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 |
|---|---|---|---|---|---|---|---|---|
[
"\\arccos \\frac{1}{18}"
] | [
"skywork"
] | 254e4cec1cabe680dc13d1f4c5331a361cf0eb591f38634a6d66cc8d54b9a57b | [
{
"content": "6. In a regular tetrahedron $ABCD$, the line segment connecting the midpoint of edge $AD$ and the centroid of face $BCD$ is $MN$, and the line segment connecting the midpoint of edge $CD$ and the centroid of face $ABC$ is $PQ$. Then the angle formed by $MN$ and $PQ$ is $\\qquad$",
"role": "use... | 6. In a regular tetrahedron $ABCD$, the line segment connecting the midpoint of edge $AD$ and the centroid of face $BCD$ is $MN$, and the line segment connecting the midpoint of edge $CD$ and the centroid of face $ABC$ is $PQ$. Then the angle formed by $MN$ and $PQ$ is $\qquad$ | "[\"\\\\arccos \\\\frac{1}{18}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3315, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17256"}] | {
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} |
[
"x_{1}=11,x_{2}=1.1"
] | [
"skywork"
] | 284328bbe966d2967852106bd9e233533f7f56bf4d5a60c74b44ed7428742998 | [
{
"content": "$7.59 \\quad \\lg ^{4}(x-1)^{2}+\\lg ^{2}(x-1)^{3}=25$.",
"role": "user"
}
] | $7.59 \quad \lg ^{4}(x-1)^{2}+\lg ^{2}(x-1)^{3}=25$. | "[\"x_{1}=11,x_{2}=1.1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3330, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17257"}] | {
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} |
[
"-4"
] | [
"skywork"
] | b29f2703eb1d00f168f4d475da867d3947de8748a40a53af092c72db95d39ef3 | [
{
"content": "Let $g(x) = 3x^4 + 2x^3 - x^2 - 4x + s$. For what value of $s$ is $g(-1) = 0$?",
"role": "user"
}
] | Let $g(x) = 3x^4 + 2x^3 - x^2 - 4x + s$. For what value of $s$ is $g(-1) = 0$? | "[\"-4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3357, "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:17258"}] | {
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[
"(0, 1), (1, 0), \\left( \\frac{-1 + \\sqrt{5}}{2}, \\frac{-1 + \\sqrt{5}}{2} \\right), \\left( \\frac{-1 - \\sqrt{5}}{2}, \\frac{-1 - \\sqrt{5}}{2} \\right)"
] | [
"skywork"
] | 73f5b50a09eeb6d8518dbebe12ca4438b4db77bd39b55e27d8ea7ee632d65a13 | [
{
"content": "The test this year was held on 13 September 2021. It consisted of 10 problems, 5 for Part 1 (each problem worth 4 points, or 1 point if the answer is correct but unjustified), and the other 5 for Part 2 (where each problem is worth 7 points). Part 1 takes 60 minutes to complete, whereas part 2 tak... | The test this year was held on 13 September 2021. It consisted of 10 problems, 5 for Part 1 (each problem worth 4 points, or 1 point if the answer is correct but unjustified), and the other 5 for Part 2 (where each problem is worth 7 points). Part 1 takes 60 minutes to complete, whereas part 2 takes 150 minutes to comp... | "[\" (0, 1), (1, 0), \\\\left( \\\\frac{-1 + \\\\sqrt{5}}{2}, \\\\frac{-1 + \\\\sqrt{5}}{2} \\\\right), \\\\left( \\\\frac{-1 - \\\\sqrt{5}}{2}, \\\\frac{-1 - \\\\sqrt{5}}{2} \\\\right) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3312, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17259"}] | {
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"reference_components": 1,
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} |
[
"-2"
] | [
"skywork"
] | 478b56dadf8ebf26da23d689d9010e992f2b5c8537cccf4e2fa5f11a8b86001d | [
{
"content": "7.127. $\\log _{2}\\left(25^{x+3}-1\\right)=2+\\log _{2}\\left(5^{x+3}+1\\right)$",
"role": "user"
}
] | 7.127. $\log _{2}\left(25^{x+3}-1\right)=2+\log _{2}\left(5^{x+3}+1\right)$ | "[\"-2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3335, "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:17260"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"228"
] | [
"skywork"
] | e94aa28656d813db89f1a594c5bbf2b20caf5550ca770914952e37e04c862fe6 | [
{
"content": "Find the number of ordered pairs of integers $(a, b)$ such that the sequence\\[3, 4, 5, a, b, 30, 40, 50\\]is strictly increasing and no set of four (not necessarily consecutive) terms forms an arithmetic progression.",
"role": "user"
}
] | Find the number of ordered pairs of integers $(a, b)$ such that the sequence\[3, 4, 5, a, b, 30, 40, 50\]is strictly increasing and no set of four (not necessarily consecutive) terms forms an arithmetic progression. | "[\"228\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3331, "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:17261"}, {"dataset": "skywork", "extra_... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"734"
] | [
"skywork"
] | aedab0018e9669d9f25a65fa89eb873f62885e67bf4ddb78b19b72e413932801 | [
{
"content": "$1 \\cdot 11$ For $0 \\leqslant x \\leqslant 100$, find the number of different integer values taken by the function $f(x)=[x]+[2 x]+\\left[\\frac{5 x}{3}\\right]+ [3 x]+[4 x]$.\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the trans... | $1 \cdot 11$ For $0 \leqslant x \leqslant 100$, find the number of different integer values taken by the function $f(x)=[x]+[2 x]+\left[\frac{5 x}{3}\right]+ [3 x]+[4 x]$.
Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly. | "[\"734\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3334, "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:17262"}] | {
"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
} |
[
"36"
] | [
"skywork"
] | 2f14d2e853c13278529884f2068d7b0ba27a8678d03c6758d8bfe681fb29b564 | [
{
"content": "[ [ Relationship,\n\nIn triangle $ABC$, the three sides are given: $AB=26$, $BC=30$, and $AC=28$. Find the part of the area of this triangle enclosed between the height and the bisector drawn from vertex $B$.\n\n#",
"role": "user"
}
] | [ [ Relationship,
In triangle $ABC$, the three sides are given: $AB=26$, $BC=30$, and $AC=28$. Find the part of the area of this triangle enclosed between the height and the bisector drawn from vertex $B$.
# | "[\"36\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3333, "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:17263"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.4"
] | [
"skywork"
] | 3f1169c09c7a961031b1acf6ef8cf11a2197077d443ef7c5caaeb9393a1cf9d3 | [
{
"content": "If two lines $l' $ and $m'$ have equations $y = -3x + 9$, and $y = -5x + 9$, what is the probability that a point randomly selected in the 1st quadrant and below $l'$ will fall between $l'$ and $m'$? Express your answer as a decimal to the nearest hundredth.",
"role": "user"
}
] | If two lines $l' $ and $m'$ have equations $y = -3x + 9$, and $y = -5x + 9$, what is the probability that a point randomly selected in the 1st quadrant and below $l'$ will fall between $l'$ and $m'$? Express your answer as a decimal to the nearest hundredth. | "[\"0.4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3329, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:17264"}] | {
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} |
[
"3"
] | [
"skywork"
] | 72e11d2b9a6487fd8fcf3cac55b243529f900f121c5aed3f8322cd23aa09c8e8 | [
{
"content": "9. Given that a line passing through the focus $F$ of the parabola $y^{2}=4 x$ intersects the parabola at points $M$ and $N$, and $E(m, 0)$ is a point on the $x$-axis. The extensions of $M E$ and $N E$ intersect the parabola at points $P$ and $Q$ respectively. If the slopes $k_{1}$ and $k_{2}$ of ... | 9. Given that a line passing through the focus $F$ of the parabola $y^{2}=4 x$ intersects the parabola at points $M$ and $N$, and $E(m, 0)$ is a point on the $x$-axis. The extensions of $M E$ and $N E$ intersect the parabola at points $P$ and $Q$ respectively. If the slopes $k_{1}$ and $k_{2}$ of $M N$ and $P Q$ satisf... | "[\"3\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3325, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:17266"}, {"dataset": "skywork", "extra_in... | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"3.1415926534<\\pi<3.1415926540"
] | [
"skywork"
] | bffe630e89386611caf7a395418201391564f6f868b0076329b41787b1bd56e2 | [
{
"content": "4. It is known that the continued fraction of $\\pi$ is\n$$x=[3,7,15,1,292,1,1, \\ldots]$$\n\nTry to find its first seven convergents and their approximate values.",
"role": "user"
}
] | 4. It is known that the continued fraction of $\pi$ is
$$x=[3,7,15,1,292,1,1, \ldots]$$
Try to find its first seven convergents and their approximate values. | "[\"3.1415926534<\\\\pi<3.1415926540\"]" | train-math-numinamath1.5_number_theory | [{"dataset": "skywork", "extra_info": {"index": 3355, "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:17267"}] | {
"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
} |
[
"404"
] | [
"skywork"
] | 1e5d6809c5e4b733a839d8fa5a15a72b4ccaf48140bd29104b7d41445de51ac5 | [
{
"content": "From the integers 1 to 2020, there are a total of 1616 integers that are not multiples of 5. These 1616 numbers need to be divided into groups (each group may have a different number of elements), such that the difference (larger number minus smaller number) between any two numbers in the same gro... | From the integers 1 to 2020, there are a total of 1616 integers that are not multiples of 5. These 1616 numbers need to be divided into groups (each group may have a different number of elements), such that the difference (larger number minus smaller number) between any two numbers in the same group is a prime number. ... | "[\"404\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3345, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17268"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\{1156, 1296, 1369, 1600, 1764\\}"
] | [
"skywork"
] | 56b4be1aa071c719814fb857c9e4854081f4e25480749946550212eacfd14fcf | [
{
"content": "Let $m$ be a positive integer for which there exists a positive integer $n$ such that the multiplication $mn$ is a perfect square and $m- n$ is prime. Find all $m$ for $1000\\leq m \\leq 2021.$",
"role": "user"
}
] | Let $m$ be a positive integer for which there exists a positive integer $n$ such that the multiplication $mn$ is a perfect square and $m- n$ is prime. Find all $m$ for $1000\leq m \leq 2021.$ | "[\"\\\\{1156, 1296, 1369, 1600, 1764\\\\}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3341, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17269"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{4}{9}"
] | [
"skywork"
] | d6e1c49cd0d135d2afb432d89702aaec6269812a3819b320107fa826cb4df759 | [
