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 |
|---|---|---|---|---|---|---|---|---|
[
"18"
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"skywork"
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{
"content": "Josef, Timothy, and Anna play a game. Josef picks an integer between 1 and 1440 inclusive. Timothy states whether the quotient of 1440 divided by Josef's integer is an integer. Finally, Anna adds a twist by stating whether Josef's integer is a multiple of 5. How many integers could Josef pick such... | Josef, Timothy, and Anna play a game. Josef picks an integer between 1 and 1440 inclusive. Timothy states whether the quotient of 1440 divided by Josef's integer is an integer. Finally, Anna adds a twist by stating whether Josef's integer is a multiple of 5. How many integers could Josef pick such that both Timothy's a... | "[\"18\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 329, "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:14366"}] | {
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[
"400"
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"skywork"
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"content": "Let triangle $ABC$ be a right triangle in the xy-plane with a right angle at $C_{}$. Given that the length of the hypotenuse $AB$ is $60$, and that the medians through $A$ and $B$ lie along the lines $y=x+3$ and $y=2x+4$ respectively, find the area of triangle $ABC$.",
"role": "user"
}
] | Let triangle $ABC$ be a right triangle in the xy-plane with a right angle at $C_{}$. Given that the length of the hypotenuse $AB$ is $60$, and that the medians through $A$ and $B$ lie along the lines $y=x+3$ and $y=2x+4$ respectively, find the area of triangle $ABC$. | "[\"400\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 330, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14367"}, {"dataset": "skywork", "extra_in... | {
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[
"150"
] | [
"skywork"
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{
"content": "6. In the Thirtieth Kingdom, there are 100 cities, and no more than one road connects any two cities. One day, the tsar ordered that one-way traffic be introduced on each road, and at the same time, each road should be painted either white or black. The Minister of Transport proudly reported that ... | 6. In the Thirtieth Kingdom, there are 100 cities, and no more than one road connects any two cities. One day, the tsar ordered that one-way traffic be introduced on each road, and at the same time, each road should be painted either white or black. The Minister of Transport proudly reported that after the order was ca... | "[\"150\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 319, "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:14368"}] | {
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[
"a_{n}=n+6"
] | [
"skywork"
] | 56e554dfd3e81a9887d81d844f8d47ddff1dc88d90acd4ca1e93cb34f9bc209b | [
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"content": "9. In an arithmetic sequence $\\left\\{a_{n}\\right\\}$ with a common difference not equal to 0, $a_{4}=10$, and $a_{3}, a_{6}, a_{10}$ form a geometric sequence, then the general term formula of the sequence $\\left\\{a_{n}\\right\\}$ is $\\qquad$.",
"role": "user"
}
] | 9. In an arithmetic sequence $\left\{a_{n}\right\}$ with a common difference not equal to 0, $a_{4}=10$, and $a_{3}, a_{6}, a_{10}$ form a geometric sequence, then the general term formula of the sequence $\left\{a_{n}\right\}$ is $\qquad$. | "[\"a_{n}=n+6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 317, "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:14369"}] | {
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} |
[
"39"
] | [
"skywork"
] | 3fc2387db278c5bc4ccd97c8a80f8ff923228a0e7174cb520976e686c2686eb1 | [
{
"content": "Mattis is hosting a badminton tournament for $40$ players on $20$ courts numbered from $1$ to $20$. The players are distributed with $2$ players on each court. In each round a winner is determined on each court. Afterwards, the player who lost on court $1$, and the player who won on court $20$ sta... | Mattis is hosting a badminton tournament for $40$ players on $20$ courts numbered from $1$ to $20$. The players are distributed with $2$ players on each court. In each round a winner is determined on each court. Afterwards, the player who lost on court $1$, and the player who won on court $20$ stay in place. For the re... | "[\"39\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 322, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14370"}] | {
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[
"4"
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"skywork"
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{
"content": "1. The number $x$ satisfies $x^{2}-4 x+2=0$. What is the value of $x+\\frac{2}{x}$ ?",
"role": "user"
}
] | 1. The number $x$ satisfies $x^{2}-4 x+2=0$. What is the value of $x+\frac{2}{x}$ ? | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 344, "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:14371"}] | {
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[
"1010000"
] | [
"skywork"
] | 9d15de971bb6b8eee1ddded85248ff9d2647d14b03414387b4853e8a15128ed4 | [
{
"content": "Given \\(\\sum^{100}_{i=1} \\sum^{100}_{j=1} (i+j)\\), find the value of the expression.",
"role": "user"
}
] | Given \(\sum^{100}_{i=1} \sum^{100}_{j=1} (i+j)\), find the value of the expression. | "[\"1010000\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 336, "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:14372"}] | {
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[
"240"
] | [
"skywork"
] | f765b62a575591b0a93726c9f2c3410a1850ba05ab04dc3d59813bf78fe186a0 | [
{
"content": "35. Xiao Le and Xiao Xi jump rope together. Xiao Xi jumps for 2 minutes first, then both of them jump for 3 minutes, and they jump a total of 780 times. Xiao Xi jumps 12 more times per minute than Xiao Le. How many more times does Xiao Xi jump than Xiao Le? \n\nFill in the blank with the answer.",... | 35. Xiao Le and Xiao Xi jump rope together. Xiao Xi jumps for 2 minutes first, then both of them jump for 3 minutes, and they jump a total of 780 times. Xiao Xi jumps 12 more times per minute than Xiao Le. How many more times does Xiao Xi jump than Xiao Le?
Fill in the blank with the answer. | "[\"240\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 345, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14373"}] | {
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} |
[
"104"
] | [
"skywork"
] | 58c3748fc79f1be23a49d0aceae03b6f0f345f68006e2472fd8a9982ab4fb256 | [
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"content": "12. Five cards have the numbers $101,102,103,104$ and 105 on their fronts.\n101\n102\n103\n104\n105\nOn the reverse, each card has one of five different positive integers: $a, b, c, d$ and $e$ respectively. We know that $a+2=b-2=2 c=\\frac{d}{2}=e^{2}$.\nGina picks up the card which has the larges... | 12. Five cards have the numbers $101,102,103,104$ and 105 on their fronts.
101
102
103
104
105
On the reverse, each card has one of five different positive integers: $a, b, c, d$ and $e$ respectively. We know that $a+2=b-2=2 c=\frac{d}{2}=e^{2}$.
