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 |
|---|---|---|---|---|---|---|---|---|
[
"1093"
] | [
"skywork"
] | 23304171c11cf30c1df608f3e0db102c688e1a3886adb26e4b1d6b1de606b67d | [
{
"content": "In the sum $+1+3+9+27+81+243+729$, any addends can be crossed out and the signs before some of the remaining numbers can be changed from \"+\" to \"-\". Masha wants to use this method to first get an expression whose value is 1, then, starting over, get an expression whose value is 2, then (starti... | In the sum $+1+3+9+27+81+243+729$, any addends can be crossed out and the signs before some of the remaining numbers can be changed from "+" to "-". Masha wants to use this method to first get an expression whose value is 1, then, starting over, get an expression whose value is 2, then (starting over again) get 3, and ... | "[\"1093\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1181, "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:15195"}] | {
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[
"25"
] | [
"skywork"
] | 1d76bbfa83be5109042504263d185dbd522c3e263779015262ae6a7c10717a2a | [
{
"content": "Given that $7^{-1} \\equiv 55 \\pmod{101}$, find $49^{-1} \\pmod{101}$, as a residue modulo 101 (Give an answer between 0 and 100, inclusive).",
"role": "user"
}
] | Given that $7^{-1} \equiv 55 \pmod{101}$, find $49^{-1} \pmod{101}$, as a residue modulo 101 (Give an answer between 0 and 100, inclusive). | "[\"25\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1188, "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:15196"}] | {
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[
"\\sqrt{2}"
] | [
"skywork"
] | 5e209f16ac9cf793c2d79c469bbc7081cc4c1798da84f7e3ec9a2df68b364b8b | [
{
"content": "$\\left[\\begin{array}{l}\\text { Algebraic inequalities (miscellaneous) } \\\\ {[\\quad \\text { Case analysis }}}\\end{array}\\right]$\n\n$x, y>0$. Let $S$ denote the smallest of the numbers $x, 1 / y, y+1 / x$. What is the maximum value that $S$ can take?",
"role": "user"
}
] | $\left[\begin{array}{l}\text { Algebraic inequalities (miscellaneous) } \\ {[\quad \text { Case analysis }}}\end{array}\right]$
$x, y>0$. Let $S$ denote the smallest of the numbers $x, 1 / y, y+1 / x$. What is the maximum value that $S$ can take? | "[\"\\\\sqrt{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1190, "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:15197"}] | {
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[
"37"
] | [
"skywork"
] | 92d834206e2988e8f2ecad841666e33cfcddcda37441a18c70413ffec3002a3a | [
{
"content": "Let $p$ be the probability that, in the process of repeatedly flipping a fair coin, one will encounter a run of 5 heads before one encounters a run of 2 tails. Given that $p$ can be written in the form $m/n$ where $m$ and $n$ are relatively prime positive integers, find $m+n$.",
"role": "user... | Let $p$ be the probability that, in the process of repeatedly flipping a fair coin, one will encounter a run of 5 heads before one encounters a run of 2 tails. Given that $p$ can be written in the form $m/n$ where $m$ and $n$ are relatively prime positive integers, find $m+n$. | "[\"37\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1186, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:15198"}, {"dataset": "skywork", "extra_inf... | {
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} |
[
"540"
] | [
"skywork"
] | f686edb726a46196ba58dc753b5aa0687d1aa99cb9e70b1211bebd7d29863e2f | [
{
"content": "Four siblings inherited a plot of land shaped like a convex quadrilateral. By connecting the midpoints of the opposite sides of the plot, they divided the inheritance into four quadrilaterals. The first three siblings received plots of $360 \\, \\mathrm{m}^{2}$, $720 \\, \\mathrm{m}^{2}$, and $900... | Four siblings inherited a plot of land shaped like a convex quadrilateral. By connecting the midpoints of the opposite sides of the plot, they divided the inheritance into four quadrilaterals. The first three siblings received plots of $360 \, \mathrm{m}^{2}$, $720 \, \mathrm{m}^{2}$, and $900 \, \mathrm{m}^{2}$ respec... | "[\"540\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1163, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:15199"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2520"
] | [
"skywork"
] | 00ae0d092b0ff293d474264f9f6b53c40882d4fa04f9348d6a3ba4e16b75d611 | [
{
"content": "Find the number of ordered pairs of integers $(a, b)$ such that $a, b$ are divisors of 720 but $a b$ is not.",
"role": "user"
}
] | Find the number of ordered pairs of integers $(a, b)$ such that $a, b$ are divisors of 720 but $a b$ is not. | "[\"2520\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1183, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15200"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | d500332c084900d5b9921fbb69cee13cd81cd95604c7de9146aff7855a3dfc99 | [
{
"content": "Suppose $p$ and $q$ are inversely proportional. If $p=25$ when $q=6$, find the value of $p$ when $q=15$.",
"role": "user"
}
] | Suppose $p$ and $q$ are inversely proportional. If $p=25$ when $q=6$, find the value of $p$ when $q=15$. | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1213, "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:15201"}] | {
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"reference_components": 1,
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} |
[
"890"
] | [
"skywork"
] | fbb47d98ab337017eae0ad246f2612daeeb36a5043d210a7da25795e9cc77d43 | [
{
"content": "What is that largest positive integer $n$ for which $n^3+100$ is divisible by $n+10$ ?",
"role": "user"
}
] | What is that largest positive integer $n$ for which $n^3+100$ is divisible by $n+10$ ? | "[\"890\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 1204, "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:15202"}, {"dataset": "skywork", "extra_inf... | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"\\frac{3 \\sqrt{14}}{5}"
] | [
"skywork"
] | 5ff9ba9f923265e84dbd1df1e5f882fddccce97342c3a60a59c577394ece539a | [
{
"content": "Let $A B C$ be a triangle with $A B=5, A C=4, B C=6$. The angle bisector of $C$ intersects side $A B$ at $X$. Points $M$ and $N$ are drawn on sides $B C$ and $A C$, respectively, such that $\\overline{X M} \\| \\overline{A C}$ and $\\overline{X N} \\| \\overline{B C}$. Compute the length $M N$.",
... | Let $A B C$ be a triangle with $A B=5, A C=4, B C=6$. The angle bisector of $C$ intersects side $A B$ at $X$. Points $M$ and $N$ are drawn on sides $B C$ and $A C$, respectively, such that $\overline{X M} \| \overline{A C}$ and $\overline{X N} \| \overline{B C}$. Compute the length $M N$. | "[\"\\\\frac{3 \\\\sqrt{14}}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1189, "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:15203"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"90"
] | [
"skywork"
] | 4eec1b98cc1e208adb9b40857bdf13373150169fad62c3183ea562c016493806 | [
{
"content": "73. Put 235 matches into three boxes, so that $\\frac{3}{4}$ of the matches in the first box equals $\\frac{1}{3}$ of the matches in the second box, and $\\frac{1}{2}$ of the matches in the second box equals $\\frac{3}{7}$ of the matches in the third box, then the second box has $\\qquad$ matches?... | 73. Put 235 matches into three boxes, so that $\frac{3}{4}$ of the matches in the first box equals $\frac{1}{3}$ of the matches in the second box, and $\frac{1}{2}$ of the matches in the second box equals $\frac{3}{7}$ of the matches in the third box, then the second box has $\qquad$ matches? | "[\"90\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1194, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15204"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | 73e02a1721037a858821c2343a151f5d37152670a3b4e469c2beb15cfa22c65b | [
{
"content": "24. Let the polynomial $x^{3}-a x^{2}+b x-a$ where $(a, b \\in \\mathbf{R})$ have all real roots. If $a$ is the smallest positive real number that satisfies this condition, and for this real number $a$, the real number $b$ is uniquely determined, then the value of $b$ is ( ).\n(A) 8\n(B) 9\n(C) 10... | 24. Let the polynomial $x^{3}-a x^{2}+b x-a$ where $(a, b \in \mathbf{R})$ have all real roots. If $a$ is the smallest positive real number that satisfies this condition, and for this real number $a$, the real number $b$ is uniquely determined, then the value of $b$ is ( ).
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12 | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1196, "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:15205"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | 9ad060ca905974a1ce27769711ba5f652305e5d556c3d0313f5b25d80be85d2e | [
{
"content": "3. The AC-2016 calculator can perform two operations: taking the cube root and calculating the tangent. Initially, the number $2^{-243}$ was entered into the calculator. What is the minimum number of operations required to obtain a number greater than 1?",
"role": "user"
}
] | 3. The AC-2016 calculator can perform two operations: taking the cube root and calculating the tangent. Initially, the number $2^{-243}$ was entered into the calculator. What is the minimum number of operations required to obtain a number greater than 1? | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1203, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15206"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 63df87b21505a500bb603702e73a3c3578ea880ddbd8226bc6abd6578202a746 | [
{
"content": "If $(2,12)$ and $(8,3)$ are the coordinates of two opposite vertices of a rectangle, what is the sum of the $x$-coordinates of the other two vertices?",
"role": "user"
}
] | If $(2,12)$ and $(8,3)$ are the coordinates of two opposite vertices of a rectangle, what is the sum of the $x$-coordinates of the other two vertices? | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1209, "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:15207"}] | {
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"reference_present": true
} |
[
"11"
] | [
"skywork"
] | 495c89a959362268afb88e97bf4ec733d68438c0c299abeb1a8e5bd8e0b9da22 | [
{
"content": "What is the minimum number of three-cell corners that can be placed in an $8 \\times 8$ square so that no more such corners can be placed in this square?",
"role": "user"
}
] | What is the minimum number of three-cell corners that can be placed in an $8 \times 8$ square so that no more such corners can be placed in this square? | "[\"11\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1198, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15208"}] | {
"all_reference_components_parse": true,
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"reference_components": 1,
"reference_present": true
} |
[
"18"
] | [
"skywork"
] | 28a27599c5ee5b692e6224c0184277979ec8a41f0fa44d34f0304ff03cba3880 | [
{
"content": "Let $d(m)$ denote the number of positive integer divisors of a positive integer $m$. If $r$ is the number of integers $n \\leqslant 2023$ for which $\\sum_{i=1}^{n} d(i)$ is odd. , find the sum of digits of $r.$",
"role": "user"
}
] | Let $d(m)$ denote the number of positive integer divisors of a positive integer $m$. If $r$ is the number of integers $n \leqslant 2023$ for which $\sum_{i=1}^{n} d(i)$ is odd. , find the sum of digits of $r.$ | "[\"18\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1182, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15209"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"110"
] | [
"skywork"
] | a7fff3143c97a1d049e1460dc5ad0f1e81b293867f0fd1ac6f65d031fea57c84 | [
{
"content": "1. Given $f(x)=x^{2}+(\\lg a+2) x+\\lg b$, and $f(-1)=-2$, also $f(x) \\geqslant 2 x$ for all $x \\in R$. Then $a+b=(\\quad)$.\n(A) 100\n(B) 110\n(C) 120\n(D) 130",
"role": "user"
}
] | 1. Given $f(x)=x^{2}+(\lg a+2) x+\lg b$, and $f(-1)=-2$, also $f(x) \geqslant 2 x$ for all $x \in R$. Then $a+b=(\quad)$.
