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 |
|---|---|---|---|---|---|---|---|---|
[
"357"
] | [
"skywork"
] | 1dc46f43c1094ff94e9524a3fbbb431517ca5da32977ac790f136027809162d5 | [
{
"content": "25. Find the number of $0-1$ binary sequences formed by six 0 's and six 1 's such that no three 0's are together. For example, 110010100101 is such a sequence but 101011000101 and 110101100001 are not.",
"role": "user"
}
] | 25. Find the number of $0-1$ binary sequences formed by six 0 's and six 1 's such that no three 0's are together. For example, 110010100101 is such a sequence but 101011000101 and 110101100001 are not. | "[\"357\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1399, "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:15403"}, {"dataset": "skywork", "extra_inf... | {
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[
"120^\\circ"
] | [
"skywork"
] | f641e96b1992c33e41929b211f2afba390432b5b0169967e0a848cefaf175cdc | [
{
"content": "In $\\triangle PQR,$ the sum of $\\angle P$ and $\\angle Q$ is $60^\\circ.$ What is the measure of $\\angle R?$",
"role": "user"
}
] | In $\triangle PQR,$ the sum of $\angle P$ and $\angle Q$ is $60^\circ.$ What is the measure of $\angle R?$ | "[\"120^\\\\circ\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1411, "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:15404"}] | {
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[
"1"
] | [
"skywork"
] | d6c48eeea1dad2ca722248a9dc9c594009581d81a070d410718646f7cd9c56d1 | [
{
"content": "16.1. Calculate: $2^{15}-2^{14}-2^{13}-\\ldots-2^{1}-1$.\n\n$$\n\\text { (6-7 grades) }\n$$",
"role": "user"
}
] | 16.1. Calculate: $2^{15}-2^{14}-2^{13}-\ldots-2^{1}-1$.
$$
\text { (6-7 grades) }
$$ | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1416, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15405"}] | {
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[
"x^2 + 2py = 0"
] | [
"skywork"
] | 7e36b3ff895136b8a55d1037f0280b8357fcb6c97e98fc01c65b18a529f6b0f4 | [
{
"content": "$(BEL 1)$ A parabola $P_1$ with equation $x^2 - 2py = 0$ and parabola $P_2$ with equation $x^2 + 2py = 0, p > 0$, are given. A line $t$ is tangent to $P_2.$ Find the locus of pole $M$ of the line $t$ with respect to $P_1.$",
"role": "user"
}
] | $(BEL 1)$ A parabola $P_1$ with equation $x^2 - 2py = 0$ and parabola $P_2$ with equation $x^2 + 2py = 0, p > 0$, are given. A line $t$ is tangent to $P_2.$ Find the locus of pole $M$ of the line $t$ with respect to $P_1.$ | "[\" x^2 + 2py = 0 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1408, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:15406"}] | {
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} |
[
"18:17"
] | [
"skywork"
] | 83c60a6a49843d82f6be5bbfc1060df2ce74dd6a307e32f64ad130d644a1a38c | [
{
"content": "On the edges $D A, D B$ and $D C$ of the pyramid $A B C D$, points $K, L$ and $M$ are taken respectively, such that $D K=\\frac{1}{2} D A, D L=\\frac{2}{5} D B$ and $D M=\\frac{3}{4} D C, G-$ is the point of intersection of the medians of triangle $A B C$. In what ratio does the plane $K L M$ divi... | On the edges $D A, D B$ and $D C$ of the pyramid $A B C D$, points $K, L$ and $M$ are taken respectively, such that $D K=\frac{1}{2} D A, D L=\frac{2}{5} D B$ and $D M=\frac{3}{4} D C, G-$ is the point of intersection of the medians of triangle $A B C$. In what ratio does the plane $K L M$ divide the segment $D G ?$ | "[\"18:17\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1398, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15407"}] | {
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} |
[
"S_{EHFG} \\le \\dfrac{1}{4} S_{ABCD}"
] | [
"skywork"
] | 93c2e4419e954ef58ff42c46d9961e0903843c1ed545665741e9e3a3385d4316 | [
{
"content": "Let $ABCD$ be a trapezoid with $AB\\parallel CD$. Points $E,F$ lie on segments $AB,CD$ respectively. Segments $CE,BF$ meet at $H$, and segments $ED,AF$ meet at $G$. Show that $S_{EHFG}\\le \\dfrac{1}{4}S_{ABCD}$. Determine, with proof, if the conclusion still holds when $ABCD$ is just any convex q... | Let $ABCD$ be a trapezoid with $AB\parallel CD$. Points $E,F$ lie on segments $AB,CD$ respectively. Segments $CE,BF$ meet at $H$, and segments $ED,AF$ meet at $G$. Show that $S_{EHFG}\le \dfrac{1}{4}S_{ABCD}$. Determine, with proof, if the conclusion still holds when $ABCD$ is just any convex quadrilateral. | "[\"S_{EHFG} \\\\le \\\\dfrac{1}{4} S_{ABCD}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1390, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15408"}] | {
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} |
[
"18"
] | [
"skywork"
] | afcab126c6ae9711942afa3a2823e90e7ac07fbe31cc4a0b4c5e641f2db51252 | [
{
"content": "On a table, there are 30 coins: 23 ten-ruble coins and 7 five-ruble coins. Out of these, 20 coins are heads up, and the remaining 10 are tails up. What is the smallest number \\( k \\) such that among any randomly chosen \\( k \\) coins, there will always be at least one ten-ruble coin that is hea... | On a table, there are 30 coins: 23 ten-ruble coins and 7 five-ruble coins. Out of these, 20 coins are heads up, and the remaining 10 are tails up. What is the smallest number \( k \) such that among any randomly chosen \( k \) coins, there will always be at least one ten-ruble coin that is heads up? | "[\"18\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1402, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:15409"}] | {
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} |
[
"216"
] | [
"skywork"
] | c220d5e3bf97ef14303ea80eb006ef7ba522a53770fb2b712a39183d4a6da5e7 | [
{
"content": "In triangle $XYZ$, $XY = 540$ and $YZ = 360$. Points $N$ and $O$ are located on $\\overline{XY}$ and $\\overline{XZ}$ respectively, such that $XN = NY$, and $\\overline{ZO}$ is the angle bisector of angle $Z$. Let $Q$ be the point of intersection of $\\overline{YN}$ and $\\overline{ZO}$, and let $... | In triangle $XYZ$, $XY = 540$ and $YZ = 360$. Points $N$ and $O$ are located on $\overline{XY}$ and $\overline{XZ}$ respectively, such that $XN = NY$, and $\overline{ZO}$ is the angle bisector of angle $Z$. Let $Q$ be the point of intersection of $\overline{YN}$ and $\overline{ZO}$, and let $R$ be the point on line $YN... | "[\"216\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1401, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15410"}] | {
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} |
[
"6"
] | [
"skywork"
] | 097a87e30107c5cb3ab2704f99921fdf855bb300d0a6f7c049575b9e4d3e2101 | [
{
"content": "11.1. How many roots does the equation $\\sqrt{14-x^{2}}(\\sin x-\\cos 2 x)=0$ have?",
"role": "user"
}
] | 11.1. How many roots does the equation $\sqrt{14-x^{2}}(\sin x-\cos 2 x)=0$ have? | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1417, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15411"}] | {
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} |
[
"\\frac{5}{12}"
] | [
"skywork"
] | e6a6f04ecc5852c08af55225b8c62b0c4d7b27ac64d52326287e1e73d77d806c | [
{
"content": "What number is one third of the way from $\\frac14$ to $\\frac34$?",
"role": "user"
}
] | What number is one third of the way from $\frac14$ to $\frac34$? | "[\"\\\\frac{5}{12}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1440, "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:15412"}] | {
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} |
[
"n = 13"
] | [
"skywork"
] | 2dd1af456656d82369074faeb1355ac14bd4c4d29ddcf4b26ce53f774914dfb9 | [
{
"content": "For an ${n\\times n}$ matrix $A$, let $X_{i}$ be the set of entries in row $i$, and $Y_{j}$ the set of entries in column $j$, ${1\\leq i,j\\leq n}$. We say that $A$ is [i]golden[/i] if ${X_{1},\\dots ,X_{n},Y_{1},\\dots ,Y_{n}}$ are distinct sets. Find the least integer $n$ such that there exists ... | For an ${n\times n}$ matrix $A$, let $X_{i}$ be the set of entries in row $i$, and $Y_{j}$ the set of entries in column $j$, ${1\leq i,j\leq n}$. We say that $A$ is [i]golden[/i] if ${X_{1},\dots ,X_{n},Y_{1},\dots ,Y_{n}}$ are distinct sets. Find the least integer $n$ such that there exists a ${2004\times 2004}$ golde... | "[\" n = 13 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1410, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:15413"}] | {
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[
"- \\dfrac {56}{65}"
] | [
"skywork"
] | 5407da605c26679b776789ae4f90dedc2ca2d546f84101275f129395596e8d6d | [
{
"content": "Given that $\\dfrac {π}{2} < β < α < \\dfrac {3}{4}π$, $\\cos (α+β)=- \\dfrac {3}{5}$, and $\\sin (α-β)= \\dfrac {5}{13}$, find $\\cos 2β$.",
"role": "user"
}
] | Given that $\dfrac {π}{2} < β < α < \dfrac {3}{4}π$, $\cos (α+β)=- \dfrac {3}{5}$, and $\sin (α-β)= \dfrac {5}{13}$, find $\cos 2β$. | "[\"- \\\\dfrac {56}{65}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1413, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:15414"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\pi}{3}"
] | [
"skywork"
] | e9f9d4fff6189c9e0f688a27e000c3fa3e5029a68333f3c87fab1db4564eb79e | [
{
"content": "Let $I$ be the set of points $(x,y)$ in the Cartesian plane such that $$x>\\left(\\frac{y^4}{9}+2015\\right)^{1/4}$$ Let $f(r)$ denote the area of the intersection of $I$ and the disk $x^2+y^2\\le r^2$ of radius $r>0$ centered at the origin $(0,0)$. Determine the minimum possible real number $L$ s... | Let $I$ be the set of points $(x,y)$ in the Cartesian plane such that $$x>\left(\frac{y^4}{9}+2015\right)^{1/4}$$ Let $f(r)$ denote the area of the intersection of $I$ and the disk $x^2+y^2\le r^2$ of radius $r>0$ centered at the origin $(0,0)$. Determine the minimum possible real number $L$ such that $f(r)<Lr^2$ for a... | "[\"\\\\frac{\\\\pi}{3}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1420, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15415"}] | {
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} |
[
"(3,m), m \\ge 3"
] | [
"skywork"
] | 18e0c41b3d50261d1eb8fe7183e7614405ebfa0230fc88265394946b20105753 | [
{
"content": "Find all pairs $(n,m)$ $m\\geq n \\geq 3$ , for which exist such table $n\\times m$ with numbers in every cell, and sum of numbers in every $2\\times 2$ is negative and sum of numbers in every $3\\times 3$ is positive.",
"role": "user"
}
] | Find all pairs $(n,m)$ $m\geq n \geq 3$ , for which exist such table $n\times m$ with numbers in every cell, and sum of numbers in every $2\times 2$ is negative and sum of numbers in every $3\times 3$ is positive. | "[\"(3,m), m \\\\ge 3\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1397, "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:15416"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | a781a38fd861856caee408606b014fc1a308ea0a52d750e39aeb9c6027414a42 | [
{
"content": "What is the value of $3^{2}-2^{2}+1^{2}$ ?\n(A) 8\n(B) -2\n(C) 10\n(D) -5\n(E) 6",
"role": "user"
}
] | What is the value of $3^{2}-2^{2}+1^{2}$ ?
