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 |
|---|---|---|---|---|---|---|---|---|
[
"13500"
] | [
"skywork"
] | cd4a18c86973208e6d80530cb99dbfe469bf57b1982e80cc60315bb83b818ec0 | [
{
"content": "Find the sum of all the digits in the decimal representations of all the positive integers less than $1000.$",
"role": "user"
}
] | Find the sum of all the digits in the decimal representations of all the positive integers less than $1000.$ | "[\"13500\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1846, "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:15810"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
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} |
[
"m = 1010"
] | [
"skywork"
] | e29462239690448ce7a640d091c0625df118a7b846b1f3829a327459f5a82acb | [
{
"content": "Define the product $P_n=1! \\cdot 2!\\cdot 3!\\cdots (n-1)!\\cdot n!$\na) Find all positive integers $m$, such that $\\frac {P_{2020}}{m!}$ is a perfect square.\nb) Prove that there are infinite many value(s) of $n$, such that $\\frac {P_{n}}{m!}$ is a perfect square, for at least two positive int... | Define the product $P_n=1! \cdot 2!\cdot 3!\cdots (n-1)!\cdot n!$
a) Find all positive integers $m$, such that $\frac {P_{2020}}{m!}$ is a perfect square.
b) Prove that there are infinite many value(s) of $n$, such that $\frac {P_{n}}{m!}$ is a perfect square, for at least two positive integers $m$. | "[\" m = 1010 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1803, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15811"}] | {
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} |
[
"(4,6)"
] | [
"skywork"
] | 7cef4e1c3d6e77f8dd9614d75719c5b2fb35397ec6dd6de8e116bdad28ecce5f | [
{
"content": "879. Solve the equation in natural numbers\n\n$$\nx!+12=y^{2}\n$$",
"role": "user"
}
] | 879. Solve the equation in natural numbers
$$
x!+12=y^{2}
$$ | "[\"(4,6)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1834, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:15812"}] | {
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} |
[
"(x, y) = (1003, 1)"
] | [
"skywork"
] | d8779e263288b83b25679714aed2a44321f6371ded9c9e9b74072e30018b4041 | [
{
"content": "Find all positive integers $x , y$ which are roots of the equation \r\n\r\n $2 x^y-y= 2005$\r\n[u] Babis[/u]",
"role": "user"
}
] | Find all positive integers $x , y$ which are roots of the equation
$2 x^y-y= 2005$
[u] Babis[/u] | "[\"(x, y) = (1003, 1)\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1840, "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:15813"}] | {
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[
"-1"
] | [
"skywork"
] | 8949b552993ee520c47b17cd644dc9e9c941589cdb584c7b78da503f4d43e617 | [
{
"content": "7. Let $F_{1}, F_{2}$ be the left and right foci of the ellipse $E: \\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1(a>b>0)$, respectively. A line passing through point $F_{1}$ intersects the ellipse $E$ at points $A$ and $B$, with $\\left|A F_{1}\\right|=3\\left|B F_{1}\\right|$ and $\\cos \\angle A F... | 7. Let $F_{1}, F_{2}$ be the left and right foci of the ellipse $E: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)$, respectively. A line passing through point $F_{1}$ intersects the ellipse $E$ at points $A$ and $B$, with $\left|A F_{1}\right|=3\left|B F_{1}\right|$ and $\cos \angle A F_{2} B=\frac{3}{5}$. The line ... | "[\"-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1802, "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:15814"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"1-\\frac{1}{2^{10}}"
] | [
"skywork"
] | 6c1e8d47b5eab54099721c1a9a3b64209e393d55a60988b606b0a9a59bc25fe7 | [
{
"content": "Khachaturyan M.A.\n\nThe length of an adult worm is 1 meter. If a worm is adult, it can be cut into two parts in any ratio of lengths. As a result, two new worms are obtained, which immediately start growing at a rate of 1 meter per hour each. When the length of a worm reaches a meter, it becomes ... | Khachaturyan M.A.
The length of an adult worm is 1 meter. If a worm is adult, it can be cut into two parts in any ratio of lengths. As a result, two new worms are obtained, which immediately start growing at a rate of 1 meter per hour each. When the length of a worm reaches a meter, it becomes an adult and stops growi... | "[\"1-\\\\frac{1}{2^{10}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1831, "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:15815"}] | {
"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
} |
[
"240"
] | [
"skywork"
] | bf81b6d8f560cebd317756db12bdda3733a7b015751b95e2df3e0c9894377423 | [
{
"content": "18. Bumblebee flew from Cybertron to Pandora, originally planning to travel at a speed of 600,000 kilometers per hour. However, during the journey, he encountered an electronic storm, and only half of the distance could be traveled at the planned speed, while the remaining distance was traveled at... | 18. Bumblebee flew from Cybertron to Pandora, originally planning to travel at a speed of 600,000 kilometers per hour. However, during the journey, he encountered an electronic storm, and only half of the distance could be traveled at the planned speed, while the remaining distance was traveled at a speed of 400,000 ki... | "[\"240\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1826, "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:15816"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"15"
] | [
"skywork"
] | 4232b53e6d3cd64e7d4f3700d746f19e434aef91acaa605b3256c8f46ad64879 | [
{
"content": "At the mountain cabin, our coach said: \"If we continue at this comfortable pace of $4 \\mathrm{~km}$ per hour, we will arrive at the station 45 minutes after our train has left.\"\n\nThen he pointed to a group that was just passing us: \"They are using poles, and thus achieve an average speed of ... | At the mountain cabin, our coach said: "If we continue at this comfortable pace of $4 \mathrm{~km}$ per hour, we will arrive at the station 45 minutes after our train has left."
Then he pointed to a group that was just passing us: "They are using poles, and thus achieve an average speed of $6 \mathrm{~km}$ per hour. T... | "[\"15\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1832, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:15817"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.1"
] | [
"skywork"
] | 3485e5e0b36e084b86d02e9fbc3b31b5f1c238367b8a00903aaf1250455914a9 | [
{
"content": "1. How many hours is 6 minutes?\nA 0.06\nB 0.1\nC 0.6\nD 10\nE 360",
"role": "user"
}
] | 1. How many hours is 6 minutes?
A 0.06
B 0.1
C 0.6
D 10
E 360 | "[\"0.1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1848, "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:15818"}] | {
"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{3}"
] | [
"skywork"
] | c33019898aa8b755261570862a7a04d9a01e0b5877aa02269d2b15ff50e3c9c4 | [
{
"content": "In $\\triangle ABC$, $\\angle A = 60^{\\circ}$ and $AB > AC$. Point $O$ is the circumcenter. The two altitudes $BE$ and $CF$ intersect at point $H$. Points $M$ and $N$ are on segments $BH$ and $HF$ respectively, and satisfy $BM = CN$. Find the value of $\\frac{MH + NH}{OH}$.",
"role": "user"
... | In $\triangle ABC$, $\angle A = 60^{\circ}$ and $AB > AC$. Point $O$ is the circumcenter. The two altitudes $BE$ and $CF$ intersect at point $H$. Points $M$ and $N$ are on segments $BH$ and $HF$ respectively, and satisfy $BM = CN$. Find the value of $\frac{MH + NH}{OH}$. | "[\"\\\\sqrt{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1824, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:15819"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{16}{7}"
] | [
"skywork"
] | 3bf35eaaf2c8b7cebea34e531d3f4406575ff1700cab0ca20704399a5314570a | [
{
"content": "In triangle $PQR$, let the side lengths be $PQ = 7,$ $PR = 8,$ and $QR = 5$. Calculate:\n\\[\\frac{\\cos \\frac{P - Q}{2}}{\\sin \\frac{R}{2}} - \\frac{\\sin \\frac{P - Q}{2}}{\\cos \\frac{R}{2}}.\\]",
"role": "user"
}
] | In triangle $PQR$, let the side lengths be $PQ = 7,$ $PR = 8,$ and $QR = 5$. Calculate:
\[\frac{\cos \frac{P - Q}{2}}{\sin \frac{R}{2}} - \frac{\sin \frac{P - Q}{2}}{\cos \frac{R}{2}}.\] | "[\"\\\\frac{16}{7}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1842, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15820"}] | {
"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
} |
[
"326"
] | [
"skywork"
] | 48588ecb5cfaed2759bbf208c50c876c477a25008b1519e1b5712e8ed691e217 | [
{
"content": "Suppose there are $160$ pigeons and $n$ holes. The $1$ st pigeon flies to the $1$ st hole, the $2$ nd pigeon flies to the $4$ th hole, and so on, such that the $i$ th pigeon flies to the $(i^2\\text{ mod }n)$ th hole, where $k\\text{ mod }n$ is the remainder when $k$ is divided by $... | Suppose there are $160$ pigeons and $n$ holes. The $1$ st pigeon flies to the $1$ st hole, the $2$ nd pigeon flies to the $4$ th hole, and so on, such that the $i$ th pigeon flies to the $(i^2\text{ mod }n)$ th hole, where $k\text{ mod }n$ is the remainder when $k$ is divided by $n$ . What is minimum $n... | "[\"326\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1835, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15821"}] | {
"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{\\pi}{4}"
] | [
"skywork"
] | d1916769fd56f1b8963e08692e095ffdfe8f5e2832242f1916ca573bec1f4265 | [
{
"content": "10. $[\\mathbf{8}]$ Compute\n$$\n\\int_{0}^{\\infty} \\frac{e^{-x} \\sin (x)}{x} d x\n$$",
"role": "user"
}
] | 10. $[\mathbf{8}]$ Compute
$$
\int_{0}^{\infty} \frac{e^{-x} \sin (x)}{x} d x
$$ | "[\"\\\\frac{\\\\pi}{4}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1852, "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:15822"}] | {
"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
} |
[
"2020"
] | [
"skywork"
] | e30e7fc773f49c438759eda93740a04922f43f95401bdf15573cc7a03b773f55 | [
{
"content": "For all non-negative integers \\( m \\) and \\( n \\) (with \\( m \\geq n \\)), the sequence \\( a_0, a_1, \\cdots \\) satisfies\n\\[ a_{m+n} + a_{m-n} + 2m - 2n - 1 = \\frac{1}{2}(a_{2m} + a_{2n}). \\]\n\nIf \\( a_1 = 0 \\) and \\( a_p = 2019^2 \\), find the value of \\( p \\).",
"role": "use... | For all non-negative integers \( m \) and \( n \) (with \( m \geq n \)), the sequence \( a_0, a_1, \cdots \) satisfies
\[ a_{m+n} + a_{m-n} + 2m - 2n - 1 = \frac{1}{2}(a_{2m} + a_{2n}). \]
If \( a_1 = 0 \) and \( a_p = 2019^2 \), find the value of \( p \). | "[\"2020\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1838, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15823"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"8 \\cdot 3^{499}"
] | [
"skywork"
] | fbda9004fd2eaa200742f08e18519ea85b1822a41fb170c145f231a9fefa8d27 | [
{
"content": "Let $ S$ be the set of natural numbers $ n$ satisfying the following conditions:\r\n\r\n$ (i)$ $ n$ has $ 1000$ digits,\r\n$ (ii)$ all the digits of $ n$ are odd, and\r\n$ (iii)$ any two adjacent digits of $ n$ differ by $ 2$.\r\n\r\nDetermine the number of elements of $ S$.",
"role": "user"
... | Let $ S$ be the set of natural numbers $ n$ satisfying the following conditions:
$ (i)$ $ n$ has $ 1000$ digits,
$ (ii)$ all the digits of $ n$ are odd, and
$ (iii)$ any two adjacent digits of $ n$ differ by $ 2$.