(A) 100
(B) 110
(C) 120
(D) 130 | "[\"110\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1180, "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:15210"}] | {
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"reference_components": 1,
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} |
[
"461"
] | [
"skywork"
] | fc3b1039636035a278480f0272b8b8ff355091063fd6b455e4ea175025d43ecb | [
{
"content": "$1 \\cdot 411,2,3,4,5,6$ 的排列 $\\left(n_{1}, n_{2}, n_{3}, n_{4}, n_{5}, n_{6}\\right)$ 具有如下性质: 对于 $i=1,2,3,4,5,\\left(n_{1}, n_{2}, \\cdots, n_{i}\\right)$ 都不是 $(1,2, \\cdots, i)$ 的排列. 求这种排列的个数.\n\nThe permutation $\\left(n_{1}, n_{2}, n_{3}, n_{4}, n_{5}, n_{6}\\right)$ of $1, 2, 3, 4, 5, 6$ has ... | $1 \cdot 411,2,3,4,5,6$ 的排列 $\left(n_{1}, n_{2}, n_{3}, n_{4}, n_{5}, n_{6}\right)$ 具有如下性质: 对于 $i=1,2,3,4,5,\left(n_{1}, n_{2}, \cdots, n_{i}\right)$ 都不是 $(1,2, \cdots, i)$ 的排列. 求这种排列的个数.
The permutation $\left(n_{1}, n_{2}, n_{3}, n_{4}, n_{5}, n_{6}\right)$ of $1, 2, 3, 4, 5, 6$ has the following property: for $i=1,... | "[\"461\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1193, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15211"}] | {
"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
} |
[
"m = 7"
] | [
"skywork"
] | 456ed80768443a3fd9aec227f28a1d9d7d55af48b92816326dc3f3420e7ac725 | [
{
"content": "What is the greatest positive integer $m$ such that $ n^2(1+n^2-n^4)\\equiv 1\\pmod{2^m} $ for all odd integers $n$?",
"role": "user"
}
] | What is the greatest positive integer $m$ such that $ n^2(1+n^2-n^4)\equiv 1\pmod{2^m} $ for all odd integers $n$? | "[\" m = 7 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1207, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15212"}] | {
"all_reference_components_parse": true,
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"reference_components": 1,
"reference_present": true
} |
[
"22"
] | [
"skywork"
] | f2c1a663d700b8a83e57a0f672263cf5b29296279183b95c029ba914f392865e | [
{
"content": "A clock chimes 2 times at 2 o'clock, taking 2 seconds to complete. How many seconds does it take to chime 12 times at 12 o'clock?",
"role": "user"
}
] | A clock chimes 2 times at 2 o'clock, taking 2 seconds to complete. How many seconds does it take to chime 12 times at 12 o'clock? | "[\"22\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1214, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:15213"}] | {
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} |
[
"252"
] | [
"skywork"
] | fa4d453a06260f362729d64c044294055a1f287be16bd34499f8905e0bd7ee9d | [
{
"content": "3. In how many ways can you partition the set $\\{1,2, \\ldots, 12\\}$ into six mutually disjoint two-element sets in such a way that the two elements in any set are coprime?\n\n(Martin Panák)",
"role": "user"
}
] | 3. In how many ways can you partition the set $\{1,2, \ldots, 12\}$ into six mutually disjoint two-element sets in such a way that the two elements in any set are coprime?
(Martin Panák) | "[\"252\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1212, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15214"}] | {
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[
"\\sqrt{6}"
] | [
"skywork"
] | f1e6a147f193efecd6522dcb2088249d9fc12902f90df4ba7e53600da8aa04fc | [
{
"content": "11.169. A plane is drawn through the vertex of the base and the midpoints of the two lateral edges of a regular triangular pyramid. Find the ratio of the lateral surface area of the pyramid to the area of its base, given that the intersecting plane is perpendicular to the lateral face.",
"role... | 11.169. A plane is drawn through the vertex of the base and the midpoints of the two lateral edges of a regular triangular pyramid. Find the ratio of the lateral surface area of the pyramid to the area of its base, given that the intersecting plane is perpendicular to the lateral face. | "[\"\\\\sqrt{6}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1206, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15216"}] | {
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} |
[
"\\frac{1+\\sqrt{5}}{2}"
] | [
"skywork"
] | da342eecccd4f72692cea6f9e6bac80824d159006f2a0cf37560fca65d1f0f87 | [
{
"content": "$\\begin{array}{l}\\text { 10. (15 points) Given } a>0, b>0, \\\\ \\log _{a} a=\\log _{12} b=\\log _{16}(a+b) . \\\\ \\text { Find the value of } \\frac{b}{a} .\\end{array}$",
"role": "user"
}
] | $\begin{array}{l}\text { 10. (15 points) Given } a>0, b>0, \\ \log _{a} a=\log _{12} b=\log _{16}(a+b) . \\ \text { Find the value of } \frac{b}{a} .\end{array}$ | "[\"\\\\frac{1+\\\\sqrt{5}}{2}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1202, "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:15217"}] | {
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"reference_components": 1,
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} |
[
"1996050"
] | [
"skywork"
] | d58176ddd8cbe81c0a324281dd68acc1d02863dada103b7744a7d7ff13072d75 | [
{
"content": "What is the sum of all the integers from 100 to 2000?",
"role": "user"
}
] | What is the sum of all the integers from 100 to 2000? | "[\"1996050\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1230, "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:15218"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"B"
] | [
"skywork"
] | 273d440aa7dc0c1c297b71321c75f01c09c2bdb6dbf86450c3ba45c7d05c59b2 | [
{
"content": "$17 \\cdot 116 P$ is a point inside an equilateral triangle of height $h$. Let the distances from $P$ to each side be $x, y, z$. If the three segments of lengths $x, y, z$ can form a triangle, then the conditions that $x, y, z$ must satisfy are\n(A) $x<h, y<h, z<h$.\n(B) $x<\\frac{h}{2}, y<\\frac{... | $17 \cdot 116 P$ is a point inside an equilateral triangle of height $h$. Let the distances from $P$ to each side be $x, y, z$. If the three segments of lengths $x, y, z$ can form a triangle, then the conditions that $x, y, z$ must satisfy are
(A) $x<h, y<h, z<h$.
(B) $x<\frac{h}{2}, y<\frac{h}{2}, z<\frac{h}{2}$.
(C) ... | "[\"B\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1199, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:15219"}] | {
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"reference_components": 1,
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} |
[
"7"
] | [
"skywork"
] | 26eea0d7134117b2c60ce1189b5663d7f7e6822051226069130c3f66ac31a8e2 | [
{
"content": "6. Write a sequence of consecutive positive integers starting with 1 on the blackboard, and erase one of the numbers. The arithmetic mean of the remaining numbers is $35 \\frac{7}{17}$. The number erased is\nA. 7\nB. 8\nC. 9\nD. Uncertain",
"role": "user"
}
] | 6. Write a sequence of consecutive positive integers starting with 1 on the blackboard, and erase one of the numbers. The arithmetic mean of the remaining numbers is $35 \frac{7}{17}$. The number erased is
A. 7
B. 8
C. 9
D. Uncertain | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1205, "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:15220"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"2 \\sqrt{2}"
] | [
"skywork"
] | 8d27c7222673d73f8de08cebfd2eb2c58dd2f81f26e1ce294009588ad0e4e444 | [
{
"content": "3. In Rt $\\triangle A B C$, it is known that $\\angle C=90^{\\circ}, B C$ $=6, C A=3, C D$ is the angle bisector of $\\angle C$. Then $C D=$ $\\qquad$ .",
"role": "user"
}
] | 3. In Rt $\triangle A B C$, it is known that $\angle C=90^{\circ}, B C$ $=6, C A=3, C D$ is the angle bisector of $\angle C$. Then $C D=$ $\qquad$ . | "[\"2 \\\\sqrt{2}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1215, "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:15221"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"757"
] | [
"skywork"
] | 8f1a8361d3a4972eb546fcee56e4aba5f16d0e25b427f6180f5fead8984367ca | [
{
"content": "3・13 Let $a, b, c, d$ be positive integers, satisfying $a^{5}=b^{4}, c^{3}=d^{2}$, and $c-a$ $=19$. Find $d-b$.\n(3rd American Invitational Mathematics Examination, 1985)",
"role": "user"
}
] | 3・13 Let $a, b, c, d$ be positive integers, satisfying $a^{5}=b^{4}, c^{3}=d^{2}$, and $c-a$ $=19$. Find $d-b$.