(A) 8
(B) -2
(C) 10
(D) -5
(E) 6 | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1438, "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:15417"}] | {
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} |
[
"\\frac{\\pi}{3}+1-\\sqrt{3}"
] | [
"skywork"
] | a343cd296a0baefd64ad897d31327702b2791f0c0bf7b8ecf8887927bc489f43 | [
{
"content": "10. In a square lawn with side length $a$, there are sprinkler devices installed at each of the four corners. The sprinkler devices can rotate to spray water at a $90^{\\circ}$ angle, and each can spray water from one side of its corner to the other side, with an effective range of $a$. Then the p... | 10. In a square lawn with side length $a$, there are sprinkler devices installed at each of the four corners. The sprinkler devices can rotate to spray water at a $90^{\circ}$ angle, and each can spray water from one side of its corner to the other side, with an effective range of $a$. Then the proportion of the lawn t... | "[\"\\\\frac{\\\\pi}{3}+1-\\\\sqrt{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1407, "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:15418"}] | {
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} |
[
"\\pm 2, \\pm 1, 0"
] | [
"skywork"
] | b5842bbd25c614afe4036760fa42fd3ac4b41465233edf61d82677d564bd9148 | [
{
"content": "One, (20 points) Given real numbers $x$, $y$, and $a$ satisfy\n$$\nx+y=x^{3}+y^{3}=x^{5}+y^{5}=a \\text {. }\n$$\n\nFind all possible values of $a$.",
"role": "user"
}
] | One, (20 points) Given real numbers $x$, $y$, and $a$ satisfy
$$
x+y=x^{3}+y^{3}=x^{5}+y^{5}=a \text {. }
$$
Find all possible values of $a$. | "[\"\\\\pm 2, \\\\pm 1, 0\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1423, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15419"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | f73076c00f1d7bd363584e912bf91453a4c904bfb7a51c85fa5ed909eceaeebc | [
{
"content": "17. The shaded region in the diagram, bounded by two concentric circles, is called an annulus. The circles have radii $2 \\mathrm{~cm}$ and $14 \\mathrm{~cm}$.\nThe dashed circle divides the area of this annulus into two equal areas. What is its radius?\nA $9 \\mathrm{~cm} \\quad$ B $10 \\mathrm{~... | 17. The shaded region in the diagram, bounded by two concentric circles, is called an annulus. The circles have radii $2 \mathrm{~cm}$ and $14 \mathrm{~cm}$.
The dashed circle divides the area of this annulus into two equal areas. What is its radius?
A $9 \mathrm{~cm} \quad$ B $10 \mathrm{~cm} \quad$ C $11 \mathrm{~cm}... | "[\"10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1426, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15420"}] | {
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[
"\\begin{pmatrix} 26/29 \\\\ 65/29 \\end{pmatrix}"
] | [
"skywork"
] | 7bc634562c3132aca7f9e5991bddab852655d7d4c21685dd4d0366d06d39c2e6 | [
{
"content": "When the vectors $\\begin{pmatrix} 4 \\\\ 1 \\end{pmatrix}$ and $\\begin{pmatrix} -1 \\\\ 3 \\end{pmatrix}$ are both projected onto the same vector $\\mathbf{v},$ the result is $\\mathbf{p}$ in both cases. Find $\\mathbf{p}.$",
"role": "user"
}
] | When the vectors $\begin{pmatrix} 4 \\ 1 \end{pmatrix}$ and $\begin{pmatrix} -1 \\ 3 \end{pmatrix}$ are both projected onto the same vector $\mathbf{v},$ the result is $\mathbf{p}$ in both cases. Find $\mathbf{p}.$ | "[\"\\\\begin{pmatrix} 26/29 \\\\\\\\ 65/29 \\\\end{pmatrix}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1400, "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:15421"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"720"
] | [
"skywork"
] | d5201841f2933a1cb5132c149af1e702544588a0f31b74419f200f53de95ec67 | [
{
"content": "Six students are arranged into two rows, with 3 students per row, and the number of different arrangements must be calculated.",
"role": "user"
}
] | Six students are arranged into two rows, with 3 students per row, and the number of different arrangements must be calculated. | "[\"720\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1428, "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:15422"}] | {
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} |
[
"2"
] | [
"skywork"
] | e31885734da0a0f7a4818a9e7ba0472741cada3110542b81a134410be8b39f35 | [
{
"content": "25. As shown in the figure, in rhombus $A B C D$, $\\angle A B C=120^{\\circ}, E$ is the midpoint of side $A B$, $P$ is a moving point on side $A C$, the minimum value of $P B+P E$ is $\\sqrt{3}$, then the length of $A B$ is $\\qquad$.",
"role": "user"
}
] | 25. As shown in the figure, in rhombus $A B C D$, $\angle A B C=120^{\circ}, E$ is the midpoint of side $A B$, $P$ is a moving point on side $A C$, the minimum value of $P B+P E$ is $\sqrt{3}$, then the length of $A B$ is $\qquad$. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1415, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:15423"}] | {
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} |
[
"2"
] | [
"skywork"
] | 069a0f474429fac9f36f5f88500f2166f0e572c1cfab60e0ca7bb602ad9c109f | [
{
"content": "2. Real numbers $x, y, z$ satisfy the relations:\n\n$$\n4 x^{2}-2 x-30 y z=25 y^{2}+5 y+12 x z=9 z^{2}-3 z-20 x y .\n$$\n\nFind the maximum of the sum $a+b+c$, where $a=2 x+5 y, b=3 z+5 y, c=3 z-2 x$.",
"role": "user"
}
] | 2. Real numbers $x, y, z$ satisfy the relations:
$$
4 x^{2}-2 x-30 y z=25 y^{2}+5 y+12 x z=9 z^{2}-3 z-20 x y .
$$
Find the maximum of the sum $a+b+c$, where $a=2 x+5 y, b=3 z+5 y, c=3 z-2 x$. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1421, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15424"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"18396"
] | [
"skywork"
] | fada347da8524452039d4e67cfc76fe16815d80dad1089241e84db906596776e | [
{
"content": "This year is 2017, and the sum of the digits of the year is 10. Find the sum of all the years in this century whose digits sum to 10.",
"role": "user"
}
] | This year is 2017, and the sum of the digits of the year is 10. Find the sum of all the years in this century whose digits sum to 10. | "[\"18396\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1434, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15425"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 5f998311ee981e810ff3a93a5df40e95aa37f577f01558d375572f68dda93dd2 | [
{
"content": "In the convex quadrilateral \\(ABCD\\),\n\\[\n\\angle BAD = \\angle BCD = 120^\\circ, \\quad BC = CD = 10.\n\\]\n\nFind \\(AC.\\)",
"role": "user"
}
] | In the convex quadrilateral \(ABCD\),
\[
\angle BAD = \angle BCD = 120^\circ, \quad BC = CD = 10.
\]
Find \(AC.\) | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1445, "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:15426"}] | {
"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"
] | be908c23bb862676aae28354ea2dbe75c186b02fab53fca9c8445a2f3a46f37c | [
{
"content": "Ralph went to the store and bought 12 pairs of socks for a total of $24. Some of the socks he bought cost $1 a pair, some of the socks he bought cost $3 a pair, and some of the socks he bought cost $4 a pair. If he bought at least one pair of each type, how many pairs of $1 socks did Ralph buy?",
... | Ralph went to the store and bought 12 pairs of socks for a total of $24. Some of the socks he bought cost $1 a pair, some of the socks he bought cost $3 a pair, and some of the socks he bought cost $4 a pair. If he bought at least one pair of each type, how many pairs of $1 socks did Ralph buy? | "[\"7\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1439, "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:15428"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.3"
] | [
"skywork"
] | 6abc4d6ca221ce49edebb3bd50f71cfea617c478b1c32a37b3b8148b86ccb762 | [
{
"content": "599. For four independent samples of the same size \\( n=17 \\), extracted from normal general populations, the corrected sample variances are: 0.21; 0.25; 0.34; 0.40.\n\nRequired: a) at a significance level of 0.05, test the null hypothesis of homogeneity of variances (critical region - right-tai... | 599. For four independent samples of the same size \( n=17 \), extracted from normal general populations, the corrected sample variances are: 0.21; 0.25; 0.34; 0.40.
