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 |
|---|---|---|---|---|---|---|---|---|
[
"\\textbf{(E)}25"
] | [
"skywork"
] | 34e3efd9c5e3a7db293613ec1bf6ec0971199bb8ea64a8b18ea8f9b3d12be599 | [
{
"content": "Bernardo chooses a three-digit positive integer $N$ and writes both its base-5 and base-6 representations on a blackboard. Later LeRoy sees the two numbers Bernardo has written. Treating the two numbers as base-10 integers, he adds them to obtain an integer $S$. For example, if $N = 749$, Bernardo... | Bernardo chooses a three-digit positive integer $N$ and writes both its base-5 and base-6 representations on a blackboard. Later LeRoy sees the two numbers Bernardo has written. Treating the two numbers as base-10 integers, he adds them to obtain an integer $S$. For example, if $N = 749$, Bernardo writes the numbers $1... | "[\"\\\\textbf{(E)}25\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 109077, "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:118992"}] | {
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"reference_components": 1,
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} |
[
"\\sqrt[3]{9} - 1"
] | [
"skywork"
] | 29808fb7d8bf27f015bd0c9881743f2351b3e4ee70dfc0612013ba766a1093f9 | [
{
"content": "Determine the maximal value of $k$ such that the inequality\n$$\\left(k +\\frac{a}{b}\\right) \\left(k + \\frac{b}{c}\\right)\\left(k + \\frac{c}{a}\\right)\n\\le \\left( \\frac{a}{b}+ \\frac{b}{c}+ \\frac{c}{a}\\right) \\left( \\frac{b}{a}+ \\frac{c}{b}+ \\frac{a}{c}\\right)$$\nholds for all pos... | Determine the maximal value of $k$ such that the inequality
$$\left(k +\frac{a}{b}\right) \left(k + \frac{b}{c}\right)\left(k + \frac{c}{a}\right)
\le \left( \frac{a}{b}+ \frac{b}{c}+ \frac{c}{a}\right) \left( \frac{b}{a}+ \frac{c}{b}+ \frac{a}{c}\right)$$
holds for all positive reals $a, b, c$. | "[\" \\\\sqrt[3]{9} - 1 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109092, "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:118993"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\sqrt{2} + \\sqrt{6}}{2}"
] | [
"skywork"
] | bd915ea6bd0540048bdcd4a86aba271150504eff8eaefa7601e0650ff88d511f | [
{
"content": "The diagonal \\( BD \\) of quadrilateral \\( ABCD \\) is the diameter of the circle circumscribed around this quadrilateral. Find the diagonal \\( AC \\) if \\( BD = 2 \\), \\( AB = 1 \\), and \\( \\angle ABD : \\angle DBC = 4 : 3 \\).",
"role": "user"
}
] | The diagonal \( BD \) of quadrilateral \( ABCD \) is the diameter of the circle circumscribed around this quadrilateral. Find the diagonal \( AC \) if \( BD = 2 \), \( AB = 1 \), and \( \angle ABD : \angle DBC = 4 : 3 \). | "[\"\\\\frac{\\\\sqrt{2} + \\\\sqrt{6}}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109085, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:118995"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"217"
] | [
"skywork"
] | f52b9ed153acc1c34a2abbbd73f7532db9c26a677894a220ed580bbf7324c0f2 | [
{
"content": "Let \\( S = \\{1, 2, \\ldots, 280\\} \\). Find the smallest natural number \\( n \\) such that every \\( n \\)-element subset of \\( S \\) contains 5 pairwise coprime numbers.",
"role": "user"
}
] | Let \( S = \{1, 2, \ldots, 280\} \). Find the smallest natural number \( n \) such that every \( n \)-element subset of \( S \) contains 5 pairwise coprime numbers. | "[\"217\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109116, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:118996"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0, 3, -1, 4"
] | [
"skywork"
] | 2acc21bf29b76cf7b4e9ae95f2d1f95e6dbe0734f0603b09be350333f4e390be | [
{
"content": "Let $f(x) = x^2-3x$. For what values of $x$ is $f(f(x)) = f(x)$? Enter all the solutions, separated by commas.",
"role": "user"
}
] | Let $f(x) = x^2-3x$. For what values of $x$ is $f(f(x)) = f(x)$? Enter all the solutions, separated by commas. | "[\"0, 3, -1, 4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109103, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118997"}] | {
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"20000"
] | [
"skywork"
] | c354e71c1a977568128ad7e897cfc20edd4c4b776396eab21b2cccd0f52fdc65 | [
{
"content": "2005^{2} + 2 \\times 2005 \\times 1995 + 1995^{2} divided by 800.",
"role": "user"
}
] | 2005^{2} + 2 \times 2005 \times 1995 + 1995^{2} divided by 800. | "[\"20000\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109097, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118998"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"13"
] | [
"skywork"
] | a0f1fb6f4148392adcb7578774762ddf131237e71970d2832ce6a13c568414de | [
{
"content": "## Task 1 - 290611\n\nPeter wants to measure exactly 13 liters of milk from a jug that contains more than 13 liters. The exact capacity of the jug is unknown, and it is also unknown how much milk is exactly in the jug. In addition to the jug, there are exactly two more containers available. One ha... | ## Task 1 - 290611
Peter wants to measure exactly 13 liters of milk from a jug that contains more than 13 liters. The exact capacity of the jug is unknown, and it is also unknown how much milk is exactly in the jug. In addition to the jug, there are exactly two more containers available. One has a capacity of exactly ... | "[\"13\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109067, "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:118999"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"107.4\\%"
] | [
"skywork"
] | 68179cc6c25db413a75a0987f53b14322ab53642696811875914162a18eb2220 | [
{
"content": "A square has sides of length 3 units. A second square is formed having sides that are $120\\%$ longer than the sides of the first square. This process is continued sequentially to create a total of five squares. What will be the percent increase in the perimeter from the first square to the fifth ... | A square has sides of length 3 units. A second square is formed having sides that are $120\%$ longer than the sides of the first square. This process is continued sequentially to create a total of five squares. What will be the percent increase in the perimeter from the first square to the fifth square? Express your an... | "[\"107.4\\\\%\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109112, "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:119000"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"61"
] | [
"skywork"
] | f5a0a4f6ce850fbeb5cbb21147e921b47ded98a110a3d7dce6f3708c1ab970f6 | [
{
"content": "2.81 The sum of the following 7 numbers is exactly 19:\n$$\\begin{array}{l}\na_{1}=2.56, a_{2}=2.61, a_{3}=2.65, a_{4}=2.71, a_{5}=2.79, a_{6}= \\\\\n2.82, a_{7}=2.86 .\n\\end{array}$$\n\nTo approximate $a_{i}$ with integers $A_{i}$ $(1 \\leqslant i \\leqslant 7)$, such that the sum of $A_{i}$ is ... | 2.81 The sum of the following 7 numbers is exactly 19:
$$\begin{array}{l}
a_{1}=2.56, a_{2}=2.61, a_{3}=2.65, a_{4}=2.71, a_{5}=2.79, a_{6}= \\
2.82, a_{7}=2.86 .
\end{array}$$
To approximate $a_{i}$ with integers $A_{i}$ $(1 \leqslant i \leqslant 7)$, such that the sum of $A_{i}$ is still 19, and the maximum value $M... | "[\"61\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 109091, "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:119001"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"skywork"
] | 942443b99dd7ce9bb6a4dab5c5d7d5f23f15b78fe01a09262d3253d6942826cc | [
{
"content": "The region consisting of all points in three-dimensional space within 3 units of line segment $\\overline{AB}$ has volume $216\\pi$. What is the length $\\textit{AB}$?",
"role": "user"
}
] | The region consisting of all points in three-dimensional space within 3 units of line segment $\overline{AB}$ has volume $216\pi$. What is the length $\textit{AB}$? | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109111, "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:119003"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9217"
] | [
"skywork"
] | e39868ac705735097824024d45829a6ceb4fe62ea9a96d557469e69f167bb6c1 | [
{
"content": "The very hungry caterpillar lives on the number line. For each non-zero integer $i$, a fruit sits on the point with coordinate $i$. The caterpillar moves back and forth; whenever he reaches a point with food, he eats the food, increasing his weight by one pound, and turns around. The caterpillar m... | The very hungry caterpillar lives on the number line. For each non-zero integer $i$, a fruit sits on the point with coordinate $i$. The caterpillar moves back and forth; whenever he reaches a point with food, he eats the food, increasing his weight by one pound, and turns around. The caterpillar moves at a speed of $2^... | "[\"9217\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109090, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119004"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{2}"
] | [
"skywork"
] | c1938370a594aea5b9727ff9e8329db11e13a807780b4536ae4b9b3cb063f1e1 | [
{
"content": "Consider an isosceles right triangle with leg lengths of 1 each. Inscribed in this triangle is a square in such a way that one vertex of the square coincides with the right-angle vertex of the triangle. Another square with side length $y$ is inscribed in an identical isosceles right triangle where... | Consider an isosceles right triangle with leg lengths of 1 each. Inscribed in this triangle is a square in such a way that one vertex of the square coincides with the right-angle vertex of the triangle. Another square with side length $y$ is inscribed in an identical isosceles right triangle where one side of the squar... | "[\"\\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109089, "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:119005"}] | {
"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
} |
[
"B"
] | [
"skywork"
] | 5c4333605fa838120ac586b99453098802e004babbb441e394f13bef45475830 | [
{
"content": "17-183 If the three sides of $\\triangle A B C$ are $a, b, c$ and simultaneously satisfy\n$$\na^{4}=b^{4}+c^{4}-b^{2} c^{2}, b^{4}=c^{4}+a^{4}-a^{2} c^{2} \\text {. }\n$$\n\nthen $\\triangle A B C$ is\n(A) a scalene triangle.\n(B) an equilateral triangle.\n(C) a right triangle.\n(D) an obtuse tria... | 17-183 If the three sides of $\triangle A B C$ are $a, b, c$ and simultaneously satisfy
$$
a^{4}=b^{4}+c^{4}-b^{2} c^{2}, b^{4}=c^{4}+a^{4}-a^{2} c^{2} \text {. }
$$
then $\triangle A B C$ is
(A) a scalene triangle.
(B) an equilateral triangle.
(C) a right triangle.