(3rd American Invitational Mathematics Examination, 1985) | "[\"757\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1192, "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:15222"}] | {
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"reference_present": true
} |
[
"90"
] | [
"skywork"
] | 606587cd9d56c9bb7944612c464cb88dd5cbd29459f3c70c2071461e4e890f33 | [
{
"content": "Mr. Rose, Mr. Stein, and Mr. Schwartz start at the same point around a circular track and run clockwise. Mr. Stein completes each lap in $6$ minutes, Mr. Rose in $10$ minutes, and Mr. Schwartz in $18$ minutes. How many minutes after the start of the race are the runners at identical points around ... | Mr. Rose, Mr. Stein, and Mr. Schwartz start at the same point around a circular track and run clockwise. Mr. Stein completes each lap in $6$ minutes, Mr. Rose in $10$ minutes, and Mr. Schwartz in $18$ minutes. How many minutes after the start of the race are the runners at identical points around the track (that is, th... | "[\"90\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1216, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "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:15223"}, {"dataset": "skywork", "extra_inf... | {
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"reference_components": 1,
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} |
[
"\\frac{x-\\sqrt{x}-6}{x-9}"
] | [
"skywork"
] | 65cc1fa077c5b95af800eda933ef53d6ba739ae78eeb98446e1989314d66e07f | [
{
"content": "A3. Let $x \\in \\mathbb{R}$ and $x>0, x \\neq 4, x \\neq 9$. Which expression is equivalent to $\\left((2+\\sqrt{x})^{-1}+1\\right)^{-1}$?\n(A) $\\frac{x+\\sqrt{x}-6}{x-9}$\n(B) $\\frac{x-\\sqrt{x}-6}{x-9}$\n(C) $\\frac{x-\\sqrt{x}+6}{x-9}$\n(D) $\\frac{x-\\sqrt{x}-6}{x-4}$\n(E) $\\frac{x-\\sqrt{... | A3. Let $x \in \mathbb{R}$ and $x>0, x \neq 4, x \neq 9$. Which expression is equivalent to $\left((2+\sqrt{x})^{-1}+1\right)^{-1}$?
(A) $\frac{x+\sqrt{x}-6}{x-9}$
(B) $\frac{x-\sqrt{x}-6}{x-9}$
(C) $\frac{x-\sqrt{x}+6}{x-9}$
(D) $\frac{x-\sqrt{x}-6}{x-4}$
(E) $\frac{x-\sqrt{x}+6}{x-4}$ | "[\"\\\\frac{x-\\\\sqrt{x}-6}{x-9}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1208, "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:15224"}] | {
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"reference_components": 1,
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} |
[
"\\arccos\\frac{1}{\\sqrt{3}}"
] | [
"skywork"
] | ae987637b86d7964b411f8e2a192cf6db2337fce57b2b3f67bf19347f55c3db8 | [
{
"content": "[Law of Cosines] [Law of Sines]\n\nIn a right triangle $KLM$, a segment $MD$ is drawn connecting the vertex of the right angle to point $D$ on the hypotenuse $KL$ such that the lengths of segments $DL, DM$, and $DK$ are distinct and form a geometric progression in the given order with a common rat... | [Law of Cosines] [Law of Sines]
In a right triangle $KLM$, a segment $MD$ is drawn connecting the vertex of the right angle to point $D$ on the hypotenuse $KL$ such that the lengths of segments $DL, DM$, and $DK$ are distinct and form a geometric progression in the given order with a common ratio of $\sqrt{2}$, and $D... | "[\"\\\\arccos\\\\frac{1}{\\\\sqrt{3}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1197, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15225"}] | {
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"plain_numeric_reference": false,
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} |
[
"-2+3i"
] | [
"skywork"
] | e78bd07c7c557f3a4f7ecfb970aeb72bd99b38d77938e634f6ac1676cb161087 | [
{
"content": "Simplify $\\dfrac{5+12i}{2-3i}$. Your answer should be of the form $a+bi$, where $a$ and $b$ are both real numbers and written as improper fractions (if necessary).",
"role": "user"
}
] | Simplify $\dfrac{5+12i}{2-3i}$. Your answer should be of the form $a+bi$, where $a$ and $b$ are both real numbers and written as improper fractions (if necessary). | "[\"-2+3i\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1232, "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:15226"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"159"
] | [
"skywork"
] | 42b2b02ec55e1f4ffa4c9b5946d1170ee7dda84d71e15994559c9be43631814e | [
{
"content": "How many real numbers $x^{}_{}$ satisfy the equation $\\frac{1}{5}\\log_2 x = \\sin (5\\pi x)$ ?",
"role": "user"
}
] | How many real numbers $x^{}_{}$ satisfy the equation $\frac{1}{5}\log_2 x = \sin (5\pi x)$ ? | "[\"159\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 1226, "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:15227"}, {"dataset": "skywork", "extra_... | {
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"reference_components": 1,
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} |
[
"6\\mathrm{~}"
] | [
"skywork"
] | f44a214e844acbcc38c0dd6c4c46e9d4372e92d7115cfeeb5a90eb3db1e67f09 | [
{
"content": "A rectangle with a width of $2 \\mathrm{~cm}$ and a length of $18 \\mathrm{~cm}$ has the same area as a square with a side length of\n(A) $6 \\mathrm{~cm}$\n(B) $12 \\mathrm{~cm}$\n(C) $9 \\mathrm{~cm}$\n(D) $10 \\mathrm{~cm}$\n(E) $8 \\mathrm{~cm}$",
"role": "user"
}
] | A rectangle with a width of $2 \mathrm{~cm}$ and a length of $18 \mathrm{~cm}$ has the same area as a square with a side length of
(A) $6 \mathrm{~cm}$
(B) $12 \mathrm{~cm}$
(C) $9 \mathrm{~cm}$
(D) $10 \mathrm{~cm}$
(E) $8 \mathrm{~cm}$ | "[\"6\\\\mathrm{~}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1223, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15228"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"(1, 2), (1, 3), (2, 1), (2, 2), (2, 5), (3, 1), (3, 5), (5, 2), (5, 3)"
] | [
"skywork"
] | 9f7f87e6381325ec01026f457198ac5e7cda84778b118a1ef44b732d7b5e5e5b | [
{
"content": "Find all ordered pairs $ (m,n)$ where $ m$ and $ n$ are positive integers such that $ \\frac {n^3 \\plus{} 1}{mn \\minus{} 1}$ is an integer.",
"role": "user"
}
] | Find all ordered pairs $ (m,n)$ where $ m$ and $ n$ are positive integers such that $ \frac {n^3 \plus{} 1}{mn \minus{} 1}$ is an integer. | "[\"(1, 2), (1, 3), (2, 1), (2, 2), (2, 5), (3, 1), (3, 5), (5, 2), (5, 3)\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1217, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:15229"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"f(n)=0"
] | [
"skywork"
] | 035012261a991e9f4e32c26e37b277d50afe387cd7f7f9837a8616c5291ef3c4 | [
{
"content": "1. Find all functions $f: \\mathbf{Z}^{*} \\rightarrow \\mathbf{R}$ (where $\\mathbf{Z}^{*}$ is the set of non-negative integers) that satisfy $f(n+m)+f(n-m)=f(3 n), m, n \\in \\mathbf{Z}^{*}, n \\geqslant m$.\n(1979 Austrian-Polish Competition)",
"role": "user"
}
] | 1. Find all functions $f: \mathbf{Z}^{*} \rightarrow \mathbf{R}$ (where $\mathbf{Z}^{*}$ is the set of non-negative integers) that satisfy $f(n+m)+f(n-m)=f(3 n), m, n \in \mathbf{Z}^{*}, n \geqslant m$.
(1979 Austrian-Polish Competition) | "[\"f(n)=0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1220, "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:15230"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | bce924342bee2da2bd7f8454b6926bd7103fdd78768d65bcf5cec8ea03305735 | [
{
"content": "In a given plane, points $A$ and $B$ are $10$ units apart. How many points $C$ are there in the plane such that the perimeter of $\\triangle ABC$ is $50$ units and the area of $\\triangle ABC$ is $100$ square units?",
"role": "user"
}
] | In a given plane, points $A$ and $B$ are $10$ units apart. How many points $C$ are there in the plane such that the perimeter of $\triangle ABC$ is $50$ units and the area of $\triangle ABC$ is $100$ square units? | "[\"0\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1229, "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:15231"}] | {
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[
"f(x)=\\frac{1}{3}\\cosx"
] | [
"skywork"
] | fbf0f834dd368d41e43d7094e825255d78024d2374c175daf08c251943186e16 | [
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"content": "Problem 6. Suppose $T$ is the period of the function $y=f(x)$. From the condition, we get:\n\n$$\n\\cos x=f(x)-2 f(x-\\pi)=f(x-T)-2 f(x-T-\\pi)=\\cos (x-T)\n$$\n\nSince this equality holds for all $x$, the number $T$ is the period of the function $y=\\cos x$, i.e., $T=2 \\pi n$, where $n$ is some ... | Problem 6. Suppose $T$ is the period of the function $y=f(x)$. From the condition, we get:
$$
\cos x=f(x)-2 f(x-\pi)=f(x-T)-2 f(x-T-\pi)=\cos (x-T)
$$
Since this equality holds for all $x$, the number $T$ is the period of the function $y=\cos x$, i.e., $T=2 \pi n$, where $n$ is some natural number. From the given equ... | "[\"f(x)=\\\\frac{1}{3}\\\\cosx\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1210, "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:15232"}] | {
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[
"C"
] | [
"skywork"
] | 69e860061e2ad84c13922283734a56c8439bc7e5f1e83565e0aa18d62ed6f914 | [
{
"content": "1. Let $[x]$ denote the greatest integer not greater than $x$. Let the set $A=\\left\\{x \\mid x^{2}-[x]=2\\right\\}, B=\\{x|| x \\mid<$ $2\\}$. Then $A \\cap B=(\\quad)$.\n(A) $(-2,2)$\n(B) $[-2,2]$\n(C) $\\{\\sqrt{3},-1\\}$\n(D) $\\{-\\sqrt{3}, 1\\}$",
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}
] | 1. Let $[x]$ denote the greatest integer not greater than $x$. Let the set $A=\left\{x \mid x^{2}-[x]=2\right\}, B=\{x|| x \mid<$ $2\}$. Then $A \cap B=(\quad)$.