Required: a) at a significance level of 0.05, test the null hypothesis of homogeneity of variances (critical region - right-tailed); b) estimate the popu... | "[\"0.3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1446, "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:15429"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"[\\frac{\\sqrt{2}}{2},+\\infty)"
] | [
"skywork"
] | 51e2e536b725cbaa0e2d4db9b04be0e2adf63d1e48d10a93cfa7ae1b2197d55e | [
{
"content": "72 The increasing interval of the function $y=2\\left(\\log _{\\frac{1}{2}} x\\right)^{2}-2 \\log _{\\frac{1}{2}} x+1$ is\nA. $\\left(0, \\frac{1}{2}\\right)$\nB. $\\left[\\frac{1}{2}, \\frac{\\sqrt{2}}{2}\\right)$\nC. $\\left[\\frac{\\sqrt{2}}{2},+\\infty\\right)$\nD. does not exist",
"role":... | 72 The increasing interval of the function $y=2\left(\log _{\frac{1}{2}} x\right)^{2}-2 \log _{\frac{1}{2}} x+1$ is
A. $\left(0, \frac{1}{2}\right)$
B. $\left[\frac{1}{2}, \frac{\sqrt{2}}{2}\right)$
C. $\left[\frac{\sqrt{2}}{2},+\infty\right)$
D. does not exist | "[\"[\\\\frac{\\\\sqrt{2}}{2},+\\\\infty)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1425, "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:15430"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3600"
] | [
"skywork"
] | d9f5edaf5a292fe988547eda72c74628996930cf83a63c8e914551e5a476772f | [
{
"content": "8. For a finite set\n$$\nA=\\left\\{a_{i} \\mid 1 \\leqslant i \\leqslant n, i \\in \\mathbf{Z}_{+}\\right\\}\\left(n \\in \\mathbf{Z}_{+}\\right) \\text {, }\n$$\n\nlet $S=\\sum_{i=1}^{n} a_{i}$, then $S$ is called the \"sum\" of set $A$, denoted as\n$|A|$. Given the set $P=\\{2 n-1 \\mid n=1,2, ... | 8. For a finite set
$$
A=\left\{a_{i} \mid 1 \leqslant i \leqslant n, i \in \mathbf{Z}_{+}\right\}\left(n \in \mathbf{Z}_{+}\right) \text {, }
$$
let $S=\sum_{i=1}^{n} a_{i}$, then $S$ is called the "sum" of set $A$, denoted as
$|A|$. Given the set $P=\{2 n-1 \mid n=1,2, \cdots, 10\}$,
all the subsets of $P$ containin... | "[\"3600\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1427, "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:15431"}, {"dataset": "skywork", "extra_inf... | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2n^3 + 7n^2 + 7n + 3"
] | [
"skywork"
] | 810d5380abd50e6f354ead9b1945e912ff68852989ea21afc3403cdceb1eb34d | [
{
"content": "Let $n$ be a positive integer. \n- Find, in terms of $n$, the number of pairs $(x,y)$ of positive integers that are solutions of the equation : $$x^2-y^2=10^2.30^{2n}$$\n- Prove further that this number is never a square",
"role": "user"
}
] | Let $n$ be a positive integer.
- Find, in terms of $n$, the number of pairs $(x,y)$ of positive integers that are solutions of the equation : $$x^2-y^2=10^2.30^{2n}$$
- Prove further that this number is never a square | "[\" 2n^3 + 7n^2 + 7n + 3 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1418, "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:15432"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"41"
] | [
"skywork"
] | 9d841b740f960e3147dcbd1a98619d24d32091eb3f14dc2c1885b919a8019454 | [
{
"content": "Example 8 Let $X$ be a set with 56 elements. Find the smallest positive integer $n$, such that for any 15 subsets of $X$, if the union of any seven of these subsets has at least $n$ elements, then there must exist three of these 15 subsets whose intersection is non-empty. ${ }^{[2]}$\n(2006, China... | Example 8 Let $X$ be a set with 56 elements. Find the smallest positive integer $n$, such that for any 15 subsets of $X$, if the union of any seven of these subsets has at least $n$ elements, then there must exist three of these 15 subsets whose intersection is non-empty. ${ }^{[2]}$
(2006, China Mathematical Olympiad) | "[\"41\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1437, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:15433"}] | {
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} |
[
"8117"
] | [
"skywork"
] | 9b34c75c0a9fd839db12bf6864c599d5059157d3458f99468a6ebe106af9fe17 | [
{
"content": "Let the function $f: \\mathbb{Z} \\rightarrow \\mathbb{Z}$ take only integer inputs and have integer outputs. For any integers $x$ and $y$, $f$ satisfies $f(x)+f(y)=f(x+1)+f(y-1)$. If $f(2016)=6102$ and $f(6102)=2016$, what is $f(1)$?",
"role": "user"
}
] | Let the function $f: \mathbb{Z} \rightarrow \mathbb{Z}$ take only integer inputs and have integer outputs. For any integers $x$ and $y$, $f$ satisfies $f(x)+f(y)=f(x+1)+f(y-1)$. If $f(2016)=6102$ and $f(6102)=2016$, what is $f(1)$? | "[\"8117\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1429, "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:15434"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | ed1b608bdf2d1c443ed317edc72d9f9a6169fde1bbed43e6802cbc7676dad9f6 | [
{
"content": "Find the sum of the infinite series $\\frac{1}{3^{2}-1^{2}}\\left(\\frac{1}{1^{2}}-\\frac{1}{3^{2}}\\right)+\\frac{1}{5^{2}-3^{2}}\\left(\\frac{1}{3^{2}}-\\frac{1}{5^{2}}\\right)+\\frac{1}{7^{2}-5^{2}}\\left(\\frac{1}{5^{2}}-\\frac{1}{7^{2}}\\right)+$",
"role": "user"
}
] | Find the sum of the infinite series $\frac{1}{3^{2}-1^{2}}\left(\frac{1}{1^{2}}-\frac{1}{3^{2}}\right)+\frac{1}{5^{2}-3^{2}}\left(\frac{1}{3^{2}}-\frac{1}{5^{2}}\right)+\frac{1}{7^{2}-5^{2}}\left(\frac{1}{5^{2}}-\frac{1}{7^{2}}\right)+$ | "[\"1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1436, "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:15435"}] | {
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} |
[
"\\left(x-\\frac{1}{2}\\right)^{2}+\\left(y+\\frac{7}{2}\\right)^{2}=\\frac{178}{4}"
] | [
"skywork"
] | 74aef924ec0e8576e515fa817480e58629180baeae26940469c959a750433e99 | [
{
"content": "2. Find the equation of the circle passing through the intersection points of the two circles\n$$\nx^{2}+y^{2}+6 x-4=0 \\text { and } x^{2}+y^{2}+6 y-28=0\n$$\n\nand whose center lies on the line $x-y-4=0$.",
"role": "user"
}
] | 2. Find the equation of the circle passing through the intersection points of the two circles
$$
x^{2}+y^{2}+6 x-4=0 \text { and } x^{2}+y^{2}+6 y-28=0
$$
and whose center lies on the line $x-y-4=0$. | "[\"\\\\left(x-\\\\frac{1}{2}\\\\right)^{2}+\\\\left(y+\\\\frac{7}{2}\\\\right)^{2}=\\\\frac{178}{4}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1443, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15436"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2}"
] | [
"skywork"
] | 5a4eed1136e0aff4cfd1fc39b2ff79bf84e341a234a435495e631898cd5af074 | [
{
"content": "3. Given $\\arcsin (\\sin \\alpha+\\sin \\beta)+\\arcsin (\\sin \\alpha-\\sin \\beta)=\\frac{\\pi}{2}, \\sin ^{2} \\alpha+\\sin ^{2} \\beta=$",
"role": "user"
}
] | 3. Given $\arcsin (\sin \alpha+\sin \beta)+\arcsin (\sin \alpha-\sin \beta)=\frac{\pi}{2}, \sin ^{2} \alpha+\sin ^{2} \beta=$ | "[\"\\\\frac{1}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1433, "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:15437"}] | {
"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
} |
[
"63"
] | [
"skywork"
] | 80fdfae9f52fe38eb2b7aa5e25c99e53baf56e1842e89aaafbe16d9520c932d8 | [
{
"content": "The number of real solutions to the equation \\[ \\frac{x}{100} = \\sin x \\] is\n\n$\\text{(A)} \\ 61 \\qquad \\text{(B)} \\ 62 \\qquad \\text{(C)} \\ 63 \\qquad \\text{(D)} \\ 64 \\qquad \\text{(E)} \\ 65$",
"role": "user"
}
] | The number of real solutions to the equation \[ \frac{x}{100} = \sin x \] is
$\text{(A)} \ 61 \qquad \text{(B)} \ 62 \qquad \text{(C)} \ 63 \qquad \text{(D)} \ 64 \qquad \text{(E)} \ 65$ | "[\"63\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1432, "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:15438"}] | {
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[
"\\frac{3}{4}"
] | [
"skywork"
] | 34e0db23a7776ec167fa1b89a4cb3cab927842814b037b6217eff6af38add752 | [
{