Gina picks up the card which has the largest integer on its reverse. What... | "[\"104\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 313, "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:14374"}] | {
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} |
[
"\\frac{729\\pi}{6}"
] | [
"skywork"
] | ced6215cb4b15439cca5e610f8e8240d3394b12212ec9ce66a6d71393d6609e8 | [
{
"content": "A bowling ball must have a diameter of 9 inches. Calculate both the surface area and the volume of the bowling ball before the finger holes are drilled. Express your answers as common fractions in terms of \\(\\pi\\).",
"role": "user"
}
] | A bowling ball must have a diameter of 9 inches. Calculate both the surface area and the volume of the bowling ball before the finger holes are drilled. Express your answers as common fractions in terms of \(\pi\). | "[\"\\\\frac{729\\\\pi}{6}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 321, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14376"}] | {
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} |
[
"\\frac{2}{3}"
] | [
"skywork"
] | 40436657ededdb8c513bce5aab719c0c0a9400a352c539a029c4b617be82c45a | [
{
"content": "Franklin has four bags, numbered 1 through 4. Initially, the first bag contains fifteen balls, numbered 1 through 15 , and the other bags are empty. Franklin randomly pulls a pair of balls out of the first bag, throws away the ball with the lower number, and moves the ball with the higher number i... | Franklin has four bags, numbered 1 through 4. Initially, the first bag contains fifteen balls, numbered 1 through 15 , and the other bags are empty. Franklin randomly pulls a pair of balls out of the first bag, throws away the ball with the lower number, and moves the ball with the higher number into the second bag. He... | "[\"\\\\frac{2}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 327, "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:14377"}] | {
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[
"45"
] | [
"skywork"
] | 253ec073f93188baf29a3dfb862e490379a0cfb5d0f588b47f3507c1ad7d4741 | [
{
"content": "[Decimal numeral system]\n\nHow many two-digit numbers exist where the digit in the tens place is greater than the digit in the units place?\n\n#",
"role": "user"
}
] | [Decimal numeral system]
How many two-digit numbers exist where the digit in the tens place is greater than the digit in the units place?
# | "[\"45\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 359, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14378"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"C"
] | [
"skywork"
] | 3781a1ec181bd14cb6d1020d21675e7857b78c8887420ea438cc767a47d9e53f | [
{
"content": "5.12 The roots of the equation $x^{2}-2 x=0$ can be found graphically, that is, equal to finding the x-coordinates of the intersection points of the following sets of equations, with one exception:\n(A) $y=x^{2}, y=2 x$.\n(B) $y=x^{2}-2 x, y=0$.\n(C) $y=x, y=x-2$.\n(D) $y=x^{2}-2 x+1, y=1$.\n(E) $... | 5.12 The roots of the equation $x^{2}-2 x=0$ can be found graphically, that is, equal to finding the x-coordinates of the intersection points of the following sets of equations, with one exception:
(A) $y=x^{2}, y=2 x$.
(B) $y=x^{2}-2 x, y=0$.
(C) $y=x, y=x-2$.
(D) $y=x^{2}-2 x+1, y=1$.
(E) $y=x^{2}-1, y=2 x-1$.
(2nd A... | "[\"C\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 335, "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:14379"}] | {
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} |
[
"\\frac{1}{3}"
] | [
"skywork"
] | f405e74961678b3a1a0ff1a731b8e817440f7c4066e9de53ce8fc0e08b28a393 | [
{
"content": "(1) Solve the inequality $|x+1| + 2|x-1| < 3x + 5$.\n(2) Given $a, b \\in [0, 1]$, find the maximum value of $ab + (1-a-b)(a+b)$.",
"role": "user"
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] | (1) Solve the inequality $|x+1| + 2|x-1| < 3x + 5$.
(2) Given $a, b \in [0, 1]$, find the maximum value of $ab + (1-a-b)(a+b)$. | "[\"\\\\frac{1}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 343, "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:14380"}] | {
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} |
[
"8\\sqrt{2}"
] | [
"skywork"
] | e67b798c88d947f429c89ffd877f03e679fb4034b51e1352199e575eba0a1247 | [
{
"content": "Task B-2.2. On a circle with a radius of $9 \\mathrm{~cm}$, the center of another circle with a radius of $6 \\mathrm{~cm}$ is located. Determine the length of the common chord of these two circles.",
"role": "user"
}
] | Task B-2.2. On a circle with a radius of $9 \mathrm{~cm}$, the center of another circle with a radius of $6 \mathrm{~cm}$ is located. Determine the length of the common chord of these two circles. | "[\"8\\\\sqrt{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 356, "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:14381"}] | {
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[
"140"
] | [
"skywork"
] | 74baaab8f28ce0bf88948acd1b5f90cb1d066a305a08eed5dbce22fc5107818c | [
{
"content": "2. From points $A$ and $B$, which are 300 km apart, two cars set off simultaneously. The speed of the car that left from $A$ is 40 km/h. Determine the speed of the second car, given that after two hours the distance between them was 100 km.",
"role": "user"
}
] | 2. From points $A$ and $B$, which are 300 km apart, two cars set off simultaneously. The speed of the car that left from $A$ is 40 km/h. Determine the speed of the second car, given that after two hours the distance between them was 100 km. | "[\"140\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 347, "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:14383"}] | {
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[
"5/2"
] | [
"skywork"
] | 4d7aca67a756a725eaacce5ac1c6764020b26381fd694b47a9c5f53940f2d3c8 | [
{
"content": "A finite arithmetic progression \\( a_1, a_2, \\ldots, a_n \\) with a positive common difference has a sum of \\( S \\), and \\( a_1 > 0 \\). It is known that if the common difference of the progression is increased by 3 times while keeping the first term unchanged, the sum \\( S \\) doubles. By h... | A finite arithmetic progression \( a_1, a_2, \ldots, a_n \) with a positive common difference has a sum of \( S \), and \( a_1 > 0 \). It is known that if the common difference of the progression is increased by 3 times while keeping the first term unchanged, the sum \( S \) doubles. By how many times will \( S \) incr... | "[\"5/2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 339, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14384"}] | {
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} |
[
"0<b \\leqslant 1"
] | [
"skywork"
] | 2cf1b9b1a5a8be562dcc3e0bcb18b828b46684114769b5d490d616da3be17b29 | [
{
"content": "18. Given the line $y=b$ (where $b$ is a real number) intersects the graph of the function $y=\\left|x^{2}-4 x+3\\right|$ at least at three points. Then the range of the real number $b$ is",
"role": "user"
}
] | 18. Given the line $y=b$ (where $b$ is a real number) intersects the graph of the function $y=\left|x^{2}-4 x+3\right|$ at least at three points. Then the range of the real number $b$ is | "[\"0<b \\\\leqslant 1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 338, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14385"}] | {
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} |
[
"963"
] | [
"skywork"
] | 336af95253ce499973787da0ed76b19aeaffb1f85fb25ecc132c810bbb89bff2 | [
{
"content": "Let $M$ be the greatest integer multiple of 9, no two of whose digits are the same. What is the remainder when $M$ is divided by 1000?",
"role": "user"
}
] | Let $M$ be the greatest integer multiple of 9, no two of whose digits are the same. What is the remainder when $M$ is divided by 1000? | "[\"963\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 346, "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:14386"}] | {
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"reference_components": 1,
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[
"15"
] | [
"skywork"
] | 06564dde981f27efbdfadb74710597cafb847c54625435d7ba5ec375bff9f35c | [
{
"content": "A book of one hundred pages has its pages numbered from 1 to 100. How many sheets of this book have the digit 5 in their numbering? (NOTE: a sheet has two pages.)\n(a) 13\n(b) 14\n(c) 15\n(d) 16\n(e) 17",
"role": "user"
}
] | A book of one hundred pages has its pages numbered from 1 to 100. How many sheets of this book have the digit 5 in their numbering? (NOTE: a sheet has two pages.)