Determine the number of elements of $ S$. | "[\"8 \\\\cdot 3^{499}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1847, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15824"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"n"
] | [
"skywork"
] | 07669f48502c07d0d92a4599c607501b770c9c2e7d69db9ed269cc41be653570 | [
{
"content": "There are several candles of the same size on the Chapel of Bones. On the first day a candle is lit for a hour. On the second day two candles are lit for a hour, on the third day three candles are lit for a hour, and successively, until the last day, when all the candles are lit for a hour. On the... | There are several candles of the same size on the Chapel of Bones. On the first day a candle is lit for a hour. On the second day two candles are lit for a hour, on the third day three candles are lit for a hour, and successively, until the last day, when all the candles are lit for a hour. On the end of that day, all ... | "[\" n \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1841, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15825"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{13}{7}"
] | [
"skywork"
] | 11a8f2c44b5aa9882d2238eaeb15ca03ac0f438e37f0ae0d12e8dac736cb9852 | [
{
"content": "Let $m$ and $n$ satisfy $mn = 6$ and $m+n = 7$. Additionally, suppose $m^2 - n^2 = 13$. Find the value of $|m-n|$.",
"role": "user"
}
] | Let $m$ and $n$ satisfy $mn = 6$ and $m+n = 7$. Additionally, suppose $m^2 - n^2 = 13$. Find the value of $|m-n|$. | "[\"\\\\frac{13}{7}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1855, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15826"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"(0, 0)"
] | [
"skywork"
] | ef03aee6f0ccbe41bba7dc07538fa77c54c1a3d47fb15387443d38f68c527491 | [
{
"content": "Find the locus of the points $ M $ that are situated on the plane where a rhombus $ ABCD $ lies, and satisfy:\n$$ MA\\cdot MC+MB\\cdot MD=AB^2 $$\n\n\n[i]Ovidiu Pop[/i]",
"role": "user"
}
] | Find the locus of the points $ M $ that are situated on the plane where a rhombus $ ABCD $ lies, and satisfy:
$$ MA\cdot MC+MB\cdot MD=AB^2 $$
[i]Ovidiu Pop[/i] | "[\" (0, 0) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1843, "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:15827"}] | {
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[
"\\frac{1}{5}"
] | [
"skywork"
] | c4edae63394db714b21920915a30e0864e14b672cbdd756a844ab8d8cd87fc76 | [
{
"content": "If $f(x) = \\frac{1 + x}{1 - 3x}, f_1(x) = f(f(x)), f_2(x) = f(f_1(x)),$ and in general $f_n(x) = f(f_{n-1}(x)),$ then $f_{1993}(3)=$",
"role": "user"
}
] | If $f(x) = \frac{1 + x}{1 - 3x}, f_1(x) = f(f(x)), f_2(x) = f(f_1(x)),$ and in general $f_n(x) = f(f_{n-1}(x)),$ then $f_{1993}(3)=$ | "[\"\\\\frac{1}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1854, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15828"}] | {
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[
"\\frac{1}{3}"
] | [
"skywork"
] | 4a892500e5f1d969706c49bb9bea9452cf1ef571b0a32af269f88eb47945e720 | [
{
"content": "(9) Given the inequality $\\frac{x-5}{x+1}<0$ with the solution set $M$, if $x_{0} \\in M$, then the probability of $\\log _{2}\\left(x_{0}+\\right.$ 1) $<1$ is ( ).\n(A) $\\frac{1}{4}$\n(B) $\\frac{1}{3}$\n(C) $\\frac{1}{5}$\n(D) $\\frac{2}{5}$",
"role": "user"
}
] | (9) Given the inequality $\frac{x-5}{x+1}<0$ with the solution set $M$, if $x_{0} \in M$, then the probability of $\log _{2}\left(x_{0}+\right.$ 1) $<1$ is ( ).
(A) $\frac{1}{4}$
(B) $\frac{1}{3}$
(C) $\frac{1}{5}$
(D) $\frac{2}{5}$ | "[\"\\\\frac{1}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1836, "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:15829"}] | {
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[
"89"
] | [
"skywork"
] | 382f98c97446275d5b5e30ec97f0617d8f7be31305d7a34cbd1a037da42bb784 | [
{
"content": "Four whole numbers, when added three at a time, give the sums $180, 197, 208$ and $222$. What is the largest of the four numbers?",
"role": "user"
}
] | Four whole numbers, when added three at a time, give the sums $180, 197, 208$ and $222$. What is the largest of the four numbers? | "[\"89\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1872, "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:15830"}] | {
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} |
[
"\\frac{13}{9}"
] | [
"skywork"
] | 0cba232ddec22a0e30cf629a94db4ddf01bdf5b89daa692538e468eb60c51666 | [
{
"content": "Calculate the sum of $0.\\overline{6}$ and $0.\\overline{7}$ as a common fraction.",
"role": "user"
}
] | Calculate the sum of $0.\overline{6}$ and $0.\overline{7}$ as a common fraction. | "[\"\\\\frac{13}{9}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1878, "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:15831"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"150"
] | [
"skywork"
] | 058f8a84c34bcace2026e78ad1666f54fda35ad7cae6a2b98440b38f7437206b | [
{
"content": "A solid wooden rectangular prism measures $3 \\times 5 \\times 12$. The prism is cut in half by a vertical cut through four vertices, creating two congruent triangular-based prisms. What is the surface area of one of these triangular-based prisms?",
"role": "user"
}
] | A solid wooden rectangular prism measures $3 \times 5 \times 12$. The prism is cut in half by a vertical cut through four vertices, creating two congruent triangular-based prisms. What is the surface area of one of these triangular-based prisms? | "[\"150\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1876, "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:15832"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"30"
] | [
"skywork"
] | 1f3aa09504bcab5a168719ae660fd20c1338a57bda5f170f902aebff026a86a5 | [
{
"content": "A necklace is strung with gems in the order of A, B, C, D, E, F, G, H. Now, we want to select 8 gems from it in two rounds, with the requirement that only 4 gems can be taken each time, and at most two adjacent gems can be taken (such as A, B, E, F). How many ways are there to do this (answer with... | A necklace is strung with gems in the order of A, B, C, D, E, F, G, H. Now, we want to select 8 gems from it in two rounds, with the requirement that only 4 gems can be taken each time, and at most two adjacent gems can be taken (such as A, B, E, F). How many ways are there to do this (answer with a number)? | "[\"30\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1845, "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:15834"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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[
"m-1"
] | [
"skywork"
] | 82f95f341dfe844f78e124587eb40e4c32b99542fdd9c546bd92d7b995a76ecc | [
{
"content": "Let $m$ be a positive integer. Find the number of real solutions of the equation\n$$|\\sum_{k=0}^{m} \\binom{2m}{2k}x^k|=|x-1|^m$$",
"role": "user"
}
] | Let $m$ be a positive integer. Find the number of real solutions of the equation
$$|\sum_{k=0}^{m} \binom{2m}{2k}x^k|=|x-1|^m$$ | "[\" m-1 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1860, "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:15835"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"665"
] | [
"skywork"
] | fe56d170aed02512f4d7ebcb6cfe6971d3dc546297edb3e010e1d1e5b1cb6aaa | [
{
"content": "The Fibonacci sequence is defined $F_1 = F_2 = 1$ and $F_n = F_{n - 1} + F_{n - 2}$ for all $n \\ge 3.$\n\nThe Fibonacci numbers $F_a,$ $F_b,$ $F_c$ form an increasing arithmetic sequence. If $a + b + c = 2000,$ compute $a.$",
"role": "user"
}
] | The Fibonacci sequence is defined $F_1 = F_2 = 1$ and $F_n = F_{n - 1} + F_{n - 2}$ for all $n \ge 3.$
The Fibonacci numbers $F_a,$ $F_b,$ $F_c$ form an increasing arithmetic sequence. If $a + b + c = 2000,$ compute $a.$ | "[\"665\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1851, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:15836"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"skywork"
] | e5dc9f6cd4332ceb939c1f17b69490bba553b03c3e99c0400b6b80f59cd68216 | [
{
"content": "Although I am certain that my watch is 5 minutes fast, it is actually 10 minutes slow. On the other hand, my friend's watch is actually 5 minutes fast, although he thinks it is correct. We made a plan to meet at 10 o'clock and intend to arrive punctually. Who will arrive first? How long after will... | Although I am certain that my watch is 5 minutes fast, it is actually 10 minutes slow. On the other hand, my friend's watch is actually 5 minutes fast, although he thinks it is correct. We made a plan to meet at 10 o'clock and intend to arrive punctually. Who will arrive first? How long after will the other arrive? | "[\"20\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1863, "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:15837"}] | {
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[
"\\$3.54"
] | [
"skywork"
] | c52bb559f2b3bbd85fb52014a08ba6a25ae1d3610327627dee5456a86dcaa814 | [
{
"content": "Ramon sells two enchiladas and three tacos for $\\$$2.50 and he sells three enchiladas and two tacos for $\\$$2.70. Assuming a fixed price per item, what is the cost, in dollars, of three enchiladas and four tacos? Express your answer as a decimal to the nearest hundredth.",
"role": "user"
}... | Ramon sells two enchiladas and three tacos for $\$$2.50 and he sells three enchiladas and two tacos for $\$$2.70. Assuming a fixed price per item, what is the cost, in dollars, of three enchiladas and four tacos? Express your answer as a decimal to the nearest hundredth. | "[\"\\\\$3.54\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1875, "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:15838"}] | {
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"reference_components": 1,
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} |
[
"-1"
] | [
"skywork"
] | 927e4b8a6c532593f352a9e4c5471110b9c07065c3ace8b46b78cb286681230e | [
{
"content": "11. In the following expression each $\\square$ is to be replaced with either + or - in such a way that the result of the calculation is 100 .\n123\n45\n67\n89\n\nThe number of + signs used is $p$ and the number of - signs used is $m$. What is the value of $p-m$ ?\nA -3\nB $\\quad-1$\nC 0\nD 1\nE ... | 11. In the following expression each $\square$ is to be replaced with either + or - in such a way that the result of the calculation is 100 .
