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 |
|---|---|---|---|---|---|---|---|---|
[
"-\\frac{132}{125}"
] | [
"skywork"
] | 32f88d6c134eded44338b22d27fca9d3a0a5ff67f9570a973545102ee2587241 | [
{
"content": "Given $-π < x < 0$, $\\sin x + \\cos x = \\frac{1}{5}$,\n(1) Find the value of $\\sin x - \\cos x$;\n(2) Find the value of $\\frac{3\\sin^2 \\frac{x}{2} - 2\\sin \\frac{x}{2}\\cos \\frac{x}{2} + \\cos^2 \\frac{x}{2}}{\\tan x + \\frac{1}{\\tan x}}$.",
"role": "user"
}
] | Given $-π < x < 0$, $\sin x + \cos x = \frac{1}{5}$,
(1) Find the value of $\sin x - \cos x$;
(2) Find the value of $\frac{3\sin^2 \frac{x}{2} - 2\sin \frac{x}{2}\cos \frac{x}{2} + \cos^2 \frac{x}{2}}{\tan x + \frac{1}{\tan x}}$. | "[\"-\\\\frac{132}{125}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2345, "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:16326"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-3"
] | [
"skywork"
] | 2b3154658150416adc176c2611a0be763753fc2bd684f0ca6f3a1bbb6e19ab3b | [
{
"content": "1. Let the side length of the regular hexagon $A B C D E F$ be 1. Then $(\\overrightarrow{A B}+\\overrightarrow{D C}) \\cdot(\\overrightarrow{A D}+\\overrightarrow{B E})=$ $\\qquad$ .",
"role": "user"
}
] | 1. Let the side length of the regular hexagon $A B C D E F$ be 1. Then $(\overrightarrow{A B}+\overrightarrow{D C}) \cdot(\overrightarrow{A D}+\overrightarrow{B E})=$ $\qquad$ . | "[\"-3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2352, "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:16327"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"34"
] | [
"skywork"
] | 098cb1a7b8b66062e8f87be92ad13b0e340ec00951ad8359daa0795872fe80e0 | [
{
"content": "Let \\(a, b, c, d\\) be distinct positive odd numbers. What is the minimum value of\n\n\\[\n2abcd - (abc + abd + acd + bcd)\n\\]",
"role": "user"
}
] | Let \(a, b, c, d\) be distinct positive odd numbers. What is the minimum value of
\[
2abcd - (abc + abd + acd + bcd)
\] | "[\"34\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2361, "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:16328"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{103}{2520}"
] | [
"skywork"
] | 94493c90b760aeead3d6b4647d87af1a169127371099472318ebeb1a481bfd9f | [
{
"content": "10. (20 points) The rules of a card game are as follows: Arrange nine cards labeled $1,2, \\cdots, 9$ in a random row. If the number on the first card (from the left) is $k$, then reverse the order of the first $k$ cards, which is considered one operation. The game stops when no operation can be p... | 10. (20 points) The rules of a card game are as follows: Arrange nine cards labeled $1,2, \cdots, 9$ in a random row. If the number on the first card (from the left) is $k$, then reverse the order of the first $k$ cards, which is considered one operation. The game stops when no operation can be performed (i.e., the num... | "[\"\\\\frac{103}{2520}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2354, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16329"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"247"
] | [
"skywork"
] | 35ea1b7dfa8f9c97333edd4333f6e0e0f5b3651a23f1fc0786de9ed14a4ec2b1 | [
{
"content": "7. (7 points) Use the digits $1,2,3,4,5,6,7,8$ to form two different four-digit numbers (each digit is used only once) so that their difference is the smallest. What is this difference? $\\qquad$ .",
"role": "user"
}
] | 7. (7 points) Use the digits $1,2,3,4,5,6,7,8$ to form two different four-digit numbers (each digit is used only once) so that their difference is the smallest. What is this difference? $\qquad$ . | "[\"247\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2369, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16330"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"f_{n}=2n!-(n+1)"
] | [
"skywork"
] | a0be76be3e1aa5613fc2958ffb0fcedb692c92d8e7e6266a5b96088f977586aa | [
{
"content": "Example 8 The sequence $a_{n}$ is defined as follows: $a_{1}=0, a_{2}=1$\n$$\na_{n}=\\frac{1}{2} n a_{n-1}+\\frac{1}{2} n(n-1) a_{n-2}+(-1)^{n}\\left(1-\\frac{n}{2}\\right)(n \\geqslant 3)\n$$\n\nTry to find the simplest expression for $f_{n}=a_{n}+2 C_{n}^{1} a_{n-1}+3 C_{n}^{n} a_{n-2}+\\cdots+(... | Example 8 The sequence $a_{n}$ is defined as follows: $a_{1}=0, a_{2}=1$
$$
a_{n}=\frac{1}{2} n a_{n-1}+\frac{1}{2} n(n-1) a_{n-2}+(-1)^{n}\left(1-\frac{n}{2}\right)(n \geqslant 3)
$$
Try to find the simplest expression for $f_{n}=a_{n}+2 C_{n}^{1} a_{n-1}+3 C_{n}^{n} a_{n-2}+\cdots+(n-1) C_{n}^{n-2} a_{2}+n C_{n}^{n-... | "[\"f_{n}=2n!-(n+1)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2355, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16331"}] | {
"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
} |
[
"112015=521\\cdot215"
] | [
"skywork"
] | bee40157c6b3a4810bcc8a19194106ffca44008067732501b94665902d095c1e | [
{
"content": "4. On the board, the product of the numbers $\\overline{\\text{IKS}}$ and $\\overline{\\text{KSI}}$ is written, where the letters correspond to different non-zero decimal digits. This product contains three digits $C$ and one each of $I$, $K$, and 0, and its leading digit is $C$. What is written o... | 4. On the board, the product of the numbers $\overline{\text{IKS}}$ and $\overline{\text{KSI}}$ is written, where the letters correspond to different non-zero decimal digits. This product contains three digits $C$ and one each of $I$, $K$, and 0, and its leading digit is $C$. What is written on the board? | "[\"112015=521\\\\cdot215\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2362, "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:16332"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2 \\text{ inches and } 1 \\text{ fraction of an inch}"
] | [
"skywork"
] | ff055b1171add0c83c504962066bf2e1b3ad93431bd59497521bf96cfc541c1f | [
{
"content": "15. A rectangular piece of wood is 3 feet 5 inches 7 points long, 1 foot and 5 points wide, and 8 inches 4 points thick. It needs to be cut into equally sized cubic blocks, with the volume of each block being as large as possible. What is the edge length of the block?",
"role": "user"
}
] | 15. A rectangular piece of wood is 3 feet 5 inches 7 points long, 1 foot and 5 points wide, and 8 inches 4 points thick. It needs to be cut into equally sized cubic blocks, with the volume of each block being as large as possible. What is the edge length of the block? | "[\"2 \\\\text{ inches and } 1 \\\\text{ fraction of an inch}\"]" | train-math-numinamath1.5_number_theory | [{"dataset": "skywork", "extra_info": {"index": 2365, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16334"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3.56, 74, 83, 92"
] | [
"skywork"
] | 39f1cfc80c3b78d2a0713e788250e8ac4bb03f7eb79e11a6cd0ba309658eb6fc | [
{
"content": "3. Please select eight different digits to form four two-digit numbers, and make the sum of each two-digit number and the two-digit number obtained by reversing its digits a perfect square. Try to find these four two-digit numbers.\n\nTranslate the above text into English, please keep the line bre... | 3. Please select eight different digits to form four two-digit numbers, and make the sum of each two-digit number and the two-digit number obtained by reversing its digits a perfect square. Try to find these four two-digit numbers.
Translate the above text into English, please keep the line breaks and format of the so... | "[\"3.56, 74, 83, 92\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2363, "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:16335"}] | {
"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
} |
[
"54"
] | [
"skywork"
] | 8797ef10a21da236c00d7111c2d65583d31aafd6647ec8010518f216e5a93b6c | [
{
"content": "How many four-digit positive integers exist, all of whose digits are 0's, 2's, and/or 5's, and the number does not start with 0?",
"role": "user"
}
] | How many four-digit positive integers exist, all of whose digits are 0's, 2's, and/or 5's, and the number does not start with 0? | "[\"54\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2389, "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:16336"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2}"
] | [
"skywork"
] | 5a069bc244437820b3108ca8f9f0796d886b4353b073a66e849ecff7fdf6921e | [
{
"content": "The value of $\\frac{7+21}{14+42}$ is\n(A) $\\frac{1}{3}$\n(B) $\\frac{1}{6}$\n(C) $\\frac{1}{2}$\n(D) $\\frac{2}{3}$\n(E) 1",
"role": "user"
}
] | The value of $\frac{7+21}{14+42}$ is
(A) $\frac{1}{3}$
(B) $\frac{1}{6}$
(C) $\frac{1}{2}$
(D) $\frac{2}{3}$
(E) 1 | "[\"\\\\frac{1}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2385, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16337"}] | {
"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
} |
[
"\\{1000, 1000, 10, 7, 1\\}"
] | [
"skywork"
] | a646c478fb0840c1ebd7190cc97bc6fe680a2b915c4f329a55cd51dcbffb5b8a | [
{
"content": "Find all sets of positive integers $A=\\big\\{ a_1,a_2,...a_{19}\\big\\}$ which satisfy the following:\n$1\\big) a_1+a_2+...+a_{19}=2017;$\n$2\\big) S(a_1)=S(a_2)=...=S(a_{19})$ where $S\\big(n\\big)$ denotes digit sum of number $n$.",
"role": "user"
}
] | Find all sets of positive integers $A=\big\{ a_1,a_2,...a_{19}\big\}$ which satisfy the following:
$1\big) a_1+a_2+...+a_{19}=2017;$
$2\big) S(a_1)=S(a_2)=...=S(a_{19})$ where $S\big(n\big)$ denotes digit sum of number $n$. | "[\" \\\\{1000, 1000, 10, 7, 1\\\\} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2375, "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:16338"}] | {
"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
} |
[
"736"
] | [
"skywork"
] | 8787536e97bb5dd0e2dbc127961df82eace9b0acf634e14fe701a8b8f7292558 | [
{
"content": "A marathon is $26$ miles and $312$ yards. One mile equals $1760$ yards.\n\nJoanna has run eight marathons in her life. If the total distance Joanna covered in these marathons is $m$ miles and $y$ yards, where $0 \\le y < 1760$, what is the value of $y$?",
"role": "user"
}
] | A marathon is $26$ miles and $312$ yards. One mile equals $1760$ yards.