(D) an obtuse triangle.
(E) an isosceles right trian... | "[\"B\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109102, "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:119007"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | a7a4c45cbb01282c4210edd3d356c478bfe8c98040a4bd0f4de40467d8f9f5c1 | [
{
"content": "10. Equation\n$$\n\\begin{array}{l}\n\\frac{(x-1)(x-4)(x-9)}{(x+1)(x+4)(x+9)}+ \\\\\n\\frac{2}{3}\\left[\\frac{x^{3}+1}{(x+1)^{3}}+\\frac{x^{3}+4^{3}}{(x+4)^{3}}+\\frac{x^{3}+9^{3}}{(x+9)^{3}}\\right]=1\n\\end{array}\n$$\n\nThe number of distinct non-zero integer solutions is",
"role": "user"
... | 10. Equation
$$
\begin{array}{l}
\frac{(x-1)(x-4)(x-9)}{(x+1)(x+4)(x+9)}+ \\
\frac{2}{3}\left[\frac{x^{3}+1}{(x+1)^{3}}+\frac{x^{3}+4^{3}}{(x+4)^{3}}+\frac{x^{3}+9^{3}}{(x+9)^{3}}\right]=1
\end{array}
$$
The number of distinct non-zero integer solutions is | "[\"4\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 109106, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:119008"}] | {
"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
} |
[
"4.5"
] | [
"skywork"
] | 8a9f7295a1dae2281541ddb9461995e8547a3eb1ffef712660cbeaec5ff8a41d | [
{
"content": "Given triangle $ABC$ with vertices $A = (3,0)$, $B = (0,3)$, and $C$ lying on the line $x + 2y = 8$, find the area of triangle $ABC$.",
"role": "user"
}
] | Given triangle $ABC$ with vertices $A = (3,0)$, $B = (0,3)$, and $C$ lying on the line $x + 2y = 8$, find the area of triangle $ABC$. | "[\"4.5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109105, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:119009"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2006"
] | [
"skywork"
] | 88020792d5c168bc3c13d2ba4db8ce6bc383f9efc10243f56f88742983eb62f4 | [
{
"content": "Given that $x\\_1$ is a root of the equation $x \\ln x = 2006$ and $x\\_2$ is a root of the equation $xe^{x} = 2006$, find the value of $x\\_1 \\cdot x\\_2$.",
"role": "user"
}
] | Given that $x\_1$ is a root of the equation $x \ln x = 2006$ and $x\_2$ is a root of the equation $xe^{x} = 2006$, find the value of $x\_1 \cdot x\_2$. | "[\"2006\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109095, "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:119010"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | 42680b0f28947df71abe8cf26433bb8eb80beaa1269137a28e148896070596bd | [
{
"content": "One. (20 points) Given that $a$, $b$, and $c$ are three distinct real numbers, and the three quadratic equations\n\\[\n\\begin{array}{l}\nx^{2} + a x + b = 0, \\\\\nx^{2} + b x + c = 0, \\\\\nx^{2} + c x + a = 0\n\\end{array}\n\\]\n\neach pair of which has exactly one common root. Find the value o... | One. (20 points) Given that $a$, $b$, and $c$ are three distinct real numbers, and the three quadratic equations
\[
\begin{array}{l}
x^{2} + a x + b = 0, \\
x^{2} + b x + c = 0, \\
x^{2} + c x + a = 0
\end{array}
\]
each pair of which has exactly one common root. Find the value of $a^{2} + b^{2} + c^{2}$. | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109109, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:119011"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{3}"
] | [
"skywork"
] | 624bc9761be9b7541a0b597792e25ed6029975dca0d3e38f49c13f149cee5ed9 | [
{
"content": "$ABCD$ is a regular tetrahedron. Let $N$ be the midpoint of $\\overline{AB}$, and let $G$ be the centroid of triangle $ACD$. What is $\\cos \\angle BNG$?",
"role": "user"
}
] | $ABCD$ is a regular tetrahedron. Let $N$ be the midpoint of $\overline{AB}$, and let $G$ be the centroid of triangle $ACD$. What is $\cos \angle BNG$? | "[\"\\\\frac{1}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109113, "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:119012"}] | {
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[
"90"
] | [
"skywork"
] | 92992cf053674d14378a02b9c27a44a53e795fba4e48ba7cddfc65cfcdd1ddce | [
{
"content": "Point D is from AC of triangle ABC so that 2AD=DC. Let DE be perpendicular to BC and AE\nintersects BD at F. It is known that triangle BEF is equilateral. Find <ADB?",
"role": "user"
}
] | Point D is from AC of triangle ABC so that 2AD=DC. Let DE be perpendicular to BC and AE
intersects BD at F. It is known that triangle BEF is equilateral. Find <ADB? | "[\"90\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109086, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119013"}] | {
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[
"35"
] | [
"skywork"
] | 948dcc696d2609f5c4e4166a6840951e1d1abc7d823a55a383c2410506e6f92f | [
{
"content": "Help Neznaika restore the division example of two numbers, if it is known that the quotient is five times smaller than the dividend and seven times larger than the divisor.\n\n#",
"role": "user"
}
] | Help Neznaika restore the division example of two numbers, if it is known that the quotient is five times smaller than the dividend and seven times larger than the divisor.
# | "[\"35\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109099, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119014"}] | {
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[
"1180990"
] | [
"skywork"
] | 3ce6d7efa02cf27fd3db212ab7fb4eee781bbf33de05ca0fc00329c2bf6dd987 | [
{
"content": "An organization initially consists of 10 leaders and a certain number of regular members. Each year, all leaders are replaced, and each regular member recruits two new members. After this, 10 new leaders are elected from outside the organization. Initially, there are 30 people in total in the orga... | An organization initially consists of 10 leaders and a certain number of regular members. Each year, all leaders are replaced, and each regular member recruits two new members. After this, 10 new leaders are elected from outside the organization. Initially, there are 30 people in total in the organization. How many peo... | "[\"1180990\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109114, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:119015"}] | {
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[
"\\frac{3}{5}"
] | [
"skywork"
] | b90d7279edcbab3b117c56646abf8dd03783002246d34fd03de569f523c85ae1 | [
{
"content": "Given that $\\sin \\alpha$ is a root of the equation $5x^2 - 7x - 6 = 0$, find the value of $\\frac{\\sin \\left(\\alpha - \\frac{\\pi}{2}\\right)\\sin^2\\left(-\\alpha + \\pi\\right)\\sin \\left( \\frac{3\\pi}{2}-\\alpha\\right)\\tan \\left(\\alpha - \\pi\\right)}{\\sin \\left( \\frac{\\pi}{2}-\\... | Given that $\sin \alpha$ is a root of the equation $5x^2 - 7x - 6 = 0$, find the value of $\frac{\sin \left(\alpha - \frac{\pi}{2}\right)\sin^2\left(-\alpha + \pi\right)\sin \left( \frac{3\pi}{2}-\alpha\right)\tan \left(\alpha - \pi\right)}{\sin \left( \frac{\pi}{2}-\alpha\right)\cos \left(\alpha + \frac{\pi}{2}\right)... | "[\"\\\\frac{3}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109081, "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:119017"}] | {
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[
"a=-2, b=-3, c=2"
] | [
"skywork"
] | 35c5e8c931e1e0c529fe1e3e43d71503f896daf7e87e1077be2222cd7d73849b | [
{
"content": "Example 3 Given three different real numbers $a, b, c$, satisfying $a-b+c=3$, the equations\n$$\nx^{2}+a x+1=0 \\text { and } x^{2}+b x+c=0\n$$\n\nhave one common real root, and the equations\n$$\nx^{2}+x+a=0 \\text { and } x^{2}+c x+b=0\n$$\n\nalso have one common real root. Find the values of $a... | Example 3 Given three different real numbers $a, b, c$, satisfying $a-b+c=3$, the equations
$$
x^{2}+a x+1=0 \text { and } x^{2}+b x+c=0
$$
have one common real root, and the equations
$$
x^{2}+x+a=0 \text { and } x^{2}+c x+b=0
$$
also have one common real root. Find the values of $a, b, c$. | "[\"a=-2, b=-3, c=2\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 109115, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:119018"}] | {
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[
"r = \\frac{2}{n + 4}"
] | [
"skywork"
] | ce820493a18bb8354aa371c5da1428f10955f8321c42d9cb766fe6c8d0f381ea | [
{
"content": "Consider the situation such that $ n$ circles with radius $ r$ are contained between 2 concentric circles with radius $ 1,\\ 1\\minus{}2r$ without intersecting one anoyher.Let $ r$ vary with being fixed $ n\\geq 2.$\r\n\r\n(1) Show that $ r$ should be satisfied $ 0<r\\leq \\frac{\\sin \\frac{\\pi}... | Consider the situation such that $ n$ circles with radius $ r$ are contained between 2 concentric circles with radius $ 1,\ 1\minus{}2r$ without intersecting one anoyher.Let $ r$ vary with being fixed $ n\geq 2.$
(1) Show that $ r$ should be satisfied $ 0<r\leq \frac{\sin \frac{\pi}{n}}{1\plus{}\sin \frac{\pi}{n}}.$... | "[\"r = \\\\frac{2}{n + 4}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109071, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119019"}] | {
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[
"39"
] | [
"skywork"
] | 259c0697f7b59e87c9ab5a97f2be3897773460223aadd06e0a369732cb02a8f5 | [
{
"content": "Example 2 As shown in Figure 1-10, 5 beads are strung together to form a necklace. Now, there are 3 colors of beads available for use. How many different necklaces can be made?",
"role": "user"
}
] | Example 2 As shown in Figure 1-10, 5 beads are strung together to form a necklace. Now, there are 3 colors of beads available for use. How many different necklaces can be made? | "[\"39\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109107, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119020"}] | {
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[
"18"
] | [
"skywork"
] | d31639d0ffab1d1db42154bd346ad11c356f5c61572c8f01ac4d4e19c755822f | [
{
"content": "Johan has a large number of identical cubes. He has made a structure by taking a single cube and then sticking another cube to each face. He wants to make an extended structure in the same way so that each face of the current structure will have a cube stuck to it. How many extra cubes will he nee... | Johan has a large number of identical cubes. He has made a structure by taking a single cube and then sticking another cube to each face. He wants to make an extended structure in the same way so that each face of the current structure will have a cube stuck to it. How many extra cubes will he need to complete his exte... | "[\"18\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109117, "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:119021"}] | {