123
45
67
89
The number of + signs used is $p$ and the number of - signs used is $m$. What is the value of $p-m$ ?
A -3
B $\quad-1$
C 0
D 1
E 3 | "[\"-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1857, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15839"}] | {
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[
"120"
] | [
"skywork"
] | cbea4f498f3373abb09cecf1a9be098e18ed00635a999fe84c45b05f82fe0179 | [
{
"content": "The cheetah takes strides of 2 meters each and the fox takes strides of 1 meter each. The time it takes for the cheetah to run 2 strides is the same as the time it takes for the fox to run 3 strides. Given that the distance between the cheetah and the fox is 30 meters, find the distance the cheeta... | The cheetah takes strides of 2 meters each and the fox takes strides of 1 meter each. The time it takes for the cheetah to run 2 strides is the same as the time it takes for the fox to run 3 strides. Given that the distance between the cheetah and the fox is 30 meters, find the distance the cheetah must run to catch up... | "[\"120\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1849, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15840"}] | {
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[
"100"
] | [
"skywork"
] | 10a22bc1fc31161ca8b3ae2da84c7b7aa441626baa7097258559a9f16596fee3 | [
{
"content": "Example 7 Given $a+b+c=1$,\n$$\n\\frac{1}{a+1}+\\frac{1}{b+3}+\\frac{1}{c+5}=0 \\text {. }\n$$\n\nFind the value of $(a+1)^{2}+(b+3)^{2}+(c+5)^{2}$.",
"role": "user"
}
] | Example 7 Given $a+b+c=1$,
$$
\frac{1}{a+1}+\frac{1}{b+3}+\frac{1}{c+5}=0 \text {. }
$$
Find the value of $(a+1)^{2}+(b+3)^{2}+(c+5)^{2}$. | "[\"100\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1862, "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:15841"}] | {
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[
"142857"
] | [
"skywork"
] | 69472524480735c70a7b36c6a786cb128bd7d60bf7078edef9fd9008ce2e109d | [
{
"content": "Given the positive integer \\( A = \\overline{a_{n} a_{n-1} \\cdots a_{1} a_{0}} \\), where \\( a_{n}, a_{n-1}, \\ldots, a_{0} \\) are all non-zero and not all equal (with \\( n \\) being a positive integer), consider the following cyclic permutations of \\( A \\):\n$$\n\\begin{array}{l}\nA_{1}=\\... | Given the positive integer \( A = \overline{a_{n} a_{n-1} \cdots a_{1} a_{0}} \), where \( a_{n}, a_{n-1}, \ldots, a_{0} \) are all non-zero and not all equal (with \( n \) being a positive integer), consider the following cyclic permutations of \( A \):
$$
\begin{array}{l}
A_{1}=\overline{a_{n-1} \cdots a_{1} a_{0} a_... | "[\"142857\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1856, "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:15842"}] | {
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[
"\\frac{216 \\pi^{3}-2187 \\sqrt{3}}{8 \\pi^{2}}"
] | [
"skywork"
] | 7753669964e598e53894a4a174269b852ba76fd38993780dbe40b8693100cf47 | [
{
"content": "A wealthy king has his blacksmith fashion him a large cup, whose inside is a cone of height 9 inches and base diameter 6 inches. At one of his many feasts, he orders the mug to be filled to the brim with cranberry juice. For each positive integer $n$, the king stirs his drink vigorously and takes ... | A wealthy king has his blacksmith fashion him a large cup, whose inside is a cone of height 9 inches and base diameter 6 inches. At one of his many feasts, he orders the mug to be filled to the brim with cranberry juice. For each positive integer $n$, the king stirs his drink vigorously and takes a sip such that the he... | "[\"\\\\frac{216 \\\\pi^{3}-2187 \\\\sqrt{3}}{8 \\\\pi^{2}}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1839, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15843"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"\\dfrac{\\pi}{12}"
] | [
"skywork"
] | 3983cc4521689e530ed9b7d3e4ff9d341fdf1dd9fa61724362cc4d7b02de4aab | [
{
"content": "Given the graph of $y=\\sqrt{2}\\sin 3x$, calculate the horizontal shift required to obtain the graph of $y=\\sin 3x+\\cos 3x$.",
"role": "user"
}
] | Given the graph of $y=\sqrt{2}\sin 3x$, calculate the horizontal shift required to obtain the graph of $y=\sin 3x+\cos 3x$. | "[\"\\\\dfrac{\\\\pi}{12}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1853, "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:15844"}] | {
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} |
[
"There does not exist a real $3 \\times 3$ matrix $A$ such that $\\operatorname{tr}(A) = 0$ and $A^2 + A^t = I$."
] | [
"skywork"
] | d2f55f909f4fcc235a4efdc9758b587e2a7ec0da2b3631d645eac4dab9acc1e1 | [
{
"content": "Does there exist a real $3 \\times 3$ matrix $A$ such that \\operatorname{tr}(\\mathrm{A})=0$ and $A^{2}+A^{t}=I$ ? (tr $(\\mathrm{A})$ denotes the trace of $A$, $A^{t}$ is the transpose of $A$, and $I$ is the identity matrix.)",
"role": "user"
}
] | Does there exist a real $3 \times 3$ matrix $A$ such that \operatorname{tr}(\mathrm{A})=0$ and $A^{2}+A^{t}=I$ ? (tr $(\mathrm{A})$ denotes the trace of $A$, $A^{t}$ is the transpose of $A$, and $I$ is the identity matrix.) | "[\"There does not exist a real $3 \\\\times 3$ matrix $A$ such that $\\\\operatorname{tr}(A) = 0$ and $A^2 + A^t = I$.\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 1868, "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:15845"}] | {
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} |
[
"n"
] | [
"skywork"
] | bbf9a16e39846a074a977e0a54cbf671e3edffeea2c93e7831116b6318b2bdd6 | [
{
"content": "Let $P$ be a set of $n\\ge 3$ points in the plane, no three of which are on a line. How many possibilities are there to choose a set $T$ of $\\binom{n-1}{2}$ triangles, whose vertices are all in $P$, such that each triangle in $T$ has a side that is not a side of any other triangle in $T$?",
"... | Let $P$ be a set of $n\ge 3$ points in the plane, no three of which are on a line. How many possibilities are there to choose a set $T$ of $\binom{n-1}{2}$ triangles, whose vertices are all in $P$, such that each triangle in $T$ has a side that is not a side of any other triangle in $T$? | "[\" n \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1864, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15846"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"19"
] | [
"skywork"
] | 9d64f21f0c580d505723b46c2dd61520c639272f3d7b2719ed5685d1434b013b | [
{
"content": "A particle is located on the coordinate plane at $(5,0)$ . Define a move for the particle as a counterclockwise rotation of $\\pi/4$ radians about the origin followed by a translation of $10$ units in the positive $x$ -direction. Given that the particle's position after $150$ moves is $(p,q)$ , fi... | A particle is located on the coordinate plane at $(5,0)$ . Define a move for the particle as a counterclockwise rotation of $\pi/4$ radians about the origin followed by a translation of $10$ units in the positive $x$ -direction. Given that the particle's position after $150$ moves is $(p,q)$ , find the greatest integer... | "[\"19\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 1870, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15847"}, {"dataset": "skywork", "extra_in... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{9}{8} \\cdot \\sqrt[4]{3}"
] | [
"skywork"
] | 22a523631b6aa329d73c08673e838660822d1a9205705706ca3929ab0beec945 | [
{
"content": "1. $x, y, z$ are positive real numbers, and satisfy $x^{4}+y^{4}+z^{4}=1$, find the minimum value of $\\frac{x^{3}}{1-x^{8}}+\\frac{y^{3}}{1-y^{8}}+\\frac{z^{3}}{1-z^{8}}$. (1999 Jiangsu Province Mathematical Winter Camp Problem)",
"role": "user"
}
] | 1. $x, y, z$ are positive real numbers, and satisfy $x^{4}+y^{4}+z^{4}=1$, find the minimum value of $\frac{x^{3}}{1-x^{8}}+\frac{y^{3}}{1-y^{8}}+\frac{z^{3}}{1-z^{8}}$. (1999 Jiangsu Province Mathematical Winter Camp Problem) | "[\"\\\\frac{9}{8} \\\\cdot \\\\sqrt[4]{3}\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 1869, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15848"}] | {
"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
} |
[
"102"
] | [
"skywork"
] | a6d5c2a2e14cec909bb6d3734e77ee6781dc93a985b3071a7ef3f7932dae297e | [
{