"content": "A square with a side length of $1$ is divided into one triangle and three trapezoids by joining the center of the square to points on each side. These points divide each side into segments such that the length from a vertex to the point is $\\frac{1}{4}$ and from the point to the center of the sid... | A square with a side length of $1$ is divided into one triangle and three trapezoids by joining the center of the square to points on each side. These points divide each side into segments such that the length from a vertex to the point is $\frac{1}{4}$ and from the point to the center of the side is $\frac{3}{4}$. If ... | "[\"\\\\frac{3}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1435, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15439"}] | {
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[
"$\\frac{\\sqrt{3}}{6}$"
] | [
"skywork"
] | 7eb1bc4949f1a8800d7395e1e845eac582aad810796da5e7686e06ef81b203a6 | [
{
"content": "A cube with an edge length of 1 and its circumscribed sphere intersect with a plane to form a cross section that is a circle and an inscribed equilateral triangle. What is the distance from the center of the sphere to the plane of the cross section?",
"role": "user"
}
] | A cube with an edge length of 1 and its circumscribed sphere intersect with a plane to form a cross section that is a circle and an inscribed equilateral triangle. What is the distance from the center of the sphere to the plane of the cross section? | "[\"$\\\\frac{\\\\sqrt{3}}{6}$\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1442, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:15440"}] | {
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[
"387"
] | [
"skywork"
] | 0dfca5895787cb607c276f0c4c6c4435e2619c5d96cff8c6b5d95250acf3bf6c | [
{
"content": "6. There are no fewer than 150 boys studying at the school, and there are $15 \\%$ more girls than boys. When the boys went on a trip, 6 buses were needed, and each bus had the same number of students. How many people in total study at the school, given that the total number of students is no more... | 6. There are no fewer than 150 boys studying at the school, and there are $15 \%$ more girls than boys. When the boys went on a trip, 6 buses were needed, and each bus had the same number of students. How many people in total study at the school, given that the total number of students is no more than 400? | "[\"387\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1419, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15441"}] | {
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[
"3\\sqrt{3} + 2"
] | [
"skywork"
] | 872a991ee65debd8dc5e853509ac9a052ba067d351a7f2fea69e6b322b0907df | [
{
"content": "Eight spheres of radius 2 are each tangent to the faces of an inner cube centered at the origin, with each sphere located in one of the octants, and the side length of the cube is 6. Find the radius of the smallest sphere, centered at the origin, that encloses these eight spheres.",
"role": "u... | Eight spheres of radius 2 are each tangent to the faces of an inner cube centered at the origin, with each sphere located in one of the octants, and the side length of the cube is 6. Find the radius of the smallest sphere, centered at the origin, that encloses these eight spheres. | "[\"3\\\\sqrt{3} + 2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1454, "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:15442"}] | {
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[
"12"
] | [
"skywork"
] | 6d3c0286673a0e05cc4d67bdc12f35dcec6a0d9eb7a42234747e9247d349f3ba | [
{
"content": "Find the number of integers $n$ that satisfy\n\\[10 < n^2 < 99.\\]",
"role": "user"
}
] | Find the number of integers $n$ that satisfy
\[10 < n^2 < 99.\] | "[\"12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1462, "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:15443"}] | {
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[
"C_{n}=n^{3}-n"
] | [
"skywork"
] | 296ca40081f8d40f0be1f2db1c8b5020e9c5ecf20116cfee5a96ff8d93dabb5c | [
{
"content": "We have a collection of identical spheres that we stack to form a tetrahedron whose edges all have $n$ spheres. Calculate, in terms of $n$, the total number of tangency points (contacts) between the spheres in the pile.",
"role": "user"
}
] | We have a collection of identical spheres that we stack to form a tetrahedron whose edges all have $n$ spheres. Calculate, in terms of $n$, the total number of tangency points (contacts) between the spheres in the pile. | "[\"C_{n}=n^{3}-n\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1444, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15444"}] | {
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} |
[
"3"
] | [
"skywork"
] | d0f21cdf3de9216f648f89b06f60017bd3e07a88414f5018b80bfe99e685ef52 | [
{
"content": "What is the value of $f(-1)$ if $f(x)=x^{2}-2x$?",
"role": "user"
}
] | What is the value of $f(-1)$ if $f(x)=x^{2}-2x$? | "[\"3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1469, "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:15445"}] | {
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[
"50"
] | [
"skywork"
] | 2a83b9b18a5ddd3f5eb14c374a527fd2776bebc4a368c339f46c998e3a9ad42d | [
{
"content": "If the function\n$$\nf(x) = |a \\sin x + b \\cos x - 1| + |b \\sin x - a \\cos x| \\quad (a, b \\in \\mathbf{R})\n$$\nattains a maximum value of 11, then $a^{2} + b^{2} = \\, \\, \\, $ .",
"role": "user"
}
] | If the function
$$
f(x) = |a \sin x + b \cos x - 1| + |b \sin x - a \cos x| \quad (a, b \in \mathbf{R})
$$
attains a maximum value of 11, then $a^{2} + b^{2} = \, \, \, $ . | "[\"50\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1431, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15446"}] | {
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[
"\\frac{22}{7}"
] | [
"skywork"
] | ce816f60561ab8e2baf7095f5d375d2f47bcbc91a92fbccd8a86ba4b04dfc432 | [
{
"content": "Let $\\lfloor x \\rfloor$ denotes the greatest integer less than or equal to $x$. Find $x$ such that $x\\lfloor x\\lfloor x\\lfloor x\\rfloor\\rfloor \\rfloor = 88$\n[list=1]\n[*] $\\pi$\n[*] 3.14\n\n[*] $\\frac{22}{7}$\n\n[*] All of these\n[/list]",
"role": "user"
}
] | Let $\lfloor x \rfloor$ denotes the greatest integer less than or equal to $x$. Find $x$ such that $x\lfloor x\lfloor x\lfloor x\rfloor\rfloor \rfloor = 88$
[list=1]
[*] $\pi$
[*] 3.14
[*] $\frac{22}{7}$
[*] All of these
[/list] | "[\"\\\\frac{22}{7}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1422, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:15447"}] | {
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[
"243"
] | [
"skywork"
] | 9468e1838e601f1ae1196e87a7d39b31f752c5081f829af697a4e8c4eb837340 | [
{
"content": "A8. How many three-digit integers less than 1000 have exactly two different digits in their representation (for example, 232 , or 466 )?",
"role": "user"
}
] | A8. How many three-digit integers less than 1000 have exactly two different digits in their representation (for example, 232 , or 466 )? | "[\"243\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1447, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:15448"}] | {
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[
"67"
] | [
"skywork"
] | c43fce70f5949f8da57a1bd05fc46d6e04d7c4c09f4340720f1fb3c15838677b | [
{
"content": "The set $\\{[x]+[2x]+[3x] \\mid x \\in \\mathbf{R}\\} \\bigcap \\{1, 2, \\cdots, 100\\}$ contains how many elements, where $[x]$ represents the greatest integer less than or equal to $x$.",
"role": "user"
}
] | The set $\{[x]+[2x]+[3x] \mid x \in \mathbf{R}\} \bigcap \{1, 2, \cdots, 100\}$ contains how many elements, where $[x]$ represents the greatest integer less than or equal to $x$. | "[\"67\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1451, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15449"}] | {
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} |
[
"10"
] | [
"skywork"
] | 4c6d73d394090618feb11405a573c5c8a19405824c18e64a0d3b9f41b380e077 | [
{
"content": "From a point located outside a circle, two mutually perpendicular tangents are drawn to the circle. The radius of the circle is 10. Find the length of each tangent.\n\n#",
"role": "user"
}
] | From a point located outside a circle, two mutually perpendicular tangents are drawn to the circle. The radius of the circle is 10. Find the length of each tangent.