Joanna has run eight marathons in her life. If the total distance Joanna covered in these marathons is $m$ miles and $y$ yards, where $0 \le y < 1760$, what is the value of $y$? | "[\"736\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2383, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16339"}] | {
"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
} |
[
"1004"
] | [
"skywork"
] | 84683118b98df2d50550778d7634f134f89a1c5ba148826245bd23cb76045e75 | [
{
"content": "A subset $M$ of $\\{1, 2, . . . , 2006\\}$ has the property that for any three elements $x, y, z$ of $M$ with $x < y < z$ , $x+ y$ does not divide $z$ . Determine the largest possible size of $M$ .",
"role": "user"
}
] | A subset $M$ of $\{1, 2, . . . , 2006\}$ has the property that for any three elements $x, y, z$ of $M$ with $x < y < z$ , $x+ y$ does not divide $z$ . Determine the largest possible size of $M$ . | "[\"1004\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2372, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16340"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{193}{247}"
] | [
"skywork"
] | fc45d77f34d9bbf73c325c9d87b3fe198f7858dece942503f29846c577eeb4ed | [
{
"content": "57. In a black cloth bag, there are 40 socks that feel the same, differing only in color: 10 white, 12 red, and 18 black. Now, reaching into the bag to grab socks, the probability of getting at least one pair of socks (2 socks of the same color count as 1 pair) out of the 3 socks taken is $\\qquad... | 57. In a black cloth bag, there are 40 socks that feel the same, differing only in color: 10 white, 12 red, and 18 black. Now, reaching into the bag to grab socks, the probability of getting at least one pair of socks (2 socks of the same color count as 1 pair) out of the 3 socks taken is $\qquad$ . | "[\"\\\\frac{193}{247}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2374, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16341"}] | {
"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
} |
[
"n"
] | [
"skywork"
] | 7224add9f9f3bccb127dcb48ff263e19dbbd133854d03c7355569a8f07d8b5dd | [
{
"content": "Karpov D.V.\n\nIn a deck of $n$ cards, some of them are face down, and the rest are face up. In one move, it is allowed to take several cards from the top, flip the obtained stack, and place it back on top of the deck. What is the minimum number of moves required to ensure that all cards are face ... | Karpov D.V.
In a deck of $n$ cards, some of them are face down, and the rest are face up. In one move, it is allowed to take several cards from the top, flip the obtained stack, and place it back on top of the deck. What is the minimum number of moves required to ensure that all cards are face down, regardless of the ... | "[\"n\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2376, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16342"}] | {
"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
} |
[
"1643"
] | [
"skywork"
] | c4c7d2600d42361a92cc73de89a393b7ff48cf371ca88362c93647dc225ea987 | [
{
"content": "Let \\( a \\) and \\( b \\) be positive integers. The quotient of \\( a^{2} + b^{2} \\) divided by \\( a + b \\) is \\( q \\), and the remainder is \\( r \\), such that \\( q^{2} + r = 2010 \\). Find the value of \\( ab \\).",
"role": "user"
}
] | Let \( a \) and \( b \) be positive integers. The quotient of \( a^{2} + b^{2} \) divided by \( a + b \) is \( q \), and the remainder is \( r \), such that \( q^{2} + r = 2010 \). Find the value of \( ab \). | "[\"1643\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2377, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:16343"}] | {
"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{8}{7}"
] | [
"skywork"
] | 68ecd5609e04f577191978ed1b4f481307422d56a7a8eeeb6be5151decffec15 | [
{
"content": "Let $K$ be a point on the side $[AB]$, and $L$ be a point on the side $[BC]$ of the square $ABCD$. If $|AK|=3$, $|KB|=2$, and the distance of $K$ to the line $DL$ is $3$, what is $|BL|:|LC|$?\n\n$ \\textbf{(A)}\\ \\frac78 \n\\qquad\\textbf{(B)}\\ \\frac{\\sqrt 3}2\n\\qquad\\textbf{(C)}\\ \\frac 87... | Let $K$ be a point on the side $[AB]$, and $L$ be a point on the side $[BC]$ of the square $ABCD$. If $|AK|=3$, $|KB|=2$, and the distance of $K$ to the line $DL$ is $3$, what is $|BL|:|LC|$?
$ \textbf{(A)}\ \frac78
\qquad\textbf{(B)}\ \frac{\sqrt 3}2
\qquad\textbf{(C)}\ \frac 87
\qquad\textbf{(D)}\ \frac 38
\qquad\t... | "[\"\\\\frac{8}{7}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2380, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16344"}] | {
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[
"150\\mathrm{~mL}"
] | [
"skywork"
] | 31fe6585159398dccc80720718aecc6eba5fbd28f48f40fddbc8d0cc7cb654a1 | [
{
"content": "To make pizza dough, Luca mixes $50 \\mathrm{~mL}$ of milk for every $250 \\mathrm{~mL}$ of flour. How much milk does he mix with $750 \\mathrm{~mL}$ of flour?\n(A) $100 \\mathrm{~mL}$\n(B) $125 \\mathrm{~mL}$\n(C) $150 \\mathrm{~mL}$\n(D) $200 \\mathrm{~mL}$\n(E) $250 \\mathrm{~mL}$",
"role":... | To make pizza dough, Luca mixes $50 \mathrm{~mL}$ of milk for every $250 \mathrm{~mL}$ of flour. How much milk does he mix with $750 \mathrm{~mL}$ of flour?
(A) $100 \mathrm{~mL}$
(B) $125 \mathrm{~mL}$
(C) $150 \mathrm{~mL}$
(D) $200 \mathrm{~mL}$
(E) $250 \mathrm{~mL}$ | "[\"150\\\\mathrm{~mL}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2392, "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:16345"}] | {
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[
"2^{n+2}-2"
] | [
"skywork"
] | f4796ba728f33dfe3be977839dad11ec9313d7fab8206a18a9beae911a05e79e | [
{
"content": "Find the number of different sequences with $2 n+1$ terms, where each term is $\\pm 1$ and the absolute value of the sum of any odd number of consecutive terms does not exceed 1.\n\nTranslate the above text into English, please keep the original text's line breaks and format, and output the transl... | Find the number of different sequences with $2 n+1$ terms, where each term is $\pm 1$ and the absolute value of the sum of any odd number of consecutive terms does not exceed 1.
Translate the above text into English, please keep the original text's line breaks and format, and output the translation result directly. | "[\"2^{n+2}-2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2398, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16346"}] | {
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[
"41"
] | [
"skywork"
] | b1fd7be9e7871b0155c898b9e89fe1b74e257d8d286f796f69e5888baabcfd3f | [
{
"content": "For how many positive integers $n \\leq 1000$ does $\\frac{1}{n}$ yield a terminating decimal where the thousandths digit is non-zero?",
"role": "user"
}
] | For how many positive integers $n \leq 1000$ does $\frac{1}{n}$ yield a terminating decimal where the thousandths digit is non-zero? | "[\"41\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2388, "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:16347"}] | {
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[
"2418"
] | [
"skywork"
] | 8ec53f4468057e0536e35f9e18004937565550567a3ecde3663ed68bd149c3c0 | [
{
"content": "Person A, Person B, and Person C start from point $A$ to point $B$. Person A starts at 8:00, Person B starts at 8:20, and Person C starts at 8:30. They all travel at the same speed. After Person C has been traveling for 10 minutes, Person A is exactly halfway between Person B and point $B$, and at... | Person A, Person B, and Person C start from point $A$ to point $B$. Person A starts at 8:00, Person B starts at 8:20, and Person C starts at 8:30. They all travel at the same speed. After Person C has been traveling for 10 minutes, Person A is exactly halfway between Person B and point $B$, and at that moment, Person C... | "[\"2418\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2378, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16348"}] | {
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[
"1008"
] | [
"skywork"
] | 2aaae824d3bb42fc5ce691ab22b11ecdeb60dbb5ee573de3c760bd25ae87e036 | [
{
"content": "4. In a regular 2017-gon, all diagonals are drawn. Petya randomly selects some $\\mathrm{N}$ diagonals. What is the smallest $N$ such that among the selected diagonals, there are guaranteed to be two of the same length?",
"role": "user"
}
] | 4. In a regular 2017-gon, all diagonals are drawn. Petya randomly selects some $\mathrm{N}$ diagonals. What is the smallest $N$ such that among the selected diagonals, there are guaranteed to be two of the same length? | "[\"1008\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2379, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:16349"}, {"dataset": "skywork", "extra_in... | {
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} |
[
"1099"
] | [
"skywork"
] | 295ebde45cdfdf39e33dc0951901110917290b500aac1f5c88b1ed02521010b3 | [
{
"content": "Richard likes to solve problems from the IMO Shortlist. In 2013, Richard solves $5$ problems each Saturday and $7$ problems each Sunday. He has school on weekdays, so he ``only'' solves $2$, $1$, $2$, $1$, $2$ problems on each Monday, Tuesday, Wednesday, Thursday, and Friday, respectively -- with ... | Richard likes to solve problems from the IMO Shortlist. In 2013, Richard solves $5$ problems each Saturday and $7$ problems each Sunday. He has school on weekdays, so he ``only'' solves $2$, $1$, $2$, $1$, $2$ problems on each Monday, Tuesday, Wednesday, Thursday, and Friday, respectively -- with the exception of Decem... | "[\"1099\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2382, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16350"}] | {
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} |
[
"\\frac{15}{31}"
] | [
"skywork"
] | 026e41dd36851c140c5364657fa93c3ca57ca9dd887aa4aa9f8eaee205558f86 | [
{
"content": "7. A real numbers $x$ is randomly chosen in the interval $\\left[-15 \\frac{1}{2}, 15 \\frac{1}{2}\\right]$. Find the probability that the closest integer to $x$ is odd.",
"role": "user"
}
] | 7. A real numbers $x$ is randomly chosen in the interval $\left[-15 \frac{1}{2}, 15 \frac{1}{2}\right]$. Find the probability that the closest integer to $x$ is odd. | "[\"\\\\frac{15}{31}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2395, "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:16351"}] | {
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"reference_components": 1,
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} |
[
"247"
] | [
"skywork"
] | 394be86a5b91c6828ecba1031e7eff813b1f4390a830fb0ef0f0e08ef0eeddd0 | [
{
"content": "20. The number $N=3^{16}-1$ has a divisor of 193. It also has some divisors between 75 and 85 inclusive. What is the sum of these divisors?",
"role": "user"
}
] | 20. The number $N=3^{16}-1$ has a divisor of 193. It also has some divisors between 75 and 85 inclusive. What is the sum of these divisors? | "[\"247\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2400, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16352"}] | {
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} |
[
"\\left( 4 \\sqrt{3}, \\frac{\\pi}{6} \\right)"
] | [
"skywork"
] | b214d7fa62d6fc2093f5f5bdde965f30d3db86fe9e388cce85d81dabd6c8e90c | [
{
"content": "Convert the point $(6,2 \\sqrt{3})$ in rectangular coordinates to polar coordinates. Enter your answer in the form $(r,\\theta),$ where $r > 0$ and $0 \\le \\theta < 2 \\pi.$",
"role": "user"
}