"content": "Inside a convex $n$-gon there are 100 points positioned in such a way that no three of these $n+100$ points are collinear. The polygon is divided into triangles, each having vertices among any 3 of the $n+100$ points. For what maximum value of $n$ can no more than 300 triangles be formed?",
"r... | Inside a convex $n$-gon there are 100 points positioned in such a way that no three of these $n+100$ points are collinear. The polygon is divided into triangles, each having vertices among any 3 of the $n+100$ points. For what maximum value of $n$ can no more than 300 triangles be formed? | "[\"102\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1865, "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:15849"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\exp(A+B) \\ne \\exp(A)\\exp(B)"
] | [
"skywork"
] | eab6b526fb942f10c8d1b3f6f4d6af3c778bd426bed61a91e58da9c16f761831 | [
{
"content": "For an arbitrary square matrix $M$, define\n$$\\exp(M)=I+\\frac M{1!}+\\frac{M^2}{2!}+\\frac{M^3}{3!}+\\ldots.$$Construct $2\\times2$ matrices $A$ and $B$ such that $\\exp(A+B)\\ne\\exp(A)\\exp(B)$.",
"role": "user"
}
] | For an arbitrary square matrix $M$, define
$$\exp(M)=I+\frac M{1!}+\frac{M^2}{2!}+\frac{M^3}{3!}+\ldots.$$Construct $2\times2$ matrices $A$ and $B$ such that $\exp(A+B)\ne\exp(A)\exp(B)$. | "[\" \\\\exp(A+B) \\\\ne \\\\exp(A)\\\\exp(B) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1867, "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:15850"}] | {
"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"
] | 5eda9bc375772e8c690786fba1e8a9db09c54f1ff2b036c4f7f3016f94e3407e | [
{
"content": "5. Through the vertex $D$ of the tetrahedron $ABCD$, construct a sphere with radius 1. This sphere is tangent to the circumsphere of the tetrahedron $ABCD$ at point $D$, and is also tangent to the plane $ABC$. If $AD=2\\sqrt{3}$, $\\angle BAC=60^{\\circ}$, $\\angle BAD=\\angle CAD=45^{\\circ}$, th... | 5. Through the vertex $D$ of the tetrahedron $ABCD$, construct a sphere with radius 1. This sphere is tangent to the circumsphere of the tetrahedron $ABCD$ at point $D$, and is also tangent to the plane $ABC$. If $AD=2\sqrt{3}$, $\angle BAC=60^{\circ}$, $\angle BAD=\angle CAD=45^{\circ}$, then the radius of the circums... | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1859, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:15851"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | ade3726e117ab1d1debe7ed83fd86e86c81baaee5c6109cf064709f2665e8f6d | [
{
"content": "14.47 The sequence $\\left\\{x_{n}\\right\\}$ satisfies $x_{1}=\\frac{1}{2}, x_{k+1}=x_{k}^{2}+x_{k}, k \\in N$. Find the integer part of the sum $\\frac{1}{x_{1}+1}+\\frac{1}{x_{2}+1}+\\cdots+\\frac{1}{x_{100}+1}$.\n(China National Training Team Problem, 1990)",
"role": "user"
}
] | 14.47 The sequence $\left\{x_{n}\right\}$ satisfies $x_{1}=\frac{1}{2}, x_{k+1}=x_{k}^{2}+x_{k}, k \in N$. Find the integer part of the sum $\frac{1}{x_{1}+1}+\frac{1}{x_{2}+1}+\cdots+\frac{1}{x_{100}+1}$.
(China National Training Team Problem, 1990) | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1871, "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:15852"}] | {
"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
} |
[
"8"
] | [
"skywork"
] | 51d4afd42007f0056665120fddc74692e5635d9a628e53f2d53512cf91dffe02 | [
{
"content": "1. Let the geometric sequence $z_{1}, z_{2}, \\cdots, z_{n}, \\cdots$ be such that $z_{1}=$ $1, z_{2}=a+b \\mathrm{i}, z_{3}=b \\mathrm{i}(a, b \\in \\mathbf{R}, ab>0)$. Then the smallest natural number $n$ for which $z_{1} z_{2} \\cdots z_{n}<0$ is $\\qquad$ .",
"role": "user"
}
] | 1. Let the geometric sequence $z_{1}, z_{2}, \cdots, z_{n}, \cdots$ be such that $z_{1}=$ $1, z_{2}=a+b \mathrm{i}, z_{3}=b \mathrm{i}(a, b \in \mathbf{R}, ab>0)$. Then the smallest natural number $n$ for which $z_{1} z_{2} \cdots z_{n}<0$ is $\qquad$ . | "[\"8\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1858, "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:15853"}] | {
"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}{126}"
] | [
"skywork"
] | f1d70b292c6603d43fc61b916bae3e89f525a21f5f057f27e39f8332ad6a074c | [
{
"content": "In the game of Rock Paper Scissors, typically two opponents make, with their hand, either a rock, a piece of paper, or a pair of scissors. If the two players play rock and scissors, the one who plays rock wins. If they play scissors and paper, the one who plays scissors wins, and if they play pape... | In the game of Rock Paper Scissors, typically two opponents make, with their hand, either a rock, a piece of paper, or a pair of scissors. If the two players play rock and scissors, the one who plays rock wins. If they play scissors and paper, the one who plays scissors wins, and if they play paper and rock, the one wh... | "[\"\\\\frac{1}{126}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1844, "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:15854"}] | {
"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
} |
[
"8.8"
] | [
"skywork"
] | 543f77b21a4815b9e184a5f49f5abe6be2ab253b3ab6f2c3f9f2097f52efa152 | [
{
"content": "Find all values of $b$ such that $b+\\lceil b\\rceil=17.8$.",
"role": "user"
}
] | Find all values of $b$ such that $b+\lceil b\rceil=17.8$. | "[\"8.8\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1890, "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:15855"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"(0,\\frac{25}{8}]"
] | [
"skywork"
] | 2a0f60575e240841887dd76946b10ec2801c19678512d1164629ac6930634da9 | [
{
"content": "11. (13 points) In $\\triangle A B C$, the sides $a, b, c$ opposite to $\\angle A, \\angle B, \\angle C$ form a geometric sequence,\n$$\n2 \\cos (A-C)-2 \\cos B=1 \\text {, }\n$$\n\nExtend $B C$ to point $D$ such that $B D=5$. Find:\n(1) The size of $\\angle B$;\n(2) The range of $\\overrightarrow... | 11. (13 points) In $\triangle A B C$, the sides $a, b, c$ opposite to $\angle A, \angle B, \angle C$ form a geometric sequence,
$$
2 \cos (A-C)-2 \cos B=1 \text {, }
$$
Extend $B C$ to point $D$ such that $B D=5$. Find:
(1) The size of $\angle B$;
(2) The range of $\overrightarrow{A C} \cdot \overrightarrow{C D}$.
保留... | "[\"(0,\\\\frac{25}{8}]\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1861, "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:15856"}] | {
"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
} |
[
"x^{2}z^{2}=9y^{2}"
] | [
"skywork"
] | 72fef82e45f2f14d584f9fc115907d4c78c8e39783ed2523bee864199132ff69 | [
{
"content": "If $\\frac{x}{y}=\\frac{3}{z}$, then $9 y^{2}$ is equal to:\n(a) $\\frac{x^{2}}{9}$\n(b) $x^{3} z$\n(c) $3 x^{2}$\n(d) $x^{2} z^{2}$\n(e) $\\frac{1}{9} x^{2} z^{2}$",
"role": "user"
}
] | If $\frac{x}{y}=\frac{3}{z}$, then $9 y^{2}$ is equal to:
(a) $\frac{x^{2}}{9}$
(b) $x^{3} z$
(c) $3 x^{2}$
(d) $x^{2} z^{2}$
(e) $\frac{1}{9} x^{2} z^{2}$ | "[\"x^{2}z^{2}=9y^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1885, "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:15857"}] | {
"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
} |
[
"6043"
] | [
"skywork"
] | c6e48670e554cb77a2bb1ab24e45927a07cade0f082b791b60b80002ca51dd79 | [
{
"content": "1. Calculate: $2015 \\times 2015-2014 \\times 2013=(\\quad)$.",
"role": "user"
}
] | 1. Calculate: $2015 \times 2015-2014 \times 2013=(\quad)$. | "[\"6043\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1901, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:15858"}] | {
"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
} |
[
"12"
] | [
"skywork"
] | 42544ed19f86a264c3e4e88d426f11b630753f2c2e47d2a2e1368073a35bb150 | [
{
"content": "3. Werner wants to write a number at each vertex and on each edge of the rhombus shown. He wants the sum of the numbers at the two vertices at the ends of each edge to be equal to the number written on that edge. What number should he write on the edge marked with the question mark?\nA 11\nB 12\nC... | 3. Werner wants to write a number at each vertex and on each edge of the rhombus shown. He wants the sum of the numbers at the two vertices at the ends of each edge to be equal to the number written on that edge. What number should he write on the edge marked with the question mark?