(a) 13
(b) 14
(c) 15
(d) 16
(e) 17 | "[\"15\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 351, "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:14387"}] | {
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[
"1001001"
] | [
"skywork"
] | 142ee88b09c903c85dd0d7e6e13a1f5f032cf6adb687c8972fa693971cc29e09 | [
{
"content": "Determine the greatest common divisor of all nine-digit integers formed by repeating a three-digit integer three times. For example, 256,256,256 or 691,691,691 are integers of this form.",
"role": "user"
}
] | Determine the greatest common divisor of all nine-digit integers formed by repeating a three-digit integer three times. For example, 256,256,256 or 691,691,691 are integers of this form. | "[\"1001001\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 354, "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:14388"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | b0a7d19b18d98f206227a63b72deb6daf5df6acdbde10cc0c4a634cbc8842410 | [
{
"content": "How many 0's are located to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of $\\frac{1}{2^5\\cdot5^8}$?",
"role": "user"
}
] | How many 0's are located to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of $\frac{1}{2^5\cdot5^8}$? | "[\"7\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 368, "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:14390"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"80"
] | [
"skywork"
] | 2c712b21b858f601596dc035a3ba9cbcad56261afec7e76e1296ced82396d26a | [
{
"content": "A box contains 30 red balls, 25 green balls, 23 yellow balls, 14 blue balls, 13 white balls, and 10 black balls. Calculate the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 15 balls of a single color will be drawn.",
"role": "user"
}
] | A box contains 30 red balls, 25 green balls, 23 yellow balls, 14 blue balls, 13 white balls, and 10 black balls. Calculate the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 15 balls of a single color will be drawn. | "[\"80\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 353, "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:14391"}] | {
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"reference_components": 1,
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} |
[
"P_{4}"
] | [
"skywork"
] | c9785895909e0f7774b0fc48bc319166677a372ec4a63c1b232e0396f8451ad9 | [
{
"content": "1.3. A game of Jai Alai has eight players and starts with players $P_{1}$ and $P_{2}$ on court and the other players $P_{3}, P_{4}, P_{5}, P_{6}, P_{7}, P_{8}$ waiting in a queue. After each point is played, the loser goes to the end of the queue; the winner adds 1 point to his score and stays on ... | 1.3. A game of Jai Alai has eight players and starts with players $P_{1}$ and $P_{2}$ on court and the other players $P_{3}, P_{4}, P_{5}, P_{6}, P_{7}, P_{8}$ waiting in a queue. After each point is played, the loser goes to the end of the queue; the winner adds 1 point to his score and stays on the court; and the pla... | "[\"P_{4}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 328, "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:14392"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"168"
] | [
"skywork"
] | 772c331806d40cc2b1bee8d787055125b171d0ed4e1ee6300e57c4c9a1a0dc9e | [
{
"content": "Problem 11.6. Given a convex quadrilateral $A B C D$. It is known that $\\angle C=57^{\\circ}, \\sin \\angle A+$ $\\sin \\angle B=\\sqrt{2}$ and $\\cos \\angle A+\\cos \\angle B=2-\\sqrt{2}$. How many degrees does angle $D$ measure?",
"role": "user"
}
] | Problem 11.6. Given a convex quadrilateral $A B C D$. It is known that $\angle C=57^{\circ}, \sin \angle A+$ $\sin \angle B=\sqrt{2}$ and $\cos \angle A+\cos \angle B=2-\sqrt{2}$. How many degrees does angle $D$ measure? | "[\"168\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 361, "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:14393"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 31ae1fab1e1c838e70f86f45e7000a26effa0badb498afe4f5e8ed482ff532d1 | [
{
"content": "Problem 8. For what values of the parameter $a$ does the equation\n\n$$\n5^{x^{2}+2 a x+a^{2}}=a x^{2}+2 a^{2} x+a^{3}+a^{2}-6 a+6\n$$\n\nhave exactly one solution?",
"role": "user"
}
] | Problem 8. For what values of the parameter $a$ does the equation
$$
5^{x^{2}+2 a x+a^{2}}=a x^{2}+2 a^{2} x+a^{3}+a^{2}-6 a+6
$$
have exactly one solution? | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 349, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14394"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 7d436f8c76edc86561731e9083b4e8ae894e89b81f01474df3e96d54105934cf | [
{
"content": "2. Let $f(x)=a x^{2}+b x+c$ be a quadratic trinomial with integer coefficients. If integers $m, n$ satisfy $f(m)-f(n)=1$, then $|m-n|=$ $\\qquad$ .",
"role": "user"
}
] | 2. Let $f(x)=a x^{2}+b x+c$ be a quadratic trinomial with integer coefficients. If integers $m, n$ satisfy $f(m)-f(n)=1$, then $|m-n|=$ $\qquad$ . | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 350, "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:14395"}] | {
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} |
[
"140"
] | [
"skywork"
] | e2c6f58618d1231917c2a43c30cb4b253f0d527454ff77b247577070497745dd | [
{
"content": "In $\\bigtriangleup ABC$, $D$ is a point on side $\\overline{AC}$ such that $BD=DC$ and $\\angle BCD$ measures $70^\\circ$. What is the degree measure of $\\angle ADB$?\n\n$\\textbf{(A) }100\\qquad\\textbf{(B) }120\\qquad\\textbf{(C) }135\\qquad\\textbf{(D) }140\\qquad \\textbf{(E) }150$",
"ro... | In $\bigtriangleup ABC$, $D$ is a point on side $\overline{AC}$ such that $BD=DC$ and $\angle BCD$ measures $70^\circ$. What is the degree measure of $\angle ADB$?