{
"content": "Among the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, draw one at random. The probability of drawing a prime number is ____, and the probability of drawing a composite number is ____.",
"role": "user"
}
] | Among the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, draw one at random. The probability of drawing a prime number is ____, and the probability of drawing a composite number is ____. | "[\"\\\\frac{4}{9}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3359, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:17270"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3501"
] | [
"skywork"
] | fb71452e0e3b8036a388f952e8287ce763a235985bd789c3bcc6507f4f9ca20d | [
{
"content": "Let set $\\mathcal{C}$ be a 70-element subset of $\\{1,2,3,\\ldots,120\\},$ and let $P$ be the sum of the elements of $\\mathcal{C}.$ Find the number of possible values of $P.$",
"role": "user"
}
] | Let set $\mathcal{C}$ be a 70-element subset of $\{1,2,3,\ldots,120\},$ and let $P$ be the sum of the elements of $\mathcal{C}.$ Find the number of possible values of $P.$ | "[\"3501\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3367, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17271"}] | {
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"reference_components": 1,
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} |
[
"6\\sqrt{3}"
] | [
"skywork"
] | cab58e0964e8f354acb6584a99516d02f7b909ef8eed0797f543c00d528d2483 | [
{
"content": "Let $x, y, a \\in \\mathbb{R}^*$, and when $x + 2y = 1$, the minimum value of $\\frac{3}{x} + \\frac{a}{y}$ is $6\\sqrt{3}$. Determine the minimum value of $3x + ay$ when $\\frac{1}{x} + \\frac{2}{y} = 1$.",
"role": "user"
}
] | Let $x, y, a \in \mathbb{R}^*$, and when $x + 2y = 1$, the minimum value of $\frac{3}{x} + \frac{a}{y}$ is $6\sqrt{3}$. Determine the minimum value of $3x + ay$ when $\frac{1}{x} + \frac{2}{y} = 1$. | "[\"6\\\\sqrt{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3326, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:17272"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | c54168498ef7c7a8a694551a17195e4f10db44e8268e2621a78422cefcb30ad8 | [
{
"content": "# Task 8. (16 points)\n\nHow many solutions in integers does the equation $x_{1}^{4}+x_{2}^{4}+\\cdots+x_{14}^{4}=2031$ have.",
"role": "user"
}
] | # Task 8. (16 points)
How many solutions in integers does the equation $x_{1}^{4}+x_{2}^{4}+\cdots+x_{14}^{4}=2031$ have. | "[\"0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3346, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:17274"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"Q"
] | [
"skywork"
] | e960ab050524b33bd232cdebd60f74a8a8bbc0fcd7619838fb575b86c4bb051c | [
{
"content": "Let $ABCD$ be a cyclic quadrilateral such that $AD=BD=AC$. A point $P$ moves along the circumcircle $\\omega$ of triangle $ABCD$. The lined $AP$ and $DP$ meet the lines $CD$ and $AB$ at points $E$ and $F$ respectively. The lines $BE$ and $CF$ meet point $Q$. Find the locus of $Q$.",
"role": "u... | Let $ABCD$ be a cyclic quadrilateral such that $AD=BD=AC$. A point $P$ moves along the circumcircle $\omega$ of triangle $ABCD$. The lined $AP$ and $DP$ meet the lines $CD$ and $AB$ at points $E$ and $F$ respectively. The lines $BE$ and $CF$ meet point $Q$. Find the locus of $Q$. | "[\" Q \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3338, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17275"}] | {
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[
"\\frac{5}{77}"
] | [
"skywork"
] | 51708a76d29c874d2f22ce723ef19b1c8855a5e71090381f0871083e79581684 | [
{
"content": "Example 6 Given three non-negative real numbers $a, b, c$ satisfying the conditions: $3a+2b+c=5, 2a+b-3c=1$. Let $s=$ $3a+b-7c$ have a maximum value of $M$ and a minimum value of $m$. Find $\\mathrm{Mm}$.\n(1989, Shanghai Junior High School Mathematics Competition)",
"role": "user"
}
] | Example 6 Given three non-negative real numbers $a, b, c$ satisfying the conditions: $3a+2b+c=5, 2a+b-3c=1$. Let $s=$ $3a+b-7c$ have a maximum value of $M$ and a minimum value of $m$. Find $\mathrm{Mm}$.
(1989, Shanghai Junior High School Mathematics Competition) | "[\"\\\\frac{5}{77}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3361, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17276"}] | {
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[
"34212.5"
] | [
"skywork"
] | eafa3a1e35ad7014ab9a50824d588a48f8ee61f55794525a15a15ffc9c6427e8 | [
{
"content": "4. Stanislav Petrovich, born on 05.06.1975, height 183 cm, weight 125 kg, an electrician by profession, decided to purchase life and health insurance for 5,000,000 rubles. He visited the insurance company's website, looked at the rates, and without consulting or filling out an application, conclud... | 4. Stanislav Petrovich, born on 05.06.1975, height 183 cm, weight 125 kg, an electrician by profession, decided to purchase life and health insurance for 5,000,000 rubles. He visited the insurance company's website, looked at the rates, and without consulting or filling out an application, concluded that the cost of th... | "[\"34212.5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3324, "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:17277"}] | {
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} |
[
"18.75"
] | [
"skywork"
] | 98cb340ed30c770fe196b3a1282b37609b8c8a3db504bb86fb03ebb302b74ef0 | [
{
"content": "15. A and B start from points A and B respectively at the same time and walk towards each other. A walks 60 meters per minute, and B walks 40 meters per minute. After a period of time, they meet at a point 300 meters away from the midpoint between A and B. If A stops for a while at some point duri... | 15. A and B start from points A and B respectively at the same time and walk towards each other. A walks 60 meters per minute, and B walks 40 meters per minute. After a period of time, they meet at a point 300 meters away from the midpoint between A and B. If A stops for a while at some point during the journey, they w... | "[\"18.75\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3343, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17278"}] | {
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} |
[
"8b + 9c \\leq 8"
] | [
"skywork"
] | 8f53fed02c0e9e14129e1e6bb254aad1859b634dc7792e0e8aaf2eccd696c89a | [
{
"content": "Let $P(x)$ be a polynomial such that $P(x)=x^3-2x^2+bx+c$. Roots of $P(x)$ belong to interval $(0,1)$. Prove that $8b+9c \\leq 8$. When does equality hold?",
"role": "user"
}
] | Let $P(x)$ be a polynomial such that $P(x)=x^3-2x^2+bx+c$. Roots of $P(x)$ belong to interval $(0,1)$. Prove that $8b+9c \leq 8$. When does equality hold? | "[\" 8b + 9c \\\\leq 8 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3348, "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:17279"}] | {
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[
"121"
] | [
"skywork"
] | 238f7d64dee96aa885b4fdc294cc97aa0e1ae0550d45cdf361c2fd9680eaa252 | [
{
"content": "Find the number of real solutions to the equation:\n\\[\n\\frac{1^2}{x - 1} + \\frac{2^2}{x - 2} + \\frac{3^2}{x - 3} + \\dots + \\frac{120^2}{x - 120} = x.\n\\]",
"role": "user"
}
] | Find the number of real solutions to the equation:
\[
\frac{1^2}{x - 1} + \frac{2^2}{x - 2} + \frac{3^2}{x - 3} + \dots + \frac{120^2}{x - 120} = x.
\] | "[\"121\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3353, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:17280"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 5f73cceaeaf0d9e6ab465c7d088e40aaaa3e963c4a4f3589894a118556c18f67 | [
{
"content": "2. How many positive numbers are there among the first 100 terms of the sequence: $\\sin 1^{\\circ}, \\sin 10^{\\circ}, \\sin 100^{\\circ}, \\sin 1000^{\\circ}, \\ldots ?$",
"role": "user"
}
] | 2. How many positive numbers are there among the first 100 terms of the sequence: $\sin 1^{\circ}, \sin 10^{\circ}, \sin 100^{\circ}, \sin 1000^{\circ}, \ldots ?$ | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3347, "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:17281"}] | {
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[
"437"
] | [
"skywork"
] | fbba29dd19d97cb3d616f0cb67e6417cd5559698214aadf3da25ee510846965a | [
{
"content": "[ $\\left[\\begin{array}{ll}\\text { Irreducible fractions }\\end{array}\\right]$\n\nWhat number should be subtracted from the numerator of the fraction ${ }^{537} / 463$ and added to the denominator to obtain $1 / 9$ after simplification?",
"role": "user"
}
] | [ $\left[\begin{array}{ll}\text { Irreducible fractions }\end{array}\right]$
What number should be subtracted from the numerator of the fraction ${ }^{537} / 463$ and added to the denominator to obtain $1 / 9$ after simplification? | "[\"437\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3365, "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:17282"}] | {
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[
"530"
] | [
"skywork"
] | 60c4e61634bb3f9d32fa3406dff1fc15d761d1c7bbb68c076977670ee6a18452 | [
{
"content": "Let \\( a_{1}, a_{2}, \\cdots, a_{n} \\) be distinct positive integers such that \\( a_{1} + a_{2} + \\cdots + a_{n} = 2014 \\), where \\( n \\) is some integer greater than 1. Let \\( d \\) be the greatest common divisor of \\( a_{1}, a_{2}, \\cdots, a_{n} \\). For all values of \\( n \\) and \\(... | Let \( a_{1}, a_{2}, \cdots, a_{n} \) be distinct positive integers such that \( a_{1} + a_{2} + \cdots + a_{n} = 2014 \), where \( n \) is some integer greater than 1. Let \( d \) be the greatest common divisor of \( a_{1}, a_{2}, \cdots, a_{n} \). For all values of \( n \) and \( a_{1}, a_{2}, \cdots, a_{n} \) that s... | "[\"530\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3322, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17283"}] | {
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[
"2"
] | [
"skywork"
] | 58fb881ac18ab7940662ff8ca42d30ea031be37e5c98a83396bec16571250b4c | [
{
"content": "8. (1963 24th Putnam Mathematical Competition) Suppose $x^{2}-x+a$ divides $x^{13}+x+90$, determine the value of the positive integer $a$.\n\n untranslated text remains the same as the source text.",
"role": "user"
}
] | 8. (1963 24th Putnam Mathematical Competition) Suppose $x^{2}-x+a$ divides $x^{13}+x+90$, determine the value of the positive integer $a$.