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[
"23"
] | [
"skywork"
] | 96bb6b18b720461c56ea3a12422ed36ad37f59e07ee2a74335a144f55e634822 | [
{
"content": "73. There are $N$ chess pieces placed on a circle, as shown in the figure, with a chess piece at point $B$ adjacent to the chess piece at point $A$. Xiaohong first takes away 1 chess piece from point $B$, then moves clockwise, taking away 2 chess pieces every 1 piece, and continues for 10 rounds, ... | 73. There are $N$ chess pieces placed on a circle, as shown in the figure, with a chess piece at point $B$ adjacent to the chess piece at point $A$. Xiaohong first takes away 1 chess piece from point $B$, then moves clockwise, taking away 2 chess pieces every 1 piece, and continues for 10 rounds, crossing $A$ 9 times. ... | "[\"23\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109087, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:119022"}] | {
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[
"-12"
] | [
"skywork"
] | 0d7d7e802f6e68f9177fc6150d2012b2fc6e841eaa1a217705447084ad0c9a93 | [
{
"content": "In parallelogram ABCD, AB=2AD=4, ∠BAD=60°, E is the midpoint of BC, calculate the dot product of vectors BD and AE.",
"role": "user"
}
] | In parallelogram ABCD, AB=2AD=4, ∠BAD=60°, E is the midpoint of BC, calculate the dot product of vectors BD and AE. | "[\"-12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109121, "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:119023"}] | {
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[
"9"
] | [
"skywork"
] | 6b0432f7f8928ac53fd6c1a48e57a286b7fd9c08f37288d098a43e802d2c7faa | [
{
"content": "Find the greatest positive integer $n$ for which there exist $n$ nonnegative integers $x_1, x_2,\\ldots , x_n$, not all zero, such that for any $\\varepsilon_1, \\varepsilon_2, \\ldots, \\varepsilon_n$ from the set $\\{-1, 0, 1\\}$, not all zero, $\\varepsilon_1 x_1 + \\varepsilon_2 x_2 + \\cdots ... | Find the greatest positive integer $n$ for which there exist $n$ nonnegative integers $x_1, x_2,\ldots , x_n$, not all zero, such that for any $\varepsilon_1, \varepsilon_2, \ldots, \varepsilon_n$ from the set $\{-1, 0, 1\}$, not all zero, $\varepsilon_1 x_1 + \varepsilon_2 x_2 + \cdots + \varepsilon_n x_n$ is not divi... | "[\"9\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109120, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119024"}] | {
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"reference_present": true
} |
[
"8"
] | [
"skywork"
] | de9edc710a5d31ed0a0b14e2052d9b4315ef4f24e44169a7ea589560b9d7420b | [
{
"content": "17. (10 points) Xiao Hua walks along the route of the \"Chunleibei\" bus at a constant speed, encountering a \"Chunleibei\" bus head-on every 6 minutes, and being overtaken by a \"Chunleibei\" bus from behind every 12 minutes. How often does a \"Chunleibei\" bus depart? (Assume that \"Chunleibei\"... | 17. (10 points) Xiao Hua walks along the route of the "Chunleibei" bus at a constant speed, encountering a "Chunleibei" bus head-on every 6 minutes, and being overtaken by a "Chunleibei" bus from behind every 12 minutes. How often does a "Chunleibei" bus depart? (Assume that "Chunleibei" buses depart from the terminal ... | "[\"8\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109124, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119025"}] | {
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[
"16"
] | [
"skywork"
] | e2a448112f4b3c5e214b007bc469b9deace114a22f971546de88e887c8025bfe | [
{
"content": "Example 20 (1998 Beijing Middle School Mathematics Competition Final Question) As shown in Figure 5-20, in rectangle $ABCD$, $AB=20 \\text{ cm}, BC=10 \\text{ cm}$. Take a point $M$ on $AC$ and a point $N$ on $AB$ such that the value of $BM+MN$ is minimized. Find this minimum value.",
"role": ... | Example 20 (1998 Beijing Middle School Mathematics Competition Final Question) As shown in Figure 5-20, in rectangle $ABCD$, $AB=20 \text{ cm}, BC=10 \text{ cm}$. Take a point $M$ on $AC$ and a point $N$ on $AB$ such that the value of $BM+MN$ is minimized. Find this minimum value. | "[\"16\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109122, "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:119026"}] | {
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[
"-3"
] | [
"skywork"
] | 4666c463379dc7973d137e5f22f1e16937e1757c93df02f7a32b320e40e1038a | [
{
"content": "If the inequality system about $x$ is $\\left\\{\\begin{array}{l}{\\frac{x+3}{2}≥x-1}\\\\{3x+6＞a+4}\\end{array}\\right.$ has exactly $3$ odd solutions, and the solution to the equation about $y$ is $3y+6a=22-y$ is a non-negative integer, then the product of all integers $a$ that satisfy the condit... | If the inequality system about $x$ is $\left\{\begin{array}{l}{\frac{x+3}{2}≥x-1}\\{3x+6＞a+4}\end{array}\right.$ has exactly $3$ odd solutions, and the solution to the equation about $y$ is $3y+6a=22-y$ is a non-negative integer, then the product of all integers $a$ that satisfy the conditions is ____. | "[\"-3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109074, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119027"}] | {
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[
"(1)(2)(4)"
] | [
"skywork"
] | 0e0370b75c64fb7b1ac62d55fa00280fa31202682c231fd5de2c08fbad898e3c | [
{
"content": "9. A. Given two inverse proportion functions $y=\\frac{k}{x}$ and $y=\\frac{1}{x}$, their graphs in the first quadrant are shown in Figure 4. Point $P$ is on the graph of $y=\\frac{k}{x}$, $PC \\perp x$-axis, with the foot of the perpendicular at $C$, and intersects the graph of $y=\\frac{1}{x}$ a... | 9. A. Given two inverse proportion functions $y=\frac{k}{x}$ and $y=\frac{1}{x}$, their graphs in the first quadrant are shown in Figure 4. Point $P$ is on the graph of $y=\frac{k}{x}$, $PC \perp x$-axis, with the foot of the perpendicular at $C$, and intersects the graph of $y=\frac{1}{x}$ at point $A$; $PD \perp y$-a... | "[\"(1)(2)(4)\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 109101, "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:119028"}] | {
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[
"30\\cdot6"
] | [
"skywork"
] | 8c1d807b5dd69225c377e18602fc1622e7f69182f1142bc56ea300560ca35aa1 | [
{
"content": "A8. A cozy house is divided into 6 equally large apartments. Each apartment has a bathroom that is $3 \\mathrm{~m}$ long and $2 \\mathrm{~m}$ wide, which represents exactly $20 \\%$ of the apartment's area. With which calculation do we get the area of the entire house in square meters?\n(A) $6 \\c... | A8. A cozy house is divided into 6 equally large apartments. Each apartment has a bathroom that is $3 \mathrm{~m}$ long and $2 \mathrm{~m}$ wide, which represents exactly $20 \%$ of the apartment's area. With which calculation do we get the area of the entire house in square meters?
(A) $6 \cdot \frac{1}{5}$
(B) $\frac... | "[\"30\\\\cdot6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109096, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119029"}] | {
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[
"6"
] | [
"skywork"
] | 8d548d5de458405766449d581869a42c9f8ea722cbe9cc19bc1b93c8bd9883d9 | [
{
"content": "Evan has $10$ cards numbered $1$ through $10$. He chooses some of the cards and takes the product of the numbers on them. When the product is divided by $3$, the remainder is $1$. Find the maximum number of cards he could have chose.\n\n[i]Proposed by Evan Chang [/i]",
"role": "user"
}
] | Evan has $10$ cards numbered $1$ through $10$. He chooses some of the cards and takes the product of the numbers on them. When the product is divided by $3$, the remainder is $1$. Find the maximum number of cards he could have chose.
[i]Proposed by Evan Chang [/i] | "[\"6\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109125, "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:119030"}] | {
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[
"9"
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"skywork"
] | 71a1a7a505a93f020304eb08bd1fd4a161b4c9c8417f275011593e82a0e96ddc | [
{
"content": "9. Arrange 2016 coins into a triangle. Place 1 coin in the 1st row, 2 coins in the 2nd row, …, and $N$ coins in the $N$th row. Then the sum of the digits of $N$ is $(\\quad)$.\n(A) 6\n(B) 7\n(C) 8\n(D) 9\n(E) 10",
"role": "user"
}
] | 9. Arrange 2016 coins into a triangle. Place 1 coin in the 1st row, 2 coins in the 2nd row, …, and $N$ coins in the $N$th row. Then the sum of the digits of $N$ is $(\quad)$.
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10 | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109069, "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:119031"}] | {
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[
"f(x) = x"
] | [
"skywork"
] | d2555ead820cd4bf739eeb35efa4ff355d29f40071f3f087f663e317ddeba38d | [
{
"content": "a) Consider\\[f\\text{:}\\left[ \\text{0,}\\infty \\right)\\to \\left[ \\text{0,}\\infty \\right)\\] a differentiable and convex function .Show that $f\\left( x \\right)\\le x$, for every $x\\ge 0$, than ${f}'\\left( x \\right)\\le 1$ ,for every $x\\ge 0$\nb) Determine \\[f\\text{:}\\left[ \\te... | a) Consider\[f\text{:}\left[ \text{0,}\infty \right)\to \left[ \text{0,}\infty \right)\] a differentiable and convex function .Show that $f\left( x \right)\le x$, for every $x\ge 0$, than ${f}'\left( x \right)\le 1$ ,for every $x\ge 0$
b) Determine \[f\text{:}\left[ \text{0,}\infty \right)\to \left[ \text{0,}\infty... | "[\" f(x) = x \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109061, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119032"}] | {
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[
"\\sin^4\\frac{\\alpha}{4}(2+\\cos\\frac{\\alpha}{2})"
] | [
"skywork"
] | f57afd5b3c08ed5e8714a22a5352f49f5449ba9b24de7cd9de6e69405f4a02c5 | [
{
"content": "3.105. Find the ratio of the volume of a spherical segment to the volume of the whole sphere, if the arc in the axial section of the segment corresponds to a central angle equal to $\\alpha$.\n\nTo find the ratio of the volume of a spherical segment to the volume of the whole sphere, where the arc... | 3.105. Find the ratio of the volume of a spherical segment to the volume of the whole sphere, if the arc in the axial section of the segment corresponds to a central angle equal to $\alpha$.