$\textbf{(A) }100\qquad\textbf{(B) }120\qquad\textbf{(C) }135\qquad\textbf{(D) }140\qquad \textbf{(E) }150$ | "[\"140\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 370, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14396"}] | {
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} |
[
"142857,428571"
] | [
"skywork"
] | ae9799098621fc25f181da2ae1356d145755f17d37d7d8731c8e2efa11723133 | [
{
"content": "\\section*{Problem 6 - 011016}\n\nA six-digit number begins with the digit 1 at the highest place. If this digit is removed and appended to the end of the number, the result is three times the original number.",
"role": "user"
}
] | \section*{Problem 6 - 011016}
A six-digit number begins with the digit 1 at the highest place. If this digit is removed and appended to the end of the number, the result is three times the original number. | "[\"142857,428571\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 367, "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:14397"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"75"
] | [
"skywork"
] | bcb3b23228192a2ec546f1065c5805b3fcf58f785d77afcd4ae460b2db5a07fe | [
{
"content": "An assignment of either a $ 0$ or a $ 1$ to each unit square of an $ m$x$ n$ chessboard is called $ fair$ if the total numbers of $ 0$s and $ 1$s are equal. A real number $ a$ is called $ beautiful$ if there are positive integers $ m,n$ and a fair assignment for the $ m$x$ n$ chessboard such that ... | An assignment of either a $ 0$ or a $ 1$ to each unit square of an $ m$x$ n$ chessboard is called $ fair$ if the total numbers of $ 0$s and $ 1$s are equal. A real number $ a$ is called $ beautiful$ if there are positive integers $ m,n$ and a fair assignment for the $ m$x$ n$ chessboard such that for each of the $ m$ r... | "[\"75\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 348, "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:14398"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1221"
] | [
"skywork"
] | 5b989c5c5eda351882bf75c15fed7b465391e40f229d2e7c841214f1ed3e9930 | [
{
"content": "An electronic clock always displays the date as an eight-digit number. For example, January 1, 2011, is displayed as 20110101. What is the last day of 2011 that can be evenly divided by 101? The date is displayed as $\\overline{2011 \\mathrm{ABCD}}$. What is $\\overline{\\mathrm{ABCD}}$?",
"ro... | An electronic clock always displays the date as an eight-digit number. For example, January 1, 2011, is displayed as 20110101. What is the last day of 2011 that can be evenly divided by 101? The date is displayed as $\overline{2011 \mathrm{ABCD}}$. What is $\overline{\mathrm{ABCD}}$? | "[\"1221\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 366, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14399"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"31"
] | [
"skywork"
] | 2eaa82d0eab84223f39e1e457ec3baadf7af4f377dd763897f7a3217a491e468 | [
{
"content": "Given a large circle with a radius of 11 and small circles with a radius of 1, determine the maximum number of small circles that can be placed inside the large circle, such that each small circle is internally tangent to the large circle and the small circles do not overlap.",
"role": "user"
... | Given a large circle with a radius of 11 and small circles with a radius of 1, determine the maximum number of small circles that can be placed inside the large circle, such that each small circle is internally tangent to the large circle and the small circles do not overlap. | "[\"31\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 374, "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:14400"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2x-1"
] | [
"skywork"
] | 25241ff40d3110cbcc336625c517904e40d00c7d5d0bce079ed4a9d104620924 | [
{
"content": "G8.3 If $f(x)=x^{2}$, then express $f(x)-f(x-1)$ in terms of $x$.",
"role": "user"
}
] | G8.3 If $f(x)=x^{2}$, then express $f(x)-f(x-1)$ in terms of $x$. | "[\"2x-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 375, "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:14401"}] | {
"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
} |
[
"10000"
] | [
"skywork"
] | 67ac127b235f5fbbd434553402941f8d650098976ff9dc2f4e5fae44a3929780 | [
{
"content": "A circle intersects the $y$ -axis at two points $(0, a)$ and $(0, b)$ and is tangent to the line $x+100y = 100$ at $(100, 0)$ . Compute the sum of all possible values of $ab - a - b$ .",
"role": "user"
}
] | A circle intersects the $y$ -axis at two points $(0, a)$ and $(0, b)$ and is tangent to the line $x+100y = 100$ at $(100, 0)$ . Compute the sum of all possible values of $ab - a - b$ . | "[\"10000\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 372, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14402"}, {"dataset": "skywork", "extra_inf... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{2\\sqrt{6}-4}{5}"
] | [
"skywork"
] | ab456d59537bac0e7e7f03e2244e00d92d9cdef6910b3b775b01a3e4202f89ae | [
{
"content": "16. Let the function $f(x)=x^{2}-\\left(k^{2}-5 a k+3\\right) x+7(a, k \\in \\mathbf{R})$, given that for any $k \\in[0,2]$, if $x_{1}, x_{2}$ satisfy $x_{1} \\in[k, k+a], x_{2} \\in[k+2 a, k+4 a]$, then $f\\left(x_{1}\\right) \\geqslant f\\left(x_{2}\\right)$, find the maximum value of the positi... | 16. Let the function $f(x)=x^{2}-\left(k^{2}-5 a k+3\right) x+7(a, k \in \mathbf{R})$, given that for any $k \in[0,2]$, if $x_{1}, x_{2}$ satisfy $x_{1} \in[k, k+a], x_{2} \in[k+2 a, k+4 a]$, then $f\left(x_{1}\right) \geqslant f\left(x_{2}\right)$, find the maximum value of the positive real number $a$. | "[\"\\\\frac{2\\\\sqrt{6}-4}{5}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 362, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14403"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"23000"
] | [
"skywork"
] | 78a171bd15b647aebd13425abb7e5b5e68fdf2e142b24953f0b23f3d0807f0ba | [
{