untranslated text remains the same as the source text. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3356, "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:17284"}] | {
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"plain_numeric_reference": true,
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} |
[
"\\frac{6}{7}"
] | [
"skywork"
] | f207bc553b070d051d0fc48132b522a5fd33df7ee11025b725c14d5debf9302c | [
{
"content": "In triangle $ABC$ with $AB < AC$, let $H$ be the orthocenter and $O$ be the circumcenter. Given that the midpoint of $OH$ lies on $BC$, $BC = 1$, and the perimeter of $ABC$ is 6, find the area of $ABC$.",
"role": "user"
}
] | In triangle $ABC$ with $AB < AC$, let $H$ be the orthocenter and $O$ be the circumcenter. Given that the midpoint of $OH$ lies on $BC$, $BC = 1$, and the perimeter of $ABC$ is 6, find the area of $ABC$. | "[\"\\\\frac{6}{7}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3344, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:17285"}] | {
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} |
[
"x\\in(-1;2)\\cup(2;3)"
] | [
"skywork"
] | bd4ff85d10a719db5aacee6b59f769eaafc44ae8ca4bc14e2dc6e88438cd15f3 | [
{
"content": "9.027. $(x+1)(3-x)(x-2)^{2}>0$.",
"role": "user"
}
] | 9.027. $(x+1)(3-x)(x-2)^{2}>0$. | "[\"x\\\\in(-1;2)\\\\cup(2;3)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3370, "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:17286"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"806"
] | [
"skywork"
] | 664c25c42c3e1e3c41d150971028f75720b9a8f63fb360d7273fa169dc26a8e4 | [
{
"content": "# 7. Problem 7*\n\nPetya came up with four different natural numbers, wrote down all their pairwise sums on the board, and in the row below, all their sums of three. It turned out that the sum of the two largest numbers in the top row and the two smallest numbers in the bottom row (a total of four... | # 7. Problem 7*
Petya came up with four different natural numbers, wrote down all their pairwise sums on the board, and in the row below, all their sums of three. It turned out that the sum of the two largest numbers in the top row and the two smallest numbers in the bottom row (a total of four numbers) is 2017. Find ... | "[\"806\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3350, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:17287"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"80"
] | [
"skywork"
] | b5f2a0d7cfb7e7570e07afaa46a9213c76fc02248de0d2dc535b3b2e9236be26 | [
{
"content": "19. A group of pirates (raiders, sailors and cabin boys) divided 200 gold and 600 silver coins between them. Each raider received 5 gold and 10 silver coins. Each sailor received 3 gold and 8 silver coins. Each cabin boy received 1 gold and 6 silver coins. How many pirates were there altogether?\n... | 19. A group of pirates (raiders, sailors and cabin boys) divided 200 gold and 600 silver coins between them. Each raider received 5 gold and 10 silver coins. Each sailor received 3 gold and 8 silver coins. Each cabin boy received 1 gold and 6 silver coins. How many pirates were there altogether?
A 50
B 60
C 72
D 80
E 9... | "[\"80\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3363, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17288"}] | {
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} |
[
"690"
] | [
"skywork"
] | fdeb32d7e98e7096dfaf76d630f9e189206cd02c0ca3b7e7b93d6fe34b6a8d83 | [
{
"content": "The table shown is to be filled in with integers so that\n\n- the integers in each row form an arithmetic sequence that increases from left to right,\n- the integers in each column form a geometric sequence that is increasing from top to bottom, and\n- the three geometric sequences have the same c... | The table shown is to be filled in with integers so that
- the integers in each row form an arithmetic sequence that increases from left to right,
- the integers in each column form a geometric sequence that is increasing from top to bottom, and
- the three geometric sequences have the same common ratio, which is an i... | "[\"690\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3352, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17289"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | 0e1e942303cfa59be80f3e01a5612350f3ff05035c325f67f02c15ce6b3680bf | [
{
"content": "Problem 3. Jana asked Philip how much the fish his father caught weighed. Philip replied: The head together with the tail weighs $3 \\mathrm{~kg}$, the head together with the body weighs $7 \\mathrm{~kg}$, and the body together with the tail weighs $8 \\mathrm{~kg}$. How much does the fish weigh?"... | Problem 3. Jana asked Philip how much the fish his father caught weighed. Philip replied: The head together with the tail weighs $3 \mathrm{~kg}$, the head together with the body weighs $7 \mathrm{~kg}$, and the body together with the tail weighs $8 \mathrm{~kg}$. How much does the fish weigh? | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3358, "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:17290"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{14}{3}\\sqrt{7}"
] | [
"skywork"
] | bc07d25cb2770122181d72cd1e7dc647ffa72754655d3e2b3ad40165bccc146e | [
{
"content": "10. Given two moving points $A\\left(x_{1}, y_{1}\\right)$ and $B\\left(x_{2}, y_{2}\\right)$ on the parabola $y^{2}=6 x$, where $x_{1} \\neq x_{2}$ and $x_{1}+x_{2}=4$. The perpendicular bisector of line segment $A B$ intersects the $x$-axis at point $C$. Find the maximum value of the area of $\\... | 10. Given two moving points $A\left(x_{1}, y_{1}\right)$ and $B\left(x_{2}, y_{2}\right)$ on the parabola $y^{2}=6 x$, where $x_{1} \neq x_{2}$ and $x_{1}+x_{2}=4$. The perpendicular bisector of line segment $A B$ intersects the $x$-axis at point $C$. Find the maximum value of the area of $\triangle A B C$. | "[\"\\\\frac{14}{3}\\\\sqrt{7}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3351, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17291"}] | {
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"reference_components": 1,
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} |
[
"1"
] | [
"skywork"
] | 4faced9973c3a630a41e9959e1f30726268488f323f61a5f770ad1bb6a5dd30e | [
{
"content": "Example 10 Let $a, b, c \\in \\mathbf{R}_{+}$, and $abc=1$. Find\n$$\n\\frac{1}{2a+1}+\\frac{1}{2b+1}+\\frac{1}{2c+1}\n$$\n\nthe minimum value.",
"role": "user"
}
] | Example 10 Let $a, b, c \in \mathbf{R}_{+}$, and $abc=1$. Find
$$
\frac{1}{2a+1}+\frac{1}{2b+1}+\frac{1}{2c+1}
$$
the minimum value. | "[\"1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3368, "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:17292"}] | {
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} |
[
"\\frac{3}{32}"
] | [
"skywork"
] | 156ad7ac820b4e0bfeed47a0c705b4ddb6c0141ec817bbc63420db77325138d0 | [
{
"content": "For a finite graph $G$, let $f(G)$ be the number of triangles and $g(G)$ the number of tetrahedra formed by edges of $G$. Find the least constant $c$ such that \\[g(G)^3\\le c\\cdot f(G)^4\\] for every graph $G$.\n\n[i]",
"role": "user"
}
] | For a finite graph $G$, let $f(G)$ be the number of triangles and $g(G)$ the number of tetrahedra formed by edges of $G$. Find the least constant $c$ such that \[g(G)^3\le c\cdot f(G)^4\] for every graph $G$.