To find the ratio of the volume of a spherical segment to the volume of the whole sphere, where the arc in the axial section of ... | "[\"\\\\sin^4\\\\frac{\\\\alpha}{4}(2+\\\\cos\\\\frac{\\\\alpha}{2})\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109119, "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:119033"}] | {
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[
"\\frac{256}{17}"
] | [
"skywork"
] | 1fb979aa1df2d0884aef3022b3e6891952e5230135e660dcbebe1486f5da3066 | [
{
"content": "In square \\( A B C D \\), \\( P \\) and \\( Q \\) are points on sides \\( C D \\) and \\( B C \\), respectively, such that \\( \\angle A P Q = 90^\\circ \\). If \\( A P = 4 \\) and \\( P Q = 3 \\), find the area of \\( A B C D \\).",
"role": "user"
}
] | In square \( A B C D \), \( P \) and \( Q \) are points on sides \( C D \) and \( B C \), respectively, such that \( \angle A P Q = 90^\circ \). If \( A P = 4 \) and \( P Q = 3 \), find the area of \( A B C D \). | "[\"\\\\frac{256}{17}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109129, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:119034"}] | {
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[
"2024"
] | [
"skywork"
] | 3ec6574367d20e9af5eeef68aac54a4a3c9d31ed9068cda8cf3bd0c5555637c8 | [
{
"content": "## Task A-4.5.\n\nDetermine (if it exists) the largest natural number that cannot be represented as the sum of some, not necessarily distinct, elements of the set $\\{135,136,137, \\ldots, 144\\}$.",
"role": "user"
}
] | ## Task A-4.5.
Determine (if it exists) the largest natural number that cannot be represented as the sum of some, not necessarily distinct, elements of the set $\{135,136,137, \ldots, 144\}$. | "[\"2024\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109145, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119035"}] | {
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[
"5\\pi"
] | [
"skywork"
] | 52648c645cec869e71ddb4677023d749907321d60f26f58cee7ef947e6622b70 | [
{
"content": "Pete has some trouble slicing a 20-inch (diameter) pizza. His first two cuts (from center to circumference of the pizza) make a 30º slice. He continues making cuts until he has gone around the whole pizza, each time trying to copy the angle of the previous slice but in fact adding 2º each time. Th... | Pete has some trouble slicing a 20-inch (diameter) pizza. His first two cuts (from center to circumference of the pizza) make a 30º slice. He continues making cuts until he has gone around the whole pizza, each time trying to copy the angle of the previous slice but in fact adding 2º each time. That is, he makes adjace... | "[\"5\\\\pi\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109131, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119036"}] | {
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[
"0.97"
] | [
"skywork"
] | 4de42c48b04d5cc5ff232a6ee20854342b16cc88a8f0f7932aac4488f654ac6b | [
{
"content": "Example 4. A sportsman shoots at a target divided into 3 sectors. The probability of hitting the first sector is 0.4, the second - 0.3. What is the probability of hitting either the first or the second sector?",
"role": "user"
}
] | Example 4. A sportsman shoots at a target divided into 3 sectors. The probability of hitting the first sector is 0.4, the second - 0.3. What is the probability of hitting either the first or the second sector? | "[\"0.97\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109143, "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:119037"}] | {
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[
"p = 31"
] | [
"skywork"
] | f4ae68e60654ff10f951957db4a2ddea00d8c9b4b3790dbd5696ec521b8bab92 | [
{
"content": "Determine all primes $p$ such that $5^p + 4 p^4$ is a perfect square, i.e., the square of an integer.",
"role": "user"
}
] | Determine all primes $p$ such that $5^p + 4 p^4$ is a perfect square, i.e., the square of an integer. | "[\" p = 31 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109138, "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:119038"}] | {
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[
"5"
] | [
"skywork"
] | 984884ce784dde68dc2dc2c75f24d50e8383f009ed6529b7c736d6cb0fac08d2 | [
{
"content": "15. (15 points) Train $109 T$ departs from Beijing at 19:33 and arrives in Shanghai the next day at 10:26; Train 1461 departs from Beijing at 11:58 and arrives in Shanghai the next day at 8:01. Question: What is the difference in running time between these two trains in minutes?",
"role": "use... | 15. (15 points) Train $109 T$ departs from Beijing at 19:33 and arrives in Shanghai the next day at 10:26; Train 1461 departs from Beijing at 11:58 and arrives in Shanghai the next day at 8:01. Question: What is the difference in running time between these two trains in minutes? | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109153, "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:119039"}] | {
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[
"-21600"
] | [
"skywork"
] | 82fde187225d6e8de00a7e07bad7b1fac2014798efbe3428e33f364f52d00d57 | [
{
"content": "In the expansion of \\((-xy + 2x + 3y - 6)^6\\), what is the coefficient of \\(x^4 y^3\\)? (Answer with a specific number)",
"role": "user"
}
] | In the expansion of \((-xy + 2x + 3y - 6)^6\), what is the coefficient of \(x^4 y^3\)? (Answer with a specific number) | "[\"-21600\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109154, "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:119040"}] | {
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[
"100"
] | [
"skywork"
] | caabed0b9d4db69bdbfd2bb487070dbeccc7cadaa4ddf693588409b8f4f2d68b | [
{
"content": "A bacterium develops on a $100 \\times 100$ grid. It can contaminate a new cell if and only if two adjacent cells are already contaminated. What is the minimal number of initially contaminated cells required for the bacterium to be able to spread everywhere on the grid?",
"role": "user"
}
] | A bacterium develops on a $100 \times 100$ grid. It can contaminate a new cell if and only if two adjacent cells are already contaminated. What is the minimal number of initially contaminated cells required for the bacterium to be able to spread everywhere on the grid? | "[\"100\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109133, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119041"}] | {
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[
"254"
] | [
"skywork"
] | f35b8cea422e2b477dc4f544f7136e9af67d371381b29f6b9b70cf344a83f6ad | [
{
"content": "Mom is sewing towels from fabric that is $120 \\mathrm{~cm}$ wide. The finished towel has dimensions of $60 \\mathrm{~cm} \\times 38 \\mathrm{~cm}$. When cutting the fabric, $2 \\mathrm{~cm}$ must be added to each edge for finishing. How many centimeters of fabric does Mom need to buy at a minimum... | Mom is sewing towels from fabric that is $120 \mathrm{~cm}$ wide. The finished towel has dimensions of $60 \mathrm{~cm} \times 38 \mathrm{~cm}$. When cutting the fabric, $2 \mathrm{~cm}$ must be added to each edge for finishing. How many centimeters of fabric does Mom need to buy at a minimum to sew 10 towels? | "[\"254\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109156, "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:119042"}] | {
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[
"\\sqrt{3}"
] | [
"skywork"
] | 3fc98bd97ad5cac0a5066f86d72600cb51dce142f073ac058d8f9d4149abdb9f | [
{
"content": "In acute triangle $\\triangle ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given vectors $\\overrightarrow{m} = (2, c)$ and $\\overrightarrow{n} = (\\frac{b}{2}\\cos C - \\sin A, \\cos B)$, with $b = \\sqrt{3}$ and $\\overrightarrow{m} \\p... | In acute triangle $\triangle ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given vectors $\overrightarrow{m} = (2, c)$ and $\overrightarrow{n} = (\frac{b}{2}\cos C - \sin A, \cos B)$, with $b = \sqrt{3}$ and $\overrightarrow{m} \perp \overrightarrow{n}$.