"content": "2. The robotics club accepts only those who know mathematics, physics, or programming. It is known that 8 members of the club know physics, 7 know mathematics, and 11 know programming. Additionally, it is known that at least two know both physics and mathematics, at least three know both mathemati... | 2. The robotics club accepts only those who know mathematics, physics, or programming. It is known that 8 members of the club know physics, 7 know mathematics, and 11 know programming. Additionally, it is known that at least two know both physics and mathematics, at least three know both mathematics and programming, an... | "[\"23000\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 360, "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:14404"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{35\\sqrt{11}}{396}"
] | [
"skywork"
] | 78f35e33062a6a444c63b88d86053394521eb4c1946dc20d15e5f742725f2dfe | [
{
"content": "6. The base of the pyramid $S A B C$ is an isosceles triangle $A B C$, with $A B = B C = 3$, and $A C = 5$. The height of the pyramid $S A B C$ is the segment $S O$, where $O$ is the intersection point of the line passing through vertex $B$ parallel to side $A C$ and the line passing through $C$ p... | 6. The base of the pyramid $S A B C$ is an isosceles triangle $A B C$, with $A B = B C = 3$, and $A C = 5$. The height of the pyramid $S A B C$ is the segment $S O$, where $O$ is the intersection point of the line passing through vertex $B$ parallel to side $A C$ and the line passing through $C$ perpendicular to side $... | "[\"\\\\frac{35\\\\sqrt{11}}{396}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 352, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14405"}] | {
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[
"29"
] | [
"skywork"
] | a7bfa4b5e302254bbbb5c527c261e540b8d9d8b733164c61d33d78b4d227dfa3 | [
{
"content": "A test has ten questions. Points are awarded as follows:\n\n- Each correct answer is worth 3 points.\n- Each unanswered question is worth 1 point.\n- Each incorrect answer is worth 0 points.\n\nA total score that is not possible is:",
"role": "user"
}
] | A test has ten questions. Points are awarded as follows:
- Each correct answer is worth 3 points.
- Each unanswered question is worth 1 point.
- Each incorrect answer is worth 0 points.
A total score that is not possible is: | "[\"29\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 373, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14406"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"15"
] | [
"skywork"
] | 435a0074a1ce4e9582426eb96a71f50a8ae2055c908b013b0f3ea504ae4b19c6 | [
{
"content": "It is known that there exist integers $x_{1}, x_{2}, \\cdots, x_{n}$, satisfying $x_{1}^{4}-x_{2}^{4}-\\cdots+x_{n}^{4}=1599$, then the minimum value of the positive integer $n$ is\n(A) 14\n(B) 15\n(C) 16\n(D) 1599",
"role": "user"
}
] | It is known that there exist integers $x_{1}, x_{2}, \cdots, x_{n}$, satisfying $x_{1}^{4}-x_{2}^{4}-\cdots+x_{n}^{4}=1599$, then the minimum value of the positive integer $n$ is
(A) 14
(B) 15
(C) 16
(D) 1599 | "[\"15\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 371, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14407"}] | {
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} |
[
"x\\in(\\frac{5}{3};\\infty)"
] | [
"skywork"
] | 159356bea592c372d9b2e348a87af2a78a38061470e83b120deabbc66ecdb55a | [
{
"content": "9.024. $\\log _{3} \\frac{3 x-5}{x+1} \\leq 1$.",
"role": "user"
}
] | 9.024. $\log _{3} \frac{3 x-5}{x+1} \leq 1$. | "[\"x\\\\in(\\\\frac{5}{3};\\\\infty)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 393, "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:14408"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{3}"
] | [
"skywork"
] | 0758d8746ea2c3d6bb06eef511f8a76b2d1b9f24d26ecef9cabb62e16f7e642b | [
{
"content": "Calculate the sum $$\\frac{2^1}{8^1 - 1} + \\frac{2^2}{8^2 - 1} + \\frac{2^3}{8^3 - 1} + \\frac{2^4}{8^4 - 1} + \\cdots.$$",
"role": "user"
}
] | Calculate the sum $$\frac{2^1}{8^1 - 1} + \frac{2^2}{8^2 - 1} + \frac{2^3}{8^3 - 1} + \frac{2^4}{8^4 - 1} + \cdots.$$ | "[\"\\\\frac{1}{3}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 377, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14409"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3 L"
] | [
"skywork"
] | 9b9e7fad81325be7123ef07ef63e34bbefbd593f9eb9bfa6314c16030ebaea11 | [
{
"content": "Some people like to write with larger pencils than others. Ed, for instance, likes to write with the longest pencils he can find. However, the halls of MIT are of limited height $L$ and width $L$. What is the longest pencil Ed can bring through the halls so that he can negotiate a square turn?",
... | Some people like to write with larger pencils than others. Ed, for instance, likes to write with the longest pencils he can find. However, the halls of MIT are of limited height $L$ and width $L$. What is the longest pencil Ed can bring through the halls so that he can negotiate a square turn? | "[\"3 L\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 355, "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:14410"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{2}{9}"
] | [
"skywork"
] | ebff74877af82f6d4606ad37bd6ad063a0351d3ea799e07e42bd5b20da9e3625 | [
{
"content": "Given that the circumference of a sector is $20\\,cm$ and its area is $9\\,cm^2$, find the radian measure of the central angle of the sector.",
"role": "user"
}
] | Given that the circumference of a sector is $20\,cm$ and its area is $9\,cm^2$, find the radian measure of the central angle of the sector. | "[\"\\\\frac{2}{9}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 385, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14411"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-4p^{2}"
] | [
"skywork"
] | dcec36d15f75504f6ab2201bb84ee94963bf429c45fdc74d4cdbb14e92eccd84 | [
{
"content": "13 Let $A, B$ be two distinct points on the parabola $y^{2}=2 p x(p>0)$, then $\\mid \\overrightarrow{O A}+$ $\\left.\\overrightarrow{O B}\\right|^{2}-|\\overrightarrow{A B}|^{2}$ the minimum value is",