] | Convert the point $(6,2 \sqrt{3})$ in rectangular coordinates to polar coordinates. Enter your answer in the form $(r,\theta),$ where $r > 0$ and $0 \le \theta < 2 \pi.$ | "[\"\\\\left( 4 \\\\sqrt{3}, \\\\frac{\\\\pi}{6} \\\\right)\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2410, "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:16353"}] | {
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} |
[
"3:1"
] | [
"skywork"
] | 76d195ae7a85766dac42e31d06e1089602ff0bcccad43bc8be5dc1ca96390218 | [
{
"content": "In the triangle $ABC$ , the angle bisector $AD$ divides the side $BC$ into the ratio $BD: DC = 2: 1$. In what ratio, does the median $CE$ divide this bisector?",
"role": "user"
}
] | In the triangle $ABC$ , the angle bisector $AD$ divides the side $BC$ into the ratio $BD: DC = 2: 1$. In what ratio, does the median $CE$ divide this bisector? | "[\"3:1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2393, "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:16354"}] | {
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} |
[
"10\\sqrt{13}"
] | [
"skywork"
] | 21cb4ae6efcc2f0450b21427ac862735f7b46b8414a488fa02f70404f8acb992 | [
{
"content": "In the diagram below, $ABCD$ is a trapezoid such that $\\overline{AB}\\parallel \\overline{CD}$ and $\\overline{AC}\\perp\\overline{CD}$. If $CD = 15$, $\\tan C = 2$, and $\\tan B = \\frac{3}{2}$, then what is $BD$?",
"role": "user"
}
] | In the diagram below, $ABCD$ is a trapezoid such that $\overline{AB}\parallel \overline{CD}$ and $\overline{AC}\perp\overline{CD}$. If $CD = 15$, $\tan C = 2$, and $\tan B = \frac{3}{2}$, then what is $BD$? | "[\"10\\\\sqrt{13}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2387, "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:16355"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"136"
] | [
"skywork"
] | d8366da72efee78e863711d58b0629a31dcd123e72ac3f9ec2dd57f498bbb230 | [
{
"content": "1. A warehouse has coffee packed in bags of 15 kg and 8 kg. How many bags of coffee in total does the warehouseman need to prepare to weigh out 1998 kg of coffee, with the number of 8 kg bags being the smallest possible?",
"role": "user"
}
] | 1. A warehouse has coffee packed in bags of 15 kg and 8 kg. How many bags of coffee in total does the warehouseman need to prepare to weigh out 1998 kg of coffee, with the number of 8 kg bags being the smallest possible? | "[\"136\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2413, "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:16356"}] | {
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} |
[
"\\frac{1 + \\sqrt{5}}{2}"
] | [
"skywork"
] | 6355f5aaf3cce2eb56918366cf5a47e53376fead82072cb6342e28f1a8055d88 | [
{
"content": "Solve\n\\[\\arctan \\frac{1}{x} + \\arctan \\frac{1}{x^3} = \\frac{\\pi}{4}.\\]",
"role": "user"
}
] | Solve
\[\arctan \frac{1}{x} + \arctan \frac{1}{x^3} = \frac{\pi}{4}.\] | "[\"\\\\frac{1 + \\\\sqrt{5}}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2419, "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:16357"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-1"
] | [
"skywork"
] | c8ad021ef3f9a2e569d71719ad5c76ba2d71abac4268681371825a0e846773ac | [
{
"content": "$\\quad 1-4(3-1)^{-1}$ is equal to\n(A) -1\n(B) $-\\frac{3}{2}$\n(C) 9\n(D) 6\n(E) $\\frac{11}{3}$",
"role": "user"
}
] | $\quad 1-4(3-1)^{-1}$ is equal to
(A) -1
(B) $-\frac{3}{2}$
(C) 9
(D) 6
(E) $\frac{11}{3}$ | "[\"-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2411, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16358"}] | {
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[
"-\\frac{1}{2}"
] | [
"skywork"
] | 60be7f9382692e34e145a567fc970042cff4107df1a5a102aa4754ba3b14f852 | [
{
"content": "Simplify the expression \\(\\frac{\\operatorname{tg}\\left(\\frac{5}{4} \\pi - 4 \\alpha\\right) \\sin^{2}\\left(\\frac{5}{4} \\pi + 4 \\alpha\\right)}{1 - 2 \\cos^{2} 4 \\alpha}\\).",
"role": "user"
}
] | Simplify the expression \(\frac{\operatorname{tg}\left(\frac{5}{4} \pi - 4 \alpha\right) \sin^{2}\left(\frac{5}{4} \pi + 4 \alpha\right)}{1 - 2 \cos^{2} 4 \alpha}\). | "[\"-\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2404, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16359"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1000^{999}"
] | [
"skywork"
] | 4dfd7b09792df7f94aad3f695f1e2aa37125965e402da37e8d10f7cd288a26bc | [
{
"content": "20. [11] Determine the number of sequences of sets $S_{1}, S_{2}, \\ldots, S_{999}$ such that\n$$\nS_{1} \\subseteq S_{2} \\subseteq \\cdots \\subseteq S_{999} \\subseteq\\{1,2, \\ldots, 999\\} .\n$$\n\nHere $A \\subseteq B$ means that all elements of $A$ are also elements of $B$.",
"role": "u... | 20. [11] Determine the number of sequences of sets $S_{1}, S_{2}, \ldots, S_{999}$ such that
$$
S_{1} \subseteq S_{2} \subseteq \cdots \subseteq S_{999} \subseteq\{1,2, \ldots, 999\} .
$$
Here $A \subseteq B$ means that all elements of $A$ are also elements of $B$. | "[\"1000^{999}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2386, "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:16361"}] | {
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} |
[
"17"
] | [
"skywork"
] | 1b94d9ccd8ae9eba0bf806d07a00b951e288939b0f6c1208190e7c23f66362e3 | [
{
"content": "6. (10 points) As shown in the figure, 75 small squares form a $15 \\times 5$ pattern. Some of the small squares have already been shaded. Now, we need to continue shading some of the blank small squares to ensure that in any $2 \\times 2$ square, the number of shaded small squares is more than ha... | 6. (10 points) As shown in the figure, 75 small squares form a $15 \times 5$ pattern. Some of the small squares have already been shaded. Now, we need to continue shading some of the blank small squares to ensure that in any $2 \times 2$ square, the number of shaded small squares is more than half. What is the minimum ... | "[\"17\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2381, "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:16362"}] | {
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"reference_components": 1,
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} |
[
"11"
] | [
"skywork"
] | fe82542216a3511001a8e1c784746b34ce37199948e51f68c1f27a165dbda45c | [
{
"content": "How many 7-digit positive integers are made up of the digits 0 and 1 only, and are divisible by 6?",
"role": "user"
}
] | How many 7-digit positive integers are made up of the digits 0 and 1 only, and are divisible by 6? | "[\"11\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2396, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16363"}] | {
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[
"(1,2),(2,1),(-1,-2),(-2,-1)"
] | [
"skywork"
] | 953be9bc893acec83d6a6c89d6398e6a700418d705e11cbd11f101bdd76ac1e6 | [
{
"content": "4. Determine all pairs of integers $(x, y)$ for which $2 x y$ is a square and $x^{2}+y^{2}$ is a prime number.",
"role": "user"
}
] | 4. Determine all pairs of integers $(x, y)$ for which $2 x y$ is a square and $x^{2}+y^{2}$ is a prime number. | "[\"(1,2),(2,1),(-1,-2),(-2,-1)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2407, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16364"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"731"
] | [
"skywork"
] | b0f914790c7a213f3da3386e0b2600eacd6b1ac920dde1c1ad6080c6f7d1dfb8 | [
{
"content": "In the middle of a vast prairie, a firetruck is stationed at the intersection of two perpendicular straight highways. The truck travels at $50$ miles per hour along the highways and at $14$ miles per hour across the prairie. Consider the set of points that can be reached by the firetruck within si... | In the middle of a vast prairie, a firetruck is stationed at the intersection of two perpendicular straight highways. The truck travels at $50$ miles per hour along the highways and at $14$ miles per hour across the prairie. Consider the set of points that can be reached by the firetruck within six minutes. The area of... | "[\"731\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 2397, "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:16365"}] | {
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"reference_components": 1,
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} |
[
"73"
] | [
"skywork"
] | bff8c34ae3bdfeef4421f30be14ed7ae742e09a9c5684b4decca53814f0c93df | [
{
"content": "Let $M_n$ be the $n \\times n$ matrix with entries as follows: for $1 \\le i \\le n$ , $m_{i,i} = 10$ ; for $1 \\le i \\le n - 1$ , $m_{i+1,i} = m_{i,i+1} = 3$ ; all other entries in $M_n$ are zero. Let $D_n$ be the determinant of matrix $M_n$ . Then $\\sum_{n=1}^{\\infty} \\frac{1}{8D_n+1}$ can b... | Let $M_n$ be the $n \times n$ matrix with entries as follows: for $1 \le i \le n$ , $m_{i,i} = 10$ ; for $1 \le i \le n - 1$ , $m_{i+1,i} = m_{i,i+1} = 3$ ; all other entries in $M_n$ are zero. Let $D_n$ be the determinant of matrix $M_n$ . Then $\sum_{n=1}^{\infty} \frac{1}{8D_n+1}$ can be represented as $\frac{p}{q}$... | "[\"73\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 2384, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16366"}, {"dataset": "skywork", "extra_inf... | {
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} |
[
"f(x)=0"
] | [
"skywork"
] | d90c65b08151fd45aec19e767da811d55357660eae283521880729ad9dc36463 | [
{
"content": "Problem 5. Determine all the functions $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ such that\n$$\nf\\left(x^{2}+f(y)\\right)=f(f(x))+f\\left(y^{2}\\right)+2 f(x y)\n$$\nfor all real number $x$ and $y$.",
"role": "user"
}
] | Problem 5. Determine all the functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that
$$
f\left(x^{2}+f(y)\right)=f(f(x))+f\left(y^{2}\right)+2 f(x y)
$$
for all real number $x$ and $y$. | "[\"f(x)=0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2402, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16367"}] | {
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} |
[
"0.9544"
] | [
"skywork"
] | e469127755125e82ac1e58eac691dc9494650c3d6e82813cfd7033d4d3ac47c2 | [
{
"content": "Example 23. The random variable $X$ is distributed according to the normal law. The mathematical expectation $a=0$ and the standard deviation of this variable $\\sigma=0.5$. Find the probability that the deviation of the random variable $X$ in absolute value will be less than one.",
"role": "u... | Example 23. The random variable $X$ is distributed according to the normal law. The mathematical expectation $a=0$ and the standard deviation of this variable $\sigma=0.5$. Find the probability that the deviation of the random variable $X$ in absolute value will be less than one. | "[\"0.9544\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2418, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16368"}] | {
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[
"4"
] | [
"skywork"
] | 4434e9f0c10738c6f4700f4222c7d7f641a3a26d88f996f0f25c8ad6dc811a35 | [
{
"content": "If $f(x)$ is a function, then we define the function $f^{(n)}(x)$ to be the result of $n$ applications of $f$ to $x$, where $n$ is a positive integer. For example, $f^{(3)}(x)=f(f(f(x)))$.\n\nWe define the $\\textit{order}$ of an input $x$ with respect to $f$ to be the smallest positive integer $m... | If $f(x)$ is a function, then we define the function $f^{(n)}(x)$ to be the result of $n$ applications of $f$ to $x$, where $n$ is a positive integer. For example, $f^{(3)}(x)=f(f(f(x)))$.