(1) Fin... | "[\"\\\\sqrt{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109123, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "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:119043"}] | {
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[
"68"
] | [
"skywork"
] | 98ffc68e6494a5c093e686f2528dbebe363faa6406f6ea87e83d12f1c72f15ce | [
{
"content": "2.1. The sine of the dihedral angle at the lateral edge of a regular quadrilateral pyramid is $\\frac{15}{17}$. Find the area of the lateral surface of the pyramid if the area of its diagonal section is $3 \\sqrt{34}$.",
"role": "user"
}
] | 2.1. The sine of the dihedral angle at the lateral edge of a regular quadrilateral pyramid is $\frac{15}{17}$. Find the area of the lateral surface of the pyramid if the area of its diagonal section is $3 \sqrt{34}$. | "[\"68\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109161, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119044"}] | {
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[
"100"
] | [
"skywork"
] | c642eaaabecaabe4b9b34a202cd1c0c73f051a1c18c0dae3a2748bc4f34041e5 | [
{
"content": "Let $d_1 = a^2 + 2^a + a \\cdot 2^{(a+1)/2} + a^3$ and $d_2 = a^2 + 2^a - a \\cdot 2^{(a+1)/2} + a^3$. If $1 \\le a \\le 300$, how many integral values of $a$ are there such that $d_1 \\cdot d_2$ is a multiple of $3$?",
"role": "user"
}
] | Let $d_1 = a^2 + 2^a + a \cdot 2^{(a+1)/2} + a^3$ and $d_2 = a^2 + 2^a - a \cdot 2^{(a+1)/2} + a^3$. If $1 \le a \le 300$, how many integral values of $a$ are there such that $d_1 \cdot d_2$ is a multiple of $3$? | "[\"100\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109141, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:119045"}] | {
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[
"6"
] | [
"skywork"
] | b457b133b55d5b2abb95593fdcdfd54f1bcf36918fc78f283b3dc7f0e1fdb7e0 | [
{
"content": "Let $A = (1,0)$ and $B = (5,4).$ Let $P$ be a point on the parabola $y^2 = 4x.$ Find the smallest possible value of $AP + BP.$",
"role": "user"
}
] | Let $A = (1,0)$ and $B = (5,4).$ Let $P$ be a point on the parabola $y^2 = 4x.$ Find the smallest possible value of $AP + BP.$ | "[\"6\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109148, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:119046"}] | {
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[
"E"
] | [
"skywork"
] | bd0f7c7b0c28eb080ca7622ce8d9b1c0c4e5fcd79f9a4bffeeec1b47eac7a387 | [
{
"content": "4) Andrea writes the sum of two three-digit numbers with the corresponding result. Then she replaces each digit with a letter, making the same letter correspond to the same digit and using different letters for different digits. In this way, she obtains:\n\n$\\mathrm{TRE}+\\mathrm{TRE}=$ SEI. Then... | 4) Andrea writes the sum of two three-digit numbers with the corresponding result. Then she replaces each digit with a letter, making the same letter correspond to the same digit and using different letters for different digits. In this way, she obtains:
$\mathrm{TRE}+\mathrm{TRE}=$ SEI. Then:
(A) the letter E necess... | "[\"E\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109132, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:119047"}] | {
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[
"26"
] | [
"skywork"
] | b3a31363fe567005721825b52bd02e4cfac0e52e8ccd4acfab0461413949616c | [
{
"content": "Given the set \\( S = \\{1, 2, \\cdots, 100\\} \\), determine the smallest possible value of \\( m \\) such that in any subset of \\( S \\) with \\( m \\) elements, there exists at least one number that is a divisor of the product of the remaining \\( m-1 \\) numbers.",
"role": "user"
}
] | Given the set \( S = \{1, 2, \cdots, 100\} \), determine the smallest possible value of \( m \) such that in any subset of \( S \) with \( m \) elements, there exists at least one number that is a divisor of the product of the remaining \( m-1 \) numbers. | "[\"26\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109137, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:119048"}] | {
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[
"56"
] | [
"skywork"
] | 31aa79f81fdcf172ce6e36a354bc4c83aeb1abc0ec64286d8f7158dc6f4bdeeb | [
{
"content": "Circle $\\Omega$ has radius 13. Circle $\\omega$ has radius 14 and its center $P$ lies on the boundary of circle $\\Omega$. Points $A$ and $B$ lie on $\\Omega$ such that chord $A B$ has length 24 and is tangent to $\\omega$ at point $T$. Find $A T \\cdot B T$.",
"role": "user"
}
] | Circle $\Omega$ has radius 13. Circle $\omega$ has radius 14 and its center $P$ lies on the boundary of circle $\Omega$. Points $A$ and $B$ lie on $\Omega$ such that chord $A B$ has length 24 and is tangent to $\omega$ at point $T$. Find $A T \cdot B T$. | "[\"56\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109150, "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:119049"}] | {
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[
"20"
] | [
"skywork"
] | 072923aece5e90f094584eb39af20f8b6f5327dbab87c0481a50439de78054d6 | [
{
"content": "A circular table has 60 chairs around it. There are $N$ people seated at this table in such a way that the next person seated must sit next to someone. What is the smallest possible value for $N$?\n$\\text{(A) } 15\\quad \\text{(B) } 20\\quad \\text{(C) } 30\\quad \\text{(D) } 40\\quad \\text{(E) ... | A circular table has 60 chairs around it. There are $N$ people seated at this table in such a way that the next person seated must sit next to someone. What is the smallest possible value for $N$?
$\text{(A) } 15\quad \text{(B) } 20\quad \text{(C) } 30\quad \text{(D) } 40\quad \text{(E) } 58$ | "[\"20\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 109149, "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:119050"}] | {
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[
"n\\cdot2^{n-2}"
] | [
"skywork"
] | da64f65f5f83fb0008a77510fb82a1dd31ed25db8faa472797731993d1373b3b | [
{
"content": "$1 \\cdot 71$ A circle has $n$ points $(n>1)$, connect these $n$ points, sequentially denoted as $P_{1}, P_{2}$,\n$\\cdots, P_{n}$, such that the polyline $P_{1} P_{2} \\cdots P_{n}$ does not intersect itself. How many such connection methods are there?",
"role": "user"
}
] | $1 \cdot 71$ A circle has $n$ points $(n>1)$, connect these $n$ points, sequentially denoted as $P_{1}, P_{2}$,
$\cdots, P_{n}$, such that the polyline $P_{1} P_{2} \cdots P_{n}$ does not intersect itself. How many such connection methods are there? | "[\"n\\\\cdot2^{n-2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109127, "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:119051"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"2^{997}"
] | [
"skywork"
] | 8b8ab40cfbc2619966fd01881a6887e064b42001a8664756be8e00a731f6aa70 | [
{
"content": "Example 12 Let the sequence of positive real numbers $x_{0}, x_{1}, \\cdots, x_{1995}$ satisfy the following two conditions:\n(1) $x_{0}=x_{1995}$; (2) $x_{i-1}+\\frac{2}{x_{i-1}}=2 x_{i}+\\frac{1}{x_{i}}, i=1,2, \\cdots, 1995$. Find the maximum value of $x_{0}$ in all sequences that satisfy the c... | Example 12 Let the sequence of positive real numbers $x_{0}, x_{1}, \cdots, x_{1995}$ satisfy the following two conditions:
(1) $x_{0}=x_{1995}$; (2) $x_{i-1}+\frac{2}{x_{i-1}}=2 x_{i}+\frac{1}{x_{i}}, i=1,2, \cdots, 1995$. Find the maximum value of $x_{0}$ in all sequences that satisfy the conditions. | "[\"2^{997}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109142, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119052"}] | {
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[
"39"
] | [
"skywork"
] | 86a8d18d77febfa0d5cd4138d04b924d1a49aa608bd1cfe6daa91a3a33096e9a | [
{
"content": "16. If any group of numbers is taken from $1,2, \\cdots, 50$, there will always be two different numbers whose product is an integer multiple of their sum. How many numbers must be taken at minimum?",
"role": "user"
}
] | 16. If any group of numbers is taken from $1,2, \cdots, 50$, there will always be two different numbers whose product is an integer multiple of their sum. How many numbers must be taken at minimum? | "[\"39\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109157, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119053"}] | {
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"reference_present": true
} |
[
"271"
] | [
"skywork"
] | 7fc7972e2d0a5287fa2f554e287fe9b8ce48b2e1f13396af77fd8d1606b9b337 | [
{
"content": "Find the positive integer $k$ such that the roots of $x^3 - 15x^2 + kx -1105$ are three distinct collinear points in the complex plane.",
"role": "user"
}
] | Find the positive integer $k$ such that the roots of $x^3 - 15x^2 + kx -1105$ are three distinct collinear points in the complex plane. | "[\"271\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109158, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119054"}] | {
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} |
[
"11011"
] | [
"skywork"
] | ff70e204a61fdeee3c73496f749ab8a9117e0cb61b73ffa75e0d0838a6343e6c | [
{
"content": "1. A palindrome is a natural number that reads the same from left to right as it does from right to left. Does there exist a five-digit palindrome that is equal to the sum of two four-digit palindromes?",
"role": "user"
}
] | 1. A palindrome is a natural number that reads the same from left to right as it does from right to left. Does there exist a five-digit palindrome that is equal to the sum of two four-digit palindromes? | "[\"11011\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109168, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:119055"}] | {
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} |
[
"f(x)=x"
] | [
"skywork"
] | 12dca772135dd3775010035b691c85ee99299b1d7049432eb12eb2b7ecb9ee19 | [
{
"content": "10. Find all non-constant monic polynomials $f(x)$ with integer coefficients, such that there exists a positive integer $M$, for all positive integers $n \\geqslant M$, $\\frac{f\\left(2^{n}\\right)-2^{f(n)}}{f(n)}$ is an integer.",
"role": "user"
}
] | 10. Find all non-constant monic polynomials $f(x)$ with integer coefficients, such that there exists a positive integer $M$, for all positive integers $n \geqslant M$, $\frac{f\left(2^{n}\right)-2^{f(n)}}{f(n)}$ is an integer. | "[\"f(x)=x\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109151, "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:119056"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1:1"
] | [
"skywork"
] | 0ef46ebdf2b92ed3ad1aad78def3da1ee06c14b07b6660ad11bc8e1a248d43f0 | [
{