(A) $(-2,2)$
(B) $[-2,2]$
(C) $\{\sqrt{3},-1\}$
(D) $\{-\sqrt{3}, 1\}$ | "[\"C\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1191, "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:15233"}] | {
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[
"10"
] | [
"skywork"
] | 607957fba3b733410c5ba22fc090ef00829a5bfdc6a3c3f64ecbc21927041690 | [
{
"content": "Example 2. Find the direction of the maximum increase of the function $z=3 x^{2}-2 y^{2}$ at the point $M(1,2)$. Also, find the greatest value of the derivatives in different directions at the point $M$.",
"role": "user"
}
] | Example 2. Find the direction of the maximum increase of the function $z=3 x^{2}-2 y^{2}$ at the point $M(1,2)$. Also, find the greatest value of the derivatives in different directions at the point $M$. | "[\"10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1228, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15234"}] | {
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[
"50"
] | [
"skywork"
] | 00e3960a5e0fc1945ae99e0affd32cdbfd09379257120371d5788f95a0c26805 | [
{
"content": "Given $w$ and $z$ are complex numbers such that $|w+z|=2$ and $|w^2+z^2|=18,$ find the smallest possible value of $|w^3+z^3|.$",
"role": "user"
}
] | Given $w$ and $z$ are complex numbers such that $|w+z|=2$ and $|w^2+z^2|=18,$ find the smallest possible value of $|w^3+z^3|.$ | "[\"50\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1244, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15235"}] | {
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[
"\\frac {\\sqrt {3}}{4}"
] | [
"skywork"
] | 16d6704cd12293b6cd294cb7315889bba7bd3de1bb78413fa59c027330258281 | [
{
"content": "In $\\triangle ABC$, $A=30^{\\circ}$, $AB=\\sqrt {3}$, $BC=1$, find the area of $\\triangle ABC$.",
"role": "user"
}
] | In $\triangle ABC$, $A=30^{\circ}$, $AB=\sqrt {3}$, $BC=1$, find the area of $\triangle ABC$. | "[\"\\\\frac {\\\\sqrt {3}}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1254, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:15236"}] | {
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"reference_components": 1,
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[
"128"
] | [
"skywork"
] | 876a9fa24f76ae296774057de77d22fc30d4a15f549bd976754b6063c5e27af5 | [
{
"content": "Evaluate $16^{7/4}$.",
"role": "user"
}
] | Evaluate $16^{7/4}$. | "[\"128\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1258, "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:15237"}] | {
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[
"1+\\sqrt{2}"
] | [
"skywork"
] | cd9860cc16e898d6c381d61ceaf30f030ce09f3e4660dfcf1de894fa56a765e0 | [
{
"content": "G3.3 Given that $f(n)=\\sin \\frac{n \\pi}{4}$, where $n$ is an integer. If $c=f(1)+f(2)+\\ldots+f(2003)$, find the value of $c$.",
"role": "user"
}
] | G3.3 Given that $f(n)=\sin \frac{n \pi}{4}$, where $n$ is an integer. If $c=f(1)+f(2)+\ldots+f(2003)$, find the value of $c$. | "[\"1+\\\\sqrt{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1238, "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:15238"}] | {
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[
"- \\frac {1}{2}"
] | [
"skywork"
] | ee0745978dee22e55da78403773dce4e4c9d19ae0380b65857491bce2313b3a8 | [
{
"content": "Given the function $f(x)=\\cos x\\cdot\\sin \\left(x+ \\frac {\\pi}{3}\\right)- \\sqrt {3}\\cos ^{2}x+ \\frac { \\sqrt {3}}{4}$, $x\\in\\mathbb{R}$. \n(I) Find the smallest positive period of $f(x)$. \n(II) Find the maximum and minimum values of $f(x)$ on the closed interval $\\left[- \\frac {\\... | Given the function $f(x)=\cos x\cdot\sin \left(x+ \frac {\pi}{3}\right)- \sqrt {3}\cos ^{2}x+ \frac { \sqrt {3}}{4}$, $x\in\mathbb{R}$.
(I) Find the smallest positive period of $f(x)$.
(II) Find the maximum and minimum values of $f(x)$ on the closed interval $\left[- \frac {\pi}{4}, \frac {\pi}{4}\right]$. | "[\"- \\\\frac {1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1222, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15239"}] | {
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[
"\\frac{16\\sqrt{3}}{9}"
] | [
"skywork"
] | 5376fc7978312112cdc13c0ced72de9e19ff9fd90a16f53815b8d273bf0a1ff3 | [
{
"content": "6. The maximum value of the function $y=\\sin x+\\sqrt{3} \\cos x-2 \\sin 3 x$ is $\\qquad$",
"role": "user"
}
] | 6. The maximum value of the function $y=\sin x+\sqrt{3} \cos x-2 \sin 3 x$ is $\qquad$ | "[\"\\\\frac{16\\\\sqrt{3}}{9}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1225, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15241"}] | {
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[
"15^{\\circ}"
] | [
"skywork"
] | feb6109cc2b21fa190b9a3b41873b52cfe13a85067e4c0f2389ff0197a565e7c | [
{
"content": "Five. (Full marks 20 points) Given the hyperbola $\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1(a>b>0)$ with eccentricity $e=2+\\sqrt{6}-\\sqrt{3}-\\sqrt{2}$, a line $l$ passing through its right focus $F_{2}$ and perpendicular to the $x$-axis intersects the hyperbola at points $A$ and $B$. Find the... | Five. (Full marks 20 points) Given the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1(a>b>0)$ with eccentricity $e=2+\sqrt{6}-\sqrt{3}-\sqrt{2}$, a line $l$ passing through its right focus $F_{2}$ and perpendicular to the $x$-axis intersects the hyperbola at points $A$ and $B$. Find the size of $\angle A F_{1} F_... | "[\"15^{\\\\circ}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1224, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15243"}] | {
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[
"30,951"
] | [
"skywork"
] | 68fc4b4a2250d5c975db0bec1ca7ea58c3917bf5a8c3415b5c49382e9db9c728 | [
{
"content": "How many 5-digit numbers have at least one zero?",
"role": "user"
}
] | How many 5-digit numbers have at least one zero? | "[\"30,951\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1261, "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:15244"}] | {
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"plain_numeric_reference": false,
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} |
[
"\\frac{11}{2}"
] | [
"skywork"
] | a91ceb0eb94d9b8c59df8ccf921bb55c0e5711b4098a40c04773b74450aa54db | [
{
"content": "Let $AD$ be a diameter of a circle of radius $r,$ and let $B,C$ be points on the circle such that $AB=BC=\\frac r2$ and $A\\neq C.$ Find the ratio $\\frac{CD}{r}.$",
"role": "user"
}
] | Let $AD$ be a diameter of a circle of radius $r,$ and let $B,C$ be points on the circle such that $AB=BC=\frac r2$ and $A\neq C.$ Find the ratio $\frac{CD}{r}.$ | "[\"\\\\frac{11}{2}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1241, "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:15245"}] | {
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[
"(50, 25)"
] | [
"skywork"
] | 4f21ee8bed1f6f6f7b574d0f93466c2efa22a3d359e80a2f9a3dd5307fbbc017 | [
{
"content": "Ali Barber, the carpet merchant, has a rectangular piece of carpet whose dimensions are unknown. Unfortunately, his tape measure is broken and he has no other measuring instruments. However, he finds that if he lays it flat on the floor of either of his storerooms, then each corner of the carpet t... | Ali Barber, the carpet merchant, has a rectangular piece of carpet whose dimensions are unknown. Unfortunately, his tape measure is broken and he has no other measuring instruments. However, he finds that if he lays it flat on the floor of either of his storerooms, then each corner of the carpet touches a different wal... | "[\"(50, 25)\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1231, "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:15247"}] | {
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[
"h(x)"
] | [
"skywork"
] | 7684a6f3112b9be069828630369555c9bcd74cc83a515bbe4738c7091ef59295 | [
{
"content": "The following functions are written on the board, $$F(x) = x^2 + \\frac{12}{x^2}, G(x) = \\sin(\\pi x^2), H(x) = 1.$$ If functions $f,g$ are currently on the board, we may write on the board the functions $$f(x) + g(x), f(x) - g(x), f(x)g(x), cf(x)$$ (the last for any real number $c$). Can a funct... | The following functions are written on the board, $$F(x) = x^2 + \frac{12}{x^2}, G(x) = \sin(\pi x^2), H(x) = 1.$$ If functions $f,g$ are currently on the board, we may write on the board the functions $$f(x) + g(x), f(x) - g(x), f(x)g(x), cf(x)$$ (the last for any real number $c$). Can a function $h(x)$ appear on the ... | "[\" h(x) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1234, "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:15248"}] | {
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[
"\\frac{5}{36}"
] | [
"skywork"
] | 8a6d66662601903e783915228919fd12bad2e782eef374046990cac67f7c5b3e | [
{
"content": "Alex, Mel, and Chelsea play a game that has $6$ rounds. In each round there is a single winner, and the outcomes of the rounds are independent. For each round the probability that Alex wins is $\\frac{1}{2}$, and Mel is twice as likely to win as Chelsea. What is the probability that Alex wins t... | Alex, Mel, and Chelsea play a game that has $6$ rounds. In each round there is a single winner, and the outcomes of the rounds are independent. For each round the probability that Alex wins is $\frac{1}{2}$, and Mel is twice as likely to win as Chelsea. What is the probability that Alex wins three rounds, Mel wins t... | "[\"\\\\frac{5}{36}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1251, "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:15249"}] | {
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[
"\\frac{3\\sqrt{3}}{2}"
] | [
"skywork"
] | a9b0cc547d15099471838708e0e050f8c02a8e3fbc41f731bb3ef40049e66c54 | [
{
"content": "$ AL$, $ BM$, and $ CN$ are the medians of $ \\triangle ABC$. $ K$ is the intersection of medians. If $ C,K,L,M$ are concyclic and $ AB \\equal{} \\sqrt 3$, then the median $ CN$ = ?\n\n$\\textbf{(A)}\\ 1 \\qquad\\textbf{(B)}\\ \\sqrt 3 \\qquad\\textbf{(C)}\\ \\frac {3\\sqrt3}{2} \\qquad\\textb... | $ AL$, $ BM$, and $ CN$ are the medians of $ \triangle ABC$. $ K$ is the intersection of medians. If $ C,K,L,M$ are concyclic and $ AB \equal{} \sqrt 3$, then the median $ CN$ = ?