We define the $\textit{order}$ of an input $x$ with respect to $f$ to be the smallest positive integer $m$ such that $f^{(m)}(x)=x... | "[\"4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2390, "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:16369"}] | {
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[
"3987"
] | [
"skywork"
] | b06da9546cf7382ac2bf610d980384500ff9ab6ebf75eaa541b3e5b2670e9e08 | [
{
"content": "What is the smallest integer $n > 0$ such that for any integer m in the range $1, 2, 3, ... , 1992$ we can always find an integral multiple of $\\frac{1}{n}$ in the open interval $(\\frac{m}{1993}, \\frac{m+1}{1994})$?",
"role": "user"
}
] | What is the smallest integer $n > 0$ such that for any integer m in the range $1, 2, 3, ... , 1992$ we can always find an integral multiple of $\frac{1}{n}$ in the open interval $(\frac{m}{1993}, \frac{m+1}{1994})$? | "[\"3987\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2399, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16370"}] | {
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} |
[
"0.32"
] | [
"skywork"
] | 639c7916929ac41615269cd7eaae0ad6eb3eb925b3e5438fc1410496befe9042 | [
{
"content": "4. In the box, there are 3 white cups, 3 red cups, and 2 black cups. Sonya took out 5 cups at random. What is the probability that she took out 2 white, 2 red, and 1 black cup? (Round your answer to the nearest hundredth).\n\n#",
"role": "user"
}
] | 4. In the box, there are 3 white cups, 3 red cups, and 2 black cups. Sonya took out 5 cups at random. What is the probability that she took out 2 white, 2 red, and 1 black cup? (Round your answer to the nearest hundredth).
# | "[\"0.32\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2412, "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:16371"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"504 \\pi"
] | [
"skywork"
] | 7e6e867e69063cc70f7258ab3e9f333f0bc51fa9dde6543f59fe1694b4fb536a | [
{
"content": "A circle is tangent to both branches of the hyperbola \\( x^{2} - 20y^{2} = 24 \\) as well as the \\( x \\)-axis. Compute the area of this circle.",
"role": "user"
}
] | A circle is tangent to both branches of the hyperbola \( x^{2} - 20y^{2} = 24 \) as well as the \( x \)-axis. Compute the area of this circle. | "[\"504 \\\\pi\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2406, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:16372"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"72"
] | [
"skywork"
] | 623c8b58cbfd35b0376ac6204a9ba28338f1085c0b714fe689fb5860052499ea | [
{
"content": "In how many ways can $a, b, c$, and $d$ be chosen from the set $\\{0,1,2, \\ldots, 9\\}$ so that $a<b<c<d$ and $a+b+c+d$ is a multiple of three?\n(A) 54\n(B) 64\n(C) 63\n(D) 90\n(E) 72",
"role": "user"
}
] | In how many ways can $a, b, c$, and $d$ be chosen from the set $\{0,1,2, \ldots, 9\}$ so that $a<b<c<d$ and $a+b+c+d$ is a multiple of three?
(A) 54
(B) 64
(C) 63
(D) 90
(E) 72 | "[\"72\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2403, "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:16373"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | 82bc40255aed9b338059b20d4763557f5dea0e8c53388eafd2ea4ccbd1e4f066 | [
{
"content": "$4 \\cdot 218$ In a middle school mathematics competition, three problems $A$, $B$, and $C$ were given. Among the 25 students who participated in the competition, each student solved at least one problem. Among those who did not solve $A$, the number of students who solved $B$ is twice the number ... | $4 \cdot 218$ In a middle school mathematics competition, three problems $A$, $B$, and $C$ were given. Among the 25 students who participated in the competition, each student solved at least one problem. Among those who did not solve $A$, the number of students who solved $B$ is twice the number of students who solved ... | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2401, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16374"}] | {
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"reference_components": 1,
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} |
[
"2 \\sqrt{33}"
] | [
"skywork"
] | 55fd05fd9a9a9ecd36f079a57aacae8e5ca3294ad11688b4e060bc4761ebb7ee | [
{
"content": "In a regular tetrahedron \\(ABCD\\), points \\(E\\) and \\(F\\) are on edges \\(AB\\) and \\(AC\\) respectively, satisfying \\(BE=3\\) and \\(EF=4\\), and \\(EF \\parallel\\) plane \\(BCD\\). Find the area of \\(\\triangle DEF\\).",
"role": "user"
}
] | In a regular tetrahedron \(ABCD\), points \(E\) and \(F\) are on edges \(AB\) and \(AC\) respectively, satisfying \(BE=3\) and \(EF=4\), and \(EF \parallel\) plane \(BCD\). Find the area of \(\triangle DEF\). | "[\"2 \\\\sqrt{33}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2394, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16375"}] | {
"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{27}{40}"
] | [
"skywork"
] | d42e5755bcdcba75deb234ddc9b8c0b7ac75fe97e7d4c35fe7a61d6a6d734bbc | [
{
"content": "Trapezoid $A B C D$ is inscribed in the parabola $y=x^{2}$ such that $A=\\left(a, a^{2}\\right), B=\\left(b, b^{2}\\right)$, $C=\\left(-b, b^{2}\\right)$, and $D=\\left(-a, a^{2}\\right)$ for some positive reals $a, b$ with $a>b$. If $A D+B C=A B+C D$, and $A B=\\frac{3}{4}$, what is $a$?",
"r... | Trapezoid $A B C D$ is inscribed in the parabola $y=x^{2}$ such that $A=\left(a, a^{2}\right), B=\left(b, b^{2}\right)$, $C=\left(-b, b^{2}\right)$, and $D=\left(-a, a^{2}\right)$ for some positive reals $a, b$ with $a>b$. If $A D+B C=A B+C D$, and $A B=\frac{3}{4}$, what is $a$? | "[\"\\\\frac{27}{40}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2391, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16376"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"60"
] | [
"skywork"
] | ee0b6473d0248082b893296e8f56f7302dab164382cfa6e449029ab4bc39da96 | [
{
"content": "## Task 1\n\nDetlef is saving for a bicycle. It is supposed to cost 360.00 DM.\n\nWhen asked how much money he still needs, he says: \"If I had six times as much money as I already have, I would have enough.\"\n\nHow much money has Detlef saved so far?",
"role": "user"
}
] | ## Task 1
Detlef is saving for a bicycle. It is supposed to cost 360.00 DM.
When asked how much money he still needs, he says: "If I had six times as much money as I already have, I would have enough."