"role": "user"
}
] | 13 Let $A, B$ be two distinct points on the parabola $y^{2}=2 p x(p>0)$, then $\mid \overrightarrow{O A}+$ $\left.\overrightarrow{O B}\right|^{2}-|\overrightarrow{A B}|^{2}$ the minimum value is | "[\"-4p^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 340, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "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:14412"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2S_{1}-\\frac{S}{3}"
] | [
"skywork"
] | f1d60ee459eb1179ce38bfda7e786fbc266cc6ce6d44b99852f0348d2bc702b4 | [
{
"content": "6. (5 points). Point $\\boldsymbol{D}$ lies on the extension of side $\\boldsymbol{A} \\boldsymbol{C}$ of triangle $\\boldsymbol{A B C}$, the area of which is equal to $\\boldsymbol{S}$; point $\\boldsymbol{A}$ is located between $\\boldsymbol{D}$ and $\\boldsymbol{C}$. Let $\\boldsymbol{O}$ be th... | 6. (5 points). Point $\boldsymbol{D}$ lies on the extension of side $\boldsymbol{A} \boldsymbol{C}$ of triangle $\boldsymbol{A B C}$, the area of which is equal to $\boldsymbol{S}$; point $\boldsymbol{A}$ is located between $\boldsymbol{D}$ and $\boldsymbol{C}$. Let $\boldsymbol{O}$ be the point of intersection of the ... | "[\"2S_{1}-\\\\frac{S}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 364, "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:14413"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2015028"
] | [
"skywork"
] | e2f83432b8e60116d254d5273e0b581d20c135d00a1bb7d8dd33d5380c9ad8fa | [
{
"content": "(10) Let $[x]$ denote the greatest integer not exceeding $x$, then the value of $\\sum_{k=1}^{2008}\\left[\\frac{2008 k}{2009}\\right]$ is $\\qquad$",
"role": "user"
}
] | (10) Let $[x]$ denote the greatest integer not exceeding $x$, then the value of $\sum_{k=1}^{2008}\left[\frac{2008 k}{2009}\right]$ is $\qquad$ | "[\"2015028\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 386, "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:14414"}] | {
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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{48}{625}"
] | [
"skywork"
] | bd726ca7f886b0ed905c159a478c5771492d1bce88efa43226dc68c8248cd423 | [
{
"content": "4. Katya and Pasha ask each other four tricky questions and answer them without thinking, randomly. The probability that Katya will lie to a question asked by Pasha is $\\frac{1}{3}$, regardless of the question number. Pasha gives a truthful answer to Katya's question with a probability of $\\frac... | 4. Katya and Pasha ask each other four tricky questions and answer them without thinking, randomly. The probability that Katya will lie to a question asked by Pasha is $\frac{1}{3}$, regardless of the question number. Pasha gives a truthful answer to Katya's question with a probability of $\frac{3}{5}$, independently o... | "[\"\\\\frac{48}{625}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 380, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14415"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-7"
] | [
"skywork"
] | 3d4686a161f1fed3877bd0a5200b043d7104041733c519325e6374f886bb1712 | [
{
"content": "Given $f(x) = kx + \\frac {2}{x^{3}} - 3$ $(k \\in \\mathbb{R})$, and it is known that $f(\\ln 6) = 1$. Find $f\\left(\\ln \\frac {1}{6}\\right)$.",
"role": "user"
}
] | Given $f(x) = kx + \frac {2}{x^{3}} - 3$ $(k \in \mathbb{R})$, and it is known that $f(\ln 6) = 1$. Find $f\left(\ln \frac {1}{6}\right)$. | "[\"-7\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 382, "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:14416"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"16"
] | [
"skywork"
] | ef65809acbedf348e90b4bb44e79be0d83c16fe3720a2e07c63e24d21cba4679 | [
{
"content": "A line $y = -2$ intersects the graph of $y = 5x^2 + 2x - 6$ at points $C$ and $D$. Find the distance between points $C$ and $D$, expressed in the form $\\frac{\\sqrt{p}}{q}$ where $p$ and $q$ are positive coprime integers. What is $p - q$?",
"role": "user"
}
] | A line $y = -2$ intersects the graph of $y = 5x^2 + 2x - 6$ at points $C$ and $D$. Find the distance between points $C$ and $D$, expressed in the form $\frac{\sqrt{p}}{q}$ where $p$ and $q$ are positive coprime integers. What is $p - q$? | "[\"16\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 379, "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:14417"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4\\sqrt{2}"
] | [
"skywork"
] | 0084751e15f43228b9dcee4477cb355625617844f8b5e9ce5ae35b732e88aba0 | [
{
"content": "Given a triangle \\( \\triangle ABC \\) with sides \\( a, b, c \\) opposite to angles \\( A, B, C \\) respectively, and \\( a^{2} + b^{2} = c^{2} + \\frac{2}{3}ab \\). If the circumradius of \\( \\triangle ABC \\) is \\( \\frac{3\\sqrt{2}}{2} \\), what is the maximum possible area of \\( \\triangl... | Given a triangle \( \triangle ABC \) with sides \( a, b, c \) opposite to angles \( A, B, C \) respectively, and \( a^{2} + b^{2} = c^{2} + \frac{2}{3}ab \). If the circumradius of \( \triangle ABC \) is \( \frac{3\sqrt{2}}{2} \), what is the maximum possible area of \( \triangle ABC \)? | "[\"4\\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 376, "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:14418"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{4}{9}"
] | [
"skywork"
] | cc5cdffa212bb88ed34d87cce3d677feb6a8dc4e81c92933db21c3e797ce4acb | [
{
"content": "The faces of a cubical die are marked with the numbers $1$, $2$, $3$, $3$, $4$, and $4$. Another die's faces are marked with $2$, $2$, $5$, $6$, $7$, and $8$. Find the probability that the sum of the top two numbers will be $7$, $9$, or $11$.\nA) $\\frac{1}{18}$\nB) $\\frac{1}{9}$\nC) $\\frac{1}{3... | The faces of a cubical die are marked with the numbers $1$, $2$, $3$, $3$, $4$, and $4$. Another die's faces are marked with $2$, $2$, $5$, $6$, $7$, and $8$. Find the probability that the sum of the top two numbers will be $7$, $9$, or $11$.
