^{31 \pi i/60} + e^{41\pi i /60} + e^{51 \pi i /60} \] | "[\"\\\\frac{31\\\\pi}{60}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 524, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14560"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{131}{10}"
] | [
"skywork"
] | e69d34767f9801bcef7a248380ef441314847879b5dd018f9d305a724e74511d | [
{
"content": "25. [15] Fran writes the numbers $1,2,3, \\ldots, 20$ on a chalkboard. Then she erases all the numbers by making a series of moves; in each move, she chooses a number $n$ uniformly at random from the set of all numbers still on the chalkboard, and then erases all of the divisors of $n$ that are st... | 25. [15] Fran writes the numbers $1,2,3, \ldots, 20$ on a chalkboard. Then she erases all the numbers by making a series of moves; in each move, she chooses a number $n$ uniformly at random from the set of all numbers still on the chalkboard, and then erases all of the divisors of $n$ that are still on the chalkboard (... | "[\"\\\\frac{131}{10}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 522, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14561"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"810"
] | [
"skywork"
] | 19fa1951366aa6ca1eb4704e281354807bb1e8957ca801d5660f8ccd33001889 | [
{
"content": "On square $ABCD$ , point $E$ lies on side $AD$ and point $F$ lies on side $BC$ , so that $BE=EF=FD=30$ . Find the area of the square $ABCD$ .",
"role": "user"
}
] | On square $ABCD$ , point $E$ lies on side $AD$ and point $F$ lies on side $BC$ , so that $BE=EF=FD=30$ . Find the area of the square $ABCD$ . | "[\"810\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 539, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14562"}, {"dataset": "skywork", "extra_info... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{2}"
] | [
"skywork"
] | d70ec63bcc505cb743d4f59cf3e242f556165bca7dcfbe5053c8b75a8e0406a9 | [
{
"content": "Given the function f(x) = 2sin(x - π/6)sin(x + π/3), x ∈ R.\n(1) Find the smallest positive period of the function f(x) and the center of symmetry of its graph.\n(2) In △ABC, if A = π/4, and acute angle C satisfies f(C/2 + π/6) = 1/2, find the value of BC/AB.",
"role": "user"
}
] | Given the function f(x) = 2sin(x - π/6)sin(x + π/3), x ∈ R.
(1) Find the smallest positive period of the function f(x) and the center of symmetry of its graph.
(2) In △ABC, if A = π/4, and acute angle C satisfies f(C/2 + π/6) = 1/2, find the value of BC/AB. | "[\"\\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 517, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14563"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"48"
] | [
"skywork"
] | 111d11e80eb6705582d68e572fcceb4ea82471fabc34c64a3f55b5bdf0ed6d94 | [
{
"content": "Points $P$, $Q$, $R$, and $S$ lie in the plane of the square $EFGH$ so that $EPF$, $FQG$, $GRH$, and $HSE$ are equilateral triangles inside square $EFGH$. If the side length of square $EFGH$ is 8, find the area of quadrilateral $PQRS$. Assume that the vertices $P$, $Q$, $R$, and $S$ lie on the sid... | Points $P$, $Q$, $R$, and $S$ lie in the plane of the square $EFGH$ so that $EPF$, $FQG$, $GRH$, and $HSE$ are equilateral triangles inside square $EFGH$. If the side length of square $EFGH$ is 8, find the area of quadrilateral $PQRS$. Assume that the vertices $P$, $Q$, $R$, and $S$ lie on the sides of square $EFGH$, r... | "[\"48\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 528, "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:14564"}] | {
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} |
[
"128"
] | [
"skywork"
] | 4f71c519764976b53e4c44d44fb1f4126078c8ac1ebbf525727828e8d6024bd3 | [
{
"content": "Given a rational number, write it as a fraction in lowest terms and calculate the product of the resulting numerator and denominator. For how many rational numbers between 0 and 1 will $20_{}^{}!$ be the resulting product?",
"role": "user"
}
] | Given a rational number, write it as a fraction in lowest terms and calculate the product of the resulting numerator and denominator. For how many rational numbers between 0 and 1 will $20_{}^{}!$ be the resulting product? | "[\"128\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 541, "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:14565"}, {"dataset": "skywork", "extra_info... | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"209"
] | [
"skywork"
] | 7d63a046d06f1350335fda73e2c6094f6ce9134079f2103e090b168174c5de42 | [
{