How much money has Detlef saved so far? | "[\"60\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2422, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16377"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{7}{2},\\frac{3+\\sqrt{13}}{2}"
] | [
"skywork"
] | de61f647ce1da90d288c0876b64c462265ed499d572acde15428897fb4f65311 | [
{
"content": "1. Find all values of $x$, for each of which one of the three given numbers $\\log _{x}\\left(x-\\frac{3}{2}\\right)$, $\\log _{x-\\frac{3}{2}}(x-3)$, and $\\log _{x-3} x$ is equal to the product of the other two.",
"role": "user"
}
] | 1. Find all values of $x$, for each of which one of the three given numbers $\log _{x}\left(x-\frac{3}{2}\right)$, $\log _{x-\frac{3}{2}}(x-3)$, and $\log _{x-3} x$ is equal to the product of the other two. | "[\"\\\\frac{7}{2},\\\\frac{3+\\\\sqrt{13}}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2417, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16378"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\pi }{8}"
] | [
"skywork"
] | ed228a0ff5af4bc0ef902f2099594cadb54c9bc99ad16cfaee7eaba51916313c | [
{
"content": "Given the function $y=\\cos (2x-\\frac{\\pi }{4})$, determine the horizontal translation of the graph of the function $y=\\sin 2x$.",
"role": "user"
}
] | Given the function $y=\cos (2x-\frac{\pi }{4})$, determine the horizontal translation of the graph of the function $y=\sin 2x$. | "[\"\\\\frac{\\\\pi }{8}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2414, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16379"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\sqrt{3}}{2}"
] | [
"skywork"
] | 6a8e7d994a085cdcd7ae864cc683a27958fe9147c90f1f91c4dce73a3b56cd4b | [
{
"content": "Simplify $\\frac{{1+\\cos{20}°}}{{2\\sin{20}°}}-\\sin{10°}\\left(\\frac{1}{{\\tan{5°}}}-\\tan{5°}\\right)=\\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | Simplify $\frac{{1+\cos{20}°}}{{2\sin{20}°}}-\sin{10°}\left(\frac{1}{{\tan{5°}}}-\tan{5°}\right)=\_\_\_\_\_\_$. | "[\"\\\\frac{\\\\sqrt{3}}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2429, "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:16380"}] | {
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} |
[
"\\frac{6}{7}"
] | [
"skywork"
] | 26bbb4061fe7605b014b06f7c673320388f3563211d34f4f5a4f92d840b2be98 | [
{
"content": "The sequence is $\\frac{1}{2}$, $\\frac{1}{3}$, $\\frac{2}{3}$, $\\frac{1}{4}$, $\\frac{2}{4}$, $\\frac{3}{4}$, ... , $\\frac{1}{m+1}$, $\\frac{2}{m+1}$, ... , $\\frac{m}{m+1}$, ... Find the $20^{th}$ term.",
"role": "user"
}
] | The sequence is $\frac{1}{2}$, $\frac{1}{3}$, $\frac{2}{3}$, $\frac{1}{4}$, $\frac{2}{4}$, $\frac{3}{4}$, ... , $\frac{1}{m+1}$, $\frac{2}{m+1}$, ... , $\frac{m}{m+1}$, ... Find the $20^{th}$ term. | "[\"\\\\frac{6}{7}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2416, "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:16381"}] | {
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} |
[
"k = 1, 2"
] | [
"skywork"
] | 425b1f474bcdf187c4cbd0cc4962bacda9e22f179bc4bac7807d73314d36dbf6 | [
{
"content": "Find all $k>0$ such that there exists a function $f : [0,1]\\times[0,1] \\to [0,1]$ satisfying the following conditions:\n$f(f(x,y),z)=f(x,f(y,z))$;\n$f(x,y) = f(y,x)$;\n$f(x,1)=x$;\n$f(zx,zy) = z^{k}f(x,y)$, for any $x,y,z \\in [0,1]$",
"role": "user"
}
] | Find all $k>0$ such that there exists a function $f : [0,1]\times[0,1] \to [0,1]$ satisfying the following conditions:
$f(f(x,y),z)=f(x,f(y,z))$;
$f(x,y) = f(y,x)$;
$f(x,1)=x$;
$f(zx,zy) = z^{k}f(x,y)$, for any $x,y,z \in [0,1]$ | "[\"k = 1, 2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2408, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:16382"}] | {
"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
} |
[
"64"
] | [
"skywork"
] | d0230aa7818d29ebee61dbcf2da6b4522ca74426a5fcc20e2fbd548ff9787c33 | [
{
"content": "Let $N$ be the number of minimally intersecting ordered triples of sets for which each set is a subset of $\\{1, 2, 3, 4, 5, 6, 7, 8\\}$. Here a minimally intersecting triple $(A, B, C)$ is defined by the condition that $|A \\cap B| = |B \\cap C| = |C \\cap A| = 1$ and $A \\cap B \\cap C = \\empty... | Let $N$ be the number of minimally intersecting ordered triples of sets for which each set is a subset of $\{1, 2, 3, 4, 5, 6, 7, 8\}$. Here a minimally intersecting triple $(A, B, C)$ is defined by the condition that $|A \cap B| = |B \cap C| = |C \cap A| = 1$ and $A \cap B \cap C = \emptyset$. Find the remainder when ... | "[\"64\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2415, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16383"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"f(x) = 0"
] | [
"skywork"
] | d8076957c6475ed50e9ed00b8c5e702deb4d108600775f43f3d48c58120b62ba | [
{
"content": "Find all functions $f:\\mathbb{N}_0\\to\\mathbb{N}_0$ for which $f(0)=0$ and\n\\[f(x^2-y^2)=f(x)f(y) \\]\nfor all $x,y\\in\\mathbb{N}_0$ with $x>y$.",
"role": "user"
}
] | Find all functions $f:\mathbb{N}_0\to\mathbb{N}_0$ for which $f(0)=0$ and
\[f(x^2-y^2)=f(x)f(y) \]
for all $x,y\in\mathbb{N}_0$ with $x>y$. | "[\" f(x) = 0 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2420, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:16384"}] | {
"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
} |
[
"30"
] | [
"skywork"
] | 6c84f6827984eb8cc838665cb80ea592820c9a1f9d38fe6e06c2158a16f28445 | [
{
"content": "Xiao Zhang has three watches. The first watch runs 2 minutes fast every hour, the second watch runs 6 minutes fast, and the third watch runs 16 minutes fast. If the minute hands of the three watches are currently all pointing in the same direction, after how many hours will the three minute hands ... | Xiao Zhang has three watches. The first watch runs 2 minutes fast every hour, the second watch runs 6 minutes fast, and the third watch runs 16 minutes fast. If the minute hands of the three watches are currently all pointing in the same direction, after how many hours will the three minute hands point in the same dire... | "[\"30\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2434, "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:16385"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"59"
] | [
"skywork"
] | 5e08f924a67e09637ae8df0d93667f719684785976eb0046468a63ca89ec05fa | [
{
"content": "2.4. When a natural number $n$ is divided by 3, the remainder is 2, and when it is divided by 37, the remainder is 22. What is the remainder when this number is divided by 111.",
"role": "user"
}
] | 2.4. When a natural number $n$ is divided by 3, the remainder is 2, and when it is divided by 37, the remainder is 22. What is the remainder when this number is divided by 111. | "[\"59\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2428, "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:16386"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-13-\\sqrt{57}"
] | [
"skywork"
] | 9430f8418c7a3228243906d72e0548e52877c8c44f2c73e6eb25951ca918d69e | [
{
"content": "10.1. Find the smallest of the solutions to the inequality\n\n$$\n\\frac{-\\log _{2}(120-2 x \\sqrt{32-2 x})^{2}+\\left|\\log _{2} \\frac{120-2 x \\sqrt{32-2 x}}{\\left(x^{2}-2 x+8\\right)^{3}}\\right|}{5 \\log _{7}(71-2 x \\sqrt{32-2 x})-2 \\log _{2}(120-2 x \\sqrt{32-2 x})} \\geqslant 0\n$$",
... | 10.1. Find the smallest of the solutions to the inequality
$$
\frac{-\log _{2}(120-2 x \sqrt{32-2 x})^{2}+\left|\log _{2} \frac{120-2 x \sqrt{32-2 x}}{\left(x^{2}-2 x+8\right)^{3}}\right|}{5 \log _{7}(71-2 x \sqrt{32-2 x})-2 \log _{2}(120-2 x \sqrt{32-2 x})} \geqslant 0
$$ | "[\"-13-\\\\sqrt{57}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2430, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16387"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"5b"
] | [
"skywork"
] | 2ba5b9ef5398133f5f5639715edf2c8e6c07c4d28a225914ea4b16488ef6f5c7 | [
{
"content": "9 A square is inscribed in a circle, and another square is inscribed in the segment cut off from the circle by the side of this square. Find the ratio of the lengths of the sides of these squares.\n\n#",
"role": "user"
}
] | 9 A square is inscribed in a circle, and another square is inscribed in the segment cut off from the circle by the side of this square. Find the ratio of the lengths of the sides of these squares.
# | "[\"5b\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2424, "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:16388"}] | {
"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
} |
[
"-2"
] | [
"skywork"
] | d06182f5bd22d95ff476c06c11f6de886d717fd550b041825dbfa8345f695260 | [
{
"content": "Given \\( AB \\) as the diameter of the smallest radius circle centered at \\( C(0,1) \\) that intersects the graph of \\( y = \\frac{1}{|x|-1} \\), where \\( O \\) is the origin. Find the value of \\( \\overrightarrow{OA} \\cdot \\overrightarrow{OB} \\).",
"role": "user"
}
] | Given \( AB \) as the diameter of the smallest radius circle centered at \( C(0,1) \) that intersects the graph of \( y = \frac{1}{|x|-1} \), where \( O \) is the origin. Find the value of \( \overrightarrow{OA} \cdot \overrightarrow{OB} \). | "[\"-2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2405, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:16389"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"40\\mathrm{~}"
] | [
"skywork"
] | 0714a8d290df37ee31977805a41811dfcaf3ea6cfcf9307ec46a7d8d436ee3ff | [
{
"content": "11. Usain runs twice as fast as his mum. His mum runs five times as fast as his pet tortoise, Turbo. They all set off together for a run down the same straight path. When Usain has run $100 \\mathrm{~m}$, how far apart are his mum and Turbo the tortoise?\nA $5 \\mathrm{~m}$\nB $10 \\mathrm{~m}$\nC... | 11. Usain runs twice as fast as his mum. His mum runs five times as fast as his pet tortoise, Turbo. They all set off together for a run down the same straight path. When Usain has run $100 \mathrm{~m}$, how far apart are his mum and Turbo the tortoise?
A $5 \mathrm{~m}$
B $10 \mathrm{~m}$
C $40 \mathrm{~m}$
D $50 \mat... | "[\"40\\\\mathrm{~}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2423, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:16390"}] | {
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} |
[
"1\\mathrm{~}\\times2\\mathrm{~}\\times21\\mathrm{~},1\\mathrm{~}\\times3\\mathrm{~}\\times14\\mathrm{~},1\\mathrm{~}\\times6\\mathrm{~}\\times7\\mathrm{~}"
] | [
"skywork"
] | 5b1715deeea401f216861aa4a54eecfe06ea19e22a519c1e57935141a38c5cd7 | [
{
"content": "Adam has two cuboids with volumes of $12 \\mathrm{~cm}^{3}$ and $30 \\mathrm{~cm}^{3}$, and the dimensions of each are expressed in centimeters as different whole numbers. Adam found that the cuboids can be glued together so that the glued faces coincide, resulting in a new cuboid.\n\nWhat dimensi... | Adam has two cuboids with volumes of $12 \mathrm{~cm}^{3}$ and $30 \mathrm{~cm}^{3}$, and the dimensions of each are expressed in centimeters as different whole numbers. Adam found that the cuboids can be glued together so that the glued faces coincide, resulting in a new cuboid.
What dimensions could the new cuboid h... | "[\"1\\\\mathrm{~}\\\\times2\\\\mathrm{~}\\\\times21\\\\mathrm{~},1\\\\mathrm{~}\\\\times3\\\\mathrm{~}\\\\times14\\\\mathrm{~},1\\\\mathrm{~}\\\\times6\\\\mathrm{~}\\\\times7\\\\mathrm{~}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2421, "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:16391"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 0eeb256c42bf20144569afcd6b164922af8283407138eae892c69dc344e48099 | [
{
"content": "## Task 2\n\nPetra estimates the length of the kindergarten garden to be $50 \\mathrm{~m}$. Ivo and Mario measure this distance. They lay out a measuring tape of $20 \\mathrm{~m}$ length twice and then measure another $12 \\mathrm{~m}$.\n\nBy how many meters did Petra overestimate?",
"role": "... | ## Task 2
Petra estimates the length of the kindergarten garden to be $50 \mathrm{~m}$. Ivo and Mario measure this distance. They lay out a measuring tape of $20 \mathrm{~m}$ length twice and then measure another $12 \mathrm{~m}$.