[i] | "[\"\\\\frac{3}{32}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3349, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:17293"}] | {
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[
"2025"
] | [
"skywork"
] | 6e0c0e9351968044a53786600f95506a3742757264174fb4aa2538226806c95d | [
{
"content": "Let $A$ be the sequence of zeroes and ones (binary sequence). The sequence can be modified by the following operation: we may pick a block or a contiguous subsequence where there are an unequal number of zeroes and ones, and then flip their order within the block (so block $a_1, a_2, \\ldots, a_r$... | Let $A$ be the sequence of zeroes and ones (binary sequence). The sequence can be modified by the following operation: we may pick a block or a contiguous subsequence where there are an unequal number of zeroes and ones, and then flip their order within the block (so block $a_1, a_2, \ldots, a_r$ becomes $a_r, a_{r-1},... | "[\"2025\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3339, "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:17294"}] | {
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} |
[
"\\frac{2\\sqrt{2}}{3}"
] | [
"skywork"
] | ff9386514017f8e5cb93298dbb226da32b5793af4285920a1eaefb5a3c952ad7 | [
{
"content": "In isosceles $\\triangle ABC$ with $AB=AC$, let $D$ be the midpoint of $AC$ and $BD=1$. Find the maximum area of $\\triangle ABC$.",
"role": "user"
}
] | In isosceles $\triangle ABC$ with $AB=AC$, let $D$ be the midpoint of $AC$ and $BD=1$. Find the maximum area of $\triangle ABC$. | "[\"\\\\frac{2\\\\sqrt{2}}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3375, "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:17295"}] | {
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} |
[
"4 \\sqrt{2}+2 \\sqrt{5}"
] | [
"skywork"
] | 3a3e43e3b4c8d3d4ff82e726a65c40faa264550e06530646def6c1edd5916aca | [
{
"content": "4. Given the quadratic function $y=a x^{2}(a \\geqslant 1)$, the x-coordinates of points $A$ and $B$ on its graph are $-1, 2$, respectively, and $O$ is the origin. If $\\triangle A O B$ is a right triangle, then the perimeter of $\\triangle O A B$ is $\\qquad$ .",
"role": "user"
}
] | 4. Given the quadratic function $y=a x^{2}(a \geqslant 1)$, the x-coordinates of points $A$ and $B$ on its graph are $-1, 2$, respectively, and $O$ is the origin. If $\triangle A O B$ is a right triangle, then the perimeter of $\triangle O A B$ is $\qquad$ . | "[\"4 \\\\sqrt{2}+2 \\\\sqrt{5}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3362, "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:17296"}] | {
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} |
[
"4"
] | [
"skywork"
] | 1fc0a84e570bcd5aab2e9f6002764e546eaa584913c1f23b415eedd55001949f | [
{
"content": "18. Amelia tosses a coin, with the probability of landing heads up being $\\frac{1}{3}$; Brian also tosses a coin, with the probability of landing heads up being $\\frac{2}{5}$. Amelia and Brian take turns tossing the coins, and the first one to get heads wins. All coin tosses are independent. Sta... | 18. Amelia tosses a coin, with the probability of landing heads up being $\frac{1}{3}$; Brian also tosses a coin, with the probability of landing heads up being $\frac{2}{5}$. Amelia and Brian take turns tossing the coins, and the first one to get heads wins. All coin tosses are independent. Starting with Amelia, the p... | "[\"4\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3366, "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:17297"}, {"dataset": "skywork", "extra_... | {
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[
"\\left\\lfloor \\frac{2n}{3} \\right\\rfloor"
] | [
"skywork"
] | 174901d8f628803351119bf8f02669159d851faa050650840f4449f853023d7c | [
{
"content": "Let an integer $ n > 3$. Denote the set $ T\\equal{}\\{1,2, \\ldots,n\\}.$ A subset S of T is called [i]wanting set[/i] if S has the property: There exists a positive integer $ c$ which is not greater than $ \\frac {n}{2}$ such that $ |s_1 \\minus{} s_2|\\ne c$ for every pairs of arbitrary element... | Let an integer $ n > 3$. Denote the set $ T\equal{}\{1,2, \ldots,n\}.$ A subset S of T is called [i]wanting set[/i] if S has the property: There exists a positive integer $ c$ which is not greater than $ \frac {n}{2}$ such that $ |s_1 \minus{} s_2|\ne c$ for every pairs of arbitrary elements $ s_1,s_2\in S$. How many d... | "[\" \\\\left\\\\lfloor \\\\frac{2n}{3} \\\\right\\\\rfloor \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3340, "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:17298"}] | {
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} |
[
"\\[ R = \\frac{2}{3}m \\]"
] | [
"skywork"
] | a0b35f4ee3845c79a3c8b8306e3b6eca1a4c7669f00f64f15a5f00899e654ec4 | [
{
"content": "Let $ABC$ be an isosceles triangle with $AC=BC$ , let $M$ be the midpoint of its side $AC$ , and let $Z$ be the line through $C$ perpendicular to $AB$ . The circle through the points $B$ , $C$ , and $M$ intersects the line $Z$ at the points $C$ and $Q$ . Find the radius of the circumcircle of the ... | Let $ABC$ be an isosceles triangle with $AC=BC$ , let $M$ be the midpoint of its side $AC$ , and let $Z$ be the line through $C$ perpendicular to $AB$ . The circle through the points $B$ , $C$ , and $M$ intersects the line $Z$ at the points $C$ and $Q$ . Find the radius of the circumcircle of the triangle $ABC$ in term... | "[\"\\\\[ R = \\\\frac{2}{3}m \\\\]\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3354, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17299"}] | {
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[
"B"
] | [
"skywork"
] | 2a838eb36c7399a604076b4ac2946cb70af95a5c8ab1b2f5dee21251d5735bb4 | [
{
"content": "7.84 For any function $y=f(x)$, in the same Cartesian coordinate system, the graphs of the functions $y=f(x-1)$ and $y=f(-x+1)$ are\n(A) symmetric with respect to the $x$-axis.\n(B) symmetric with respect to the line $x=1$.\n(C) symmetric with respect to the line $x=-1$.\n(D) symmetric with respec... | 7.84 For any function $y=f(x)$, in the same Cartesian coordinate system, the graphs of the functions $y=f(x-1)$ and $y=f(-x+1)$ are
(A) symmetric with respect to the $x$-axis.
(B) symmetric with respect to the line $x=1$.
(C) symmetric with respect to the line $x=-1$.
(D) symmetric with respect to the $y$-axis.
(China ... | "[\"B\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3379, "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:17301"}] | {
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[
"35"
] | [
"skywork"
] | 3af36830bf1c7b7ded1de1a8aad2db0dcc2872fdee276d6f70a196c78bf7aab7 | [
{
"content": "While doing her homework for a Momentum Learning class, Valencia draws two intersecting segments $AB = 10$ and $CD = 7$ on a plane. Across all possible configurations of those two segments, determine the maximum possible area of quadrilateral $ACBD$.",
"role": "user"
}
] | While doing her homework for a Momentum Learning class, Valencia draws two intersecting segments $AB = 10$ and $CD = 7$ on a plane. Across all possible configurations of those two segments, determine the maximum possible area of quadrilateral $ACBD$. | "[\"35\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3373, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17302"}, {"dataset": "skywork", "extra_inf... | {
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[
"\\textbf{(C)}5"
] | [
"skywork"
] | 29ae6fa401ba3a0b80d000cf7d471876cb4796dc0d8c86082820242d31262697 | [
{
"content": "Claudia has 12 coins, each of which is a 5-cent coin or a 10-cent coin. There are exactly 17 different values that can be obtained as combinations of one or more of her coins. How many 10-cent coins does Claudia have?\n$\\textbf{(A) }3\\qquad\\textbf{(B) }4\\qquad\\textbf{(C) }5\\qquad\\textbf{(D)... | Claudia has 12 coins, each of which is a 5-cent coin or a 10-cent coin. There are exactly 17 different values that can be obtained as combinations of one or more of her coins. How many 10-cent coins does Claudia have?
$\textbf{(A) }3\qquad\textbf{(B) }4\qquad\textbf{(C) }5\qquad\textbf{(D) }6\qquad\textbf{(E) }7$ | "[\"\\\\textbf{(C)}5\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 3369, "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:17303"}] | {
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[
"2"
] | [
"skywork"
] | f542b5cd8d68271dd5ad7601f4701441629028ded738add3f06082ef250bc6bb | [
{
"content": "Let $H$ be a regular hexagon of side length $x$. Call a hexagon in the same plane a \"distortion\" of $H$ if\nand only if it can be obtained from $H$ by translating each vertex of $H$ by a distance strictly less than $1$. Determine the smallest value of $x$ for which every distortion of $H$ is nec... | Let $H$ be a regular hexagon of side length $x$. Call a hexagon in the same plane a "distortion" of $H$ if
and only if it can be obtained from $H$ by translating each vertex of $H$ by a distance strictly less than $1$. Determine the smallest value of $x$ for which every distortion of $H$ is necessarily convex. | "[\"2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3372, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17304"}] | {
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} |
[
"889"
] | [
"skywork"
] | 200760254ab13c7df2d1e569d77180ebd5e50f8e84769d53408ba556937cfac7 | [
{
"content": "Let $m$ be a positive integer, and let $a_0, a_1,\\ldots,a_m$ be a sequence of reals such that $a_0=37$ , $a_1=72$ , $a_m=0$ , and \\[a_{k+1}=a_{k-1}-\\frac{3}{a_k}\\] for $k=1,2, \\dots, m-1$ . Find $m$ .",
"role": "user"
}
] | Let $m$ be a positive integer, and let $a_0, a_1,\ldots,a_m$ be a sequence of reals such that $a_0=37$ , $a_1=72$ , $a_m=0$ , and \[a_{k+1}=a_{k-1}-\frac{3}{a_k}\] for $k=1,2, \dots, m-1$ . Find $m$ . | "[\"889\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 3381, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17305"}, {"dataset": "skywork", "extra_inf... | {
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} |
[
"\\frac{1}{4}"
] | [
"skywork"
] | 484d9ff55cf981e66976f0bf7839c12dd608313f2f7d90dc937ff00c5b10f326 | [
{
"content": "Evaluate \\[\\frac{3}{\\log_8{5000^4}} + \\frac{2}{\\log_9{5000^4}},\\] giving your answer as a fraction in lowest terms.",
"role": "user"
}
] | Evaluate \[\frac{3}{\log_8{5000^4}} + \frac{2}{\log_9{5000^4}},\] giving your answer as a fraction in lowest terms. | "[\"\\\\frac{1}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3398, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17306"}] | {
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} |
[
"576"
] | [
"skywork"
] | 561e3672c6df3b409d42ca298fd28e914bcb60610dcdf83842e733abcd4dffaa | [
{
"content": "In an $8 \\times 8$ chessboard, how many ways are there to select 56 squares so that all the black squares are selected, and each row and each column has exactly seven squares selected?",
"role": "user"
}
] | In an $8 \times 8$ chessboard, how many ways are there to select 56 squares so that all the black squares are selected, and each row and each column has exactly seven squares selected? | "[\"576\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3374, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:17308"}] | {
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} |
[
"13"
] | [
"skywork"
] | 3a0396b15755af5ba7e7932fffa65cfd35034cc8130880f0e33a0af7bce2d356 | [
{
"content": "7. Builders need to tile the floor in a small house with small square tiles. The client says that the variant with more red tiles is preferable. For variants with the same number of red tiles, the one with more orange tiles is preferable; and generally, the client's preferences for colors are: red... | 7. Builders need to tile the floor in a small house with small square tiles. The client says that the variant with more red tiles is preferable. For variants with the same number of red tiles, the one with more orange tiles is preferable; and generally, the client's preferences for colors are: red, orange, yellow, gree... | "[\"13\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3384, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17309"}] | {
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} |
[
"531440"
] | [
"skywork"
] | 275913948bb5ccf9af6b5f345b5892e20f144f2bbbecc19dbdd40cae0c7ea391 | [
{
"content": "A regular dodecagon \\( Q_1 Q_2 \\dotsb Q_{12} \\) is drawn in the coordinate plane with \\( Q_1 \\) at \\( (4,0) \\) and \\( Q_7 \\) at \\( (2,0) \\). If \\( Q_n \\) is the point \\( (x_n,y_n) \\), compute the numerical value of the product\n\\[\n(x_1 + y_1 i)(x_2 + y_2 i)(x_3 + y_3 i) \\dotsm (x... | A regular dodecagon \( Q_1 Q_2 \dotsb Q_{12} \) is drawn in the coordinate plane with \( Q_1 \) at \( (4,0) \) and \( Q_7 \) at \( (2,0) \). If \( Q_n \) is the point \( (x_n,y_n) \), compute the numerical value of the product
\[
(x_1 + y_1 i)(x_2 + y_2 i)(x_3 + y_3 i) \dotsm (x_{12} + y_{12} i).