A 11
B 12
C 13
D 14
E 15 | "[\"12\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1866, "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:15859"}] | {
"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
} |
[
"2"
] | [
"skywork"
] | be8ecf9c92f4905a083e99cd3d5494b8f6329527fcaa38b2007698f681957416 | [
{
"content": "Example 7 (Question from the 12th \"Hope Cup\" Invitational Competition) The solution set of the equation $\\log _{5}\\left(3^{x}+4^{x}\\right)=\\log _{4}\\left(5^{x}-3^{x}\\right)$ is",
"role": "user"
}
] | Example 7 (Question from the 12th "Hope Cup" Invitational Competition) The solution set of the equation $\log _{5}\left(3^{x}+4^{x}\right)=\log _{4}\left(5^{x}-3^{x}\right)$ is | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1886, "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:15860"}] | {
"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
} |
[
"35"
] | [
"skywork"
] | cac104ecdd09e22275e0ba2c3d7c1eddeb6a7ef04e3f69e47066e00b58b1f1f0 | [
{
"content": "Volume $A$ equals one fourth of the sum of the volumes $B$ and $C$, while volume $B$ equals one sixth of the sum of the volumes $A$ and $C$. There are relatively prime positive integers $m$ and $n$ so that the ratio of volume $C$ to the sum of the other two volumes is $\\frac{m}{n}$. Find $m+n$.",... | Volume $A$ equals one fourth of the sum of the volumes $B$ and $C$, while volume $B$ equals one sixth of the sum of the volumes $A$ and $C$. There are relatively prime positive integers $m$ and $n$ so that the ratio of volume $C$ to the sum of the other two volumes is $\frac{m}{n}$. Find $m+n$. | "[\"35\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1873, "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:15861"}] | {
"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
} |
[
"50"
] | [
"skywork"
] | b36287d5a8e4381dabe017c156b0b5b689072f24105bb88cbe43d45f91f56ee9 | [
{
"content": "Problem 7.4. (15 points) On an island, there live knights who always tell the truth, and liars who always lie. One day, 100 residents of this island lined up, and each of them said one of the following phrases:\n\n- \"To the left of me, there are as many liars as there are knights.\"\n- \"To the l... | Problem 7.4. (15 points) On an island, there live knights who always tell the truth, and liars who always lie. One day, 100 residents of this island lined up, and each of them said one of the following phrases:
- "To the left of me, there are as many liars as there are knights."
- "To the left of me, there are 1 more ... | "[\"50\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1881, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15862"}] | {
"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
} |
[
"11"
] | [
"skywork"
] | ab47734da9d3ad964f97619396dfb61dd26c929d617dbaa055eb066841ee4301 | [
{
"content": "Let $M$ be a set consisting of $n$ points in the plane, satisfying:\ni) there exist $7$ points in $M$ which constitute the vertices of a convex heptagon; \nii) if for any $5$ points in $M$ which constitute the vertices of a convex pentagon, then there is a point in $M$ which lies in the interior o... | Let $M$ be a set consisting of $n$ points in the plane, satisfying:
i) there exist $7$ points in $M$ which constitute the vertices of a convex heptagon;
ii) if for any $5$ points in $M$ which constitute the vertices of a convex pentagon, then there is a point in $M$ which lies in the interior of the pentagon.
Find the... | "[\"11\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1879, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:15863"}] | {
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} |
[
"9"
] | [
"skywork"
] | a9dd0d802fcac8c7bf351b14e13181ca1e4f86053e3a5a3bae382cd15368acb1 | [
{
"content": "Example 2 Let $A$ be a subset of the set of positive integers $\\mathbf{N}^{*}$. For any $x, y \\in A, x \\neq y$, we have $\\mid x- y \\left\\lvert\\, \\geqslant \\frac{x y}{25}\\right.$. Find the maximum value of $|A|$. (26th IMO Shortlist)",
"role": "user"
}
] | Example 2 Let $A$ be a subset of the set of positive integers $\mathbf{N}^{*}$. For any $x, y \in A, x \neq y$, we have $\mid x- y \left\lvert\, \geqslant \frac{x y}{25}\right.$. Find the maximum value of $|A|$. (26th IMO Shortlist) | "[\"9\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 1888, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15864"}] | {
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[
"11"
] | [
"skywork"
] | cc2a0796d58d007eefd435519ed878e0c34194888e0b3c3aecba9195fa71f50e | [
{
"content": "For all positive integers $n$ , let $f(n)$ return the smallest positive integer $k$ for which $\\tfrac{n}{k}$ is not an integer. For example, $f(6) = 4$ because $1$ , $2$ , and $3$ all divide $6$ but $4$ does not. Determine the largest possible value of $f(n)$ as $n$ ranges ... | For all positive integers $n$ , let $f(n)$ return the smallest positive integer $k$ for which $\tfrac{n}{k}$ is not an integer. For example, $f(6) = 4$ because $1$ , $2$ , and $3$ all divide $6$ but $4$ does not. Determine the largest possible value of $f(n)$ as $n$ ranges over the set $\{1,2,\l... | "[\"11\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1899, "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:15865"}, {"dataset": "skywork", "extra_inf... | {
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} |
[
"\\[\n\\boxed{\\text{prime } n}\n\\]"
] | [
"skywork"
] | a340496ef6ca296c4f0491802c09a198a18b0738b6d949538057a69bdbea36d3 | [
{
"content": "Let $n\\geq3$ be an integer. We say that an arrangement of the numbers $1$ , $2$ , $\\dots$ , $n^2$ in a $n \\times n$ table is row-valid if the numbers in each row can be permuted to form an arithmetic progression, and column-valid if the numbers in each column can be permuted to form an arithmet... | Let $n\geq3$ be an integer. We say that an arrangement of the numbers $1$ , $2$ , $\dots$ , $n^2$ in a $n \times n$ table is row-valid if the numbers in each row can be permuted to form an arithmetic progression, and column-valid if the numbers in each column can be permuted to form an arithmetic progression. For what ... | "[\"\\\\[\\n\\\\boxed{\\\\text{prime } n}\\n\\\\]\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 1887, "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:15866"}] | {
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} |
[
"17"
] | [
"skywork"
] | 47f0449a7418018620cdd8636bdcac0a937d0b2d3fa79aab4d11c45462e4dd3d | [
{
"content": "3. In the sequence $\\left\\{a_{n}\\right\\}$, for $1 \\leqslant n \\leqslant 5$, we have $a_{n}=n^{2}$, and for all positive integers $n$, we have\n$$\na_{n+5}+a_{n+1}=a_{n+4}+a_{n} \\text {. }\n$$\n\nThen $a_{2023}=$ . $\\qquad$",
"role": "user"
}
] | 3. In the sequence $\left\{a_{n}\right\}$, for $1 \leqslant n \leqslant 5$, we have $a_{n}=n^{2}$, and for all positive integers $n$, we have
$$
a_{n+5}+a_{n+1}=a_{n+4}+a_{n} \text {. }
$$
Then $a_{2023}=$ . $\qquad$ | "[\"17\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1877, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:15867"}, {"dataset": "skywork", "extra_in... | {
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} |
[
"\\frac{7}{9}"
] | [
"skywork"
] | 8d13b39d37a739ea43de0bec71ccac3c4327480722d720d793c88941ed429ad4 | [
{
"content": "Simplify the expression $\\dfrac{20}{21} \\cdot \\dfrac{35}{54} \\cdot \\dfrac{63}{50}$.",
"role": "user"
}
] | Simplify the expression $\dfrac{20}{21} \cdot \dfrac{35}{54} \cdot \dfrac{63}{50}$. | "[\"\\\\frac{7}{9}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1911, "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:15868"}] | {
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"reference_components": 1,
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} |
[
"\\frac {1}{512}"
] | [
"skywork"
] | 4635febc9119137f2ab99c4cb72c2e8d728a5acad7c04a860d7ca677d96152d7 | [
{
"content": "Given a sequence $\\{a_n\\}$ satisfying $a_1=1$, $|a_n-a_{n-1}|= \\frac {1}{2^n}$ $(n\\geqslant 2,n\\in\\mathbb{N})$, and the subsequence $\\{a_{2n-1}\\}$ is decreasing, while $\\{a_{2n}\\}$ is increasing, find the value of $5-6a_{10}$.",
"role": "user"
}
] | Given a sequence $\{a_n\}$ satisfying $a_1=1$, $|a_n-a_{n-1}|= \frac {1}{2^n}$ $(n\geqslant 2,n\in\mathbb{N})$, and the subsequence $\{a_{2n-1}\}$ is decreasing, while $\{a_{2n}\}$ is increasing, find the value of $5-6a_{10}$. | "[\"\\\\frac {1}{512}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1882, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15869"}] | {
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} |
[
"\\binom{n+1}{2} 2^{n-2}"
] | [
"skywork"
] | d3caec4cfe584397b08b02d97bcb2655b1e5779de3fae926dc23f2e11b753510 | [
{
"content": "Let $ X_n\\equal{}\\{1,2,...,n\\}$,where $ n \\geq 3$. \r\nWe define the measure $ m(X)$ of $ X\\subset X_n$ as the sum of its elements.(If $ |X|\\equal{}0$,then $ m(X)\\equal{}0$).\r\nA set $ X \\subset X_n$ is said to be even(resp. odd) if $ m(X)$ is even(resp. odd).\r\n(a)Show that the number o... | Let $ X_n\equal{}\{1,2,...,n\}$,where $ n \geq 3$.
We define the measure $ m(X)$ of $ X\subset X_n$ as the sum of its elements.(If $ |X|\equal{}0$,then $ m(X)\equal{}0$).
A set $ X \subset X_n$ is said to be even(resp. odd) if $ m(X)$ is even(resp. odd).