By how many meters did Petra overestimate? | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2444, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16392"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\dfrac{3}{8}"
] | [
"skywork"
] | e1b227fac87550bcaf10a40ae2185d50e5bf4c835fb2db96f8cd8a7348f88103 | [
{
"content": "In \\\\(\\triangle ABC\\\\), \\\\(AB=BC\\\\), \\\\(\\cos B=-\\dfrac{7}{18}\\\\). If an ellipse with foci at points \\\\(A\\\\) and \\\\(B\\\\) passes through point \\\\(C\\\\), find the eccentricity of the ellipse.",
"role": "user"
}
] | In \\(\triangle ABC\\), \\(AB=BC\\), \\(\cos B=-\dfrac{7}{18}\\). If an ellipse with foci at points \\(A\\) and \\(B\\) passes through point \\(C\\), find the eccentricity of the ellipse. | "[\"\\\\dfrac{3}{8}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2426, "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:16393"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 4f721e86776f60aa7b6ba40e024fb8e6b0cc0670841e51001d4a4751ecbbbd9b | [
{
"content": "2. To walk 2 km, ride 3 km on a bicycle, and drive 20 km by car, Uncle Vanya needs 1 hour 6 minutes. If he needs to walk 5 km, ride 8 km on a bicycle, and drive 30 km by car, it will take him 2 hours 24 minutes. How much time will Uncle Vanya need to walk 4 km, ride 5 km on a bicycle, and drive 80... | 2. To walk 2 km, ride 3 km on a bicycle, and drive 20 km by car, Uncle Vanya needs 1 hour 6 minutes. If he needs to walk 5 km, ride 8 km on a bicycle, and drive 30 km by car, it will take him 2 hours 24 minutes. How much time will Uncle Vanya need to walk 4 km, ride 5 km on a bicycle, and drive 80 km by car? | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2433, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16394"}] | {
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"reference_present": true
} |
[
"280"
] | [
"skywork"
] | 523039b0498be4bfcca2d4668b2df7ca80dac50fa294bc1b95b6f03dec78dc22 | [
{
"content": "Bradley is driving at a constant speed. When he passes his school, he notices that in $20$ minutes he will be exactly $\\frac14$ of the way to his destination, and in $45$ minutes he will be exactly $\\frac13$ of the way to his destination. Find the number of minutes it takes Bradley to reach his ... | Bradley is driving at a constant speed. When he passes his school, he notices that in $20$ minutes he will be exactly $\frac14$ of the way to his destination, and in $45$ minutes he will be exactly $\frac13$ of the way to his destination. Find the number of minutes it takes Bradley to reach his destination from the poi... | "[\"280\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2436, "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:16395"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-5"
] | [
"skywork"
] | 1705b8dbef143bff0880c7056eb460162136edca7b22b78eabe78ae5f8dcc728 | [
{
"content": "32. Given real numbers $a, b, x, y$ satisfy $a+b=x+y=2, a x+b y=5$, then $\\left(a^{2}+b^{2}\\right) x y+a b\\left(x^{2}+y^{2}\\right)=$ $\\qquad$",
"role": "user"
}
] | 32. Given real numbers $a, b, x, y$ satisfy $a+b=x+y=2, a x+b y=5$, then $\left(a^{2}+b^{2}\right) x y+a b\left(x^{2}+y^{2}\right)=$ $\qquad$ | "[\"-5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2435, "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:16396"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-5"
] | [
"skywork"
] | 0082a5476dcaaf8ab3fa41f303e457df108467144ea87359d41801be5fa2baf3 | [
{
"content": "2.1. Lisa wrote a quadratic equation. Artem erased its free term, so the equation now looks like $\\operatorname{\\operatorname {mak}} 2 x^{2}+20 x+\\ldots=0$. Lisa doesn't remember what number Artem erased, but she remembers that the equation has exactly one real root. What is this root?",
"r... | 2.1. Lisa wrote a quadratic equation. Artem erased its free term, so the equation now looks like $\operatorname{\operatorname {mak}} 2 x^{2}+20 x+\ldots=0$. Lisa doesn't remember what number Artem erased, but she remembers that the equation has exactly one real root. What is this root? | "[\"-5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2409, "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:16397"}] | {
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[
"2^{1998}"
] | [
"skywork"
] | e90e073ec53fe09c9c3b796e8ec026b465e96077446136e1f7d9aca5f26c2bc1 | [
{
"content": "Problem 8.3. Find the least positive integer $m$ such that $2^{2000}$ divides $2003^{m}-$ 1.\n\nIvan Tonov",
"role": "user"
}
] | Problem 8.3. Find the least positive integer $m$ such that $2^{2000}$ divides $2003^{m}-$ 1.
Ivan Tonov | "[\"2^{1998}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2440, "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:16398"}] | {
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[
"14400"
] | [
"skywork"
] | 0b6d2aa32b7581b65f7ff6024b511e01b790fc8965abe61efe2d62e8ab43cacd | [
{
"content": "If I have a $5\\times 5$ chess board, in how many ways can I place five distinct pawns on the board such that each column and row of the board contains no more than one pawn?",
"role": "user"
}
] | If I have a $5\times 5$ chess board, in how many ways can I place five distinct pawns on the board such that each column and row of the board contains no more than one pawn? | "[\"14400\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2448, "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:16399"}, {"dataset": "skywork", "extra_inf... | {
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[
"Joint density of \\(\\left(X_{(1)}, X_{(n)}\\right)\\), joint density of \\((R, V)\\), density of \\(R\\), and density of \\(V\\) as described in the solution."
] | [
"skywork"
] | 96e79f7d9edd98b71dea2226d0aee18ed7cb884a1bbb6020c9aa2a917e7d27a3 | [
{
"content": "Assume that \\(X_{1}, \\ldots, X_{n} \\sim U[0,1]\\) (uniform distribution) are i.i.d. Denote \\(X_{(1)}=\\min _{1 \\leq k \\leq n} X_{k}\\) and \\(X_{(n)}=\\max _{1 \\leq k \\leq n} X_{k}\\). Let \\(R=X_{(n)}-X_{(1)}\\) be the sample range and \\(V=\\left(X_{(1)}+X_{(n)}\\right) / 2\\) be the sam... | Assume that \(X_{1}, \ldots, X_{n} \sim U[0,1]\) (uniform distribution) are i.i.d. Denote \(X_{(1)}=\min _{1 \leq k \leq n} X_{k}\) and \(X_{(n)}=\max _{1 \leq k \leq n} X_{k}\). Let \(R=X_{(n)}-X_{(1)}\) be the sample range and \(V=\left(X_{(1)}+X_{(n)}\right) / 2\) be the sample midvalue. (1). Find the joint density ... | "[\"Joint density of \\\\(\\\\left(X_{(1)}, X_{(n)}\\\\right)\\\\), joint density of \\\\((R, V)\\\\), density of \\\\(R\\\\), and density of \\\\(V\\\\) as described in the solution.\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 2431, "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:16400"}] | {
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} |
[
"\\frac{9}{2}"
] | [
"skywork"
] | f807d66a15b87bf7707dcb9a4b6ddd5d4ade7a8a7eb91558c76947934cc7f9ca | [
{
"content": "For any positive real numbers $x_1,\\ x_2,\\ x_3,\\ y_1,\\ y_2,\\ y_3,\\ z_1,\\ z_2,\\ z_3,$ find the maximum value of real number $A$ such that if \\[ M = (x_1^3+x_2^3+x_3^3+1)(y_1^3+y_2^3+y_3^3+1)(z_1^3+z_2^3+z_3^3+1) \\] and \\[ N = A(x_1+y_1+z_1)(x_2+y_2+z_2)(x_3+y_3+z_3), \\] then $M \\geq ... | For any positive real numbers $x_1,\ x_2,\ x_3,\ y_1,\ y_2,\ y_3,\ z_1,\ z_2,\ z_3,$ find the maximum value of real number $A$ such that if \[ M = (x_1^3+x_2^3+x_3^3+1)(y_1^3+y_2^3+y_3^3+1)(z_1^3+z_2^3+z_3^3+1) \] and \[ N = A(x_1+y_1+z_1)(x_2+y_2+z_2)(x_3+y_3+z_3), \] then $M \geq N$ always holds, then find the cond... | "[\"\\\\frac{9}{2}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2432, "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:16401"}] | {
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[
"C"
] | [
"skywork"
] | aafdada1f1815a0c14eb1f1f55a31384b4870250757035760522c132190b5038 | [
{
"content": "If $x=\\frac{-1+i\\sqrt{3}}{2}$ and $y=\\frac{-1-i\\sqrt{3}}{2}$, where $i^2=-1$, then which of the following is not correct?\n$\\mathrm{(A)\\ } x^5+y^5=-1 \\qquad \\mathrm{(B) \\ }x^7+y^7=-1 \\qquad \\mathrm{(C) \\ } x^9+y^9=-1 \\qquad$\n$\\mathrm{(D) \\ } x^{11}+y^{11}=-1 \\qquad \\mathrm{(E) ... | If $x=\frac{-1+i\sqrt{3}}{2}$ and $y=\frac{-1-i\sqrt{3}}{2}$, where $i^2=-1$, then which of the following is not correct?
$\mathrm{(A)\ } x^5+y^5=-1 \qquad \mathrm{(B) \ }x^7+y^7=-1 \qquad \mathrm{(C) \ } x^9+y^9=-1 \qquad$
$\mathrm{(D) \ } x^{11}+y^{11}=-1 \qquad \mathrm{(E) \ }x^{13}+y^{13}=-1$ | "[\"C\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 2445, "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:16402"}] | {
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} |
[
"(160, 560, 960)"
] | [
"skywork"
] | 328944bafee0a0bab463e60950aab698eb2c5bace5bde3cbb2e16887164c0293 | [
{
"content": "Find all triples of three-digit positive integers $x < y < z$ with $x,y,z$ in arithmetic progression and $x, y, z + 1000$ in geometric progression.\n\n[i]For this problem, you may use calculators or computers to gain an intuition about how to solve the problem. However, your final submission shoul... | Find all triples of three-digit positive integers $x < y < z$ with $x,y,z$ in arithmetic progression and $x, y, z + 1000$ in geometric progression.