# | "[\"10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1448, "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:15450"}] | {
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[
"11\\mathrm{~}^{2}"
] | [
"skywork"
] | 29c5773ca107626b3949600826fa677ed514abae4cbd7359939c532ad7f27dbd | [
{
"content": "A9. The diagram shows the square $P Q R S$, which has area $25 \\mathrm{~cm}^{2}$, and the rhombus $Q R T U$, which has area $20 \\mathrm{~cm}^{2}$. What is the area of the shaded region?",
"role": "user"
}
] | A9. The diagram shows the square $P Q R S$, which has area $25 \mathrm{~cm}^{2}$, and the rhombus $Q R T U$, which has area $20 \mathrm{~cm}^{2}$. What is the area of the shaded region? | "[\"11\\\\mathrm{~}^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1452, "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:15451"}] | {
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} |
[
"6"
] | [
"skywork"
] | 3514d48de36400c71abd6e6f93027661f075d4f52cb6fe5b984323c2d3ec0591 | [
{
"content": "B1. John walks from home to school with a constant speed, and his sister Joan bikes twice as fast. The distance between their home and school is $3 \\mathrm{~km}$. If Joan leaves home 15 minutes after John then they arrive to school at the same time. What is the walking speed (in $\\mathrm{km} / \... | B1. John walks from home to school with a constant speed, and his sister Joan bikes twice as fast. The distance between their home and school is $3 \mathrm{~km}$. If Joan leaves home 15 minutes after John then they arrive to school at the same time. What is the walking speed (in $\mathrm{km} / \mathrm{h}$ ) of John? | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1450, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15452"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"396"
] | [
"skywork"
] | 97a3abaf5c9a6b723ef5f19fbde61d4edc08c2b8c7c06d0089ea7e25f7ac9330 | [
{
"content": "Define a positive integer $n$ to be a factorial tail if there is some positive integer $m$ such that the decimal representation of $m!$ ends with exactly $n$ zeroes. How many positive integers less than $1992$ are not factorial tails?",
"role": "user"
}
] | Define a positive integer $n$ to be a factorial tail if there is some positive integer $m$ such that the decimal representation of $m!$ ends with exactly $n$ zeroes. How many positive integers less than $1992$ are not factorial tails? | "[\"396\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1466, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15453"}] | {
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} |
[
"4-\\pi"
] | [
"skywork"
] | 00800c66b7e77b0bba175c442392ca07ec0f3a5fb93f8b4067ee7b5a46f904a5 | [
{
"content": "In square $PQRS$ with side length 2, each of $P, Q, R$, and $S$ is the centre of a circle with radius 1. What is the area of the shaded region?",
"role": "user"
}
] | In square $PQRS$ with side length 2, each of $P, Q, R$, and $S$ is the centre of a circle with radius 1. What is the area of the shaded region? | "[\"4-\\\\pi\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1465, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15454"}] | {
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[
"\\frac{19}{125}"
] | [
"skywork"
] | 22f12ede5e751566366b4153375104a4c7f7f33b802104fb51a37e75ce6f3b2f | [
{
"content": "3. From the numbers $1,2,3,4,5$, randomly draw 3 numbers (repetition allowed) to form a three-digit number, the probability that the sum of its digits equals 9 is\nA. $\\frac{13}{125}$\nB. $\\frac{16}{125}$\nC. $\\frac{18}{125}$\nD. $\\frac{19}{125}$",
"role": "user"
}
] | 3. From the numbers $1,2,3,4,5$, randomly draw 3 numbers (repetition allowed) to form a three-digit number, the probability that the sum of its digits equals 9 is
A. $\frac{13}{125}$
B. $\frac{16}{125}$
C. $\frac{18}{125}$
D. $\frac{19}{125}$ | "[\"\\\\frac{19}{125}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1472, "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:15455"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"243"
] | [
"skywork"
] | 0d6e31b920492c8b9f76a7f5d5bdfa8da86792616cb58904bc16e13b67a6d79d | [
{
"content": "Calculate the value of $3^{12} \\cdot 3^3$ and express it as some integer raised to the third power.",
"role": "user"
}
] | Calculate the value of $3^{12} \cdot 3^3$ and express it as some integer raised to the third power. | "[\"243\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1477, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15456"}] | {
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"reference_present": true
} |
[
"z = 2^t \\cdot 3^3 \\cdot k"
] | [
"skywork"
] | 1c55a8049585740f3a046c3bdfaa6131d19aa70a799886607008d95bc301cd27 | [
{
"content": "suppose that $a=3^{100}$ and $b=5454$. how many $z$s in $[1,3^{99})$ exist such that for every $c$ that $gcd(c,3)=1$, two equations $x^z\\equiv c$ and $x^b\\equiv c$ (mod $a$) have the same number of answers?($\\frac{100}{6}$ points)",
"role": "user"
}
] | suppose that $a=3^{100}$ and $b=5454$. how many $z$s in $[1,3^{99})$ exist such that for every $c$ that $gcd(c,3)=1$, two equations $x^z\equiv c$ and $x^b\equiv c$ (mod $a$) have the same number of answers?($\frac{100}{6}$ points) | "[\" z = 2^t \\\\cdot 3^3 \\\\cdot k \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1455, "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:15457"}] | {
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[
"30"
] | [
"skywork"
] | 8c137185505dfe88c90c6b8c9e1a9310097a7523870c652b6e3a4eeafa666db7 | [
{
"content": "## Subject IV. (30 points)\n\nInside the angle $\\Varangle A O B$, points $A_{1}, A_{2}, A_{3}, \\ldots, A_{101}$ are taken such that: $m\\left(\\Varangle A O A_{1}\\right)=m\\left(\\Varangle A_{1} O A_{2}\\right)=m\\left(\\Varangle A_{2} O A_{3}\\right)=\\ldots=m\\left(\\Varangle A_{101} O B\\rig... | ## Subject IV. (30 points)
Inside the angle $\Varangle A O B$, points $A_{1}, A_{2}, A_{3}, \ldots, A_{101}$ are taken such that: $m\left(\Varangle A O A_{1}\right)=m\left(\Varangle A_{1} O A_{2}\right)=m\left(\Varangle A_{2} O A_{3}\right)=\ldots=m\left(\Varangle A_{101} O B\right)=1^{\circ} 20^{\prime}$.
a) Find th... | "[\"30\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1441, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15458"}] | {
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[
"96\\mathrm{~}^{2}"
] | [
"skywork"
] | e8b6feda80c262792734e7b18b2c9cf59badb501bfac23f0ea7ad18fb70773bc | [
{
"content": "10.102. The diagonal of an isosceles trapezoid bisects its obtuse angle. The smaller base of the trapezoid is 3 cm, and the perimeter is $42 \\mathrm{~cm}$. Find the area of the trapezoid.",
"role": "user"
}
] | 10.102. The diagonal of an isosceles trapezoid bisects its obtuse angle. The smaller base of the trapezoid is 3 cm, and the perimeter is $42 \mathrm{~cm}$. Find the area of the trapezoid. | "[\"96\\\\mathrm{~}^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1456, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15459"}] | {
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"reference_components": 1,
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} |
[
"E"
] | [
"skywork"
] | dc00e372bf316af6fd53cab0520d64cb300c7ee7e040ca514df69a6811c1efa3 | [
{
"content": "Let $S$ be the sum of the interior angles of a polygon $P$ for which each interior angle is $7\\frac{1}{2}$ times the \nexterior angle at the same vertex. Then\n$\\textbf{(A)}\\ S=2660^{\\circ} \\text{ } \\text{and} \\text{ } P \\text{ } \\text{may be regular}\\qquad \\\\ \\textbf{(B)}\\ S=2660^{\... | Let $S$ be the sum of the interior angles of a polygon $P$ for which each interior angle is $7\frac{1}{2}$ times the
exterior angle at the same vertex. Then
$\textbf{(A)}\ S=2660^{\circ} \text{ } \text{and} \text{ } P \text{ } \text{may be regular}\qquad \\ \textbf{(B)}\ S=2660^{\circ} \text{ } \text{and} \text{ } P \... | "[\"E\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 1464, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15460"}] | {
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[
"\\textbf{(A)}"
] | [
"skywork"
] | e0df928321a02169e8cbe28dee47e761d9466f5b314cd197d320199ea34b9ca6 | [
{
"content": "Consider $A = \\log (2013 + \\log (2012 + \\log (2011 + \\log (\\cdots + \\log (3 + \\log 2) \\cdots ))))$. Which of the following intervals contains $A$?\n$\\textbf{(A)} \\ (\\log 2016, \\log 2017)$\n$\\textbf{(B)} \\ (\\log 2017, \\log 2018)$\n$\\textbf{(C)} \\ (\\log 2018, \\log 2019)$\n$\\text... | Consider $A = \log (2013 + \log (2012 + \log (2011 + \log (\cdots + \log (3 + \log 2) \cdots ))))$. Which of the following intervals contains $A$?
$\textbf{(A)} \ (\log 2016, \log 2017)$
$\textbf{(B)} \ (\log 2017, \log 2018)$
$\textbf{(C)} \ (\log 2018, \log 2019)$
$\textbf{(D)} \ (\log 2019, \log 2020)$
$\textbf{(E)}... | "[\"\\\\textbf{(A)}\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 1468, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15461"}] | {
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[
"1536"
] | [
"skywork"
] | 52a17a1f88a8263119d72099abcf66aaac9dd7218ef7ae424ffc915da2b7283b | [
{
"content": "Let $P(x) = x^3 + 8x^2 - x + 3$ and let the roots of $P$ be $a, b,$ and $c.$ The roots of a monic polynomial $Q(x)$ are $ab - c^2, ac - b^2, bc - a^2.$ Find $Q(-1).$",
"role": "user"
}
] | Let $P(x) = x^3 + 8x^2 - x + 3$ and let the roots of $P$ be $a, b,$ and $c.$ The roots of a monic polynomial $Q(x)$ are $ab - c^2, ac - b^2, bc - a^2.$ Find $Q(-1).$ | "[\"1536\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1463, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15462"}] | {
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[
"7"
] | [
"skywork"
] | 9df141be63ccd1f0d76dbe2b70fe958875fefae52bbc370ff1c7b0f2984aba03 | [
{
"content": "Four girls — Mary, Alina, Tina, and Hanna — sang songs in a concert as trios, with one girl sitting out each time. Hanna sang $7$ songs, which was more than any other girl, and Mary sang $4$ songs, which was fewer than any other girl. How many songs did these trios sing?",
"role": "user"
}
] | Four girls — Mary, Alina, Tina, and Hanna — sang songs in a concert as trios, with one girl sitting out each time. Hanna sang $7$ songs, which was more than any other girl, and Mary sang $4$ songs, which was fewer than any other girl. How many songs did these trios sing? | "[\"7\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1460, "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:15463"}] | {
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[
"0"
] | [
"skywork"
] | bf5bfd7354b8d481b3b0ca773e04ae5856762550938af943ff76a00ea5c6e282 | [
{
"content": "2 Let $C$ be a circle with radius $r$, centered at the point $(\\sqrt{2}, \\sqrt{3})$, where $r$ is a positive real number. When $x, y$ are both rational numbers, the point $(x, y)$ is called a rational point. The maximum number of rational points on circle $C$ is\nA. 0\nB. 1\nC. 2\nD. 3",
"ro... | 2 Let $C$ be a circle with radius $r$, centered at the point $(\sqrt{2}, \sqrt{3})$, where $r$ is a positive real number. When $x, y$ are both rational numbers, the point $(x, y)$ is called a rational point. The maximum number of rational points on circle $C$ is
A. 0
B. 1
C. 2
D. 3 | "[\"0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1457, "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:15464"}] | {
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[
"2"
] | [
"skywork"
] | 6fbec10e38029ed77344f0959a1b9a58e36b3bd2e538a518b9e756de04b33ef7 | [
{
"content": "9. Real numbers $a, b, c$ satisfy $5^{a}=2^{b}=\\sqrt{10^{c}}$, and $a b \\neq 0, \\frac{c}{a}+\\frac{c}{b}$ has the value of $\\qquad$ .",
"role": "user"
}
] | 9. Real numbers $a, b, c$ satisfy $5^{a}=2^{b}=\sqrt{10^{c}}$, and $a b \neq 0, \frac{c}{a}+\frac{c}{b}$ has the value of $\qquad$ . | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1449, "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:15465"}] | {
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[
"256\\pi"
] | [
"skywork"
] | c9b5898a8eac9b8cea103a2c5fa61d54ea976738c0bf7137a239bf95b931d149 | [
{
"content": "Find the number of cubic centimeters in the volume of the cylinder formed by rotating a rectangle with side lengths 8 cm and 16 cm about its longer side. Express your answer in terms of \\(\\pi\\).",
"role": "user"
}
] | Find the number of cubic centimeters in the volume of the cylinder formed by rotating a rectangle with side lengths 8 cm and 16 cm about its longer side. Express your answer in terms of \(\pi\). | "[\"256\\\\pi\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1473, "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:15466"}] | {
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} |
[
"78.75"
] | [
"skywork"
] | 2c54e117aa05f9b74251dcb28046c4c261c05193a87ad3e2968e3075f0d0cd89 | [
{
"content": "The circle is divided by points \\(A, B, C, D\\) such that \\(\\sim AB: BC: CD: DA = 2: 3: 5: 6\\). Chords \\(AC\\) and \\(BD\\) are drawn, intersecting at point \\(M\\).\n\nFind the angle \\(AMB\\).",
"role": "user"
}
] | The circle is divided by points \(A, B, C, D\) such that \(\sim AB: BC: CD: DA = 2: 3: 5: 6\). Chords \(AC\) and \(BD\) are drawn, intersecting at point \(M\).