"content": "Find the greatest natural number $N$ such that, for any arrangement of the numbers $1, 2, \\ldots, 400$ in a chessboard $20 \\times 20$, there exist two numbers in the same row or column, which differ by at least $N.$",
"role": "user"
}
] | Find the greatest natural number $N$ such that, for any arrangement of the numbers $1, 2, \ldots, 400$ in a chessboard $20 \times 20$, there exist two numbers in the same row or column, which differ by at least $N.$ | "[\"209\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 547, "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:14566"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"\\frac{120}{169}"
] | [
"skywork"
] | 100dfd550ca8ca5a0a503ee7b9147dade58850a4a65f3b19b69a4a77fff8255b | [
{
"content": "Problem 11.4. It is known that $\\frac{7}{13}+\\sin \\varphi=\\cos \\varphi$ for some real $\\varphi$. What is $\\sin 2 \\varphi$?",
"role": "user"
}
] | Problem 11.4. It is known that $\frac{7}{13}+\sin \varphi=\cos \varphi$ for some real $\varphi$. What is $\sin 2 \varphi$? | "[\"\\\\frac{120}{169}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 542, "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:14567"}] | {
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"reference_components": 1,
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} |
[
"3"
] | [
"skywork"
] | 23775ab0c428a28eca17f3853cef09c936c6dee31b841d9fe27e800c6fcf913b | [
{
"content": "How many of the positive divisors of 128 are perfect squares larger than 1?",
"role": "user"
}
] | How many of the positive divisors of 128 are perfect squares larger than 1? | "[\"3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 556, "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:14568"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 4cccc17f82daa56f207f55b7e618fbaddbb8212f351bac46dcde0cef9d23d6b8 | [
{
"content": "Find the least positive integer $n$ such that \\[ \\frac 1{\\sin 45^\\circ\\sin 46^\\circ}+\\frac 1{\\sin 47^\\circ\\sin 48^\\circ}+\\cdots+\\frac 1{\\sin 133^\\circ\\sin 134^\\circ}=\\frac 1{\\sin n^\\circ}. \\]",
"role": "user"
}
] | Find the least positive integer $n$ such that \[ \frac 1{\sin 45^\circ\sin 46^\circ}+\frac 1{\sin 47^\circ\sin 48^\circ}+\cdots+\frac 1{\sin 133^\circ\sin 134^\circ}=\frac 1{\sin n^\circ}. \] | "[\"1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 540, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14569"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"2014"
] | [
"skywork"
] | b308fb7bcca944cee4a8f45cfe9d9bde1624d3ceaa894ede5ee0af9d490cd91f | [
{
"content": "91. On a long strip of paper, consecutive natural numbers $1, 2, 3, \\cdots \\cdots n$ are written in sequence. The long strip is cut into five segments, each containing some numbers (the digits of a single number will not be cut into different segments). The average of the numbers in these five s... | 91. On a long strip of paper, consecutive natural numbers $1, 2, 3, \cdots \cdots n$ are written in sequence. The long strip is cut into five segments, each containing some numbers (the digits of a single number will not be cut into different segments). The average of the numbers in these five segments are $1234, 345, ... | "[\"2014\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 536, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14570"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{15 + 5\\sqrt{5}}{2}"
] | [
"skywork"
] | d8dbc73194ac2ebb0db1852a4d37960a9163a76b18b13b05d9ffc60dd142b181 | [
{
"content": "Let $Q$ be a point outside of circle $C$. A segment is drawn from $Q$, tangent to circle $C$ at point $R$, and a different secant from $Q$ intersects $C$ at points $D$ and $E$ such that $QD < QE$. If $QD = 5$ and the length of the tangent from $Q$ to $R$ ($QR$) is equal to $DE - QD$, calculate $QE... | Let $Q$ be a point outside of circle $C$. A segment is drawn from $Q$, tangent to circle $C$ at point $R$, and a different secant from $Q$ intersects $C$ at points $D$ and $E$ such that $QD < QE$. If $QD = 5$ and the length of the tangent from $Q$ to $R$ ($QR$) is equal to $DE - QD$, calculate $QE$. | "[\"\\\\frac{15 + 5\\\\sqrt{5}}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 533, "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:14571"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"14"
] | [
"skywork"
] | 1824ea4384845182d6a464e54171f203a31166b5c097d9fba3047f41f9ee5afd | [
{
"content": "Everyone in a class of 30 students takes math and history. Seven students received an A in history and 13 received an A in math, including four that received an A in both courses. How many students did not receive an A in any of these two courses?",