$\textbf{(A)}\ 1 \qquad\textbf{(B)}\ \sqrt 3 \qquad\textbf{(C)}\ \frac {3\sqrt3}{2} \qquad\textbf{(D)}\ 3 \qquad\textbf{(E)}\ \text{Non... | "[\"\\\\frac{3\\\\sqrt{3}}{2}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1240, "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:15250"}] | {
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[
"\\text{bromine}"
] | [
"skywork"
] | fff58cb4796f361413d6916b72a2eb24b7bb9b7d62923e75087cbcd5f4784e98 | [
{
"content": "Which element is a liquid at $25^\\circ\\text{C}$ and $1.0 \\text{ atm}$?\n\n$\\textbf{(A)}\\hspace{.05in}\\text{bromine} \\qquad\\textbf{(B)}\\hspace{.05in}\\text{krypton} \\qquad\\textbf{(C)}\\hspace{.05in}\\text{phosphorus} \\qquad\\textbf{(D)}\\hspace{.05in}\\text{xenon} \\qquad$",
"role":... | Which element is a liquid at $25^\circ\text{C}$ and $1.0 \text{ atm}$?
$\textbf{(A)}\hspace{.05in}\text{bromine} \qquad\textbf{(B)}\hspace{.05in}\text{krypton} \qquad\textbf{(C)}\hspace{.05in}\text{phosphorus} \qquad\textbf{(D)}\hspace{.05in}\text{xenon} \qquad$ | "[\"\\\\text{bromine}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1237, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15251"}] | {
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[
"1"
] | [
"skywork"
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{
"content": "Suppose that for some $a,b,c$ we have $a+b+c = 1$, $ab+ac+bc = abc = -4$. What is $a^3+b^3+c^3$?",
"role": "user"
}
] | Suppose that for some $a,b,c$ we have $a+b+c = 1$, $ab+ac+bc = abc = -4$. What is $a^3+b^3+c^3$? | "[\"1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1265, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15252"}] | {
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[
"\\frac{3}{2}\\pi - 1"
] | [
"skywork"
] | bdf0498edcf99ecb62e7dba19bfa1b903980ad6e2c8cfb01755faea568e3c808 | [
{
"content": "Two semicircles of diameters 2 and 4 are placed such that the smaller is inside the larger one and their diameters are along the same line. A square of side 1 is inscribed in the larger semicircle such that one of its sides is along the diameter of the semicircles. Calculate the area of the lune f... | Two semicircles of diameters 2 and 4 are placed such that the smaller is inside the larger one and their diameters are along the same line. A square of side 1 is inscribed in the larger semicircle such that one of its sides is along the diameter of the semicircles. Calculate the area of the lune formed by the space in ... | "[\"\\\\frac{3}{2}\\\\pi - 1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1219, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15253"}] | {
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[
"10571"
] | [
"skywork"
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{
"content": "12. B. Let the positive integer $a$ satisfy $192 \\mid\\left(a^{3}+191\\right)$, and $a<2$ 009. Find the sum of all possible positive integers $a$ that meet the condition.",
"role": "user"
}
] | 12. B. Let the positive integer $a$ satisfy $192 \mid\left(a^{3}+191\right)$, and $a<2$ 009. Find the sum of all possible positive integers $a$ that meet the condition. | "[\"10571\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1249, "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:15254"}] | {
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[
"2, 3, 5"
] | [
"skywork"
] | 78f9bace7273e1b1ffac8553c96c042bbb021a59b6f00e0ffb696bb3876966ca | [
{
"content": "A positive integer $k > 1$ is called nice if for any pair $(m, n)$ of positive integers satisfying the condition $kn + m | km + n$ we have $n | m$.\n1. Prove that $5$ is a nice number.\n2. Find all the nice numbers.",
"role": "user"
}
] | A positive integer $k > 1$ is called nice if for any pair $(m, n)$ of positive integers satisfying the condition $kn + m | km + n$ we have $n | m$.
1. Prove that $5$ is a nice number.
2. Find all the nice numbers. | "[\" 2, 3, 5 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1221, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15255"}] | {
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[
"3^{377}"
] | [
"skywork"
] | 8dde6dbe17529e50eb0f877916ace6db7c70bc19cc2fe409f381ed091e12e07e | [
{
"content": "Define a new sequence \\( c_1, c_2, \\ldots \\) such that \\( c_1 = 3 \\), \\( c_2 = 3 \\), and \\( c_{n+1} = c_n \\cdot c_{n-1} \\). Calculate \\( c_{15} \\).",
"role": "user"
}
] | Define a new sequence \( c_1, c_2, \ldots \) such that \( c_1 = 3 \), \( c_2 = 3 \), and \( c_{n+1} = c_n \cdot c_{n-1} \). Calculate \( c_{15} \). | "[\"3^{377}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1260, "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:15256"}] | {
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[
"30+10 \\sqrt{17}"
] | [
"skywork"
] | e12ecbc742abdb24655ec37b8a7ed9d21eb0b3a50e6bf3721f27af261c49adbb | [
{
"content": "5. Ports $A$ and $B$ are on the south shore of a large lake, and port $C$ is on the north shore. Ports $A$, $B$, and $C$ form the vertices of an equilateral triangle. Ships from port $A$ and port $B$ start at the same time and travel in a straight line towards port $C$ at a constant speed. When sh... | 5. Ports $A$ and $B$ are on the south shore of a large lake, and port $C$ is on the north shore. Ports $A$, $B$, and $C$ form the vertices of an equilateral triangle. Ships from port $A$ and port $B$ start at the same time and travel in a straight line towards port $C$ at a constant speed. When ship B has traveled 40 k... | "[\"30+10 \\\\sqrt{17}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1247, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15257"}] | {
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[
"\\frac{\\pi}{2}"
] | [
"skywork"
] | ec7d1730e508387b4c1eb055afd52e6e759abd4936dc9fa79550b3696c7ae07d | [
{
"content": "Determine the smallest positive real number $r$ such that there exist differentiable functions $f\\colon \\mathbb{R} \\to \\mathbb{R}$ and $g\\colon \\mathbb{R} \\to \\mathbb{R}$ satisfying \\begin{enumerate} \\item[(a)] $f(0) > 0$, \\item[(b)] $g(0) = 0$, \\item[(c)] $|f'(x)| \\leq |g(x)|$ for al... | Determine the smallest positive real number $r$ such that there exist differentiable functions $f\colon \mathbb{R} \to \mathbb{R}$ and $g\colon \mathbb{R} \to \mathbb{R}$ satisfying \begin{enumerate} \item[(a)] $f(0) > 0$, \item[(b)] $g(0) = 0$, \item[(c)] $|f'(x)| \leq |g(x)|$ for all $x$, \item[(d)] $|g'(x)| \leq |f(... | "[\"\\\\frac{\\\\pi}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1245, "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:15258"}] | {
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[
"\\[ |a| = |b| \\]"
] | [
"skywork"
] | de0a4f79ed1a40c8505106dcf7b73c0d11245b2c2f559c69c576ab52b014a97f | [
{
"content": "Let $\\mathbb Z$ be the set of all integers. Find all pairs of integers $(a,b)$ for which there exist functions $f:\\mathbb Z\\rightarrow\\mathbb Z$ and $g:\\mathbb Z\\rightarrow\\mathbb Z$ satisfying \\[f(g(x))=x+a\\quad\\text{and}\\quad g(f(x))=x+b\\] for all integers $x$ .",
"role": "user"
... | Let $\mathbb Z$ be the set of all integers. Find all pairs of integers $(a,b)$ for which there exist functions $f:\mathbb Z\rightarrow\mathbb Z$ and $g:\mathbb Z\rightarrow\mathbb Z$ satisfying \[f(g(x))=x+a\quad\text{and}\quad g(f(x))=x+b\] for all integers $x$ . | "[\"\\\\[ |a| = |b| \\\\]\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1242, "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:15259"}] | {
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[
"55\\%"
] | [
"skywork"
] | 89807d88ace502bff220e1d523d1e2c3a106268a0c8cbf7eb2d940e32a695fe3 | [
{
"content": "A jar was fi\flled with jelly beans so that $54\\%$ of the beans were red, $30\\%$ of the beans were green, and $16\\%$ of the beans were blue. Alan then removed the same number of red jelly beans and green jelly beans from the jar so that now $20\\%$ of the jelly beans in the jar are blue. What p... | A jar was fi lled with jelly beans so that $54\%$ of the beans were red, $30\%$ of the beans were green, and $16\%$ of the beans were blue. Alan then removed the same number of red jelly beans and green jelly beans from the jar so that now $20\%$ of the jelly beans in the jar are blue. What percent of the jelly beans i... | "[\"55\\\\%\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1256, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15260"}] | {