"content": "A kitten bites off a quarter of a sausage from one end, then a puppy bites off a third of the remaining piece from the opposite end, then the kitten again bites off a quarter from its end, and the puppy bites off a third from its end, and so on. You need to tie a string around the sausage in advan... | A kitten bites off a quarter of a sausage from one end, then a puppy bites off a third of the remaining piece from the opposite end, then the kitten again bites off a quarter from its end, and the puppy bites off a third from its end, and so on. You need to tie a string around the sausage in advance to ensure that no o... | "[\"1:1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109136, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119057"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\sqrt{3}}{4}"
] | [
"skywork"
] | 379ab1c33ea6036d92f673921188a2d45df9e241acdd9913ff24762083970395 | [
{
"content": "Two adjacent faces of a tetrahedron, which are equilateral triangles with a side length of 1, form a dihedral angle of 45 degrees. The tetrahedron is rotated around the common edge of these faces. Find the maximum area of the projection of the rotating tetrahedron onto the plane containing this ed... | Two adjacent faces of a tetrahedron, which are equilateral triangles with a side length of 1, form a dihedral angle of 45 degrees. The tetrahedron is rotated around the common edge of these faces. Find the maximum area of the projection of the rotating tetrahedron onto the plane containing this edge. | "[\"\\\\frac{\\\\sqrt{3}}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109146, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119058"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"57"
] | [
"skywork"
] | 576150a8beca1359bb295459e1e3b5c5d584bfce7d89c70cfeb9a982564aee4a | [
{
"content": "477*. What is the greatest common divisor of all numbers $7^{n+2}+8^{2 n+1}(n \\in N)$?",
"role": "user"
}
] | 477*. What is the greatest common divisor of all numbers $7^{n+2}+8^{2 n+1}(n \in N)$? | "[\"57\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109176, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:119059"}] | {
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[
"-\\frac{2}{5}"
] | [
"skywork"
] | 01fc7f8e8721803fa6796b00d31055352d4fa55ae2f4578d6dd29367ff28f750 | [
{
"content": "Let $f(x)$ be a function defined on $\\mathbb{R}$ with a period of $2$. In the interval $[-1,1)$, $f(x)$ is defined as follows:\n$$\nf(x)=\\begin{cases} \nx + a, & -1 \\leqslant x < 0, \\\\\n\\left| \\frac{2}{5} - x \\right|, & 0 \\leqslant x < 1,\n\\end{cases}\n$$\nwhere $a \\in \\mathbb{R}$. If ... | Let $f(x)$ be a function defined on $\mathbb{R}$ with a period of $2$. In the interval $[-1,1)$, $f(x)$ is defined as follows:
$$
f(x)=\begin{cases}
x + a, & -1 \leqslant x < 0, \\
\left| \frac{2}{5} - x \right|, & 0 \leqslant x < 1,
\end{cases}
$$
where $a \in \mathbb{R}$. If $f\left( -\frac{5}{2} \right) = f\left( \... | "[\"-\\\\frac{2}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109130, "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:119060"}] | {
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[
"\\frac{21}{32}"
] | [
"skywork"
] | a7553b928793f7954b070c324b32c5aac9a27968d9772bed3d96e21c63d88d7c | [
{
"content": "Given two arithmetic sequences $\\{a\\_n\\}$ and $\\{b\\_n\\}$ with the sum of their first $n$ terms being $S\\_n$ and $T\\_n$ respectively. If $\\frac{S\\_n}{T\\_n} = \\frac{2n}{3n+1}$, find the value of $\\frac{a\\_{11}}{b\\_{11}}$.",
"role": "user"
}
] | Given two arithmetic sequences $\{a\_n\}$ and $\{b\_n\}$ with the sum of their first $n$ terms being $S\_n$ and $T\_n$ respectively. If $\frac{S\_n}{T\_n} = \frac{2n}{3n+1}$, find the value of $\frac{a\_{11}}{b\_{11}}$. | "[\"\\\\frac{21}{32}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109139, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119061"}] | {
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[
"\\frac{-a^{2}+20 a+8+\\left(a^{3}+8 a\\right) \\sqrt{a^{2}+8}}{32}"
] | [
"skywork"
] | da62459c522778dbf60b7d59ccfab08b52d1e796accb32b3067f22cf5e4586a3 | [
{
"content": "Example 3 (Self-created problem, 1988.11.03) Let $x \\in \\mathbf{R}, a \\geqslant 1$ be a constant, then\n$$|\\sin x \\cdot(\\cos x+a)| \\leqslant \\sqrt{\\frac{-a^{2}+20 a+8+\\left(a^{3}+8 a\\right) \\sqrt{a^{2}+8}}{32}}$$",
"role": "user"
}
] | Example 3 (Self-created problem, 1988.11.03) Let $x \in \mathbf{R}, a \geqslant 1$ be a constant, then
$$|\sin x \cdot(\cos x+a)| \leqslant \sqrt{\frac{-a^{2}+20 a+8+\left(a^{3}+8 a\right) \sqrt{a^{2}+8}}{32}}$$ | "[\"\\\\frac{-a^{2}+20 a+8+\\\\left(a^{3}+8 a\\\\right) \\\\sqrt{a^{2}+8}}{32}\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 109164, "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:119062"}] | {
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"reference_present": true
} |
[
"\\frac{49}{64}"
] | [
"skywork"
] | b1fa3867ed34abccba49c5081825a6f35fd09882c8944fb08dd1d86fcb1e9357 | [
{
"content": "Two fair, eight-sided dice are rolled. What is the probability that the sum of the two numbers showing is less than 12?",
"role": "user"
}
] | Two fair, eight-sided dice are rolled. What is the probability that the sum of the two numbers showing is less than 12? | "[\"\\\\frac{49}{64}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109177, "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:119064"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"120^{\\circ}"
] | [
"skywork"
] | e957032ee1dd5d5828d879c363286f7b00b526bd5828d2ca724b730dd8462099 | [
{
"content": "4. In the acute triangle $\\triangle A B C$, the lengths of the three sides $a, b, c$ are all integers, and $a<b<c, a+b+c=20$. Then $\\angle A$ $+\\angle C=$ $\\qquad$ .",
"role": "user"
}
] | 4. In the acute triangle $\triangle A B C$, the lengths of the three sides $a, b, c$ are all integers, and $a<b<c, a+b+c=20$. Then $\angle A$ $+\angle C=$ $\qquad$ . | "[\"120^{\\\\circ}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 109134, "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:119065"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"288\\pi"
] | [
"skywork"
] | 058431075d52d7475890498c6264d5ccd3dffe67d814da1a90b92068afe436fa | [
{
"content": "A right circular cone sits on a table, pointing up. The cross-section triangle, perpendicular to the base, has a vertex angle of 60 degrees. The diameter of the cone's base is $12\\sqrt{3}$ inches. A sphere is placed inside the cone so that it is tangent to the sides of the cone and sits on the ta... | A right circular cone sits on a table, pointing up. The cross-section triangle, perpendicular to the base, has a vertex angle of 60 degrees. The diameter of the cone's base is $12\sqrt{3}$ inches. A sphere is placed inside the cone so that it is tangent to the sides of the cone and sits on the table. What is the volume... | "[\"288\\\\pi\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109159, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119066"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"4013"
] | [
"skywork"
] | eb9631f0247833ffa02bf7fefe4e1a6fe09ad669de3e39cf9523b028f94207db | [
{
"content": "(solved by Anca Arnautu and Adrien Laroche). Let $\\mathscr{P}$ be the parabola in the plane with equation $y=x^{2}$. Let $\\Gamma_{1}$ be the circle of diameter 1 tangent internally to $\\mathscr{P}$ at the origin. By recurrence, we define $\\Gamma_{n+1}$ as the circle tangent to $\\Gamma_{n}$ an... | (solved by Anca Arnautu and Adrien Laroche). Let $\mathscr{P}$ be the parabola in the plane with equation $y=x^{2}$. Let $\Gamma_{1}$ be the circle of diameter 1 tangent internally to $\mathscr{P}$ at the origin. By recurrence, we define $\Gamma_{n+1}$ as the circle tangent to $\Gamma_{n}$ and twice to $\mathscr{P}$. C... | "[\"4013\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109152, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:119067"}] | {
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[
"0,-1,-2"
] | [
"skywork"
] | 94470fb40f32e3091ff8282b48d057f5a9a835c6bafa226ed617266786069b5b | [
{
"content": "24. The numbers $a, b, c$ satisfy the equations\n\n$$\na b+a+b=c, \\quad b c+b+c=a, \\quad c a+c+a=b\n$$\n\nFind all possible values of $a$.",
"role": "user"
}
] | 24. The numbers $a, b, c$ satisfy the equations
$$
a b+a+b=c, \quad b c+b+c=a, \quad c a+c+a=b
$$
Find all possible values of $a$. | "[\"0,-1,-2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109175, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119068"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 0a6d9d25f388e140d745d2d3a2799b52737f93250ebef17259f35a5aa970c279 | [
{
"content": "4. For the parabola $y^{2}=2 p x(p>0)$, the focus is $F$, the directrix is $l$, and $A, B$ are two moving points on the parabola, satisfying $\\angle A F B=\\frac{\\pi}{3}$. Let the midpoint of segment $A B$ be $M$, and the projection of $M$ on $l$ be $N$. Then the maximum value of $\\frac{|M N|}{... | 4. For the parabola $y^{2}=2 p x(p>0)$, the focus is $F$, the directrix is $l$, and $A, B$ are two moving points on the parabola, satisfying $\angle A F B=\frac{\pi}{3}$. Let the midpoint of segment $A B$ be $M$, and the projection of $M$ on $l$ be $N$. Then the maximum value of $\frac{|M N|}{|A B|}$ is $\qquad$ | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109144, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119069"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2} \\tan \\theta"
] | [
"skywork"
] | c8bb1166330e20ceaf78c78a3fbdf245a712656ac1de296e7c7fb1fbffb798ad | [
{
"content": "A hollow cylinder with a very thin wall (like a toilet paper tube) and a block are placed at rest at the top of a plane with inclination $\\theta$ above the horizontal. The cylinder rolls down the plane without slipping and the block slides down the plane; it is found that both objects reach the b... | A hollow cylinder with a very thin wall (like a toilet paper tube) and a block are placed at rest at the top of a plane with inclination $\theta$ above the horizontal. The cylinder rolls down the plane without slipping and the block slides down the plane; it is found that both objects reach the bottom of the plane simu... | "[\"\\\\frac{1}{2} \\\\tan \\\\theta\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109170, "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:119070"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"46"
] | [
"skywork"
] | ba8024e9bb32e7599230193d40dd3593535abe0fdb2cc5e35f668a7b3ffbd642 | [
{
"content": "The number $2013$ has the property that its units digit is the sum of its other digits, that is $2+0+1=3$. How many integers less than $2013$ but greater than $1000$ have this property?",
"role": "user"
}
] | The number $2013$ has the property that its units digit is the sum of its other digits, that is $2+0+1=3$. How many integers less than $2013$ but greater than $1000$ have this property? | "[\"46\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109183, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119072"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"282282"
] | [
"skywork"
] | d135f8f7a541c9a56f4b625b16fd754053a7ade2c75f728a6b2e1095ff76d3b3 | [
{