\] | "[\"531440\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3377, "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:17310"}] | {
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} |
[
"101"
] | [
"skywork"
] | 0688fb65044272d36bcc103a32640137742fd63a8fd4c58dfd4b1b424b76f140 | [
{
"content": "Let tetrahedron $ABCD$ have $AD=BC=30$, $AC=BD=40$, and $AB=CD=50$. For any point $X$ in space, suppose $g(X)=AX+BX+CX+DX$. Determine the least possible value of $g(X)$, expressed as $p\\sqrt{q}$ where $p$ and $q$ are positive integers with $q$ not divisible by the square of any prime. Report the ... | Let tetrahedron $ABCD$ have $AD=BC=30$, $AC=BD=40$, and $AB=CD=50$. For any point $X$ in space, suppose $g(X)=AX+BX+CX+DX$. Determine the least possible value of $g(X)$, expressed as $p\sqrt{q}$ where $p$ and $q$ are positive integers with $q$ not divisible by the square of any prime. Report the sum $p+q$. | "[\"101\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3382, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17311"}] | {
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} |
[
"9"
] | [
"skywork"
] | d7249bd2c71dde25f03d731d98d2e62e718f87546a2fd7fdec71f30473abdd8c | [
{
"content": "16. (UKR) Determine the smallest integer $n \\geq 4$ for which one can choose four different numbers $a, b, c$, and $d$ from any $n$ distinct integers such that $a+b-c-d$ is divisible by 20 .",
"role": "user"
}
] | 16. (UKR) Determine the smallest integer $n \geq 4$ for which one can choose four different numbers $a, b, c$, and $d$ from any $n$ distinct integers such that $a+b-c-d$ is divisible by 20 . | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3385, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17312"}] | {
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[
"x_1=2,x_2=-2"
] | [
"skywork"
] | 8067203b112f6c0543c0b18b1aafa581e63df2a2658bf6dfc0ae03b58c334ad9 | [
{
"content": "1. Solve the equation\n\n$$\n(\\sqrt{3-\\sqrt{8}})^{x}+(\\sqrt{3+\\sqrt{8}})^{x}=6\n$$",
"role": "user"
}
] | 1. Solve the equation
$$
(\sqrt{3-\sqrt{8}})^{x}+(\sqrt{3+\sqrt{8}})^{x}=6
$$ | "[\"x_1=2,x_2=-2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3396, "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:17313"}] | {
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[
"121"
] | [
"skywork"
] | 5734bbc4fb624146b68b2db024cb1830f6cbbf5209975a66ed3fcb7ef97a2da0 | [
{
"content": "8. As shown in the right figure, a square piece of paper $A B C D$ is cut into two triangles along the diagonal $B D$. In the first operation, triangle $A B D$ is translated vertically downward by 3 cm to triangle $E F G$; in the second operation, triangle $E F G$ is translated vertically downward... | 8. As shown in the right figure, a square piece of paper $A B C D$ is cut into two triangles along the diagonal $B D$. In the first operation, triangle $A B D$ is translated vertically downward by 3 cm to triangle $E F G$; in the second operation, triangle $E F G$ is translated vertically downward by another 5 cm to tr... | "[\"121\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3380, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17314"}] | {
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[
"-2\\sqrt{2}"
] | [
"skywork"
] | 23441dc34433a2bc272afa57b0add2556fc525aacd6f16d803b670a6599451d0 | [
{
"content": "If $\\sin\\theta + \\cos\\theta = \\frac{2\\sqrt{2}-1}{3}$ ($0 < \\theta < \\pi$), then $\\tan\\theta = \\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | If $\sin\theta + \cos\theta = \frac{2\sqrt{2}-1}{3}$ ($0 < \theta < \pi$), then $\tan\theta = \_\_\_\_\_\_$. | "[\"-2\\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3395, "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:17315"}] | {
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[
"10"
] | [
"skywork"
] | 2e506fe6f5a3bf5842244366c0c0467e80326741e62a1ab7ad6c19fa9a205e1b | [
{
"content": "In an isosceles trapezoid, the height is 10, and the diagonals are mutually perpendicular. Find the midsegment (the line connecting the midpoints of the non-parallel sides) of the trapezoid.",
"role": "user"
}
] | In an isosceles trapezoid, the height is 10, and the diagonals are mutually perpendicular. Find the midsegment (the line connecting the midpoints of the non-parallel sides) of the trapezoid. | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3386, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17316"}] | {
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[
"2"
] | [
"skywork"
] | a022f3bf5240e1f75fefde400dbc99919d0d2e53c62ff4fc1fa84c09fdd5fc62 | [
{
"content": "7. In $\\triangle A B C$, it is known that\n$$\n\\begin{array}{l}\n|\\overrightarrow{A B}|=\\sqrt{3},|\\overrightarrow{B C}|=1, \\\\\n|\\overrightarrow{A C}| \\cos B=|\\overrightarrow{B C}| \\cos A \\text {. } \\\\\n\\text { Then } \\overrightarrow{A C} \\cdot \\overrightarrow{A B}=\n\\end{array}\... | 7. In $\triangle A B C$, it is known that
$$
\begin{array}{l}
|\overrightarrow{A B}|=\sqrt{3},|\overrightarrow{B C}|=1, \\
|\overrightarrow{A C}| \cos B=|\overrightarrow{B C}| \cos A \text {. } \\
\text { Then } \overrightarrow{A C} \cdot \overrightarrow{A B}=
\end{array}
$$ | "[\"2\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3393, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:17317"}] | {
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[
"21"
] | [
"skywork"
] | e27608f24bb1df13906c4b5869358d37d194240b9ce23067da4a4d30eee58744 | [
{
"content": "Given set \\( A = \\{0, 1, 2, 3, 4, 5, 9\\} \\), and \\( a, b \\in A \\) where \\( a \\neq b \\). The number of functions of the form \\( y = -a x^2 + (4 - b)x \\) whose vertex lies in the first quadrant is ___.",
"role": "user"
}
] | Given set \( A = \{0, 1, 2, 3, 4, 5, 9\} \), and \( a, b \in A \) where \( a \neq b \). The number of functions of the form \( y = -a x^2 + (4 - b)x \) whose vertex lies in the first quadrant is ___. | "[\"21\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3383, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17318"}] | {
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[
"\\frac{8\\sqrt{5}}{5}"
] | [
"skywork"
] | 32fa197a4d6a4f1bd3d8a3e79148bf71816c6fd65ebfe1b0a61f7222cd05a280 | [
{
"content": "5. Given that the complex number $z$ satisfies $|z|=1$. Then the minimum value of $\\left|z^{2}-2 z+5\\right|$ is $\\qquad$\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.",
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}
] | 5. Given that the complex number $z$ satisfies $|z|=1$. Then the minimum value of $\left|z^{2}-2 z+5\right|$ is $\qquad$
Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly. | "[\"\\\\frac{8\\\\sqrt{5}}{5}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3394, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17319"}] | {
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[
"96"
] | [
"skywork"
] | 8bb29cc74a132e375f8d36502a3c6703ba6a6e26f8892f20c43125cb8cae81c1 | [
{
"content": "11.6. In a round-robin chess tournament (each chess player plays one game against each other), 20 chess players participated, 6 of whom were from Russia. It is known that Vladimir, who scored more points than anyone else, took first place. Levon from Armenia took second place, also outscoring each... | 11.6. In a round-robin chess tournament (each chess player plays one game against each other), 20 chess players participated, 6 of whom were from Russia. It is known that Vladimir, who scored more points than anyone else, took first place. Levon from Armenia took second place, also outscoring each of the other 18 chess... | "[\"96\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3378, "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:17320"}] | {
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[
"5"
] | [
"skywork"
] | 05fb8e0fa6c35371474e3c6d379cc290bb3e14af609277b08b2a304275c2ea1a | [
{
"content": "Which digit will appear in the 534th place after the decimal point in the decimal representation of $\\frac{5}{13}$?",
"role": "user"
}
] | Which digit will appear in the 534th place after the decimal point in the decimal representation of $\frac{5}{13}$? | "[\"5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3426, "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:17321"}] | {
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"reference_present": true
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[
"7.5"
] | [
"skywork"
] | c526651427421ccc0d440ef1031f7b0daddfc4bb0cb3e7d26d78dbdc0e942500 | [
{
"content": "In right triangle $DEF$, where $DE = 15$, $DF = 9$, and $EF = 12$ units, find the distance from $F$ to the midpoint of segment $DE$.",
"role": "user"
}
] | In right triangle $DEF$, where $DE = 15$, $DF = 9$, and $EF = 12$ units, find the distance from $F$ to the midpoint of segment $DE$. | "[\"7.5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3420, "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:17322"}] | {
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[
"2005"
] | [
"skywork"
] | 54ce9d1d506221a4f6d2e51be2c001f9864f6512030c6d803312967fa381b6a1 | [
{
"content": "1. A natural number has a digit sum of 2013. The next number has a smaller digit sum and is not divisible by 4. What is the digit sum of the next natural number.",
"role": "user"
}
] | 1. A natural number has a digit sum of 2013. The next number has a smaller digit sum and is not divisible by 4. What is the digit sum of the next natural number. | "[\"2005\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3387, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17323"}] | {
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} |
[
"k = n"
] | [
"skywork"
] | c577e7e93c066e8987a74d42ea0831038f7a6421c3fb4da88877f15a8bccce15 | [
{
"content": "Let $n$ be a fixed positive integer. There are $n \\geq 1$ lamps in a row, some of them are on and some are off. In a single move, we choose a positive integer $i$ ($1 \\leq i \\leq n$) and switch the state of the first $i$ lamps from the left. Determine the smallest number $k$ with the property t... | Let $n$ be a fixed positive integer. There are $n \geq 1$ lamps in a row, some of them are on and some are off. In a single move, we choose a positive integer $i$ ($1 \leq i \leq n$) and switch the state of the first $i$ lamps from the left. Determine the smallest number $k$ with the property that we can make all of th... | "[\" k = n \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3389, "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:17324"}] | {
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[
"256"
] | [
"skywork"
] | 48d6f000f7f3afc02cc6ca8d1e554c6eb777be36713dcc543640be8b2ab51032 | [
{
"content": "5. An aside: the sum of all the unit fractions\nIt is possible to show that, given any real $\\mathrm{M}$, there exists a positive integer $k$ large enough that:\n$$\n\\sum_{n=1}^{k} \\frac{1}{n}=\\frac{1}{1}+\\frac{1}{2}+\\frac{1}{3} \\ldots>M\n$$\n\nNote that this statement means that the infini... | 5. An aside: the sum of all the unit fractions
It is possible to show that, given any real $\mathrm{M}$, there exists a positive integer $k$ large enough that:
$$
\sum_{n=1}^{k} \frac{1}{n}=\frac{1}{1}+\frac{1}{2}+\frac{1}{3} \ldots>M
$$
Note that this statement means that the infinite harmonic series, $\sum_{n=1}^{\i... | "[\"256\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3388, "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:17325"}] | {
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[
"49"
] | [
"skywork"
] | 93532d52383de80b96d7a52cd71ca9ac24c67b6611fd7d2f0275d8f26b6ce1c5 | [
{
"content": "Berroov S.L.\n\nOne hundred integers are written in a circle. Each number is greater than the sum of the two numbers following it in a clockwise direction.\n\nWhat is the maximum number of positive numbers that can be among those written?\n\n#",
"role": "user"
}
] | Berroov S.L.