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[
"7"
] | [
"skywork"
] | 1f6f40abe8808c12b8c51814801768bafac49a0b52ed068f28215fb73ed3e587 | [
{
"content": "Four mayors decide to build a circular highway that passes within the boundaries of their cities. Since the four cities are not on the same circle, the mayors hire a company to develop a project for the construction of a circular highway equidistant from the four cities. What is the maximum number... | Four mayors decide to build a circular highway that passes within the boundaries of their cities. Since the four cities are not on the same circle, the mayors hire a company to develop a project for the construction of a circular highway equidistant from the four cities. What is the maximum number of geographically dis... | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1250, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15261"}] | {
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[
"1,6"
] | [
"skywork"
] | 2a5e2ded5f012119352e961abbe4ed69ce9c10dd1bb63d6ef33b67980b3ea826 | [
{
"content": "1. Find all positive integers $m$ such that $m^{2}+m+7$ is a perfect square. ${ }^{[1]}$",
"role": "user"
}
] | 1. Find all positive integers $m$ such that $m^{2}+m+7$ is a perfect square. ${ }^{[1]}$ | "[\"1,6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1271, "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:15262"}] | {
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[
"3^{666}"
] | [
"skywork"
] | a132d15425473aa322761efd1c7c68a20e65d1fec93c3ea35844caf7c35a89b1 | [
{
"content": "The sequence \\( (a_i) \\) is defined as follows: \\( a_1 = 0 \\), \\( a_2 = 2 \\), \\( a_3 = 3 \\), and for \\( n = 4, 5, 6, \\ldots \\), \\( a_n = \\max_{1 < d < n} \\{ a_d \\cdot a_{n-d} \\} \\). Determine the value of \\( a_{1998} \\).",
"role": "user"
}
] | The sequence \( (a_i) \) is defined as follows: \( a_1 = 0 \), \( a_2 = 2 \), \( a_3 = 3 \), and for \( n = 4, 5, 6, \ldots \), \( a_n = \max_{1 < d < n} \{ a_d \cdot a_{n-d} \} \). Determine the value of \( a_{1998} \). | "[\"3^{666}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1252, "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:15263"}] | {
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[
"(0;0),(2;1)"
] | [
"skywork"
] | c51bab68c60ed6e2a8ff14dadfe4cdbbbedd9b42ed952fb624e60e96791be390 | [
{
"content": "4. Solve the inequality in integers\n\n$$\n\\frac{x^{2}}{\\sqrt{x-3 y+2}}+\\frac{y^{2}}{\\sqrt{-x+2 y+1}} \\geq y^{2}+2 x^{2}-2 x-1 .\n$$",
"role": "user"
}
] | 4. Solve the inequality in integers
$$
\frac{x^{2}}{\sqrt{x-3 y+2}}+\frac{y^{2}}{\sqrt{-x+2 y+1}} \geq y^{2}+2 x^{2}-2 x-1 .
$$ | "[\"(0;0),(2;1)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1257, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:15264"}] | {
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[
"\\frac{3}{4}"
] | [
"skywork"
] | 0f958c4343b9fed3723d549b94825c95fb00a8d782713a3394f5a9677ad7b382 | [
{
"content": "Suppose that \\( f(x) \\) is a function defined for every real number \\( x \\) with \\( 0 \\leq x \\leq 1 \\) with the properties that\n\n- \\( f(1-x)=1-f(x) \\) for all real numbers \\( x \\) with \\( 0 \\leq x \\leq 1 \\),\n- \\( f\\left(\\frac{1}{3} x\\right)=\\frac{1}{2} f(x) \\) for all real... | Suppose that \( f(x) \) is a function defined for every real number \( x \) with \( 0 \leq x \leq 1 \) with the properties that
- \( f(1-x)=1-f(x) \) for all real numbers \( x \) with \( 0 \leq x \leq 1 \),
- \( f\left(\frac{1}{3} x\right)=\frac{1}{2} f(x) \) for all real numbers \( x \) with \( 0 \leq x \leq 1 \), an... | "[\"\\\\frac{3}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1248, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15265"}] | {
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[
"\\frac{17}{21}"
] | [
"skywork"
] | 76da608ff245d36e54b6ff8a62a50f81f6c2ab92c9bca404b7ee904979bd3609 | [
{
"content": "Two different natural numbers are selected from the set $\\{1, 2, 3, \\ldots, 7\\}$. What is the probability that the greatest common divisor of these two numbers is one? Express your answer as a common fraction.",
"role": "user"
}
] | Two different natural numbers are selected from the set $\{1, 2, 3, \ldots, 7\}$. What is the probability that the greatest common divisor of these two numbers is one? Express your answer as a common fraction. | "[\"\\\\frac{17}{21}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1275, "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:15266"}] | {
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[
"\\sqrt{65}"
] | [
"skywork"
] | c0cfecf88833b8c16fcb23fcdc364c1c294499f5cf7f3d9b6710f2f68f53f163 | [
{
"content": "2. Let complex numbers $z, w$ satisfy $|z|=3,(z+\\bar{w})(\\bar{z}-w)=7+4 \\mathrm{i}$, where $\\mathrm{i}$ is the imaginary unit, $\\bar{z}, \\bar{w}$ represent the conjugates of $z, w$ respectively, then the modulus of $(z+2 \\bar{w})(\\bar{z}-2 w)$ is $\\qquad$ .",
"role": "user"
}
] | 2. Let complex numbers $z, w$ satisfy $|z|=3,(z+\bar{w})(\bar{z}-w)=7+4 \mathrm{i}$, where $\mathrm{i}$ is the imaginary unit, $\bar{z}, \bar{w}$ represent the conjugates of $z, w$ respectively, then the modulus of $(z+2 \bar{w})(\bar{z}-2 w)$ is $\qquad$ . | "[\"\\\\sqrt{65}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1253, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15267"}, {"dataset": "skywork", "extra_in... | {
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"reference_components": 1,
"reference_present": true
} |
[
"308"
] | [
"skywork"
] | 312c80cb3411f60e389d7ecc7ba5445c30c47187cbc201d2256109d4bb2c0075 | [
{
"content": "Jillian drives along a straight road that goes directly from her house $(J)$ to her Grandfather's house $(G)$. Some of this road is on flat ground and some is downhill or uphill. Her car travels downhill at $99 \\mathrm{~km} / \\mathrm{h}$, on flat ground at $77 \\mathrm{~km} / \\mathrm{h}$, and u... | Jillian drives along a straight road that goes directly from her house $(J)$ to her Grandfather's house $(G)$. Some of this road is on flat ground and some is downhill or uphill. Her car travels downhill at $99 \mathrm{~km} / \mathrm{h}$, on flat ground at $77 \mathrm{~km} / \mathrm{h}$, and uphill at $63 \mathrm{~km} ... | "[\"308\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1255, "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:15268"}] | {
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[
"15"
] | [
"skywork"
] | 84b7d880d81e4305bd2c522eabbd49249f795767d7107619f718ec498fc48f1b | [
{
"content": "How many ways are there to put 4 balls in 3 boxes if the balls are not distinguishable but the boxes are?",
"role": "user"
}
] | How many ways are there to put 4 balls in 3 boxes if the balls are not distinguishable but the boxes are? | "[\"15\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1285, "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:15269"}] | {
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[
"1984"
] | [
"skywork"
] | 725d8422044bc3b1d5b902db62fce06f3825431eea93610d55fcbe921d529aba | [
{
"content": "What is the maximum value that can be taken by the sum\n\n$$\n\\left|x_{1}-1\\right|+\\left|x_{2}-2\\right|+\\ldots+\\left|x_{63}-63\\right|\n$$\n\nif $x_{1}, x_{2}, \\ldots, x_{63}$ are some permutation of the numbers $1, 2, 3, \\ldots, 63$?",
"role": "user"
}
] | What is the maximum value that can be taken by the sum
$$
\left|x_{1}-1\right|+\left|x_{2}-2\right|+\ldots+\left|x_{63}-63\right|
$$
if $x_{1}, x_{2}, \ldots, x_{63}$ are some permutation of the numbers $1, 2, 3, \ldots, 63$? | "[\"1984\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1277, "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:15270"}] | {
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[
"\\frac{3}{2}+ \\sqrt{2}"
] | [
"skywork"
] | f279267cb2dfff3b8b2fa5a6114de3c27ea664809a2bcbaceeaf2339464b493a | [
{
"content": "Given the function $f(x)=|x-1|+|x+1|$.\n(I) Solve the inequality $f(x) < 3$;\n(II) If the minimum value of $f(x)$ is $m$, let $a > 0$, $b > 0$, and $a+b=m$, find the minimum value of $\\frac{1}{a}+ \\frac{2}{b}$.",
"role": "user"
}
] | Given the function $f(x)=|x-1|+|x+1|$.