Find the angle \(AMB\). | "[\"78.75\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1453, "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:15467"}] | {
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"reference_components": 1,
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} |
[
"1415_6"
] | [
"skywork"
] | ab12f4d5ee541beb47b29b45e6fac885a52f21a05b4c0b1fa5412409a18fd092 | [
{
"content": "Find the sum of $453_6$, $436_6$, and $42_6$ in base 6.",
"role": "user"
}
] | Find the sum of $453_6$, $436_6$, and $42_6$ in base 6. | "[\"1415_6\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1485, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15468"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1006"
] | [
"skywork"
] | 406d9c65c2d5b6eb27adb8f836e2507c629890fdc60c904cfe206911a916680b | [
{
"content": "Let $M$ be a subset of the set of $2021$ integers $\\{1, 2, 3, ..., 2021\\}$ such that for any three elements (not necessarily distinct) $a, b, c$ of $M$ we have $|a + b - c | > 10$.\nDetermine the largest possible number of elements of $M$.",
"role": "user"
}
] | Let $M$ be a subset of the set of $2021$ integers $\{1, 2, 3, ..., 2021\}$ such that for any three elements (not necessarily distinct) $a, b, c$ of $M$ we have $|a + b - c | > 10$.
Determine the largest possible number of elements of $M$. | "[\"1006\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1474, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15469"}] | {
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} |
[
"94.67"
] | [
"skywork"
] | e9b1f3bdcc2d0fa8c162d19cefb4a1e6c7e18d6743d1b8c07785180d897bd510 | [
{
"content": "Four scores belong to Alex and the other three to Morgan: 78, 82, 90, 95, 98, 102, 105. Alex's mean score is 91.5. What is Morgan's mean score?",
"role": "user"
}
] | Four scores belong to Alex and the other three to Morgan: 78, 82, 90, 95, 98, 102, 105. Alex's mean score is 91.5. What is Morgan's mean score? | "[\"94.67\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1476, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15470"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 6cd30e059f7c3fc670435101153dd8fab7aed90cd8af7d2c8feffc12ac4b1353 | [
{
"content": "22.1. Calculate the expression $2 x^{4}+3 x^{2} y^{2}+y^{4}+y^{2}$, given that $x^{2}+y^{2}=1$.\n\n$$\n\\text { (7-8 grades) }\n$$",
"role": "user"
}
] | 22.1. Calculate the expression $2 x^{4}+3 x^{2} y^{2}+y^{4}+y^{2}$, given that $x^{2}+y^{2}=1$.
$$
\text { (7-8 grades) }
$$ | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1478, "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:15471"}] | {
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[
"220 + 20\\sqrt{22}"
] | [
"skywork"
] | cc181e59a100d2df70afab58875c503bcddea57d383b847903f05f1d1537ebb5 | [
{
"content": "A spider is on the edge of a ceiling of a circular room with a radius of 65 feet. The spider moves straight across the ceiling to the opposite edge, passing through the circle's center. It then moves directly to another point on the edge of the circle, not passing through the center. The final seg... | A spider is on the edge of a ceiling of a circular room with a radius of 65 feet. The spider moves straight across the ceiling to the opposite edge, passing through the circle's center. It then moves directly to another point on the edge of the circle, not passing through the center. The final segment of the journey is... | "[\"220 + 20\\\\sqrt{22}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1461, "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:15472"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"2\\sqrt{3}"
] | [
"skywork"
] | 42fd246b8a02b8520ea37d85da538594d3947f4674c5500832ce25e56238e657 | [
{
"content": "8. Let $A B C$ be an equilateral triangle of side length 2 . Let $\\omega$ be its circumcircle, and let $\\omega_{A}, \\omega_{B}, \\omega_{C}$ be circles congruent to $\\omega$ centered at each of its vertices. Let $R$ be the set of all points in the plane contained in exactly two of these four c... | 8. Let $A B C$ be an equilateral triangle of side length 2 . Let $\omega$ be its circumcircle, and let $\omega_{A}, \omega_{B}, \omega_{C}$ be circles congruent to $\omega$ centered at each of its vertices. Let $R$ be the set of all points in the plane contained in exactly two of these four circles. What is the area of... | "[\"2\\\\sqrt{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1471, "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:15473"}] | {
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} |
[
"[1,3] \\text{ or } \\left[-2-\\sqrt{17}, \\frac{13}{4}\\right]"
] | [
"skywork"
] | 603b097248ba0053c2b97e3330cc2c36debbda4811ff012154cb44f68e63fa1e | [
{
"content": "5. If the function $f(x)=-\\frac{1}{2} x^{2}+\\frac{13}{2}$ has a minimum value of $2a$ and a maximum value of $2b$ on the interval $[a, b]$, find $[a, b]$.\n(2000, National High School Mathematics Competition)",
"role": "user"
}
] | 5. If the function $f(x)=-\frac{1}{2} x^{2}+\frac{13}{2}$ has a minimum value of $2a$ and a maximum value of $2b$ on the interval $[a, b]$, find $[a, b]$.
(2000, National High School Mathematics Competition) | "[\"[1,3] \\\\text{ or } \\\\left[-2-\\\\sqrt{17}, \\\\frac{13}{4}\\\\right]\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1467, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15474"}] | {
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"reference_components": 1,
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[
"\\sqrt{13}"
] | [
"skywork"
] | 2b7da8d1c215546b729ba4f6ccdd207c85226ca7676f6ab038afb231e63bafe7 | [
{
"content": "Given a triangle $ABC$ with $\\angle B = \\frac{\\pi}{3}$, \n(I) if $AB=8\\sqrt{3}$ and $AC=12$, find the area of $\\triangle ABC$; \n(II) if $AB=4$ and $\\vec{BM} = \\vec{MN} = \\vec{NC}$ with $AN=2\\sqrt{3}BM$, find the length of $AM$.",
"role": "user"
}
] | Given a triangle $ABC$ with $\angle B = \frac{\pi}{3}$,
(I) if $AB=8\sqrt{3}$ and $AC=12$, find the area of $\triangle ABC$;
(II) if $AB=4$ and $\vec{BM} = \vec{MN} = \vec{NC}$ with $AN=2\sqrt{3}BM$, find the length of $AM$. | "[\"\\\\sqrt{13}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1459, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15475"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"12769"
] | [
"skywork"
] | 2cd42a4921d8b62e09bf0de3c0d47b74c858f995ff2345d7dedd74c0f82cfa2e | [
{
"content": "Problem 6. Vanya is coming up with a number consisting of non-repeating digits without zeros - a password for his phone. The password works as follows: if, without lifting his finger from the screen, he sequentially connects the points corresponding to the digits of the password with line segments... | Problem 6. Vanya is coming up with a number consisting of non-repeating digits without zeros - a password for his phone. The password works as follows: if, without lifting his finger from the screen, he sequentially connects the points corresponding to the digits of the password with line segments, the phone will unloc... | "[\"12769\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1470, "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:15476"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | 2f569b50ad28a33585addcb021009adc9e0a2964ff5606b7b8a89e3348b9e110 | [
{
"content": "## Task A-1.2.\n\nLet $x$ and $y$ be real numbers such that $x+y=1$ and $x^{3}+y^{3}=13$. What is $x^{2}+y^{2}$?",
"role": "user"
}
] | ## Task A-1.2.