One hundred integers are written in a circle. Each number is greater than the sum of the two numbers following it in a clockwise direction.
What is the maximum number of positive numbers that can be among those written?
# | "[\"49\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3399, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17326"}] | {
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[
"83.5"
] | [
"skywork"
] | 4ff356ee247cc9657a46c452dd682073060d00f7cde79d2886b7d99260d7b619 | [
{
"content": "The mean of the set of numbers $\\{87,85,80,83,84,x\\}$ is 83.5. What is the median of the set of six numbers? Express your answer as a decimal to the nearest tenth.",
"role": "user"
}
] | The mean of the set of numbers $\{87,85,80,83,84,x\}$ is 83.5. What is the median of the set of six numbers? Express your answer as a decimal to the nearest tenth. | "[\"83.5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3416, "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:17327"}] | {
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[
"The composite positive integers \\( n \\) for which it is possible to arrange all divisors of \\( n \\) that are greater than 1 in a circle so that no two adjacent divisors are relatively prime are those \\( n \\) that are not of the form \\( pq \\) where \\( p \\) and \\( q \\) are distinct primes."
] | [
"skywork"
] | 4c6cc9464a86c840d96b977b3a031dd59e0ce1cb8af267f4bdac6f6a5512fdcd | [
{
"content": "( Zuming Feng ) Determine all composite positive integers $n$ for which it is possible to arrange all divisors of $n$ that are greater than 1 in a circle so that no two adjacent divisors are relatively prime.",
"role": "user"
}
] | ( Zuming Feng ) Determine all composite positive integers $n$ for which it is possible to arrange all divisors of $n$ that are greater than 1 in a circle so that no two adjacent divisors are relatively prime. | "[\"The composite positive integers \\\\( n \\\\) for which it is possible to arrange all divisors of \\\\( n \\\\) that are greater than 1 in a circle so that no two adjacent divisors are relatively prime are those \\\\( n \\\\) that are not of the form \\\\( pq \\\\) where \\\\( p \\\\) and \\\\( q \\\\) are distinct... | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 3391, "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:17328"}] | {
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[
"4"
] | [
"skywork"
] | 8b1028eacf9c9abfd6d08f08ed425ca2eb501509128b99464e360285ee685e40 | [
{
"content": "7.5. If $a, b, c, d, e, f, g, h, k$ are all 1 or -1, try to find the maximum possible value of\n$$\na e k - a f h + b f g - b d k + c d h - c e g\n$$",
"role": "user"
}
] | 7.5. If $a, b, c, d, e, f, g, h, k$ are all 1 or -1, try to find the maximum possible value of
$$
a e k - a f h + b f g - b d k + c d h - c e g
$$ | "[\"4\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3408, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17329"}] | {
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[
"f(x) = k(a^x - a^{-x})"
] | [
"skywork"
] | 99156522f506e6a1e277d7d2217d063dff07654436422253f02b610f047b6269 | [
{
"content": "Find all functions $f:\\mathbb{Q}\\rightarrow\\mathbb{R}$ such that\n \\[\n f(x)^2-f(y)^2=f(x+y)\\cdot f(x-y),\n \\]\n for all $x,y\\in \\mathbb{Q}$.\n\n[i]Proposed by Portugal.[/i]",
"role": "user"
}
] | Find all functions $f:\mathbb{Q}\rightarrow\mathbb{R}$ such that
\[
f(x)^2-f(y)^2=f(x+y)\cdot f(x-y),
\]
for all $x,y\in \mathbb{Q}$.
[i]Proposed by Portugal.[/i] | "[\" f(x) = k(a^x - a^{-x}) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3402, "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:17330"}] | {
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} |
[
"3,4,6"
] | [
"skywork"
] | 7b4ddb43f74167672744a655118c78e0f654c7d401bc775765004e701c6e4b1b | [
{
"content": "Vasilev N.B.\n\nFor which $n$ can a regular $n$-gon be placed on a sheet of lined paper so that all its vertices lie on the lines?\n\n(The lines are parallel and are spaced at equal distances from each other.)",
"role": "user"
}
] | Vasilev N.B.
For which $n$ can a regular $n$-gon be placed on a sheet of lined paper so that all its vertices lie on the lines?
(The lines are parallel and are spaced at equal distances from each other.) | "[\"3,4,6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3397, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17331"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"2\\sqrt{3}-1"
] | [
"skywork"
] | 7a994880d5107d6e16208351231ed7668ddfae5e003bb4e4bc8f671df785cb17 | [
{
"content": "9. If the domain of functions $f(x)$ and $g(x)$ is the set of non-negative real numbers, for any $x \\geqslant 0$, it is defined that $f(x) \\cdot g(x)=$ $\\min \\{f(x), g(x)\\}$. If $f(x)=3-x, g(x)=\\sqrt{2 x+5}$, then the maximum value of $f(x) \\cdot g(x)$ is $\\qquad$ .",
"role": "user"
... | 9. If the domain of functions $f(x)$ and $g(x)$ is the set of non-negative real numbers, for any $x \geqslant 0$, it is defined that $f(x) \cdot g(x)=$ $\min \{f(x), g(x)\}$. If $f(x)=3-x, g(x)=\sqrt{2 x+5}$, then the maximum value of $f(x) \cdot g(x)$ is $\qquad$ . | "[\"2\\\\sqrt{3}-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3390, "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:17332"}] | {
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"reference_components": 1,
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} |
[
"1"
] | [
"skywork"
] | 43f2d8333ddc81998af4947c69271f9da208132006e70968a6451390ef6cb12a | [
{
"content": "Find the remainder when the polynomial $x^{1000}$ is divided by the polynomial $(x^2 + 1)(x + 1).$",
"role": "user"
}
] | Find the remainder when the polynomial $x^{1000}$ is divided by the polynomial $(x^2 + 1)(x + 1).$ | "[\"1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3425, "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:17333"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{8}{25}"
] | [
"skywork"
] | 4ed5cf777610d11d69390c9a5110d820f945bc7934baa944ac2926bd129afde7 | [
{
"content": "Given that 600 athletes are numbered from 001 to 600 and divided into three color groups (red: 001 to 311, white: 312 to 496, and yellow: 497 to 600), calculate the probability of randomly drawing an athlete wearing white clothing.",
"role": "user"
}
] | Given that 600 athletes are numbered from 001 to 600 and divided into three color groups (red: 001 to 311, white: 312 to 496, and yellow: 497 to 600), calculate the probability of randomly drawing an athlete wearing white clothing. | "[\"\\\\frac{8}{25}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3412, "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:17334"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"7+1=8;9-6=3;4\\times5=20"
] | [
"skywork"
] | e873cbfb5c1a83110ad3738aaa39c7338c766615c49f999f9e46e2c784ffa16e | [
{
"content": "131. Juggling with numbers. Compose three simple arithmetic expressions from ten digits, using three of the four arithmetic operations - addition, subtraction, multiplication, and division. (In writing the expressions, only the symbols of the three chosen arithmetic operations are allowed.) Let us... | 131. Juggling with numbers. Compose three simple arithmetic expressions from ten digits, using three of the four arithmetic operations - addition, subtraction, multiplication, and division. (In writing the expressions, only the symbols of the three chosen arithmetic operations are allowed.) Let us clarify this with an ... | "[\"7+1=8;9-6=3;4\\\\times5=20\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3376, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17335"}] | {
"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
} |
[
"2n-2, n-2, -2"
] | [
"skywork"
] | a4788748a7fc2c15c555430d7623e36f8b3eb29c2f642c14e7c6a4cdcbbb698c | [
{
"content": "Non-zero numbers are arranged in $n \\times n$ square ($n>2$). Every number is exactly $k$ times less than the sum of all the other numbers in the same cross (i.e., $2n-2$ numbers written in the same row or column with this number). \nFind all possible $k$.\n\n[i]Proposed by D. Rostovsky, A. Khrab... | Non-zero numbers are arranged in $n \times n$ square ($n>2$). Every number is exactly $k$ times less than the sum of all the other numbers in the same cross (i.e., $2n-2$ numbers written in the same row or column with this number).