"content": "Find the least positive integer of the form <u>a</u> <u>b</u> <u>a</u> <u>a</u> <u>b</u> <u>a</u>, where a and b are distinct digits, such that the integer can be written as a product of six distinct primes",
"role": "user"
}
] | Find the least positive integer of the form <u>a</u> <u>b</u> <u>a</u> <u>a</u> <u>b</u> <u>a</u>, where a and b are distinct digits, such that the integer can be written as a product of six distinct primes | "[\"282282\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109174, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119073"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | ecb2620471fd23188c620976b1eaf684250be4dfc4a9499a3061a90574deeceb | [
{
"content": "(4) (Total 20 points) In the right triangle $\\triangle ABC$, $\\angle ACB=90^{\\circ}$, $M$ is a point on $AB$, and $AM^2 + BM^2 + CM^2 = 2AM + 2BM + 2CM - 3$. If $P$ is a moving point on the segment $AC$, and $\\odot O$ is the circle passing through points $P, M, C$, and a line through $P$ paral... | (4) (Total 20 points) In the right triangle $\triangle ABC$, $\angle ACB=90^{\circ}$, $M$ is a point on $AB$, and $AM^2 + BM^2 + CM^2 = 2AM + 2BM + 2CM - 3$. If $P$ is a moving point on the segment $AC$, and $\odot O$ is the circle passing through points $P, M, C$, and a line through $P$ parallel to $AB$ intersects $\o... | "[\"1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 109135, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119075"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{17}{8}"
] | [
"skywork"
] | 4524c4b0950183238d6eecbd3c1beabd797385928591f194fd3f6ea9f454cd21 | [
{
"content": "A line $l$ passing through the focus of the parabola $y=4x^2$ intersects the parabola at points $A(x_1, y_1)$ and $B(x_2, y_2)$. If $y_1+y_2=2$, then the length of segment $AB$ equals \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | A line $l$ passing through the focus of the parabola $y=4x^2$ intersects the parabola at points $A(x_1, y_1)$ and $B(x_2, y_2)$. If $y_1+y_2=2$, then the length of segment $AB$ equals \_\_\_\_\_\_. | "[\"\\\\frac{17}{8}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109162, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119076"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"$f(x) = x^2 \\text{ and } f(x) = 0$"
] | [
"skywork"
] | eca6a5c17738d8ee29f22150c69d7577c88b0b63fb1dbafc9099f3ee3bb0a24e | [
{
"content": "Determine all the functions $f : \\mathbb{R} \\to \\mathbb{R}$ such that\n\\[ f(x^2 + f(y)) = f(f(x)) + f(y^2) + 2f(xy) \\]\nfor all real numbers $x$ and $y$.",
"role": "user"
}
] | Determine all the functions $f : \mathbb{R} \to \mathbb{R}$ such that
\[ f(x^2 + f(y)) = f(f(x)) + f(y^2) + 2f(xy) \]
for all real numbers $x$ and $y$. | "[\"$f(x) = x^2 \\\\text{ and } f(x) = 0$\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109184, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119077"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"576=(4!)^{2}"
] | [
"skywork"
] | e8e6243636240d374601ccfe42398cc3683f7c24907ff1256fcd084d4ecbadf5 | [
{
"content": "10.2. Find the number of different arrangements of 8 rooks on different white squares of an 8 by 8 chessboard such that no rook attacks another. A chess rook attacks all squares in the row and column it occupies.",
"role": "user"
}
] | 10.2. Find the number of different arrangements of 8 rooks on different white squares of an 8 by 8 chessboard such that no rook attacks another. A chess rook attacks all squares in the row and column it occupies. | "[\"576=(4!)^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109182, "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:119078"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{\\frac{401}{5}}"
] | [
"skywork"
] | 00bcf4c4ea496e29b955936014e45347f77c1f78906bf9289ffbb8feb0bcd687 | [
{
"content": "The points $A=\\left(4, \\frac{1}{4}\\right)$ and $B=\\left(-5,-\\frac{1}{5}\\right)$ lie on the hyperbola $x y=1$. The circle with diameter $A B$ intersects this hyperbola again at points $X$ and $Y$. Compute $X Y$.",
"role": "user"
}
] | The points $A=\left(4, \frac{1}{4}\right)$ and $B=\left(-5,-\frac{1}{5}\right)$ lie on the hyperbola $x y=1$. The circle with diameter $A B$ intersects this hyperbola again at points $X$ and $Y$. Compute $X Y$. | "[\"\\\\sqrt{\\\\frac{401}{5}}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109169, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:119079"}] | {
"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
} |
[
"160"
] | [
"skywork"
] | 40f6135864e0af185fcbd199dc30a260a108a13012e3f9dcd6f7fb3a4985dd00 | [
{
"content": "In triangle \\(ABC\\), the sides opposite to angles \\(A, B,\\) and \\(C\\) are denoted by \\(a, b,\\) and \\(c\\) respectively. Given that \\(c = 10\\) and \\(\\frac{\\cos A}{\\cos B} = \\frac{b}{a} = \\frac{4}{3}\\). Point \\(P\\) is a moving point on the incircle of triangle \\(ABC\\), and \\(d... | In triangle \(ABC\), the sides opposite to angles \(A, B,\) and \(C\) are denoted by \(a, b,\) and \(c\) respectively. Given that \(c = 10\) and \(\frac{\cos A}{\cos B} = \frac{b}{a} = \frac{4}{3}\). Point \(P\) is a moving point on the incircle of triangle \(ABC\), and \(d\) is the sum of the squares of the distances ... | "[\"160\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109178, "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:119080"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | 9a677c430f330788d735ecc1dc3846a916277a317c35dbf72c1630b46f7ca6af | [
{
"content": "3. If $x^{2}-13 x+1=0$, then the unit digit of $x^{4}+x^{-4}$ is\n(A) 1 ;\n(B) 3 ;\n(C) 5 ;\n(D) 7 .",
"role": "user"
}
] | 3. If $x^{2}-13 x+1=0$, then the unit digit of $x^{4}+x^{-4}$ is
(A) 1 ;
(B) 3 ;
(C) 5 ;
(D) 7 . | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109173, "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:119081"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{4}"
] | [
"skywork"
] | 92a61432c7c7269a71b2320a2b9cdd82e1b824c6dca34222a8c32183135f8acc | [
{
"content": "In a certain business district parking lot, the temporary parking fee is charged by time period. The fee is 6 yuan for each car if the parking duration does not exceed 1 hour, and each additional hour (or a fraction thereof is rounded up to a full hour) costs 8 yuan. It is known that two individua... | In a certain business district parking lot, the temporary parking fee is charged by time period. The fee is 6 yuan for each car if the parking duration does not exceed 1 hour, and each additional hour (or a fraction thereof is rounded up to a full hour) costs 8 yuan. It is known that two individuals, A and B, parked in... | "[\"\\\\frac{1}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109167, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119082"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 34691992875ee7f49a2d910aa38ad0bb8ec687ee9d183e29318bdfde04997299 | [
{
"content": "Given two equiangular polygons $P_1$ and $P_2$ with different numbers of sides; each angle of $P_1$ is $x$ degrees and each angle of $P_2$ is $kx$ degrees, where $k$ is an integer greater than $1$. The number of possibilities for the pair $(x, k)$ is:",
"role": "user"
}
] | Given two equiangular polygons $P_1$ and $P_2$ with different numbers of sides; each angle of $P_1$ is $x$ degrees and each angle of $P_2$ is $kx$ degrees, where $k$ is an integer greater than $1$. The number of possibilities for the pair $(x, k)$ is: | "[\"1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109165, "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:119083"}] | {
"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
} |
[
"6-2\\sqrt{73}"
] | [
"skywork"
] | 965cbc811d6567984482e9ae16e172b656598044f7322b20fc8479f8c77dbe4c | [
{
"content": "Given that point $P(x,y)$ is a moving point on the circle $x^{2}+y^{2}=2y$,\n(1) Find the range of $z=2x+y$;\n(2) If $x+y+a\\geqslant 0$ always holds, find the range of real numbers $a$;\n(3) Find the maximum and minimum values of $x^{2}+y^{2}-16x+4y$.",
"role": "user"
}
] | Given that point $P(x,y)$ is a moving point on the circle $x^{2}+y^{2}=2y$,
(1) Find the range of $z=2x+y$;
(2) If $x+y+a\geqslant 0$ always holds, find the range of real numbers $a$;
(3) Find the maximum and minimum values of $x^{2}+y^{2}-16x+4y$. | "[\"6-2\\\\sqrt{73}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109140, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119084"}] | {
"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
} |
[
"200"
] | [
"skywork"
] | e00ae649763e977393d6da588ac70f1ffe75835bddda3bde22819dbc1bbe5efc | [
{
"content": "9.1. Petya had a large wooden cube with dimensions $30 \\times 30 \\times 30$ cm $^{3}$. Petya decided to paint the entire cube, which took 100 grams of paint. Later, Petya needed smaller cubes, so he cut the large cube with 6 cuts, parallel to the faces of the cube (2 cuts parallel to each pair o... | 9.1. Petya had a large wooden cube with dimensions $30 \times 30 \times 30$ cm $^{3}$. Petya decided to paint the entire cube, which took 100 grams of paint. Later, Petya needed smaller cubes, so he cut the large cube with 6 cuts, parallel to the faces of the cube (2 cuts parallel to each pair of faces), into 27 cubes ... | "[\"200\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109181, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:119085"}] | {
"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
} |
[
"81"
] | [
"skywork"
] | 71a9ecb0782a608aa1510cd96e6d110bd4729d44b7c185601d46a076d16ed7e5 | [
{
"content": "5 Let $x_{1}, x_{2}, x_{3}, x_{4}$ all be positive real numbers, and $x_{1}+x_{2}+x_{3}+x_{4}=\\pi$. Find the minimum value of \n$A=\\left(2 \\sin ^{2} x_{1}+\\frac{1}{\\sin ^{2} x_{1}}\\right)\\left(2 \\sin ^{2} x_{2}+\\frac{1}{\\sin ^{2} x_{2}}\\right)\\left(2 \\sin ^{2} x_{3}+\\frac{1}{\\sin ^{... | 5 Let $x_{1}, x_{2}, x_{3}, x_{4}$ all be positive real numbers, and $x_{1}+x_{2}+x_{3}+x_{4}=\pi$. Find the minimum value of
$A=\left(2 \sin ^{2} x_{1}+\frac{1}{\sin ^{2} x_{1}}\right)\left(2 \sin ^{2} x_{2}+\frac{1}{\sin ^{2} x_{2}}\right)\left(2 \sin ^{2} x_{3}+\frac{1}{\sin ^{2} x_{3}}\right)\left(2 \sin ^{2} x_{4... | "[\"81\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 109179, "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:119086"}] | {
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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"
] | [
"skywork"
] | 875e5674cd080577c232cfb567161bc16f0cbb723c888d54e51f1a3b8702876d | [
{
"content": "Let $\\{a_n\\}$ be a sequence of integers satisfying the following conditions. \n[list]\n[*] $a_1=2021^{2021}$\n[*] $0 \\le a_k < k$ for all integers $k \\ge 2$\n[*] $a_1-a_2+a_3-a_4+ \\cdots + (-1)^{k+1}a_k$ is multiple of $k$ for all positive integers $k$. \n[/list]\nDetermine the $2021^{2022}$t... | Let $\{a_n\}$ be a sequence of integers satisfying the following conditions.
[list]
[*] $a_1=2021^{2021}$
[*] $0 \le a_k < k$ for all integers $k \ge 2$
[*] $a_1-a_2+a_3-a_4+ \cdots + (-1)^{k+1}a_k$ is multiple of $k$ for all positive integers $k$.