Let $x$ and $y$ be real numbers such that $x+y=1$ and $x^{3}+y^{3}=13$. What is $x^{2}+y^{2}$? | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1503, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15477"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"n = 2^{2014}k - 1"
] | [
"skywork"
] | 01443c52bb015bd0ef282d47d1fce60afe87d3e7ce653d59940ff369a1206b61 | [
{
"content": "Find all positive integers $n$ for which $n^{n-1} - 1$ is divisible by $2^{2015}$, but not by $2^{2016}$.",
"role": "user"
}
] | Find all positive integers $n$ for which $n^{n-1} - 1$ is divisible by $2^{2015}$, but not by $2^{2016}$. | "[\" n = 2^{2014}k - 1 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1488, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15478"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"0 \\leqslant y \\leqslant 4"
] | [
"skywork"
] | 0e1b43ac8973955ba97acea3256f75d9ead2a1d1568e6673c761b3d92b363716 | [
{
"content": "5. Let $0 \\leqslant x \\leqslant 8$, then the range of the function $f(x)$ $=\\frac{\\sqrt{x\\left(x^{2}+8\\right)(8-x)}}{x+1}$ is",
"role": "user"
}
] | 5. Let $0 \leqslant x \leqslant 8$, then the range of the function $f(x)$ $=\frac{\sqrt{x\left(x^{2}+8\right)(8-x)}}{x+1}$ is | "[\"0 \\\\leqslant y \\\\leqslant 4\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1482, "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:15479"}] | {
"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
} |
[
"137"
] | [
"skywork"
] | 67bd60aa91018bb3478171d820e3a25611b5acf4ebde88fc23867ccb5f4a864e | [
{
"content": "What is the largest possible distance between two points, one on the sphere of radius 19 with center $(-2,-10,5)$ and the other on the sphere of radius 87 with center $(12,8,-16)$?",
"role": "user"
}
] | What is the largest possible distance between two points, one on the sphere of radius 19 with center $(-2,-10,5)$ and the other on the sphere of radius 87 with center $(12,8,-16)$? | "[\"137\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1498, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:15480"}, {"dataset": "skywork", "extra_inf... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"62"
] | [
"skywork"
] | a7945592c33774cc94df7eb58d0c9e64d96d6fbfa3fb1e6d1503109f1416cd44 | [
{
"content": "Vera has several identical matches, from which she makes a triangle. Vera wants any two sides of this triangle to differ in length by at least $10$ matches, but it turned out that it is impossible to add such a triangle from the available matches (it is impossible to leave extra matches). What is ... | Vera has several identical matches, from which she makes a triangle. Vera wants any two sides of this triangle to differ in length by at least $10$ matches, but it turned out that it is impossible to add such a triangle from the available matches (it is impossible to leave extra matches). What is the maximum number of ... | "[\"62\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1458, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15481"}, {"dataset": "skywork", "extra_in... | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"83"
] | [
"skywork"
] | c25ffdf09c2b379794f4a078613762a66c9ca61338ccc25a1bd03d49089b6ee7 | [
{
"content": "Each of the numbers 1, 2, 3, and 4 is substituted, in some order, for \\( p, q, r \\), and \\( s \\). Find the greatest possible value of \\( p^q + r^s \\).",
"role": "user"
}
] | Each of the numbers 1, 2, 3, and 4 is substituted, in some order, for \( p, q, r \), and \( s \). Find the greatest possible value of \( p^q + r^s \). | "[\"83\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1480, "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:15482"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"60"
] | [
"skywork"
] | 6f2335db2b6fd0c0e24b18309aaed8d0a8080464e3d1b2afac2eb8b9ca196083 | [
{
"content": "Problem 3. In the rectangle $A B C D$, with a perimeter of $60 \\mathrm{~cm}$, it is given that $\\overline{B C}=$ $\\frac{2}{3} \\overline{A B}$. On side $A B$, there is a point $E$ such that $\\overline{A E}=\\frac{1}{3} \\overline{A B}$, and on side $B C$, there is a point $F$ such that $\\over... | Problem 3. In the rectangle $A B C D$, with a perimeter of $60 \mathrm{~cm}$, it is given that $\overline{B C}=$ $\frac{2}{3} \overline{A B}$. On side $A B$, there is a point $E$ such that $\overline{A E}=\frac{1}{3} \overline{A B}$, and on side $B C$, there is a point $F$ such that $\overline{B F}=\frac{2}{3} \overlin... | "[\"60\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1475, "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:15483"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"80"
] | [
"skywork"
] | 4677e35049ff83851af61a4f4592d3b6f434dc283895696a065652bd1f35d3a6 | [
{
"content": "If an integer $n > 8$ is a solution of the equation $x^2 - ax+b=0$ and the representation of $a$ in the base-$n$ number system is $18$, \nthen the base-n representation of $b$ is\n$\\textbf{(A)}\\ 18 \\qquad \\textbf{(B)}\\ 20 \\qquad \\textbf{(C)}\\ 80 \\qquad \\textbf{(D)}\\ 81 \\qquad \\textbf{... | If an integer $n > 8$ is a solution of the equation $x^2 - ax+b=0$ and the representation of $a$ in the base-$n$ number system is $18$,
then the base-n representation of $b$ is
$\textbf{(A)}\ 18 \qquad \textbf{(B)}\ 20 \qquad \textbf{(C)}\ 80 \qquad \textbf{(D)}\ 81 \qquad \textbf{(E)}\ 280$ | "[\"80\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 1487, "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:15484"}] | {
"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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[
"C"
] | [
"skywork"
] | 33cbdb2c0e0c496f5867fb882f5747e14aca217c30d1698e7d36295e4af51698 | [
{
"content": "2.99 The number of real roots of the equation $\\left|x^{2}-1\\right|=\\frac{1}{10}\\left(x+\\frac{9}{10}\\right)$ is\n(A) 4.\n(B) 3.\n(C) 2.\n(D) 1.\n(2nd \"Hope Cup\" National Mathematics Invitational, 1991)",
"role": "user"
}
] | 2.99 The number of real roots of the equation $\left|x^{2}-1\right|=\frac{1}{10}\left(x+\frac{9}{10}\right)$ is
(A) 4.
(B) 3.
(C) 2.
(D) 1.
(2nd "Hope Cup" National Mathematics Invitational, 1991) | "[\"C\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1507, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:15485"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"0.2311203"
] | [
"skywork"
] | 32de216d94bf9d7841340016666c3ad20fa37348babf4962552d07da1b740b1a | [
{
"content": "Ha $9^{-1 \\frac{1}{6}}=0.0770401$, what is $9^{-\\frac{2}{3}}$?",
"role": "user"
}
] | Ha $9^{-1 \frac{1}{6}}=0.0770401$, what is $9^{-\frac{2}{3}}$? | "[\"0.2311203\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1492, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15486"}] | {
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"reference_components": 1,
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} |
[
"2016"
] | [
"skywork"
] | 72d3e8311c6a24dd4b19c1d6eb64e2745e7604b7dd07f6777e9547c669d28b5e | [
{
"content": "Let the sequence $\\{a_n\\}$ satisfy $a_1=2$, $a_2=6$, and $a_{n+2}-2a_{n+1}+a_n=2$. If $\\lfloor x \\rfloor$ represents the greatest integer not exceeding $x$, calculate $$\\left\\lfloor \\frac{2017}{a_1} + \\frac{2017}{a_2} + \\ldots + \\frac{2017}{a_{2017}} \\right\\rfloor.$$",
"role": "use... | Let the sequence $\{a_n\}$ satisfy $a_1=2$, $a_2=6$, and $a_{n+2}-2a_{n+1}+a_n=2$. If $\lfloor x \rfloor$ represents the greatest integer not exceeding $x$, calculate $$\left\lfloor \frac{2017}{a_1} + \frac{2017}{a_2} + \ldots + \frac{2017}{a_{2017}} \right\rfloor.$$ | "[\"2016\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1484, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15487"}] | {
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"reference_components": 1,
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[
"2"
] | [
"skywork"
] | 2797deb333438c27e1bc9e8b3fbcb352c56ac433bad8b914605d5d8beb19bc0c | [
{
"content": "7.218. $\\left(\\frac{3}{5}\\right)^{2 \\log _{9}(x+1)} \\cdot\\left(\\frac{125}{27}\\right)^{\\log _{27}(x-1)}=\\frac{\\log _{5} 27}{\\log _{5} 243}$.",
"role": "user"
}
] | 7.218. $\left(\frac{3}{5}\right)^{2 \log _{9}(x+1)} \cdot\left(\frac{125}{27}\right)^{\log _{27}(x-1)}=\frac{\log _{5} 27}{\log _{5} 243}$. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1505, "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:15488"}] | {
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[
"n = 10, 34, 342, 19"
] | [
"skywork"
] | 64ad6de66f9dac96dc48d0a1d5a9275da9110baedeff19dd3aafe0b447ae8d90 | [
{
"content": "Find all integers $n$ for which the polynomial $p(x) = x^5 -nx -n -2$ can be represented as a product of two non-constant polynomials with integer coefficients.",
"role": "user"
}
] | Find all integers $n$ for which the polynomial $p(x) = x^5 -nx -n -2$ can be represented as a product of two non-constant polynomials with integer coefficients. | "[\" n = 10, 34, 342, 19 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1513, "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:15489"}] | {
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[
"20/13"
] | [
"skywork"
] | 6929d7883fcf5d7c5bce36054e148e5d1ee58cd4de617a0cc8909c71c7c637e6 | [
{
"content": "Equilateral triangle \\( \\triangle ABC \\) has side length 6. Let \\( \\omega \\) be the circle through \\( A \\) and \\( B \\) such that \\( CA \\) and \\( CB \\) are both tangent to \\( \\omega \\). A point \\( D \\) on \\( \\omega \\) satisfies \\( CD = 4 \\). Let \\( E \\) be the intersection... | Equilateral triangle \( \triangle ABC \) has side length 6. Let \( \omega \) be the circle through \( A \) and \( B \) such that \( CA \) and \( CB \) are both tangent to \( \omega \). A point \( D \) on \( \omega \) satisfies \( CD = 4 \). Let \( E \) be the intersection of line \( CD \) with segment \( AB \). What is... | "[\"20/13\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1489, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15490"}] | {
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[
"2\\sqrt{3}"
] | [
"skywork"