"role": "user"
}
] | Everyone in a class of 30 students takes math and history. Seven students received an A in history and 13 received an A in math, including four that received an A in both courses. How many students did not receive an A in any of these two courses? | "[\"14\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 553, "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:14572"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"15"
] | [
"skywork"
] | ae6c2a207cc177ef62a56567c4efca03ef1e47f3ca4b71eb89a1e1f8d699d397 | [
{
"content": "In a round-robin chess tournament with $x$ players, two players dropped out after playing three matches each. The tournament ended with a total of 84 matches played. How many players were there initially?",
"role": "user"
}
] | In a round-robin chess tournament with $x$ players, two players dropped out after playing three matches each. The tournament ended with a total of 84 matches played. How many players were there initially? | "[\"15\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 532, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:14573"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{(p+1)^{2}}{4}"
] | [
"skywork"
] | 684dd41ed33a8cbaf49985152e4a0c9febb8218795077f840052d5d082c5bfbc | [
{
"content": "110) Let $p$ be a given odd prime, and let the positive integer $k$ be such that $\\sqrt{k^{2}-p k}$ is also a positive integer. Then $k=$ $\\qquad$",
"role": "user"
}
] | 110) Let $p$ be a given odd prime, and let the positive integer $k$ be such that $\sqrt{k^{2}-p k}$ is also a positive integer. Then $k=$ $\qquad$ | "[\"\\\\frac{(p+1)^{2}}{4}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 537, "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:14574"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3:2"
] | [
"skywork"
] | 01f321a6c3f111487fb2bb8a91006f43890e042417e52bff430d9bd4ab0a2bb9 | [
{
"content": "13. The diagram shows a triangle joined to a square to form an irregular pentagon. The triangle has the same perimeter as the square.\nWhat is the ratio of the perimeter of the pentagon to the perimeter of the square?\nA 2:1\nB $3: 2$\nC 4:3\nD 5:4\nE 6: 5",
"role": "user"
}
] | 13. The diagram shows a triangle joined to a square to form an irregular pentagon. The triangle has the same perimeter as the square.
What is the ratio of the perimeter of the pentagon to the perimeter of the square?
A 2:1
B $3: 2$
C 4:3
D 5:4
E 6: 5 | "[\"3:2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 543, "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:14575"}] | {
"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
} |
[
"131"
] | [
"skywork"
] | f0b0b69c27f0ac3a6d679ca829d7d56fd17d93e33ee4f5e819a48803d688f582 | [
{
"content": "3. Let the pair of positive integers $(x, y)$ be such that $\\frac{x^{2}+y^{2}}{11}$ is an integer, and satisfies the condition $\\frac{x^{2}+y^{2}}{11} \\leqslant 1991$. Find the number of such pairs of positive integers $(x, y)$ (when $a \\neq b$, $(a, b)$ and $(b, a)$ are considered different p... | 3. Let the pair of positive integers $(x, y)$ be such that $\frac{x^{2}+y^{2}}{11}$ is an integer, and satisfies the condition $\frac{x^{2}+y^{2}}{11} \leqslant 1991$. Find the number of such pairs of positive integers $(x, y)$ (when $a \neq b$, $(a, b)$ and $(b, a)$ are considered different pairs). | "[\"131\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 534, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:14576"}] | {
"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
} |
[
"84"
] | [
"skywork"
] | f6d97c414277259a7210872f22b69f34b13d661fc95e5148f42b3f8f3de76674 | [
{
"content": "When Phil and Shelley stand on a scale together, the scale reads $151$ pounds. When Shelley and Ryan stand on the same scale together, the scale reads $132$ pounds. When Phil and Ryan stand on the same scale together, the scale reads $115$ pounds. Find the number of pounds Shelley weighs.",
"r... | When Phil and Shelley stand on a scale together, the scale reads $151$ pounds. When Shelley and Ryan stand on the same scale together, the scale reads $132$ pounds. When Phil and Ryan stand on the same scale together, the scale reads $115$ pounds. Find the number of pounds Shelley weighs. | "[\"84\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 568, "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:14577"}] | {
"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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