[i]For this problem, you may use calculators or computers to gain an intuition about how to solve the problem. However, your final submission should include mathematical d... | "[\"(160, 560, 960)\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2438, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16403"}] | {
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[
"\\frac{1}{2}"
] | [
"skywork"
] | ff4ef5937ae0917c71dc52fbd3478b77eb9dab2fcfa291a3a4bb162ebb4cc4e8 | [
{
"content": "Sally rolls an $8$-sided die with faces numbered $1$ through $8$. Compute the probability that she gets a power of $2$.",
"role": "user"
}
] | Sally rolls an $8$-sided die with faces numbered $1$ through $8$. Compute the probability that she gets a power of $2$. | "[\"\\\\frac{1}{2}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2467, "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:16404"}] | {
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[
"12"
] | [
"skywork"
] | 92587a758e2d313918be731eb57fd94ce1d59ce82afcaac9247e62327d7064ab | [
{
"content": "G6.3 If $n$ is a positive integer, $m^{2 n}=2$ and $c=2 m^{6 n}-4$, find the value of $c$.",
"role": "user"
}
] | G6.3 If $n$ is a positive integer, $m^{2 n}=2$ and $c=2 m^{6 n}-4$, find the value of $c$. | "[\"12\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2441, "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:16405"}] | {
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[
"\\frac{\\sqrt{15}+3}{2}"
] | [
"skywork"
] | d3a684186e940122f62cc38dfe2ac78b3951f74afbfa10918def1580f4c935c8 | [
{
"content": "4.4. Quadrilateral $K L M N$ with sides $M N=6, K L=2, L M=5$ is inscribed in a circle. Determine the distance between the midpoint of side $K N$ and the line $L M$, if the lines $K M$ and $L N$ are perpendicular. Round the answer to two decimal places if necessary.",
"role": "user"
}
] | 4.4. Quadrilateral $K L M N$ with sides $M N=6, K L=2, L M=5$ is inscribed in a circle. Determine the distance between the midpoint of side $K N$ and the line $L M$, if the lines $K M$ and $L N$ are perpendicular. Round the answer to two decimal places if necessary. | "[\"\\\\frac{\\\\sqrt{15}+3}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2447, "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:16406"}] | {
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[
"\\frac{5\\pi}{6}"
] | [
"skywork"
] | 84565319d557e4d252da9ad9ea88021032d9d4b4875a8448ef25493fe8b205fe | [
{
"content": "Given vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ that satisfy $|\\overrightarrow{a}| = 1$, $|\\overrightarrow{b}| = 2$, and $\\overrightarrow{a} \\cdot \\overrightarrow{b} = -\\sqrt{3}$, find the angle between $\\overrightarrow{a}$ and $\\overrightarrow{b}$.",
"role": "user"
}
] | Given vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ that satisfy $|\overrightarrow{a}| = 1$, $|\overrightarrow{b}| = 2$, and $\overrightarrow{a} \cdot \overrightarrow{b} = -\sqrt{3}$, find the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$. | "[\"\\\\frac{5\\\\pi}{6}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2466, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16407"}] | {
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} |
[
"307"
] | [
"skywork"
] | cf3d3cfefe813ca3e58021dc83de92495f1cf465f3db54d6188a4fb81c0f2006 | [
{
"content": "Square $ABCD$ has center $O$, $AB=900$, $E$ and $F$ are on $AB$ with $AE<BF$ and $E$ between $A$ and $F$, $m\\angle EOF =45^\\circ$, and $EF=400$. Given that $BF=p+q\\sqrt{r}$, wherer $p,q,$ and $r$ are positive integers and $r$ is not divisible by the square of any prime, find $p+q+r$.",
"rol... | Square $ABCD$ has center $O$, $AB=900$, $E$ and $F$ are on $AB$ with $AE<BF$ and $E$ between $A$ and $F$, $m\angle EOF =45^\circ$, and $EF=400$. Given that $BF=p+q\sqrt{r}$, wherer $p,q,$ and $r$ are positive integers and $r$ is not divisible by the square of any prime, find $p+q+r$. | "[\"307\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2439, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16408"}, {"dataset": "skywork", "extra_in... | {
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[
"16"
] | [
"skywork"
] | 2106f7b8949fee189f55e013f2a8f529a7e2e94bbb5f5ab9147bc587446128fd | [
{
"content": "In the permutation \\(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\\) of \\(1, 2, 3, 4, 5\\), how many permutations are there that satisfy \\(a_{1} < a_{2}, a_{2} > a_{3}, a_{3} < a_{4}, a_{4} > a_{5}\\)?",
"role": "user"
}
] | In the permutation \(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\) of \(1, 2, 3, 4, 5\), how many permutations are there that satisfy \(a_{1} < a_{2}, a_{2} > a_{3}, a_{3} < a_{4}, a_{4} > a_{5}\)? | "[\"16\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2460, "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:16409"}] | {
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[
"216"
] | [
"skywork"
] | d48e4e17794791c72cdcb01f96ec4b284f1187f3ad37fc23b049e264c021eb69 | [
{
"content": "Problem 11.4. Senya has three straight sticks, each 24 centimeters long. Senya broke one of them into two pieces so that he could form the outline of a right-angled triangle with the two pieces of this stick and the two whole sticks. How many square centimeters is the area of this triangle?",
... | Problem 11.4. Senya has three straight sticks, each 24 centimeters long. Senya broke one of them into two pieces so that he could form the outline of a right-angled triangle with the two pieces of this stick and the two whole sticks. How many square centimeters is the area of this triangle? | "[\"216\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2475, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16410"}] | {
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[
"0"
] | [
"skywork"
] | 9d86f7faebf6e70dd3ff4c0d20d319502e641b21353356d8a7173d7e02efaea5 | [
{
"content": "Real numbers $x,y,z$ are chosen such that $$\\frac{1}{|x^2+2yz|} ,\\frac{1}{|y^2+2zx|} ,\\frac{1}{|x^2+2xy|} $$ \nare lengths of a non-degenerate triangle .\nFind all possible values of $xy+yz+zx$ .\n\n[i]Proposed by Michael Rolínek[/i]",
"role": "user"
}
] | Real numbers $x,y,z$ are chosen such that $$\frac{1}{|x^2+2yz|} ,\frac{1}{|y^2+2zx|} ,\frac{1}{|x^2+2xy|} $$
are lengths of a non-degenerate triangle .
Find all possible values of $xy+yz+zx$ .
[i]Proposed by Michael Rolínek[/i] | "[\"0\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2461, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16411"}] | {
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[
"37/72"
] | [
"skywork"
] | ed9f6a1a153fc4fa7bfc6707ecf48f006ba09ebfe12fe444ae7dfcad105c5bd7 | [
{
"content": "\\(A, B, C, D\\) are consecutive vertices of a parallelogram. Points \\(E, F, P, H\\) lie on sides \\(AB\\), \\(BC\\), \\(CD\\), and \\(AD\\) respectively. Segment \\(AE\\) is \\(\\frac{1}{3}\\) of side \\(AB\\), segment \\(BF\\) is \\(\\frac{1}{3}\\) of side \\(BC\\), and points \\(P\\) and \\(H\... | \(A, B, C, D\) are consecutive vertices of a parallelogram. Points \(E, F, P, H\) lie on sides \(AB\), \(BC\), \(CD\), and \(AD\) respectively. Segment \(AE\) is \(\frac{1}{3}\) of side \(AB\), segment \(BF\) is \(\frac{1}{3}\) of side \(BC\), and points \(P\) and \(H\) bisect the sides they lie on. Find the ratio of t... | "[\"37/72\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2452, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16412"}] | {
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[
"216\\sqrt{3}\\approx374.12"
] | [
"skywork"
] | e9c6953f9faf18888acf0f62fc762111e5f3613a4bd976646bd627ae957bbceb | [
{
"content": "7.1. Find the volume of a regular triangular pyramid, the midpoint of the height of which is at a distance of 2 and $\\sqrt{12}$ from the lateral face and the lateral edge, respectively. Round your answer to two decimal places if necessary.",
"role": "user"
}
] | 7.1. Find the volume of a regular triangular pyramid, the midpoint of the height of which is at a distance of 2 and $\sqrt{12}$ from the lateral face and the lateral edge, respectively. Round your answer to two decimal places if necessary. | "[\"216\\\\sqrt{3}\\\\approx374.12\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2453, "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:16413"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"z<y<x"
] | [
"skywork"
] | 756266b47e0a1c2234ae8c428bbfc3a30d437c0df5f4d21827aa7c55fb05319e | [
{
"content": "1. Let $a>b>c>d>0$, and\n$$\n\\begin{array}{l}\nx=\\sqrt{a b}+\\sqrt{c d}, y=\\sqrt{a c}+\\sqrt{b d}, \\\\\nz=\\sqrt{a d}+\\sqrt{b c} .\n\\end{array}\n$$\n\nThen the size relationship of $x, y, z$ is ( ).\n(A) $x<z<y$\n(B) $y<z<x$\n(C) $x<y<z$\n(D) $z<y<x$",
"role": "user"
}
] | 1. Let $a>b>c>d>0$, and
$$
\begin{array}{l}
x=\sqrt{a b}+\sqrt{c d}, y=\sqrt{a c}+\sqrt{b d}, \\
z=\sqrt{a d}+\sqrt{b c} .
\end{array}
$$
Then the size relationship of $x, y, z$ is ( ).
(A) $x<z<y$
(B) $y<z<x$
(C) $x<y<z$
(D) $z<y<x$ | "[\"z<y<x\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2458, "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:16414"}] | {
"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
} |
[
"181"
] | [
"skywork"
] | 78ffc167506ef3583ef14ad32e47e2da154939bcfa0b92ac855bdbc6ddc3527b | [
{
"content": "4. 144 If $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$ satisfy the following system of equations\n$$\\left\\{\\begin{array}{l}\n2 x_{1}+x_{2}+x_{3}+x_{4}+x_{5}=6, \\\\\nx_{1}+2 x_{2}+x_{3}+x_{4}+x_{5}=12, \\\\\nx_{1}+x_{2}+2 x_{3}+x_{4}+x_{5}=24, \\\\\nx_{1}+x_{2}+x_{3}+2 x_{4}+x_{5}=48 \\\\\nx_{1}+x_{2}+x... | 4. 144 If $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$ satisfy the following system of equations
$$\left\{\begin{array}{l}
2 x_{1}+x_{2}+x_{3}+x_{4}+x_{5}=6, \\
x_{1}+2 x_{2}+x_{3}+x_{4}+x_{5}=12, \\
x_{1}+x_{2}+2 x_{3}+x_{4}+x_{5}=24, \\
x_{1}+x_{2}+x_{3}+2 x_{4}+x_{5}=48 \\
x_{1}+x_{2}+x_{3}+x_{4}+2 x_{5}=96 .