] | ae1ef5ff9354178186ad1fac19aa6c10e074a122a6ed8797784721d3e37cdada | [
{
"content": "In triangle $\\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively, with $c=4$. Point $D$ is on $CD\\bot AB$, and $c\\cos C\\cos \\left(A-B\\right)+4=c\\sin ^{2}C+b\\sin A\\sin C$. Find the maximum value of the length of segment $CD$.",
"role": "user"... | In triangle $\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively, with $c=4$. Point $D$ is on $CD\bot AB$, and $c\cos C\cos \left(A-B\right)+4=c\sin ^{2}C+b\sin A\sin C$. Find the maximum value of the length of segment $CD$. | "[\"2\\\\sqrt{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1490, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:15491"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{12(3 - \\sqrt{2})}{7}"
] | [
"skywork"
] | c7da4d4c14cf2646a02352489aa3fe21fd050849037c08700c068f55e1fc2f7c | [
{
"content": "In an isosceles trapezoid \\(ABCD\\), the larger base \\(AD = 12\\) and \\(AB = 6\\). Find the distance from point \\(O\\), the intersection of the diagonals, to point \\(K\\), the intersection of the extensions of the lateral sides, given that the extensions of the lateral sides intersect at a ri... | In an isosceles trapezoid \(ABCD\), the larger base \(AD = 12\) and \(AB = 6\). Find the distance from point \(O\), the intersection of the diagonals, to point \(K\), the intersection of the extensions of the lateral sides, given that the extensions of the lateral sides intersect at a right angle. | "[\"\\\\frac{12(3 - \\\\sqrt{2})}{7}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1479, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15492"}] | {
"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
} |
[
"7"
] | [
"skywork"
] | 4718198129e04d6a7017fa09d243a1d9771c14f28f5c6cdf3b2e5873b705b456 | [
{
"content": "1. Place $1,2, \\cdots, n$ on a circle such that the absolute difference between any two adjacent numbers is 3, 4, or 5. Find the smallest $n$ that allows such an arrangement.",
"role": "user"
}
] | 1. Place $1,2, \cdots, n$ on a circle such that the absolute difference between any two adjacent numbers is 3, 4, or 5. Find the smallest $n$ that allows such an arrangement. | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1500, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:15493"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"1990"
] | [
"skywork"
] | 027a2a3fd5a6008bbb3c77ce01b572f89863f89b9029c4c51a9142c3ef6a01a1 | [
{
"content": "$6 \\cdot 90$ Let the numbers $x_{1}, \\cdots, x_{1991}$ satisfy the condition\n$$\n\\left|x_{1}-x_{2}\\right|+\\cdots+\\left|x_{1990}-x_{1991}\\right|=1991 \\text {, }\n$$\n\nand $y_{k}=\\frac{1}{k}\\left(x_{1}+\\cdots+x_{k}\\right), k=1, \\cdots, 1991$. Try to find the maximum value that the fol... | $6 \cdot 90$ Let the numbers $x_{1}, \cdots, x_{1991}$ satisfy the condition
$$
\left|x_{1}-x_{2}\right|+\cdots+\left|x_{1990}-x_{1991}\right|=1991 \text {, }
$$
and $y_{k}=\frac{1}{k}\left(x_{1}+\cdots+x_{k}\right), k=1, \cdots, 1991$. Try to find the maximum value that the following expression can achieve.
$$
\left|... | "[\"1990\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1483, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15494"}] | {
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"reference_present": true
} |
[
"1009"
] | [
"skywork"
] | c8b314e867bc19ef57a671a07dcf02a4da25842ef71d5dac77d03f7fef14fbd7 | [
{
"content": ". Positive integers $x_{1}, \\ldots, x_{m}$ (not necessarily distinct) are written on a blackboard. It is known that each of the numbers $F_{1}, \\ldots, F_{2018}$ can be represented as a sum of one or more of the numbers on the blackboard. What is the smallest possible value of $m$ ?\n\n(Here $F_... | . Positive integers $x_{1}, \ldots, x_{m}$ (not necessarily distinct) are written on a blackboard. It is known that each of the numbers $F_{1}, \ldots, F_{2018}$ can be represented as a sum of one or more of the numbers on the blackboard. What is the smallest possible value of $m$ ?
(Here $F_{1}, \ldots, F_{2018}$ are... | "[\"1009\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1491, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15495"}, {"dataset": "skywork", "extra_i... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"skywork"
] | 3c66ad544057df50365e99030428f1017aebcf3f45d6c4c0ac4fa7c67252dd41 | [
{
"content": "2. (8 points) A large cube with an edge length of 5 is cut into 125 smaller cubes with an edge length of 1. The total surface area of these smaller cubes is $\\qquad$ times the surface area of the original large cube.",
"role": "user"
}
] | 2. (8 points) A large cube with an edge length of 5 is cut into 125 smaller cubes with an edge length of 1. The total surface area of these smaller cubes is $\qquad$ times the surface area of the original large cube. | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1502, "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:15496"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 895f70628a6c5295e9f3f7f6f4f23e6d9428614322e9522431c3ca7b1a8b3452 | [
{
"content": "9.1. Several numbers are written on the board. It is known that the square of any written number is greater than the product of any two other written numbers. What is the maximum number of numbers that can be on the board\n\n#",
"role": "user"
}
] | 9.1. Several numbers are written on the board. It is known that the square of any written number is greater than the product of any two other written numbers. What is the maximum number of numbers that can be on the board
# | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1495, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15497"}] | {
"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"
] | 6b678f9fde2b753e6319b7e4e5cd747277f84677f493999bd199cd5051a73225 | [
{
"content": "1. (10 points) Simplify: $1 \\div\\left[a+1 \\div\\left(b+\\frac{1}{\\mathrm{c}}\\right)\\right] \\div \\frac{\\mathrm{b}}{\\mathrm{ab}+1}-\\frac{1}{\\mathrm{~b}(\\mathrm{abc}+\\mathrm{a}+\\mathrm{c})}=$",
"role": "user"
}
] | 1. (10 points) Simplify: $1 \div\left[a+1 \div\left(b+\frac{1}{\mathrm{c}}\right)\right] \div \frac{\mathrm{b}}{\mathrm{ab}+1}-\frac{1}{\mathrm{~b}(\mathrm{abc}+\mathrm{a}+\mathrm{c})}=$ | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1497, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15498"}] | {
"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
} |
[
"55"
] | [
"skywork"
] | 1ad477985e60d42df6ec58ae3d4ff9bd2b78a01ec7343124cc11b08aad057120 | [
{
"content": "Consider numbers of the form $1a1$ , where $a$ is a digit. How many pairs of such numbers are there such that their sum is also a palindrome?\n\n*Note: A palindrome is a number which reads the same from left to right and from right to left. Examples: $353$ , $91719$ .*",
"role": "user"
... | Consider numbers of the form $1a1$ , where $a$ is a digit. How many pairs of such numbers are there such that their sum is also a palindrome?
*Note: A palindrome is a number which reads the same from left to right and from right to left. Examples: $353$ , $91719$ .* | "[\"55\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1510, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15499"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2}(S_{1}+S_{2}+\\sqrt{(S_{1}+S_{2})^{2}-4S_{1}S_{2}\\sin^{2}\\alpha})"
] | [
"skywork"
] | 9c67a59c9512397abb525eecfc33eb3bcd7cb24b74d9f6214a7dd775297ef753 | [
{
"content": "[ Area of a Triangle (using two sides and the angle between them)] Area\n\nOn the segment $AB$ lie points $C$ and $D$, with point $C$ between points $A$ and $D$. Point $M$ is taken such that lines $AM$ and $MD$ are perpendicular, and lines $CM$ and $MB$ are also perpendicular. Find the area of tri... | [ Area of a Triangle (using two sides and the angle between them)] Area
On the segment $AB$ lie points $C$ and $D$, with point $C$ between points $A$ and $D$. Point $M$ is taken such that lines $AM$ and $MD$ are perpendicular, and lines $CM$ and $MB$ are also perpendicular. Find the area of triangle $AMB$, given that ... | "[\"\\\\frac{1}{2}(S_{1}+S_{2}+\\\\sqrt{(S_{1}+S_{2})^{2}-4S_{1}S_{2}\\\\sin^{2}\\\\alpha})\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1486, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15500"}] | {
"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
} |
[
"pq^{2}"
] | [
"skywork"
] | 8ced3e49f0134ab45cedcde9e59df5de6a3247bf06ecf71d67d7d5d73faddc5d | [
{
"content": "Let $p$ and $q$ be two distinct odd prime numbers. Determine the multiplicative order of $1+p q$ modulo $p^{2} q^{3}$.",
"role": "user"
}
] | Let $p$ and $q$ be two distinct odd prime numbers. Determine the multiplicative order of $1+p q$ modulo $p^{2} q^{3}$. | "[\"pq^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1506, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15501"}] | {
"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
} |
[
"135"
] | [
"skywork"
] | 65d3ae193b5f6c574c7f49ddf653a8cc59671bedfc1b9458498b476c52857a45 | [
{
"content": "A positive integer $n$ is *funny* if for all positive divisors $d$ of $n$ , $d+2$ is a prime number. Find all funny numbers with the largest possible number of divisors.",
"role": "user"
}
] | A positive integer $n$ is *funny* if for all positive divisors $d$ of $n$ , $d+2$ is a prime number. Find all funny numbers with the largest possible number of divisors. | "[\"135\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1494, "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:15502"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | 3ec883b474490cdf19245a6e7c38bb70a58c4ab711ca8519a17b78ccac34f653 | [
{
"content": "5. Calculate:\n$$\n\\sum_{k=0}^{2013}(-1)^{k+1}(k+1) \\frac{1}{\\mathrm{C}_{2014}^{k}}=\n$$\n$\\qquad$",
"role": "user"
}
] | 5. Calculate:
$$
\sum_{k=0}^{2013}(-1)^{k+1}(k+1) \frac{1}{\mathrm{C}_{2014}^{k}}=
$$
$\qquad$ | "[\"0\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1515, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15503"}] | {
"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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