(a)Show that the number of even sets equals the number of odd... | "[\"\\\\binom{n+1}{2} 2^{n-2}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1884, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15870"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"\\frac{10}{91}"
] | [
"skywork"
] | d9ef7cdb424fc5a19170d3c31a27659cf6414b47a596b74019a206f8124190c3 | [
{
"content": "Rectangle $ABCD$ has $AB=5$ and $BC=4$. Point $E$ lies on $\\overline{AB}$ so that $EB=1$, point $G$ lies on $\\overline{BC}$ so that $CG=1$, and point $F$ lies on $\\overline{CD}$ so that $DF=2$. Segments $\\overline{AG}$ and $\\overline{AC}$ intersect $\\overline{EF}$ at $Q$ and $P$, respectivel... | Rectangle $ABCD$ has $AB=5$ and $BC=4$. Point $E$ lies on $\overline{AB}$ so that $EB=1$, point $G$ lies on $\overline{BC}$ so that $CG=1$, and point $F$ lies on $\overline{CD}$ so that $DF=2$. Segments $\overline{AG}$ and $\overline{AC}$ intersect $\overline{EF}$ at $Q$ and $P$, respectively. What is the value of $\fr... | "[\"\\\\frac{10}{91}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1891, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15871"}] | {
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"12"
] | [
"skywork"
] | 879937ec27aeaccd1960154afd04bf2e976a4b00edc346025a9224e2f666ad4a | [
{
"content": "Of the numbers 1, 2, 3, ..., 15, which number has the greatest number of divisors (the dots mean that we are including all the integers between 1 and 15)?",
"role": "user"
}
] | Of the numbers 1, 2, 3, ..., 15, which number has the greatest number of divisors (the dots mean that we are including all the integers between 1 and 15)? | "[\"12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1907, "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:15872"}] | {
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} |
[
"\\frac{10}{3}"
] | [
"skywork"
] | 7ccc2a26ad3fd34ee99854841c89e52e7d1ada14f5fbf2c0cbadefb9ff2875e0 | [
{
"content": "22. As shown in Figure 4, in the right triangle $\\triangle ABC$, $AC=12, BC=5, \\angle C=90^{\\circ}$, inside the triangle, a semicircle $\\odot O$ with its diameter on side $AC$ is tangent to $AB$. Then the radius $r$ of the semicircle is ( ).\n(A) $\\frac{7}{6}$\n(B) $\\frac{13}{5}$\n(C) $\\fra... | 22. As shown in Figure 4, in the right triangle $\triangle ABC$, $AC=12, BC=5, \angle C=90^{\circ}$, inside the triangle, a semicircle $\odot O$ with its diameter on side $AC$ is tangent to $AB$. Then the radius $r$ of the semicircle is ( ).
(A) $\frac{7}{6}$
(B) $\frac{13}{5}$
(C) $\frac{59}{18}$
(D) $\frac{10}{3}$
(E... | "[\"\\\\frac{10}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1889, "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:15873"}] | {
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | b1534cf125c604cffafd3314a5622e038ceb9627e63af7c4ec193d5f309ffa71 | [
{
"content": "The digits in a two-digit positive integer are reversed. The new two-digit integer minus the original integer equals 54. What is the positive difference between the two digits of the original integer?",
"role": "user"
}
] | The digits in a two-digit positive integer are reversed. The new two-digit integer minus the original integer equals 54. What is the positive difference between the two digits of the original integer? | "[\"6\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1910, "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:15874"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"340"
] | [
"skywork"
] | dece48d80525a3b7dc2c513a959e54b3c2606e8c27c82c2aed8753f4a4550d31 | [
{
"content": "13.400 On the highway, points D, A, C, and B are arranged sequentially. A motorcyclist and a cyclist set off from A and B simultaneously, heading to C and D, respectively. Meeting at E, they exchanged vehicles and each continued their journey. As a result, the first one spent 6 hours on the trip f... | 13.400 On the highway, points D, A, C, and B are arranged sequentially. A motorcyclist and a cyclist set off from A and B simultaneously, heading to C and D, respectively. Meeting at E, they exchanged vehicles and each continued their journey. As a result, the first one spent 6 hours on the trip from A to C, while the ... | "[\"340\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1893, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15875"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"-38"
] | [
"skywork"
] | 8bcc29b717878220f7ecc62a916cc5c8f2d25fce9584dc9ec521001472bbb940 | [
{
"content": "The polynomial $P(x) = 2x^3 + ax^2 + bx + c$ has the property that the mean of its zeros, the product of its zeros, and the sum of the coefficients are all equal. The $y$-intercept of the graph of $y = P(x)$ is 8. What is $b$?",
"role": "user"
}
] | The polynomial $P(x) = 2x^3 + ax^2 + bx + c$ has the property that the mean of its zeros, the product of its zeros, and the sum of the coefficients are all equal. The $y$-intercept of the graph of $y = P(x)$ is 8. What is $b$? | "[\"-38\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1874, "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:15876"}] | {
"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"
] | 5c70f98cd5e4d84ec884051eac400bfe870238022aab590b842cc61cfeb7f64f | [
{
"content": "3. Solve for $x$ in $3=\\sqrt{x+\\sqrt{x+\\sqrt{x+\\cdots}}}$.",
"role": "user"
}
] | 3. Solve for $x$ in $3=\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}$. | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1898, "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:15877"}] | {
"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
} |
[
"11"
] | [
"skywork"
] | 1f691e5bc983d449ce3a50a372fade36cf2bc026e0ad6567b5e787d7d519f2e1 | [
{
"content": "The list of integers $4,4, x, y, 13$ has been arranged from least to greatest. How many different possible ordered pairs $(x, y)$ are there so that the average (mean) of these 5 integers is itself an integer?\n(A) 7\n(B) 8\n(C) 9\n(D) 10\n(E) 11",
"role": "user"
}
] | The list of integers $4,4, x, y, 13$ has been arranged from least to greatest. How many different possible ordered pairs $(x, y)$ are there so that the average (mean) of these 5 integers is itself an integer?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11 | "[\"11\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1905, "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:15878"}] | {
"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
} |
[
"29"
] | [
"skywork"
] | 7ba40cf2d9f5ebbab4491db457b73da880129385bfad9a50b1b941cdd61b5e94 | [
{
"content": "What integer $n$ satisfies $0\\le n<{101}$ and $$100n\\equiv 72\\pmod {101}~?$$",
"role": "user"
}
] | What integer $n$ satisfies $0\le n<{101}$ and $$100n\equiv 72\pmod {101}~?$$ | "[\"29\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1917, "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:15879"}] | {
"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}{16}"
] | [
"skywork"
] | 6ce6d0277262e439d4418bd7877a1fd6ec73b88f946ab3abe850c7020baa415c | [
{
"content": "When two fair 12-sided dice are tossed, the numbers $a$ and $b$ are obtained. What is the probability that both the two-digit number $ab$ (where $a$ and $b$ are digits) and each of $a$ and $b$ individually are divisible by 4?",
"role": "user"
}
] | When two fair 12-sided dice are tossed, the numbers $a$ and $b$ are obtained. What is the probability that both the two-digit number $ab$ (where $a$ and $b$ are digits) and each of $a$ and $b$ individually are divisible by 4? | "[\"\\\\frac{1}{16}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1896, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15880"}] | {
"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
} |
[
"15987"
] | [
"skywork"
] | d96e613a2fdfe7a0d8737e88b2702be0be6e99b30550577832cd2a116f933246 | [
{
"content": "There are 294 distinct cards with numbers \\(7, 11, 7^{2}, 11^{2}, \\ldots, 7^{147}, 11^{147}\\) (each card has exactly one number, and each number appears exactly once). How many ways can two cards be selected so that the product of the numbers on the selected cards is a perfect square?",
"ro... | There are 294 distinct cards with numbers \(7, 11, 7^{2}, 11^{2}, \ldots, 7^{147}, 11^{147}\) (each card has exactly one number, and each number appears exactly once). How many ways can two cards be selected so that the product of the numbers on the selected cards is a perfect square? | "[\"15987\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1895, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:15881"}] | {
"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
} |
[
"2222"
] | [
"skywork"
] | 7daec2f45b49a6fed597bfba1798c1b5764630c2e13d982ee15ec988a714b73e | [
{
"content": "Let $a$, $b$, $c$, and $d$ be digits such that $b = a + 2$, $c = a + 4$, and $d = a + 6$. Form the numbers $abcd$ and $dcba$, where these represent four-digit numbers created by these digits. What is the greatest common divisor of all numbers of the form $abcd + dcba$?",
"role": "user"
}
] | Let $a$, $b$, $c$, and $d$ be digits such that $b = a + 2$, $c = a + 4$, and $d = a + 6$. Form the numbers $abcd$ and $dcba$, where these represent four-digit numbers created by these digits. What is the greatest common divisor of all numbers of the form $abcd + dcba$? | "[\"2222\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1894, "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:15882"}] | {
"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
} |
[
"BC"
] | [
"skywork"
] | 1ebda5b8b2af1ed29f148e0dd93e6aa1914d68d4c898f243c1136e31330d65ae | [
{
"content": "Let triangle $ ABC$ acutangle, with $ m \\angle ACB\\leq\\ m \\angle ABC$. $ M$ the midpoint of side $ BC$ and $ P$ a point over the side $ MC$. Let $ C_{1}$ the circunference with center $ C$. Let $ C_{2}$ the circunference with center $ B$. $ P$ is a point of $ C_{1}$ and $ C_{2}$. Let $ X$ a po... | Let triangle $ ABC$ acutangle, with $ m \angle ACB\leq\ m \angle ABC$. $ M$ the midpoint of side $ BC$ and $ P$ a point over the side $ MC$. Let $ C_{1}$ the circunference with center $ C$. Let $ C_{2}$ the circunference with center $ B$. $ P$ is a point of $ C_{1}$ and $ C_{2}$. Let $ X$ a point on the opposite semipl... | "[\" BC \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1883, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:15883"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"100"
] | [
"skywork"