A) $\frac{1}{18}$
B) $\frac{1}{9}$
C) $\frac{1}{3}$
D) $\frac{4}{9}$
E) $\fra... | "[\"\\\\frac{4}{9}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 381, "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:14419"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 3e874b4a8e643de59ae07abe040277f0be6b010cc6e1c858ff63e6812d313cf4 | [
{
"content": "Let \\( f: \\mathbb{N}^{*} \\rightarrow \\mathbb{N}^{*} \\) be a function that satisfies the following conditions:\n\n1. \\( f(1)=1 \\)\n2. \\( f(2n)=f(n) \\)\n3. \\( f(2n+1)=f(n)+1 \\)\n\nWhat is the greatest value of \\( f(n) \\) for \\( 1 \\leqslant n \\leqslant 2018 \\) ?",
"role": "user"
... | Let \( f: \mathbb{N}^{*} \rightarrow \mathbb{N}^{*} \) be a function that satisfies the following conditions:
1. \( f(1)=1 \)
2. \( f(2n)=f(n) \)
3. \( f(2n+1)=f(n)+1 \)
What is the greatest value of \( f(n) \) for \( 1 \leqslant n \leqslant 2018 \) ? | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 378, "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:14420"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"6e^{-x}+2e^{3x}"
] | [
"skywork"
] | 25cf87e8aa1fe003ecb147bfbf381b1e5e2b149f2f9b94385595f6d80346bf3d | [
{
"content": "140. Find the particular solution of the equations $y^{\\prime \\prime}-2 y^{\\prime}-3 y=0$, if $y=8$ and $y^{\\prime}=0$ when $x=0$.",
"role": "user"
}
] | 140. Find the particular solution of the equations $y^{\prime \prime}-2 y^{\prime}-3 y=0$, if $y=8$ and $y^{\prime}=0$ when $x=0$. | "[\"6e^{-x}+2e^{3x}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 396, "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:14421"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{2\\sqrt{2}}{3}"
] | [
"skywork"
] | 992250d9700d4266742822a8273915b42c58641c504c41569ccca82d07317b61 | [
{
"content": "Let $a$ be real number. A circle $C$ touches the line $y=-x$ at the point $(a, -a)$ and passes through the point $(0,\\ 1).$\nDenote by $P$ the center of $C$. When $a$ moves, find the area of the figure enclosed by the locus of $P$ and the line $y=1$.",
"role": "user"
}
] | Let $a$ be real number. A circle $C$ touches the line $y=-x$ at the point $(a, -a)$ and passes through the point $(0,\ 1).$
Denote by $P$ the center of $C$. When $a$ moves, find the area of the figure enclosed by the locus of $P$ and the line $y=1$. | "[\"\\\\frac{2\\\\sqrt{2}}{3}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 358, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14422"}] | {
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[
"P(x) = Q\\left(\\frac{1}{2} - x\\right) + \\frac{1}{2}"
] | [
"skywork"
] | 10d9b4854f1d92b96c784eec040b9a834e22b19c6c1e7a0472be5bfa2643b3d5 | [
{
"content": "Find the solution of the functional equation $P(x)+P(1-x)=1$ with power $2015$\n\nP.S: $P(y)=y^{2015}$ is also a function with power $2015$",
"role": "user"
}
] | Find the solution of the functional equation $P(x)+P(1-x)=1$ with power $2015$
P.S: $P(y)=y^{2015}$ is also a function with power $2015$ | "[\" P(x) = Q\\\\left(\\\\frac{1}{2} - x\\\\right) + \\\\frac{1}{2} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 357, "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:14423"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"176"
] | [
"skywork"
] | 5d25af705bbee61858bbb40f937459b4f8b625c64b2e0093ccc3e7fa0f8ba3ad | [
{
"content": "Kelvin the Frog is trying to hop across a river. The river has 10 lilypads on it, and he must hop on them in a specific order (the order is unknown to Kelvin). If Kelvin hops to the wrong lilypad at any point, he will be thrown back to the wrong side of the river and will have to start over. Assum... | Kelvin the Frog is trying to hop across a river. The river has 10 lilypads on it, and he must hop on them in a specific order (the order is unknown to Kelvin). If Kelvin hops to the wrong lilypad at any point, he will be thrown back to the wrong side of the river and will have to start over. Assuming Kelvin is infinite... | "[\"176\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 369, "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:14424"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | a3107fc4f014b75b88e059501ec5ab71faede193575541d03795db894be6e126 | [
{
"content": "Ashley, Betty, Carlos, Dick, and Elgin went shopping. Each had a whole number of dollars to spend, and together they had $56$ dollars. The absolute difference between the amounts Ashley and Betty had to spend was $19$ dollars. The absolute difference between the amounts Betty and Carlos had was $7... | Ashley, Betty, Carlos, Dick, and Elgin went shopping. Each had a whole number of dollars to spend, and together they had $56$ dollars. The absolute difference between the amounts Ashley and Betty had to spend was $19$ dollars. The absolute difference between the amounts Betty and Carlos had was $7$ dollars, between Car... | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 365, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:14425"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"11"
] | [
"skywork"
] | 645472f0f32769749b292ad2ca249e62ad6c0d7034367c64122d1af496f4e4f7 | [
{
"content": "6 A country has $n$ airports, served by $k$ airlines, with some airports connected by direct flights (direct flights are bidirectional, meaning one can travel from $A$ to $B$ and from $B$ to $A$). If two airports are not directly connected, they can still be reached via connecting flights.\n(1) To... | 6 A country has $n$ airports, served by $k$ airlines, with some airports connected by direct flights (direct flights are bidirectional, meaning one can travel from $A$ to $B$ and from $B$ to $A$). If two airports are not directly connected, they can still be reached via connecting flights.