Find all possible $k$.
[i]Proposed by D. Rostovsky, A. Khrabrov, S. Berlov [/i] | "[\"2n-2, n-2, -2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3392, "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:17336"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"150"
] | [
"skywork"
] | ac561ab50c6c9ae2a210466edc6a9306f8e949803601dd09ea017769a1dcd7e2 | [
{
"content": "13.041. A 30% hydrochloric acid solution was mixed with a 10% solution to obtain 600 g of a 15% solution. How many grams of each solution were taken?",
"role": "user"
}
] | 13.041. A 30% hydrochloric acid solution was mixed with a 10% solution to obtain 600 g of a 15% solution. How many grams of each solution were taken? | "[\"150\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3419, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17337"}] | {
"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
} |
[
"f(n)=\\frac{1}{2} n(n+1)"
] | [
"skywork"
] | d6f8c47b3a004f52bb4be6889bd70f6f80bb5e529d2cc3fc42597b114c7dd8ab | [
{
"content": "Example 5. Try to find the function $f(x)$ defined on the set of natural numbers, such that $f(x+y)=f(x)+f(y)+xy, f(1)=1$.\n\n untranslated portion: \n\n将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。\n\nTranslation:\n\nExample 5. Try to find the function $f(x)$ defined on the set of natural numbers, such that... | Example 5. Try to find the function $f(x)$ defined on the set of natural numbers, such that $f(x+y)=f(x)+f(y)+xy, f(1)=1$.
untranslated portion:
将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。
Translation:
Example 5. Try to find the function $f(x)$ defined on the set of natural numbers, such that $f(x+y)=f(x)+f(y)+xy, f(1)=1$... | "[\"f(n)=\\\\frac{1}{2} n(n+1)\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3415, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17338"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{25}"
] | [
"skywork"
] | 81d3e51ab921630474f3306dd521b8315153d2d6161d033c20e6039814c73792 | [
{
"content": "A square $ABCD$ with side length $1$ is inscribed in a circle. A smaller square lies in the circle with two vertices lying on segment $AB$ and the other two vertices lying on minor arc $AB$. Compute the area of the smaller square.",
"role": "user"
}
] | A square $ABCD$ with side length $1$ is inscribed in a circle. A smaller square lies in the circle with two vertices lying on segment $AB$ and the other two vertices lying on minor arc $AB$. Compute the area of the smaller square. | "[\"\\\\frac{1}{25}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3401, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17339"}] | {
"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{16x\\sqrt{x}}{(1-x^{2})(x-1)}"
] | [
"skywork"
] | d04f61d2fd3322894604c99b435377db0dd8e32fca75c66325b37c570f1b6d2a | [
{
"content": "2.011. $\\left(\\frac{1+\\sqrt{x}}{\\sqrt{1+x}}-\\frac{\\sqrt{1+x}}{1+\\sqrt{x}}\\right)^{2}-\\left(\\frac{1-\\sqrt{x}}{\\sqrt{1+x}}-\\frac{\\sqrt{1+x}}{1-\\sqrt{x}}\\right)^{2}$.",
"role": "user"
}
] | 2.011. $\left(\frac{1+\sqrt{x}}{\sqrt{1+x}}-\frac{\sqrt{1+x}}{1+\sqrt{x}}\right)^{2}-\left(\frac{1-\sqrt{x}}{\sqrt{1+x}}-\frac{\sqrt{1+x}}{1-\sqrt{x}}\right)^{2}$. | "[\"\\\\frac{16x\\\\sqrt{x}}{(1-x^{2})(x-1)}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3409, "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:17340"}] | {
"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
} |
[
"20"
] | [
"skywork"
] | 4651b44283f2248dbfadc382c505f027ceb7b755e94e1ccb02b8e7bf9b882926 | [
{
"content": "A chess team has $26$ members. However, only $16$ members attended the last meeting: half of the girls attended but all of the boys attended. How many girls are on the chess team?",
"role": "user"
}
] | A chess team has $26$ members. However, only $16$ members attended the last meeting: half of the girls attended but all of the boys attended. How many girls are on the chess team? | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3411, "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:17341"}] | {
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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{3}{2}"
] | [
"skywork"
] | 12adbb6ac1268fbee15abffc6ca84b1a3e2426579a9539b064b17a2c45a460b5 | [
{
"content": "Suppose $S = \\{1, 2, 3, x\\}$ is a set with four distinct real numbers for which the difference between the largest and smallest values of $S$ is equal to the sum of elements of $S.$ What is the value of $x?$\n$$\n\\mathrm a. ~ {-1}\\qquad \\mathrm b.~{-3/2}\\qquad \\mathrm c. ~{-2} \\qquad \\mat... | Suppose $S = \{1, 2, 3, x\}$ is a set with four distinct real numbers for which the difference between the largest and smallest values of $S$ is equal to the sum of elements of $S.$ What is the value of $x?$
$$
\mathrm a. ~ {-1}\qquad \mathrm b.~{-3/2}\qquad \mathrm c. ~{-2} \qquad \mathrm d. ~{-2/3} \qquad \mathrm e. ... | "[\"-\\\\frac{3}{2}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3421, "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:17342"}] | {
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"any_reference_component_parses": true,
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"reference_components": 1,
"reference_present": true
} |
[
"72"
] | [
"skywork"
] | 2d3decfa0e3969ee5cc6a44f76b09219ea28db5b41db10620e148c3dc73925df | [
{
"content": "Ben and Anna each have some CDs. If Anna gives six of her CDs to Ben, he would then have twice as many CDs as Anna. If, instead, Anna takes six CDs from Ben, then both would have the same number of the CDs. What is the total number of CDs that Ben and Anna have?\n(A) 42\n(B) 30\n(C) 72\n(D) 18\n(E... | Ben and Anna each have some CDs. If Anna gives six of her CDs to Ben, he would then have twice as many CDs as Anna. If, instead, Anna takes six CDs from Ben, then both would have the same number of the CDs. What is the total number of CDs that Ben and Anna have?
(A) 42
(B) 30
(C) 72
(D) 18
(E) 36 | "[\"72\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3413, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17343"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"60^\\circ"
] | [
"skywork"
] | 9744a94e7769a635b642e09795bf65c5a9628ff2eab6142e363a4d60bc3ec527 | [
{
"content": "In a triangle with sides of lengths $a,$ $b,$ and $c,$\n\\[(a + b + c)(a + b - c) = 3ab.\\]Find the angle opposite the side of length $c,$ in degrees.",
"role": "user"
}
] | In a triangle with sides of lengths $a,$ $b,$ and $c,$
\[(a + b + c)(a + b - c) = 3ab.\]Find the angle opposite the side of length $c,$ in degrees. | "[\"60^\\\\circ\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3410, "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:17345"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | eda8e7649ea7dae6e30b55dca0f4014049f18001926e1789449ee233e5b0db07 | [
{
"content": "2. A cat can catch 5 mice in 6 days. How many days will it take for 2 cats to catch 3 mice?",
"role": "user"
}
] | 2. A cat can catch 5 mice in 6 days. How many days will it take for 2 cats to catch 3 mice? | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3414, "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:17346"}] | {
"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
} |
[
"37500"
] | [
"skywork"
] | f7decb8646dc1f9df3669cb88d3c2ce8e1e8ce3d00d16782b24fe45e724d3e9f | [
{
"content": "Last year Mr. Jon Q. Public received an inheritance. He paid $20\\%$ in federal taxes on the inheritance, and paid $10\\%$ of what he had left in state taxes. He paid a total of $\\textdollar10500$ for both taxes. How many dollars was his inheritance?",
"role": "user"
}
] | Last year Mr. Jon Q. Public received an inheritance. He paid $20\%$ in federal taxes on the inheritance, and paid $10\%$ of what he had left in state taxes. He paid a total of $\textdollar10500$ for both taxes. How many dollars was his inheritance? | "[\"37500\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3424, "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:17347"}] | {
"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
} |
[
"25\\pi"
] | [
"skywork"
] | 87eb7d3be0c3ed28c7b68beda5bdcab5d4b348ef02f5836c16d0ccc7b0024eb7 | [
{
"content": "In the tetrahedron \\( P-ABC \\), \\( \\triangle ABC \\) is an equilateral triangle with a side length of \\( 2\\sqrt{3} \\), \\( PB = PC = \\sqrt{5} \\), and the dihedral angle between \\( P-BC \\) and \\( BC-A \\) is \\( 45^\\circ \\). Find the surface area of the circumscribed sphere around the... | In the tetrahedron \( P-ABC \), \( \triangle ABC \) is an equilateral triangle with a side length of \( 2\sqrt{3} \), \( PB = PC = \sqrt{5} \), and the dihedral angle between \( P-BC \) and \( BC-A \) is \( 45^\circ \). Find the surface area of the circumscribed sphere around the tetrahedron \( P-ABC \). | "[\"25\\\\pi\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3400, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17348"}] | {
"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
} |
[
"123"
] | [
"skywork"
] | f53d3483b54c10f7efcb6de3c47c2363fcbac26779e1f6776b44795221aa9319 | [
{
"content": "1. The price of one pencil is a whole number of eurocents. The total price of 9 pencils is greater than 11, but less than 12 euros, while the total price of 13 pencils is greater than 15, but less than 16 euros. How much does one pencil cost?",
"role": "user"
}
] | 1. The price of one pencil is a whole number of eurocents. The total price of 9 pencils is greater than 11, but less than 12 euros, while the total price of 13 pencils is greater than 15, but less than 16 euros. How much does one pencil cost? | "[\"123\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3427, "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:17349"}] | {
"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 { \\sqrt {15}}{4}"
] | [
"skywork"
] | 43e336ad20ba6964f6d2b9b066d570ffafae221b542a13ef0934c0a144bac32e | [
{
"content": "Given: In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are respectively $a$, $b$, and $c$, and it is known that $\\frac {\\cos A-2\\cos C}{\\cos B}= \\frac {2c-a}{b}$. \n$(1)$ Find the value of $\\frac {\\sin C}{\\sin A}$; \n$(2)$ If $\\cos B= \\frac {1}{4}$ and $b=2$, find t... | Given: In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are respectively $a$, $b$, and $c$, and it is known that $\frac {\cos A-2\cos C}{\cos B}= \frac {2c-a}{b}$.