] | 4d9c162fe9b5fddad9a811870aa9bee53cd0aadf9b60e24ca1a2a3a494c0bb5c | [
{
"content": "Let $\\alpha$ and $\\beta$ be real numbers. Find the minimum value of\n\\[(2 \\cos \\alpha + 5 \\sin \\beta - 8)^2 + (2 \\sin \\alpha + 5 \\cos \\beta - 15)^2.\\]",
"role": "user"
}
] | Let $\alpha$ and $\beta$ be real numbers. Find the minimum value of
\[(2 \cos \alpha + 5 \sin \beta - 8)^2 + (2 \sin \alpha + 5 \cos \beta - 15)^2.\] | "[\"100\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1906, "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:15884"}] | {
"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
} |
[
"-4030,-2012,2018,4036"
] | [
"skywork"
] | fd3688e8ad7fb3788964c87e263d11b612953e955da837b4b8b67edd6d3d710a | [
{
"content": "3. Let the integer $k$ be such that the quadratic equation in $x$\n$$\n2 x^{2}+(11-5 k) x+3 k^{2}-13 k-2003=0\n$$\n\nhas at least one integer root. Then all such integers $k$ are\n$\\qquad$",
"role": "user"
}
] | 3. Let the integer $k$ be such that the quadratic equation in $x$
$$
2 x^{2}+(11-5 k) x+3 k^{2}-13 k-2003=0
$$
has at least one integer root. Then all such integers $k$ are
$\qquad$ | "[\"-4030,-2012,2018,4036\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1909, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:15885"}] | {
"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
} |
[
"90^{\\circ}"
] | [
"skywork"
] | ef3df8cc37fb6d55dbec4236078b5c5c137b58e2fcd8668ad8f20f7d6ca19125 | [
{
"content": "Four. (20 points) Let $A\\left(x_{0}, y_{0}\\right)$ be a point on the ellipse $C_{1}$:\n$$\n\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1(a>b>0)\n$$\n\nPoints $B$, $C$, and $D$ are the reflections of point $A$ across the $y$-axis, the origin, and the $x$-axis, respectively. Point $E$ is a point on ... | Four. (20 points) Let $A\left(x_{0}, y_{0}\right)$ be a point on the ellipse $C_{1}$:
$$
\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)
$$
Points $B$, $C$, and $D$ are the reflections of point $A$ across the $y$-axis, the origin, and the $x$-axis, respectively. Point $E$ is a point on the ellipse $C_{1}$ such that $... | "[\"90^{\\\\circ}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1892, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15886"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"68"
] | [
"skywork"
] | 79a5b3a54ea76e014402e6a7e12ae45dd04d8cd960c40f7ff8010850b854c55d | [
{
"content": "15. For any positive integer $m$, the set\n$$\n\\{m, m+1, m+2, \\cdots, m+99\\}\n$$\n\nhas the property that in any $n(n \\geqslant 3)$-element subset, there are always three elements that are pairwise coprime. Find the minimum value of $n$.",
"role": "user"
}
] | 15. For any positive integer $m$, the set
$$
\{m, m+1, m+2, \cdots, m+99\}
$$
has the property that in any $n(n \geqslant 3)$-element subset, there are always three elements that are pairwise coprime. Find the minimum value of $n$. | "[\"68\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1912, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15887"}] | {
"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{5}{324}"
] | [
"skywork"
] | f68e9e7a676ace0449236fa82535a97fa3321d404e9f4ccb6b64de81fa0ad9c7 | [
{
"content": "If I roll a fair, regular six-sided die four times, what is the probability that I will roll the number $1$ exactly three times?",
"role": "user"
}
] | If I roll a fair, regular six-sided die four times, what is the probability that I will roll the number $1$ exactly three times? | "[\"\\\\frac{5}{324}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1919, "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:15888"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"432"
] | [
"skywork"
] | 6a59d90b7896f0bc6f66606ce7b39c73a068cf7967a8ea0311c9e8f07749f20d | [
{
"content": "In right triangle $\\triangle ABC$ with $\\angle BAC = 90^\\circ$, medians $\\overline{AD}$ and $\\overline{BE}$ are given such that $AD = 18$ and $BE = 24$. If $\\overline{AD}$ is the altitude from $A$, find the area of $\\triangle ABC$.",
"role": "user"
}
] | In right triangle $\triangle ABC$ with $\angle BAC = 90^\circ$, medians $\overline{AD}$ and $\overline{BE}$ are given such that $AD = 18$ and $BE = 24$. If $\overline{AD}$ is the altitude from $A$, find the area of $\triangle ABC$. | "[\"432\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1900, "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:15889"}] | {
"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
} |
[
"41"
] | [
"skywork"
] | 37d333a7c69fe040530883f0e3365fe4efc068ea6cf691ce91ef78cfa3fad649 | [
{
"content": "In triangle $XYZ$, $XY=15$, $YZ=18$, and $ZX=21$. Point $G$ is on $\\overline{XY}$, $H$ is on $\\overline{YZ}$, and $I$ is on $\\overline{ZX}$. Let $XG = p \\cdot XY$, $YH = q \\cdot YZ$, and $ZI = r \\cdot ZX$, where $p$, $q$, and $r$ are positive and satisfy $p+q+r=3/4$ and $p^2+q^2+r^2=1/2$. Th... | In triangle $XYZ$, $XY=15$, $YZ=18$, and $ZX=21$. Point $G$ is on $\overline{XY}$, $H$ is on $\overline{YZ}$, and $I$ is on $\overline{ZX}$. Let $XG = p \cdot XY$, $YH = q \cdot YZ$, and $ZI = r \cdot ZX$, where $p$, $q$, and $r$ are positive and satisfy $p+q+r=3/4$ and $p^2+q^2+r^2=1/2$. The ratio of the area of trian... | "[\"41\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1904, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15890"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | c9adfe9708fcead7b0456e1b949d638b01b1d242f9ff946f6cd3ba7dd2698b25 | [
{
"content": "What is the sum of the roots of $x^2 - 4x + 3 = 0$?",
"role": "user"
}
] | What is the sum of the roots of $x^2 - 4x + 3 = 0$? | "[\"4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1942, "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:15891"}] | {
"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
} |
[
"51"
] | [
"skywork"
] | 53daefb5cbc9c7500ec7bb48f78d09a71f485c76ef40b82801d8a6ade3d52428 | [
{
"content": "Compute the sum $S=\\sum_{i=0}^{101} \\frac{x_{i}^{3}}{1-3 x_{i}+3 x_{i}^{2}}$ for $x_{i}=\\frac{i}{101}$.",
"role": "user"
}
] | Compute the sum $S=\sum_{i=0}^{101} \frac{x_{i}^{3}}{1-3 x_{i}+3 x_{i}^{2}}$ for $x_{i}=\frac{i}{101}$. | "[\"51\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1931, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15892"}] | {
"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
} |
[
"-2036162"
] | [
"skywork"
] | f83ddae796a1c9bb4741544701fd72fa0f72763f786e77dc99af5a4d083ffe6b | [
{
"content": "Let $x$ and $y$ be positive real numbers. Find the minimum value of\n\\[\\left( x + \\frac{1}{y} \\right) \\left( x + \\frac{1}{y} - 2018 \\right) + \\left( y + \\frac{1}{x} \\right) \\left( y + \\frac{1}{x} - 2018 \\right).\\]",
"role": "user"
}
] | Let $x$ and $y$ be positive real numbers. Find the minimum value of
\[\left( x + \frac{1}{y} \right) \left( x + \frac{1}{y} - 2018 \right) + \left( y + \frac{1}{x} \right) \left( y + \frac{1}{x} - 2018 \right).\] | "[\"-2036162\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1925, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15893"}] | {
"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}{3}"
] | [
"skywork"
] | 2d8b7cb81b634c4768440f57f08a2f0e798c23c88d2d92442d54e33e5fd0592e | [
{
"content": "Let $ABCD$ be a square and $X$ a point such that $A$ and $X$ are on opposite sides of $CD$ . The lines $AX$ and $BX$ intersect $CD$ in $Y$ and $Z$ respectively. If the area of $ABCD$ is $1$ and the area of $XYZ$ is $\\frac{2}{3}$ , determine the length of $YZ$",
"rol... | Let $ABCD$ be a square and $X$ a point such that $A$ and $X$ are on opposite sides of $CD$ . The lines $AX$ and $BX$ intersect $CD$ in $Y$ and $Z$ respectively. If the area of $ABCD$ is $1$ and the area of $XYZ$ is $\frac{2}{3}$ , determine the length of $YZ$ | "[\"\\\\frac{2}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1902, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15894"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{5}{8}"
] | [
"skywork"
] | ccea1b9e306779619d96ad701726cc7cb92744aa30e7ff660bde3e0f8ef4c1f2 | [
{
"content": "13. A frog starts a series of jumps from point $(1,2)$, with each jump parallel to one of the coordinate axes and 1 unit in length. It is known that the direction of each jump (up, down, right, or left) is randomly chosen. The frog stops jumping when it reaches the boundary of the square with vert... | 13. A frog starts a series of jumps from point $(1,2)$, with each jump parallel to one of the coordinate axes and 1 unit in length. It is known that the direction of each jump (up, down, right, or left) is randomly chosen. The frog stops jumping when it reaches the boundary of the square with vertices at $(0,0)$, $(0,4... | "[\"\\\\frac{5}{8}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1922, "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:15895"}] | {
"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
} |
[
"5"
] | [
"skywork"
] | 3b4198287e19c6fec1e4928339c15988a245cc4166fedc83e08a167ee8b67237 | [
{
"content": "Task B-2.3. Andrea and Mirela are preparing for a math competition. When their teacher asked them how many problems they solved yesterday, they did not answer directly. He only found out that Andrea solved fewer problems than Mirela, and each of them solved at least one problem. They also said tha... | Task B-2.3. Andrea and Mirela are preparing for a math competition. When their teacher asked them how many problems they solved yesterday, they did not answer directly. He only found out that Andrea solved fewer problems than Mirela, and each of them solved at least one problem. They also said that the product of the n... | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1921, "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:15896"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"f(n)=n^{2}-n+2"
] | [
"skywork"
] | 138ddf98156fcd804a3c2275390f9f0e4b0b6a77dd3c809a4076cede2223e1a7 | [
{
"content": "2. There are $n$ circles on a plane, each pair of which intersects at two points, and no three circles have a common point. They divide the plane into $f(n)$ regions, such as $f(1)=2, f(2)=4$, etc. The expression for $f(n)$ is ( ).\nA. $2^{n}$\nB. $n^{2}-n+2$\nC. $2^{n}-(n-1)(n-2)(n-3)$\nD. $n^{3}... | 2. There are $n$ circles on a plane, each pair of which intersects at two points, and no three circles have a common point. They divide the plane into $f(n)$ regions, such as $f(1)=2, f(2)=4$, etc. The expression for $f(n)$ is ( ).