(I) Solve the inequality $f(x) < 3$;
(II) If the minimum value of $f(x)$ is $m$, let $a > 0$, $b > 0$, and $a+b=m$, find the minimum value of $\frac{1}{a}+ \frac{2}{b}$. | "[\"\\\\frac{3}{2}+ \\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1243, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15271"}] | {
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[
"y=2x^2-x"
] | [
"skywork"
] | 35bdbef4dfe0eddc81f177cfb9a93eda980201c96e43442e2670b4c554845cae | [
{
"content": "Example 5. Through the origin, any line intersects the parabola $y^{2}=x^{2}-x+3$ at points $A$ and $B$. Find the locus of the midpoint of $AB$.\n\nKeep the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | Example 5. Through the origin, any line intersects the parabola $y^{2}=x^{2}-x+3$ at points $A$ and $B$. Find the locus of the midpoint of $AB$.
Keep the original text's line breaks and format, and output the translation result directly. | "[\"y=2x^2-x\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1270, "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:15272"}] | {
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[
"\\frac{1}{2}"
] | [
"skywork"
] | 8d68eb9fbe1c764500a91af0ed6582620b1f49292cb3d0369073f58fa1d270b3 | [
{
"content": "The area of the triangle formed by the tangent to the curve $y=\\ln(x)-2x$ at the point $(1, -2)$ and the coordinate axes.",
"role": "user"
}
] | The area of the triangle formed by the tangent to the curve $y=\ln(x)-2x$ at the point $(1, -2)$ and the coordinate axes. | "[\"\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1264, "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:15273"}] | {
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[
"2\\sqrt{13-6\\sqrt{3}}"
] | [
"skywork"
] | a5a5837f616ae8c85d6a0f96006a5d8e4fa2ccae2028e0e17693f884edba7f46 | [
{
"content": "10. Triangle $A B C$ is inscribed in a circle $\\omega$. Let the bisector of angle $A$ meet $\\omega$ at $D$ and $B C$ at $E$. Let the reflections of $A$ across $D$ and $C$ be $D^{\\prime}$ and $C^{\\prime}$, respectively. Suppose that $\\angle A=60^{\\circ}, A B=3$, and $A E=4$. If the tangent to... | 10. Triangle $A B C$ is inscribed in a circle $\omega$. Let the bisector of angle $A$ meet $\omega$ at $D$ and $B C$ at $E$. Let the reflections of $A$ across $D$ and $C$ be $D^{\prime}$ and $C^{\prime}$, respectively. Suppose that $\angle A=60^{\circ}, A B=3$, and $A E=4$. If the tangent to $\omega$ at $A$ meets line ... | "[\"2\\\\sqrt{13-6\\\\sqrt{3}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1269, "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:15274"}] | {
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[
"\\frac{42}{5}"
] | [
"skywork"
] | 856eafca4ae53468ad2a26fd791d22e607ef53290dc7871e654a9c5480f42acc | [
{
"content": "502. Find the smallest fraction, which when divided by each of the fractions $\\frac{21}{25}$ and $\\frac{14}{15}$, results in a natural number.\n\nThe conditions of this problem are unique: here two fractions are mentioned, one of which divides the other exactly.",
"role": "user"
}
] | 502. Find the smallest fraction, which when divided by each of the fractions $\frac{21}{25}$ and $\frac{14}{15}$, results in a natural number.
The conditions of this problem are unique: here two fractions are mentioned, one of which divides the other exactly. | "[\"\\\\frac{42}{5}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1279, "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:15275"}] | {
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[
"\\frac{1}{30}"
] | [
"skywork"
] | 2c726e73904cf9ab406b1bba6d6effd6f561b680d9c39ff7f5e290126669c052 | [
{
"content": "If you pick a random $3$-digit number, what is the probability that its hundreds digit is triple the ones digit?",
"role": "user"
}
] | If you pick a random $3$-digit number, what is the probability that its hundreds digit is triple the ones digit? | "[\"\\\\frac{1}{30}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1268, "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:15276"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"1482"
] | [
"skywork"
] | 14d9f87e8a17cfbc165d91ecad9290749bc0c4dfea723400817bbf75aaa69b59 | [
{
"content": "The numbers 2, 3, 5, 7, 11, 13, 17, 19 are arranged in a multiplication table, with four along the top and the other four down the left. The multiplication table is completed and the sum of the sixteen entries is tabulated. What is the largest possible sum of the sixteen entries?\n\n\\[\n\\begin{a... | The numbers 2, 3, 5, 7, 11, 13, 17, 19 are arranged in a multiplication table, with four along the top and the other four down the left. The multiplication table is completed and the sum of the sixteen entries is tabulated. What is the largest possible sum of the sixteen entries?
\[
\begin{array}{c||c|c|c|c|}
\times &... | "[\"1482\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1263, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15277"}] | {
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} |
[
"\\frac{45}{2}"
] | [
"skywork"
] | bca1e0d62adacfd9cae45d236e64bb4defb600ba0b020ca524a5f18a0ab74da4 | [
{
"content": "1. When $2 x^{2}$ was added to the quadratic trinomial $f(x)$, its maximum value increased by 10, and when $5 x^{2}$ was subtracted from it, its maximum value decreased by $\\frac{15}{2}$. How will the maximum value of $f(x)$ change if $3 x^{2}$ is added to it?",
"role": "user"
}
] | 1. When $2 x^{2}$ was added to the quadratic trinomial $f(x)$, its maximum value increased by 10, and when $5 x^{2}$ was subtracted from it, its maximum value decreased by $\frac{15}{2}$. How will the maximum value of $f(x)$ change if $3 x^{2}$ is added to it? | "[\"\\\\frac{45}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1235, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:15278"}] | {
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} |
[
"10"
] | [
"skywork"
] | c59e72f0d26a310b4ba99e37986c5b696c7f16c001faa4589139e982719e70c9 | [
{
"content": "Solve the equation $\\frac{n!}{2}=k!+l!$ in natural numbers $n$, $k$, and $l$, where $n! = 1 \\cdot 2 \\cdots n$. In your answer, indicate 0 if there are no solutions, specify the value of $n$ if there is only one solution, or provide the sum of all $n$ values if there are multiple solutions. Reca... | Solve the equation $\frac{n!}{2}=k!+l!$ in natural numbers $n$, $k$, and $l$, where $n! = 1 \cdot 2 \cdots n$. In your answer, indicate 0 if there are no solutions, specify the value of $n$ if there is only one solution, or provide the sum of all $n$ values if there are multiple solutions. Recall that a solution is a t... | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1266, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15279"}] | {
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[
"10.5"
] | [
"skywork"
] | ae6257962914284bfdc4a1305358089c85a51b2e170c3be796f23f41e777b51c | [
{
"content": "A three-digit number is composed of three different non-zero digits in base ten. When divided by the sum of these three digits, the smallest quotient value is what?",
"role": "user"
}
] | A three-digit number is composed of three different non-zero digits in base ten. When divided by the sum of these three digits, the smallest quotient value is what? | "[\"10.5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1272, "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:15280"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"35"
] | [
"skywork"
] | 76c7a0b1e51467a2a73764ecaeb8a59f893fb27d60fdc9c181f99f4d2e886ff6 | [
{
"content": "How many positive integers less than $800$ are either a perfect cube or a perfect square?",
"role": "user"
}
] | How many positive integers less than $800$ are either a perfect cube or a perfect square? | "[\"35\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1281, "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:15281"}] | {
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} |
[
"198"
] | [
"skywork"
] | 7606d935636bd12f35d345d9874c8fcf427100d42dc5b747e0ea6b4ae2c70f31 | [
{
"content": "Example 5 A mall installs an escalator between the first and second floors, which travels upwards at a uniform speed. A boy and a girl start walking up the escalator to the second floor (the escalator itself is also moving). If the boy and the girl both move at a uniform speed, and the boy walks t... | Example 5 A mall installs an escalator between the first and second floors, which travels upwards at a uniform speed. A boy and a girl start walking up the escalator to the second floor (the escalator itself is also moving). If the boy and the girl both move at a uniform speed, and the boy walks twice as many steps per... | "[\"198\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1246, "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:15283"}] | {
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} |
[
"\\frac{\\sqrt{10}}{2}"
] | [
"skywork"
] | 1d1df2f514d9d28cc50e3edbbd94625bec1eb8f56f24d0faadd01954cba21564 | [
{
"content": "Example 5 Let $a, b, c$ all be positive numbers, $a+b+4c^2=1$, find the maximum value of $\\sqrt{a}+\\sqrt{b}+\\sqrt{2}c$.\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | Example 5 Let $a, b, c$ all be positive numbers, $a+b+4c^2=1$, find the maximum value of $\sqrt{a}+\sqrt{b}+\sqrt{2}c$.
Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly. | "[\"\\\\frac{\\\\sqrt{10}}{2}\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 1288, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15284"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"\\dfrac{36}{7}"
] | [
"skywork"
] | 38e2d7436bb54f60440bfa442d9672782ccd1688a5f67cc3ca45f441e1a2921e | [
{
"content": "Given that $F$ is the right focus of the hyperbola $C$: ${{x}^{2}}-\\dfrac{{{y}^{2}}}{8}=1$, and $P$ is a point on the left branch of $C$, $A(0,4)$. When the perimeter of $\\Delta APF$ is minimized, the area of this triangle is \\_\\_\\_.",
"role": "user"
}
] | Given that $F$ is the right focus of the hyperbola $C$: ${{x}^{2}}-\dfrac{{{y}^{2}}}{8}=1$, and $P$ is a point on the left branch of $C$, $A(0,4)$. When the perimeter of $\Delta APF$ is minimized, the area of this triangle is \_\_\_. | "[\"\\\\dfrac{36}{7}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1287, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:15285"}] | {
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} |
[
"19152"
] | [
"skywork"
] | eae9db6a21a4734d8a3fce1b379dfa2121bb233c18a5ee566ad61f6811492bc7 | [
{
"content": "Two toads named Gamakichi and Gamatatsu are sitting at the points $(0,0)$ and $(2,0)$ respectively. Their goal is to reach $(5,5)$ and $(7,5)$ respectively by making one unit jumps in positive $x$ or $y$ direction at a time. How many ways can they do this while ensuring that there is no point on t... | Two toads named Gamakichi and Gamatatsu are sitting at the points $(0,0)$ and $(2,0)$ respectively. Their goal is to reach $(5,5)$ and $(7,5)$ respectively by making one unit jumps in positive $x$ or $y$ direction at a time. How many ways can they do this while ensuring that there is no point on the plane where both Ga... | "[\"19152\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1259, "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:15286"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"45"
] | [
"skywork"
] | eb4502b275816d91d17a85f10b8674cde32b3fdf35cab877d4f860ad12969d8c | [
{
"content": "1. Let $A B C$ be an acute angled triangle. The circle $\\Gamma$ with $B C$ as diameter intersects $A B$ and $A C$ again at $P$ and $Q$, respectively. Determine $\\angle B A C$ given that the orthocenter of triangle $A P Q$ lies on $\\Gamma$.",
"role": "user"
}
] | 1. Let $A B C$ be an acute angled triangle. The circle $\Gamma$ with $B C$ as diameter intersects $A B$ and $A C$ again at $P$ and $Q$, respectively. Determine $\angle B A C$ given that the orthocenter of triangle $A P Q$ lies on $\Gamma$. | "[\"45\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1276, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:15287"}] | {
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} |
[
"3"
] | [
"skywork"
] | ee54804a5cc84e0e7f709ba1c03bcbf9a0637b3d005b0efd4e3ea78cb10926a8 | [
{
"content": "489*. Three cyclists set off simultaneously: the first and second from point A, and the third towards them from point B. After 1.5 hours, the first cyclist was at an equal distance from the other two, and after 2 hours from the start, the third cyclist was at an equal distance from the first and s... | 489*. Three cyclists set off simultaneously: the first and second from point A, and the third towards them from point B. After 1.5 hours, the first cyclist was at an equal distance from the other two, and after 2 hours from the start, the third cyclist was at an equal distance from the first and second. How many hours ... | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1274, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15288"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-1"
] | [
"skywork"
] | fc56315e4370cbc8673d5fe29ca227776335466b9670783a0a64ba1e5c8f7d88 | [
{
"content": "$2.14 \\sqrt{15-x}+\\sqrt{3-x}=6$.",
"role": "user"
}
] | $2.14 \sqrt{15-x}+\sqrt{3-x}=6$. | "[\"-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1295, "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:15289"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | 25edca57235dbacbda4c79fb0be23e5c03a5eaa345d5dd8fe1e8c4ee91f4ecb3 | [
{
"content": "Donna has $n$ boxes of doughnuts. Each box contains $13$ doughnuts.\n\nAfter eating one doughnut, Donna is able to rearrange the remaining doughnuts into bags so that each bag contains $9$ doughnuts, and none are left over. What is the smallest possible value of $n$?",
"role": "user"
}
] | Donna has $n$ boxes of doughnuts. Each box contains $13$ doughnuts.
After eating one doughnut, Donna is able to rearrange the remaining doughnuts into bags so that each bag contains $9$ doughnuts, and none are left over. What is the smallest possible value of $n$? | "[\"7\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1291, "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:15290"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
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"reference_components": 1,
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} |
[
"7^11"
] | [
"skywork"
] | ecd1013fe87ce3cbb3ea6c7aaf4e7883a68e662d543d304b2918d7c6887c359f | [
{
"content": "Given sets \\( A, B, C \\) (not necessarily distinct) such that \\( A \\cup B \\cup C = \\{1, 2, 3, \\ldots, 11\\} \\), find the number of ordered pairs \\((A, B, C)\\) that satisfy this condition.",
"role": "user"
}
] | Given sets \( A, B, C \) (not necessarily distinct) such that \( A \cup B \cup C = \{1, 2, 3, \ldots, 11\} \), find the number of ordered pairs \((A, B, C)\) that satisfy this condition. | "[\"7^11\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1262, "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:15291"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"220"
] | [
"skywork"
] | 6b7317d2d63b251d6a021a1b3dff44106cef5eef29a7ad53df4b5e3683d10a79 | [
{
"content": "Suppose $f$ is a function that satisfies $f(2)=20$ and $f(2 n)+n f(2)=f(2 n+2)$ for all positive integers $n$. What is the value of $f(10)$ ?",
"role": "user"
}
] | Suppose $f$ is a function that satisfies $f(2)=20$ and $f(2 n)+n f(2)=f(2 n+2)$ for all positive integers $n$. What is the value of $f(10)$ ? | "[\"220\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1289, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15292"}] | {
"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
} |
[
"314"
] | [
"skywork"
] | cc56adecab41a4d1e70c0a230116869c99d87ef89404fc89a5a1ca0b28a39b32 | [
{
"content": "Ed has eight identical green marbles, and a large supply of identical red marbles. He arranges the green marbles and some of the red ones in a row and finds that the number of marbles whose left-hand neighbor is the same color as themselves is equal to the number of marbles whose left-hand neighbo... | Ed has eight identical green marbles, and a large supply of identical red marbles. He arranges the green marbles and some of the red ones in a row and finds that the number of marbles whose left-hand neighbor is the same color as themselves is equal to the number of marbles whose left-hand neighbor is of a different co... | "[\"314\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1267, "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:15293"}] | {
"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
} |
[
"105"
] | [
"skywork"
] | 6e03a1f5e041cd3fd7cfeff66c0c7bc2ceca72dfb895ab559aae4ffbe6da738e | [
{
"content": "Let $\\triangle ABC$ with $AB=AC$ and $BC=14$ be inscribed in a circle $\\omega$ . Let $D$ be the point on ray $BC$ such that $CD=6$ . Let the intersection of $AD$ and $\\omega$ be $E$ . Given that $AE=7$ , find $AC^2$ .\n\n*Proposed by Ephram Chun and Euhan Kim*",
"role": "... | Let $\triangle ABC$ with $AB=AC$ and $BC=14$ be inscribed in a circle $\omega$ . Let $D$ be the point on ray $BC$ such that $CD=6$ . Let the intersection of $AD$ and $\omega$ be $E$ . Given that $AE=7$ , find $AC^2$ .
*Proposed by Ephram Chun and Euhan Kim* | "[\"105\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1280, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15294"}] | {
"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
} |
[
"1680"
] | [
"skywork"
] | e3b657288eb8394c9dd26cc65410e4963fa9b6db39ef07eca76106df03e67739 | [
{
"content": "For any positive integer $a$, define $M(a)$ to be the number of positive integers $b$ for which $a+b$ divides $ab$. Find all integer(s) $a$ with $1\\le a\\le 2013$ such that $M(a)$ attains the largest possible value in the range of $a$.",
"role": "user"
}
] | For any positive integer $a$, define $M(a)$ to be the number of positive integers $b$ for which $a+b$ divides $ab$. Find all integer(s) $a$ with $1\le a\le 2013$ such that $M(a)$ attains the largest possible value in the range of $a$. | "[\"1680\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1283, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:15295"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"a>\\frac{1}{2}"
] | [
"skywork"
] | 24fa1a796eaf9010f294317004d4fa384c68cdc379e570fe01bed1d90b7637bb | [
{
"content": "What describes the set of values of $a$ for which the curves $x^2+y^2=a^2$ and $y=x^2-a$ in the real $xy$-plane intersect at exactly 3 points?",
"role": "user"
}
] | What describes the set of values of $a$ for which the curves $x^2+y^2=a^2$ and $y=x^2-a$ in the real $xy$-plane intersect at exactly 3 points? | "[\"a>\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1294, "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:15296"}, {"dataset": "skywork", "extra_inf... | {
"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
} |
[
"75"
] | [
"skywork"
] | bacec4c331c04ecd32bc9764e6ec771e3bcdbd846a3553f28e97d387a9c4ba52 | [
{
"content": "13.213. Usually, two mechanisms are involved in performing a certain task simultaneously. The productivity of these mechanisms is not the same, and when working together, they complete the task in 30 hours. However, this time the joint operation of the two mechanisms lasted only 6 hours, after whi... | 13.213. Usually, two mechanisms are involved in performing a certain task simultaneously. The productivity of these mechanisms is not the same, and when working together, they complete the task in 30 hours. However, this time the joint operation of the two mechanisms lasted only 6 hours, after which the first mechanism... | "[\"75\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1286, "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:15297"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"512"
] | [
"skywork"
] | 9aa8bc281292846092bf547f83985b097e6eef9e9b8d0212e0fa468baadb9d9e | [
{
"content": "Shen A.X.\n\nA strip of $1 \\times 10$ is divided into unit squares. The numbers $1, 2, \\ldots, 10$ are written in the squares. First, the number 1 is written in one of the squares, then the number 2 is written in one of the adjacent squares, then the number 3 is written in one of the adjacent sq... | Shen A.X.
A strip of $1 \times 10$ is divided into unit squares. The numbers $1, 2, \ldots, 10$ are written in the squares. First, the number 1 is written in one of the squares, then the number 2 is written in one of the adjacent squares, then the number 3 is written in one of the adjacent squares to the already occup... | "[\"512\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1278, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "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:15298"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 726bd3d77e6a010099d3a4782f6a1f3f53801246206d5665daa1ba3b14176352 | [
{
"content": "Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the greatest number of additional cars she must buy in order to be able to arrange all her cars this way?",
"role": "user"
}
] | Danica wants to arrange her model cars in rows with exactly 6 cars in each row. She now has 23 model cars. What is the greatest number of additional cars she must buy in order to be able to arrange all her cars this way? | "[\"1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1300, "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:15299"}] | {
"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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