$(1)$ Find the value of $\frac {\sin C}{\sin A}$;
$(2)$ If $\cos B= \frac {1}{4}$ and $b=2$, find the area $S$ of $\triangle ABC$. | "[\"\\\\frac { \\\\sqrt {15}}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3407, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17350"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"572"
] | [
"skywork"
] | 7bbdf264f7fff65ed4f5cbabe32dca9b359b4313b0a45aad1ed92c095cb126ff | [
{
"content": "\\section*{Problem 4 - 251034}\n\nA natural number \\(x\\) is required to satisfy the following conditions (1) to (5):\n\n(1) The number \\(x\\), when written in the binary system (base 2), has exactly ten digits.\n\n(2) When \\(x\\) is written in the ternary system, the second digit is 1.\n\n(3) ... | \section*{Problem 4 - 251034}
A natural number \(x\) is required to satisfy the following conditions (1) to (5):
(1) The number \(x\), when written in the binary system (base 2), has exactly ten digits.
(2) When \(x\) is written in the ternary system, the second digit is 1.
(3) When \(x\) is written in the quaterna... | "[\"572\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3403, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17351"}] | {
"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
} |
[
"280"
] | [
"skywork"
] | 9d448c4bbe0e3eb6fc8b77694da84f91245395740e960eaa7e381e7d43f87076 | [
{
"content": "2. A white rabbit and a gray rabbit started picking mushrooms at the same time. The white rabbit picks 4 mushrooms per minute, and the gray rabbit picks 3 mushrooms per minute. After 10 minutes, the white rabbit gives half of the mushrooms it has picked to the gray rabbit, and then they continue p... | 2. A white rabbit and a gray rabbit started picking mushrooms at the same time. The white rabbit picks 4 mushrooms per minute, and the gray rabbit picks 3 mushrooms per minute. After 10 minutes, the white rabbit gives half of the mushrooms it has picked to the gray rabbit, and then they continue picking. When the two r... | "[\"280\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3404, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:17352"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | c66fbee1ac71e44aa3f577b948fa882257e231dca7239370172bb02fc6b53a47 | [
{
"content": "Harriet ran a $1000 \\mathrm{~m}$ course in 380 seconds. She ran the first $720 \\mathrm{~m}$ of the course at a constant speed of $3 \\mathrm{~m} / \\mathrm{s}$. She ran the remaining part of the course at a constant speed of $v \\mathrm{~m} / \\mathrm{s}$. What is the value of $v$ ?\n(A) 2\n(B) ... | Harriet ran a $1000 \mathrm{~m}$ course in 380 seconds. She ran the first $720 \mathrm{~m}$ of the course at a constant speed of $3 \mathrm{~m} / \mathrm{s}$. She ran the remaining part of the course at a constant speed of $v \mathrm{~m} / \mathrm{s}$. What is the value of $v$ ?
(A) 2
(B) 1.5
(C) 3
(D) 1
(E) 4.5 | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3417, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17353"}] | {
"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: 5"
] | [
"skywork"
] | b1ee427c317a103f2d1aebed0854cd24bdd7c3c404a56375922e2d6a7874c5b6 | [
{
"content": "Given that $E$ is the midpoint of the diagonal $BD$ of the square $ABCD$, point $F$ is taken on $AD$ such that $DF = \\frac{1}{3} DA$. Connecting $E$ and $F$, the ratio of the area of $\\triangle DEF$ to the area of quadrilateral $ABEF$ is:",
"role": "user"
}
] | Given that $E$ is the midpoint of the diagonal $BD$ of the square $ABCD$, point $F$ is taken on $AD$ such that $DF = \frac{1}{3} DA$. Connecting $E$ and $F$, the ratio of the area of $\triangle DEF$ to the area of quadrilateral $ABEF$ is: | "[\"1: 5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3428, "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:17354"}] | {
"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{3}{2}"
] | [
"skywork"
] | d229ca620f4f3c42a589275af5d4c7cc3e6be7862a0a743e2f695dbf13a221ad | [
{
"content": "2. If the difference between the maximum and minimum elements of the real number set $\\{1,2,3, x\\}$ equals the sum of all elements in the set, then the value of $x$ is $\\qquad$ ـ.",
"role": "user"
}
] | 2. If the difference between the maximum and minimum elements of the real number set $\{1,2,3, x\}$ equals the sum of all elements in the set, then the value of $x$ is $\qquad$ ـ. | "[\"-\\\\frac{3}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3422, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17355"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"S"
] | [
"skywork"
] | 4c8a517036e0908041df616ded440acf87b4d0112d1890f334a6d4484c4120ef | [
{
"content": "Points $ A’,B,C’ $ are arbitrarily taken on edges $ SA,SB, $ respectively, $ SC $ of a tetrahedron $ SABC. $ Plane forrmed by $ ABC $ intersects the plane $ \\rho , $ formed by $ A’B’C’, $ in a line $ d. $ Prove that, meanwhile the plane $ \\rho $ rotates around $ d, $ the lines $ AA’,BB’ $ and $ ... | Points $ A’,B,C’ $ are arbitrarily taken on edges $ SA,SB, $ respectively, $ SC $ of a tetrahedron $ SABC. $ Plane forrmed by $ ABC $ intersects the plane $ \rho , $ formed by $ A’B’C’, $ in a line $ d. $ Prove that, meanwhile the plane $ \rho $ rotates around $ d, $ the lines $ AA’,BB’ $ and $ CC’ $ are, and remain co... | "[\"S\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3406, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17356"}] | {
"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
} |
[
"18"
] | [
"skywork"
] | 9066e7b7bb0e24918c2c2188c3c0477dff3d17d7268fa67cd8fbfc1ffdda7685 | [
{
"content": "24. Jake wrote six consecutive numbers on six white pieces of paper, one number on each piece. He stuck these bits of paper onto the top and bottom of three coins. Then he tossed these three coins three times. On the first toss, he saw the numbers 6,7 and 8 and then coloured them red. On the secon... | 24. Jake wrote six consecutive numbers on six white pieces of paper, one number on each piece. He stuck these bits of paper onto the top and bottom of three coins. Then he tossed these three coins three times. On the first toss, he saw the numbers 6,7 and 8 and then coloured them red. On the second toss, the sum of the... | "[\"18\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3405, "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:17357"}] | {
"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
} |
[
"52"
] | [
"skywork"
] | 330afe7fb78e68460a1b682c4453e5b0ba9cfb9e86438aaa6644535b18d96a85 | [
{
"content": "3. A person adds the page numbers of a book in the order $1,2,3, \\cdots$, with one page number being added an extra time, resulting in an incorrect total sum of 2005. Then the page number that was added extra is $\\qquad$ .",
"role": "user"
}
] | 3. A person adds the page numbers of a book in the order $1,2,3, \cdots$, with one page number being added an extra time, resulting in an incorrect total sum of 2005. Then the page number that was added extra is $\qquad$ . | "[\"52\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3430, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "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:17358"}] | {
"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"
] | 6a6785afdf193bf9a3cf6a719c35066192f903530f9882b96e09916b9e3046ff | [
{
"content": "2. If the function $f(x)$ is an odd function with a period of 3, and when $x \\in[0,1)$, $f(x)=3^{x}-1$, then $f\\left(\\log _{\\frac{1}{3}} 54\\right)=$ $\\qquad$ .",
"role": "user"
}
] | 2. If the function $f(x)$ is an odd function with a period of 3, and when $x \in[0,1)$, $f(x)=3^{x}-1$, then $f\left(\log _{\frac{1}{3}} 54\right)=$ $\qquad$ . | "[\"-1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3434, "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:17359"}] | {
"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{48}{25}"
] | [
"skywork"
] | bfc4370a651d5d2ff26b1804ae32bd91023fe7fadf4fffb4ddd76866908c25e9 | [
{
"content": "Task B-2.7. Let $A B C$ be a right triangle with a right angle at vertex $C$. The height $C N$ is drawn to the side $A B$ and from point $N$ we draw the height $N P$ to the side $B C$ in triangle $B C N$. If the lengths of the legs are $|A C|=3$ and $|B C|=4$, what is the length of the height $N P... | Task B-2.7. Let $A B C$ be a right triangle with a right angle at vertex $C$. The height $C N$ is drawn to the side $A B$ and from point $N$ we draw the height $N P$ to the side $B C$ in triangle $B C N$. If the lengths of the legs are $|A C|=3$ and $|B C|=4$, what is the length of the height $N P$? | "[\"\\\\frac{48}{25}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3437, "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:17360"}] | {
"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
} |
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