A. $2^{n}$
B. $n^{2}-n+2$
C. $2^{n}-(n-1)(n-2)(n-3)$
D. $n^{3}-5 n^{2}+10 n-4$ | "[\"f(n)=n^{2}-n+2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1903, "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:15897"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"18"
] | [
"skywork"
] | 8d3a306a705fdf2f8bfc83762a5484dd4ef8cdd52cec3314b443397f94a7bed5 | [
{
"content": "Problem 130. Given an angle of $54^{\\circ}$. Divide it into three equal parts using a compass and a straightedge.",
"role": "user"
}
] | Problem 130. Given an angle of $54^{\circ}$. Divide it into three equal parts using a compass and a straightedge. | "[\"18\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1914, "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:15898"}] | {
"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
} |
[
"8"
] | [
"skywork"
] | c9e5dde844892e1168eb54cf0254bbaa8b7d40b244328420703f42b85d720a81 | [
{
"content": "Tony has an old sticky toy spider that very slowly \"crawls\" down a wall after being stuck to the wall. In fact, left untouched, the toy spider crawls down at a rate of one inch for every two hours it's left stuck to the wall. One morning, at around $9$ o' clock, Tony sticks the spider to the w... | Tony has an old sticky toy spider that very slowly "crawls" down a wall after being stuck to the wall. In fact, left untouched, the toy spider crawls down at a rate of one inch for every two hours it's left stuck to the wall. One morning, at around $9$ o' clock, Tony sticks the spider to the wall in the living room t... | "[\"8\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1929, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15899"}] | {
"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
} |
[
"104"
] | [
"skywork"
] | eb55ac3a2c50291eb9d41e8a4109be73b7c511aa06ea3073e36d03cc21e1c9df | [
{
"content": "1. There were 21 consecutive natural numbers written on the board. When one of the numbers was erased, the sum of the remaining numbers became 2017. Which number was erased?",
"role": "user"
}
] | 1. There were 21 consecutive natural numbers written on the board. When one of the numbers was erased, the sum of the remaining numbers became 2017. Which number was erased? | "[\"104\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1927, "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:15900"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | e19b1a0a9c7b66d0aa85def4134b1501b0c805b8b642f767beac22d2e44a950f | [
{
"content": "4. If $x, y, z$ are real numbers, satisfying\n$$\nx+\\frac{1}{y}=2 y+\\frac{2}{z}=3 z+\\frac{3}{x}=k \\text{, and } x y z=3 \\text{, }\n$$\n\nthen $k=$ . $\\qquad$",
"role": "user"
}
] | 4. If $x, y, z$ are real numbers, satisfying
$$
x+\frac{1}{y}=2 y+\frac{2}{z}=3 z+\frac{3}{x}=k \text{, and } x y z=3 \text{, }
$$
then $k=$ . $\qquad$ | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1932, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15901"}, {"dataset": "skywork", "extra_in... | {
"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
} |
[
"749"
] | [
"skywork"
] | cef068cc1cc684cf4416ce966f7b99aa5906835a3e3a88f11397dd2c77372339 | [
{
"content": "Seven cubes, whose volumes are $1$, $8$, $27$, $64$, $125$, $216$, and $343$ cubic units, are stacked vertically to form a tower in which the volumes of the cubes decrease from bottom to top. Except for the bottom cube, the bottom face of each cube lies completely on top of the cube below it. What... | Seven cubes, whose volumes are $1$, $8$, $27$, $64$, $125$, $216$, and $343$ cubic units, are stacked vertically to form a tower in which the volumes of the cubes decrease from bottom to top. Except for the bottom cube, the bottom face of each cube lies completely on top of the cube below it. What is the total surface ... | "[\"749\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1908, "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:15902"}] | {
"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
} |
[
"21"
] | [
"skywork"
] | 4afb629d219c12c2691dcac699e24b13906087869d281a4bc1826dca91363186 | [
{
"content": "36. Each side of an equilateral triangle is divided into 30 equal parts. Lines drawn through the division points parallel to the sides of the triangle divide it into 900 small triangles. What is the maximum number of vertices of the partition, no two of which lie on the same drawn line or side?",
... | 36. Each side of an equilateral triangle is divided into 30 equal parts. Lines drawn through the division points parallel to the sides of the triangle divide it into 900 small triangles. What is the maximum number of vertices of the partition, no two of which lie on the same drawn line or side? | "[\"21\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1939, "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:15903"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\sqrt{3591}}{24}"
] | [
"skywork"
] | 084cb85fa7cd3e10c156538eba16e591d3b217a17047211f0f448c415f3a93b6 | [
{
"content": "In triangle $ABC$, $AB = 12$, $AC = 10$, and $BC = 16$. The centroid $G$ of triangle $ABC$ divides each median in the ratio $2:1$. Calculate the length $GP$, where $P$ is the foot of the perpendicular from point $G$ to side $BC$.",
"role": "user"
}
] | In triangle $ABC$, $AB = 12$, $AC = 10$, and $BC = 16$. The centroid $G$ of triangle $ABC$ divides each median in the ratio $2:1$. Calculate the length $GP$, where $P$ is the foot of the perpendicular from point $G$ to side $BC$. | "[\"\\\\frac{\\\\sqrt{3591}}{24}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1928, "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:15904"}] | {
"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
} |
[
"4ab"
] | [
"skywork"
] | d623de41b77a89de96e5e87046534d6ce981c5e81d467a3ac73382239ea4e55a | [
{
"content": "[ Re-grouping areas $]$\n[ Properties of symmetries and axes of symmetry ]\n\nAuthors: Galperin G.A., Vasilyev N.B.\n\n$F$ - a convex figure with two mutually perpendicular axes of symmetry. Through a point $M$, lying inside the figure and at distances $a$ and $b$ from the axes, lines parallel to ... | [ Re-grouping areas $]$
[ Properties of symmetries and axes of symmetry ]
Authors: Galperin G.A., Vasilyev N.B.
$F$ - a convex figure with two mutually perpendicular axes of symmetry. Through a point $M$, lying inside the figure and at distances $a$ and $b$ from the axes, lines parallel to the axes are drawn. These l... | "[\"4ab\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1918, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15905"}] | {
"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
} |
[
"\\binom{2037171}{2019}"
] | [
"skywork"
] | 202a236ddeef3d4c0d48d9f13febfcb13ca17646766786cf02cdc408fbc6a6dc | [
{
"content": "How many decreasing sequences $a_1, a_2, \\ldots, a_{2019}$ of positive integers are there such that $a_1\\le 2019^2$ and $a_n + n$ is even for each $1 \\le n \\le 2019$ ?",
"role": "user"
}
] | How many decreasing sequences $a_1, a_2, \ldots, a_{2019}$ of positive integers are there such that $a_1\le 2019^2$ and $a_n + n$ is even for each $1 \le n \le 2019$ ? | "[\"\\\\binom{2037171}{2019}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1916, "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:15907"}, {"dataset": "skywork", "extra_... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"20\\sqrt{5}"
] | [
"skywork"
] | 5edc172d40fbc0da52e4aca029e804e59d2bf08372eed4fb0b63efbfd201b35e | [
{
"content": "Given the parabola $C: x^{2}=2py\\left(p \\gt 0\\right)$ with focus $F$, and the minimum distance between $F$ and a point on the circle $M: x^{2}+\\left(y+4\\right)^{2}=1$ is $4$.<br/>$(1)$ Find $p$;<br/>$(2)$ If point $P$ lies on $M$, $PA$ and $PB$ are two tangents to $C$ with points $A$ and $B$ ... | Given the parabola $C: x^{2}=2py\left(p \gt 0\right)$ with focus $F$, and the minimum distance between $F$ and a point on the circle $M: x^{2}+\left(y+4\right)^{2}=1$ is $4$.<br/>$(1)$ Find $p$;<br/>$(2)$ If point $P$ lies on $M$, $PA$ and $PB$ are two tangents to $C$ with points $A$ and $B$ as the points of tangency, ... | "[\"20\\\\sqrt{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1915, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:15908"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"0\\leqb\\leq2"
] | [
"skywork"
] | 52c326affbc666cc325ed77c8b41afe1ad5566b266156e1d018a68af2dfa1134 | [
{
"content": "10.2. Find all values of the parameter $b$, for each of which the system of equations\n\n$$\n\\left\\{\\begin{array}{l}\nx^{2}-2 x+y^{2}=0 \\\\\na x+y=a b\n\\end{array}\\right.\n$$\n\nhas a solution for any $a$.",
"role": "user"
}
] | 10.2. Find all values of the parameter $b$, for each of which the system of equations
$$
\left\{\begin{array}{l}
x^{2}-2 x+y^{2}=0 \\
a x+y=a b
\end{array}\right.
$$
has a solution for any $a$. | "[\"0\\\\leqb\\\\leq2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1930, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15909"}] | {
"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
} |
[
"6"
] | [
"skywork"
] | 45576287f1a26746464d3079eef9f1ea6f9c671b1b3a624ae5694a6091276cd8 | [
{
"content": "10. The teacher took out 13 cards, with the numbers on the cards ranging from 1 to 13. After keeping one of the cards, the teacher distributed the remaining 12 cards to three students, Jia, Yi, and Bing, with each receiving 4 cards. It is known that the sum of the numbers on the cards in Jia's han... | 10. The teacher took out 13 cards, with the numbers on the cards ranging from 1 to 13. After keeping one of the cards, the teacher distributed the remaining 12 cards to three students, Jia, Yi, and Bing, with each receiving 4 cards. It is known that the sum of the numbers on the cards in Jia's hand and the sum of the n... | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1924, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15910"}] | {
"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
} |
[
"27\\frac{43}{120}"
] | [
"skywork"
] | 56740f677d28951e9e40374f229db398fdb4061637de9c557375baf29182ac2b | [
{
"content": "1. (10 points) $3 \\frac{3}{4}+5 \\frac{5}{6}+7 \\frac{7}{8}+9 \\frac{9}{10}=$",
"role": "user"
}
] | 1. (10 points) $3 \frac{3}{4}+5 \frac{5}{6}+7 \frac{7}{8}+9 \frac{9}{10}=$ | "[\"27\\\\frac{43}{120}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1944, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15911"}] | {
"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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