[/list]
Determine the $2021^{2022}$th term of the sequence $\{a_n\}$. | "[\"0\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109166, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "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:119087"}] | {
"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
} |
[
"b_{n}=(-1)[(-1)^{n-1}+(-1)^{n}]"
] | [
"skywork"
] | 8c41a03656d873c3cadb1598a65a61f5d4722b19733ca2641560616b2b42adbe | [
{
"content": "Example 3 Color each vertex of an $n(n \\geqslant 3)$-sided polygon with one color, such that the endpoints of the same edge have different colors. If there are $m(m \\geqslant 3)$ colors available, then the total number of different coloring methods is\n$$\nb_{n}=(m-1)\\left[(m-1)^{n-1}+(-1)^{n}\... | Example 3 Color each vertex of an $n(n \geqslant 3)$-sided polygon with one color, such that the endpoints of the same edge have different colors. If there are $m(m \geqslant 3)$ colors available, then the total number of different coloring methods is
$$
b_{n}=(m-1)\left[(m-1)^{n-1}+(-1)^{n}\right] .
$$ | "[\"b_{n}=(-1)[(-1)^{n-1}+(-1)^{n}]\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109172, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119088"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"40"
] | [
"skywork"
] | a8e1edbeb29f5003a4e6bae99506f2ac9e3c008a75e2b557f47ad1f9f138a8ea | [
{
"content": "8. Let $a_{1}, a_{2}, a_{3}, a_{4}$ be 4 distinct numbers from $1,2, \\cdots, 100$, satisfying\n$$\n\\left(a_{1}^{2}+a_{2}^{2}+a_{3}^{2}\\right)\\left(a_{2}^{2}+a_{3}^{2}+a_{4}^{2}\\right)=\\left(a_{1} a_{2}+a_{2} a_{3}+a_{3} a_{4}\\right)^{2},\n$$\n\nthen the number of such ordered quadruples $\\... | 8. Let $a_{1}, a_{2}, a_{3}, a_{4}$ be 4 distinct numbers from $1,2, \cdots, 100$, satisfying
$$
\left(a_{1}^{2}+a_{2}^{2}+a_{3}^{2}\right)\left(a_{2}^{2}+a_{3}^{2}+a_{4}^{2}\right)=\left(a_{1} a_{2}+a_{2} a_{3}+a_{3} a_{4}\right)^{2},
$$
then the number of such ordered quadruples $\left(a_{1}, a_{2}, a_{3}, a_{4}\rig... | "[\"40\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109171, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119089"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 7a0ac56b2f5b3271ee688f46c165dcc90ca3bab4e7ea7756601a312002f79fab | [
{
"content": "Condition of the problem\n\nCalculate the limit of the function:\n\n$\\lim _{x \\rightarrow 1}\\left(\\frac{x^{3}-1}{x-1}\\right)^{\\frac{1}{x^{2}}}$",
"role": "user"
}
] | Condition of the problem
Calculate the limit of the function:
$\lim _{x \rightarrow 1}\left(\frac{x^{3}-1}{x-1}\right)^{\frac{1}{x^{2}}}$ | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109193, "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:119090"}] | {
"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
} |
[
"432"
] | [
"skywork"
] | 27180716fbb9d89900902823d46ce7c3967c63e50fbdeec2fb87280565936e7d | [
{
"content": "In a press conference before a championship game, ten players from four teams will be taking questions. The teams are as follows: three Celtics, three Lakers, two Warriors, and two Nuggets. If teammates insist on sitting together and one specific Warrior must sit at the end of the row on the left,... | In a press conference before a championship game, ten players from four teams will be taking questions. The teams are as follows: three Celtics, three Lakers, two Warriors, and two Nuggets. If teammates insist on sitting together and one specific Warrior must sit at the end of the row on the left, how many ways can the... | "[\"432\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109192, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:119091"}] | {
"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"
] | 8de1aacc5c13dce90220bdc9e7f5f1afd74563dd0c98c8df9e11ddbdb443c81b | [
{
"content": "Example 9 If $x, y, z$ are real numbers, and\n$$\n\\begin{aligned}\n(y-z)^{2} & +(z-x)^{2}+(x-y)^{2} \\\\\n= & (y+z-2 x)^{2}+(z+x-2 y)^{2} \\\\\n& +(x+y-2 z)^{2},\n\\end{aligned}\n$$\n\nfind the value of $M=\\frac{(y z+1)(z x+1)(x y+1)}{\\left(x^{2}+1\\right)\\left(y^{2}+1\\right)\\left(z^{2}+1\\r... | Example 9 If $x, y, z$ are real numbers, and
$$
\begin{aligned}
(y-z)^{2} & +(z-x)^{2}+(x-y)^{2} \\
= & (y+z-2 x)^{2}+(z+x-2 y)^{2} \\
& +(x+y-2 z)^{2},
\end{aligned}
$$
find the value of $M=\frac{(y z+1)(z x+1)(x y+1)}{\left(x^{2}+1\right)\left(y^{2}+1\right)\left(z^{2}+1\right)}$. | "[\"1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 109196, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119092"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{193}{71}"
] | [
"skywork"
] | d9f1149ca0f3115c8ae1dca664dae8eee6cff7ae1a87638d619c40a93051611b | [
{
"content": "4. The infinite simple continued fraction expansion of the number $e$ is\n$$e=[2 ; 1,2,1,1,4,1,1,6,1,1,8, \\ldots]$$\na) Find the first eight convergents of the continued fraction of $e$.\nb) Find the best rational approximation to $e$ having a denominator less than 100.",
"role": "user"
}
] | 4. The infinite simple continued fraction expansion of the number $e$ is
$$e=[2 ; 1,2,1,1,4,1,1,6,1,1,8, \ldots]$$
a) Find the first eight convergents of the continued fraction of $e$.
b) Find the best rational approximation to $e$ having a denominator less than 100. | "[\"\\\\frac{193}{71}\"]" | train-math-numinamath1.5_number_theory | [{"dataset": "skywork", "extra_info": {"index": 109200, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119093"}] | {
"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
} |
[
"\\arcsin\\frac{4}{5}"
] | [
"skywork"
] | ff290152ce8d588fd702560650d76169fde1755ede33431aaf7ecc7cdb2ca626 | [
{
"content": "12.238. A sphere is inscribed in a truncated cone. The sum of the lengths of the diameters of the upper and lower bases of the cone is five times the length of the radius of the sphere. Find the angle between the generatrix of the cone and the plane of the base.",
"role": "user"
}
] | 12.238. A sphere is inscribed in a truncated cone. The sum of the lengths of the diameters of the upper and lower bases of the cone is five times the length of the radius of the sphere. Find the angle between the generatrix of the cone and the plane of the base. | "[\"\\\\arcsin\\\\frac{4}{5}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 109189, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119094"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1170 \\sqrt{37}}{1379}"
] | [
"skywork"
] | 412ac3fa6c2368676daa5a9dcfdd6fedd63927ecefb88b0de56c4c54eac690b6 | [
{
"content": "Let $A B C$ be a triangle with $A B=13, A C=14$, and $B C=15$. Let $G$ be the point on $A C$ such that the reflection of $B G$ over the angle bisector of $\\angle B$ passes through the midpoint of $A C$. Let $Y$ be the midpoint of $G C$ and $X$ be a point on segment $A G$ such that $\\frac{A X}{X ... | Let $A B C$ be a triangle with $A B=13, A C=14$, and $B C=15$. Let $G$ be the point on $A C$ such that the reflection of $B G$ over the angle bisector of $\angle B$ passes through the midpoint of $A C$. Let $Y$ be the midpoint of $G C$ and $X$ be a point on segment $A G$ such that $\frac{A X}{X G}=3$. Construct $F$ and... | "[\"\\\\frac{1170 \\\\sqrt{37}}{1379}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109185, "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:119095"}] | {
"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
} |
[
"798"
] | [
"skywork"
] | 68ab35fd03568e11b69ed49aab084f37b1b9009a3e2c22c40bc9e855aea579f4 | [
{
"content": "A three-digit number \\( X \\) was composed of three different digits, \\( A, B, \\) and \\( C \\). Four students made the following statements:\n\n- Petya: \"The largest digit in the number \\( X \\) is \\( B \\).\"\n- Vasya: \"\\( C = 8 \\).\"\n- Tolya: \"The largest digit is \\( C \\).\"\n- Dim... | A three-digit number \( X \) was composed of three different digits, \( A, B, \) and \( C \). Four students made the following statements:
- Petya: "The largest digit in the number \( X \) is \( B \)."
- Vasya: "\( C = 8 \)."
- Tolya: "The largest digit is \( C \)."
- Dima: "\( C \) is the arithmetic mean of the digit... | "[\"798\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 109188, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119096"}] | {
"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
} |
[
"30"
] | [
"skywork"
] | b032c440bd08fe90ddd27a4202aa921b836de38e6ca9b211ecd74eaa430d70a8 | [
{
"content": "5. If the odd function $y=f(x)$ defined on $\\mathbf{R}$ is symmetric about the line $x=1$, and when $0<x \\leqslant 1$, $f(x)=\\log _{3} x$, then the sum of all real roots of the equation $f(x)=-\\frac{1}{3}+f(0)$ in the interval $(0,10)$ is . $\\qquad$",
"role": "user"
}
] | 5. If the odd function $y=f(x)$ defined on $\mathbf{R}$ is symmetric about the line $x=1$, and when $0<x \leqslant 1$, $f(x)=\log _{3} x$, then the sum of all real roots of the equation $f(x)=-\frac{1}{3}+f(0)$ in the interval $(0,10)$ is . $\qquad$ | "[\"30\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 109186, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119097"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"84"
] | [
"skywork"
] | a1b8cb8dd110d16b8962367560b2aa80cb8d39214c6f9528b23d332228a43bc1 | [
{
"content": "How many integers $n$ with $10 \\le n \\le 500$ have the property that the hundreds digit of $17n$ and $17n+17$ are different?\n\n[i]Proposed by Evan Chen[/i]",
"role": "user"
}
] | How many integers $n$ with $10 \le n \le 500$ have the property that the hundreds digit of $17n$ and $17n+17$ are different?
[i]Proposed by Evan Chen[/i] | "[\"84\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 109205, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:119098"}] | {
"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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