\end{array}\rig... | "[\"181\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 2465, "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:16415"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"400"
] | [
"skywork"
] | 2dd28be266684e67f90ce4c3fb7bdc12cadc27776993d8e10c8b1aad3b8344c0 | [
{
"content": "In a right-angled triangle \\(ABC\\) (with right angle at \\(A\\)), the bisectors of the acute angles intersect at point \\(P\\). The distance from \\(P\\) to the hypotenuse is \\(\\sqrt{80000}\\). What is the distance from \\(P\\) to \\(A\\)?",
"role": "user"
}
] | In a right-angled triangle \(ABC\) (with right angle at \(A\)), the bisectors of the acute angles intersect at point \(P\). The distance from \(P\) to the hypotenuse is \(\sqrt{80000}\). What is the distance from \(P\) to \(A\)? | "[\"400\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2462, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16416"}] | {
"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
} |
[
"-170"
] | [
"skywork"
] | da4b88b3803773f400fb1d9c0cdecffc128482d20978cddb13dbd0ad82eb134a | [
{
"content": "Given that the plane vectors $\\boldsymbol{\\alpha}$ and $\\boldsymbol{\\beta}$ satisfy $|\\boldsymbol{\\alpha} + 2\\boldsymbol{\\beta}| = 3$ and $|2\\boldsymbol{\\alpha} + 3\\boldsymbol{\\beta}| = 4$, find the minimum value of $\\boldsymbol{\\alpha} \\cdot \\boldsymbol{\\beta}$.",
"role": "us... | Given that the plane vectors $\boldsymbol{\alpha}$ and $\boldsymbol{\beta}$ satisfy $|\boldsymbol{\alpha} + 2\boldsymbol{\beta}| = 3$ and $|2\boldsymbol{\alpha} + 3\boldsymbol{\beta}| = 4$, find the minimum value of $\boldsymbol{\alpha} \cdot \boldsymbol{\beta}$. | "[\"-170\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2470, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16417"}] | {
"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
} |
[
"n+1"
] | [
"skywork"
] | 44b19d29071924ee53e203ee3018cbba191c761307ed7fd9febc45b8ba1d4d04 | [
{
"content": "Let $ n$ be an integer greater than $ 3.$ Points $ V_{1},V_{2},...,V_{n},$ with no three collinear, lie on a plane. Some of the segments $ V_{i}V_{j},$ with $ 1 \\le i < j \\le n,$ are constructed. Points $ V_{i}$ and $ V_{j}$ are [i]neighbors[/i] if $ V_{i}V_{j}$ is constructed. Initially, ches... | Let $ n$ be an integer greater than $ 3.$ Points $ V_{1},V_{2},...,V_{n},$ with no three collinear, lie on a plane. Some of the segments $ V_{i}V_{j},$ with $ 1 \le i < j \le n,$ are constructed. Points $ V_{i}$ and $ V_{j}$ are [i]neighbors[/i] if $ V_{i}V_{j}$ is constructed. Initially, chess pieces $ C_{1},C_{2},.... | "[\"n+1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2451, "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:16418"}] | {
"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\\pi}{8}"
] | [
"skywork"
] | 085d960d342e97c3153465c8853fc8580567549ff1203f876272501209df4b17 | [
{
"content": "Suppose that $f$ is a function from $\\mathbb{R}$ to $\\mathbb{R}$ such that \\[ f(x) + f\\left( 1 - \\frac{1}{x} \\right) = \\arctan x \\] for all real $x \\neq 0$. (As usual, $y = \\arctan x$ means $-\\pi/2 < y < \\pi/2$ and $\\tan y = x$.) Find \\[ \\int_0^1 f(x)\\,dx. \\]",
"role": "user"
... | Suppose that $f$ is a function from $\mathbb{R}$ to $\mathbb{R}$ such that \[ f(x) + f\left( 1 - \frac{1}{x} \right) = \arctan x \] for all real $x \neq 0$. (As usual, $y = \arctan x$ means $-\pi/2 < y < \pi/2$ and $\tan y = x$.) Find \[ \int_0^1 f(x)\,dx. \] | "[\"\\\\frac{3\\\\pi}{8}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2446, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16419"}] | {
"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
} |
[
"1/16"
] | [
"skywork"
] | 7a9a0ed8f356beaac20810315eafe7ad51077ed19b430f03a6a9e42b2ea64930 | [
{
"content": "A one-meter gas pipe has rusted through in two places. Determine the probability that all three resulting parts can be used as connectors to gas stoves, given that according to regulations, the stove must not be closer than 25 cm to the main gas pipe.",
"role": "user"
}
] | A one-meter gas pipe has rusted through in two places. Determine the probability that all three resulting parts can be used as connectors to gas stoves, given that according to regulations, the stove must not be closer than 25 cm to the main gas pipe. | "[\"1/16\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2442, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:16420"}] | {
"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
} |
[
"1914"
] | [
"skywork"
] | 1eccdf7ee823856262784f1b7f3a528f5121e1e5edd4deeeefc565ce91b191fd | [
{
"content": "Example 2.2.3 In the sequence $1,9,81, \\cdots, 9^{2005}$, delete the terms whose highest digit is 9. How many terms are left in the remaining sequence?",
"role": "user"
}
] | Example 2.2.3 In the sequence $1,9,81, \cdots, 9^{2005}$, delete the terms whose highest digit is 9. How many terms are left in the remaining sequence? | "[\"1914\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2457, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16421"}] | {
"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
} |
[
"112.5"
] | [
"skywork"
] | 686e73f2f3f28c1dc4e0d8dd774ec7fae94dff4895d4a15ad09f18b4e0d1ffeb | [
{
"content": "4. Point $M$ is the midpoint of the leg $A B$ of an isosceles right triangle $A B C$ with a right angle $\\angle B$. The bisector of angle $\\angle A$ intersects the circumcircle of the triangle at point $L$. Point $H$ is the foot of the perpendicular dropped from $L$ to the line $A C$. Find the a... | 4. Point $M$ is the midpoint of the leg $A B$ of an isosceles right triangle $A B C$ with a right angle $\angle B$. The bisector of angle $\angle A$ intersects the circumcircle of the triangle at point $L$. Point $H$ is the foot of the perpendicular dropped from $L$ to the line $A C$. Find the angle $\angle A M H$. | "[\"112.5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2450, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16422"}] | {
"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{2\\pi}{3}"
] | [
"skywork"
] | b8e7d4ac8921fd955fbdb123e1068f4262d011722ac487e2eb8dab1029cacf6a | [
{
"content": "B3. Let $\\operatorname{tg} \\alpha=\\frac{a+2 b}{a \\sqrt{3}}, \\operatorname{tg} \\beta=\\frac{b+2 a}{b \\sqrt{3}}, a>0, b>0, \\alpha, \\beta \\in\\left[0, \\frac{\\pi}{2}\\right]$. Determine $\\alpha+\\beta$.",
"role": "user"
}
] | B3. Let $\operatorname{tg} \alpha=\frac{a+2 b}{a \sqrt{3}}, \operatorname{tg} \beta=\frac{b+2 a}{b \sqrt{3}}, a>0, b>0, \alpha, \beta \in\left[0, \frac{\pi}{2}\right]$. Determine $\alpha+\beta$. | "[\"\\\\frac{2\\\\pi}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2476, "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:16423"}] | {
"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
} |
[
"198"
] | [
"skywork"
] | b250e41de0b94d8c70ce81db95fb90da00ac87ccba2cd20b8d4e167a06646fd3 | [
{
"content": "Find $c$ if $a$, $b$, and $c$ are positive integers which satisfy $c=(a + bi)^3 - 107i$, where $i^2 = -1$.",
"role": "user"
}
] | Find $c$ if $a$, $b$, and $c$ are positive integers which satisfy $c=(a + bi)^3 - 107i$, where $i^2 = -1$. | "[\"198\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2463, "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:16424"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"67"
] | [
"skywork"
] | 72b94bbae4dff69400b5b561aef9b45b03cf55a91ac8330e0660123962e110fd | [
{
"content": "The square $BCDE$ is inscribed in circle $\\omega$ with center $O$ . Point $A$ is the reflection of $O$ over $B$ . A \"hook\" is drawn consisting of segment $AB$ and the major arc $\\widehat{BE}$ of $\\omega$ (passing through $C$ and $D$ ). Assume $BCDE$ has area $200$ . To... | The square $BCDE$ is inscribed in circle $\omega$ with center $O$ . Point $A$ is the reflection of $O$ over $B$ . A "hook" is drawn consisting of segment $AB$ and the major arc $\widehat{BE}$ of $\omega$ (passing through $C$ and $D$ ). Assume $BCDE$ has area $200$ . To the nearest integer, what ... | "[\"67\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2443, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16425"}] | {
"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
} |
[
"768"
] | [
"skywork"
] | 3d1b61efcc2a9bb00a216a4439467bde3aee65c64be8af9dd14df3dfc8327bde | [
{
"content": "3. For each positive number, define the function $f(n)=\\left\\{\\begin{array}{l}0, \\text { when } n \\text { is a perfect square, } \\\\ {\\left[\\frac{1}{\\{\\sqrt{n}\\}}\\right], \\text { when } n \\text { is not a perfect square, }}\\end{array}\\right.$ where $[x]$ is the greatest integer not... | 3. For each positive number, define the function $f(n)=\left\{\begin{array}{l}0, \text { when } n \text { is a perfect square, } \\ {\left[\frac{1}{\{\sqrt{n}\}}\right], \text { when } n \text { is not a perfect square, }}\end{array}\right.$ where $[x]$ is the greatest integer not exceeding $x$, $\{x\}=x-[x]$, find the... | "[\"768\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2459, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16426"}] | {
"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
} |
[
"\\sqrt{399}"
] | [
"skywork"
] | b08321009eb133b29123694c16a5070fc60ed10d6757964ea838b73ba7460d17 | [
{
"content": "Suppose that the angles of triangle $ABC$ satisfy\n\\[\\cos 3A + \\cos 3B + \\cos 3C = 1.\\]Two sides of the triangle have lengths 10 and 13. Find the maximum length of the third side.",
"role": "user"
}
] | Suppose that the angles of triangle $ABC$ satisfy
\[\cos 3A + \cos 3B + \cos 3C = 1.\]Two sides of the triangle have lengths 10 and 13. Find the maximum length of the third side. | "[\"\\\\sqrt{399}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2464, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16427"}] | {
"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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