(1) To connect these $n$ airp... | "[\"11\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 363, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14426"}] | {
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} |
[
"16815"
] | [
"skywork"
] | c89194523f55ba71e07f1abd266c099703ef8b2ba4a5af78daffea8f5c9f935e | [
{
"content": "1. Take every two distinct numbers from the set $\\{1,2, \\cdots, 19\\}$ and multiply them. Then the sum of all such products is $\\qquad$",
"role": "user"
}
] | 1. Take every two distinct numbers from the set $\{1,2, \cdots, 19\}$ and multiply them. Then the sum of all such products is $\qquad$ | "[\"16815\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 390, "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:14427"}] | {
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"reference_components": 1,
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} |
[
"y^3 + 15y^2 - 198y + 1"
] | [
"skywork"
] | 96083e5dbbb45ef368579a3cb3fbcc189206de48b368f7df28e8aebe17b8918e | [
{
"content": "Let $P (x) = x^{3}-3x+1.$ Find the polynomial $Q$ whose roots are the fifth powers of the roots of $P$.",
"role": "user"
}
] | Let $P (x) = x^{3}-3x+1.$ Find the polynomial $Q$ whose roots are the fifth powers of the roots of $P$. | "[\"y^3 + 15y^2 - 198y + 1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 394, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14428"}] | {
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} |
[
"\\frac{125}{671}"
] | [
"skywork"
] | 94a36e6632e9ac32964ee6516fadd0ad90cde064ffba7ac1232f8d79e7ce27f8 | [
{
"content": "Alice, Bob, Carol, and David repeatedly take turns tossing a die, starting with Alice, followed by Bob, then Carol, and finally David. The sequence repeats in the same order. Find the probability that Carol will be the first to toss a six.",
"role": "user"
}
] | Alice, Bob, Carol, and David repeatedly take turns tossing a die, starting with Alice, followed by Bob, then Carol, and finally David. The sequence repeats in the same order. Find the probability that Carol will be the first to toss a six. | "[\"\\\\frac{125}{671}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 391, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:14429"}] | {
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"plain_numeric_reference": false,
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} |
[
"None"
] | [
"skywork"
] | 9b52c7fd6438f00c4cb14634373d03fc8ca312a6a667755780c4356a4dbc4334 | [
{
"content": "Tyler has two calculators, both of which initially display zero. The first calculators has only two buttons, $[+1]$ and $[\\times 2]$. The second has only the buttons $[+1]$ and $[\\times 4]$. Both calculators update their displays immediately after each keystroke. \n\nA positive integer $n$ is... | Tyler has two calculators, both of which initially display zero. The first calculators has only two buttons, $[+1]$ and $[\times 2]$. The second has only the buttons $[+1]$ and $[\times 4]$. Both calculators update their displays immediately after each keystroke.
A positive integer $n$ is called [i]ambivalent[/i] ... | "[\"None\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 388, "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:14430"}] | {
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} |
[
"\\frac{15}{23}"
] | [
"skywork"
] | 7dd49afa9a48000ab365d26c47875e6d921dd3680b1adbecb0977b688640c700 | [
{
"content": "2. Find the fraction of the form $\\frac{n}{23}$ that is closest to the fraction $\\frac{37}{57}$ ( $n$ - integer).",
"role": "user"
}
] | 2. Find the fraction of the form $\frac{n}{23}$ that is closest to the fraction $\frac{37}{57}$ ( $n$ - integer). | "[\"\\\\frac{15}{23}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 402, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:14431"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"25"
] | [
"skywork"
] | b18045b341f363c6701f82cc402d1c0db2f9879346a4f6354c8c494de5992bb8 | [
{
"content": "Let $x,y$ be real numbers such that $xy=1$. Let $T$ and $t$ be the largest and smallest values of the expression \\\\\n$\\hspace{2cm} \\frac{(x+y)^2-(x-y)-2}{(x+y)^2+(x-y)-2}$\\\\.\n\\\\\nIf $T+t$ can be expressed in the form $\\frac{m}{n}$ where $m,n$ are nonzero integers with $GCD(m,n)=1$, find ... | Let $x,y$ be real numbers such that $xy=1$. Let $T$ and $t$ be the largest and smallest values of the expression \\
$\hspace{2cm} \frac{(x+y)^2-(x-y)-2}{(x+y)^2+(x-y)-2}$\\.
\\
If $T+t$ can be expressed in the form $\frac{m}{n}$ where $m,n$ are nonzero integers with $GCD(m,n)=1$, find the value of $m+n$. | "[\"25\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 384, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:14432"}] | {
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[
"2005"
] | [
"skywork"
] | 833864723b823f3a717aecfc6382dd0e9f038b10a6cf296f7662954147dacb50 | [
{
"content": "12. Find the exact value of $\\sqrt{\\frac{x-2}{6}}$ when $x=2006^{3}-2004^{3}$.",
"role": "user"
}
] | 12. Find the exact value of $\sqrt{\frac{x-2}{6}}$ when $x=2006^{3}-2004^{3}$. | "[\"2005\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 404, "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:14433"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"26"
] | [
"skywork"
] | f3ab512ce278d3c983135eb5ab0b74af5ca72599d3962d76f9a90e694325b6d9 | [
{
"content": "Let $x_1, x_2, \\ldots, x_n$ be real numbers which satisfy $|x_i| < 1$ for $i = 1, 2, \\dots, n,$ and \\[|x_1| + |x_2| + \\dots + |x_n| = 25 + |x_1 + x_2 + \\dots + x_n|.\\] What is the smallest possible value of $n$?",
"role": "user"
}
] | Let $x_1, x_2, \ldots, x_n$ be real numbers which satisfy $|x_i| < 1$ for $i = 1, 2, \dots, n,$ and \[|x_1| + |x_2| + \dots + |x_n| = 25 + |x_1 + x_2 + \dots + x_n|.\] What is the smallest possible value of $n$? | "[\"26\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 400, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14435"}] | {
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"reference_present": true
} |
[
"7"
] | [
"skywork"
] | 947615fb678e01f518e2b94b895bc3fb18480030702060b25e515199edaa9da7 | [
{
"content": "Find the smallest positive integer $x$ which is greater than $1$ and relatively prime to $120$ (recall that relatively prime means that the GCD of $x$ and $120$ is $1$)",
"role": "user"
}
] | Find the smallest positive integer $x$ which is greater than $1$ and relatively prime to $120$ (recall that relatively prime means that the GCD of $x$ and $120$ is $1$) | "[\"7\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 405, "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:14436"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\pi}{3}"
] | [
"skywork"
] | a206daf7172e18e50ec9a9006b572ed053a46f312a2aa688500a3bf1b7f347b2 | [
{
"content": "Given non-zero vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfy $|\\overrightarrow{a}|=2|\\overrightarrow{b}|$, and $(\\overrightarrow{a}-\\overrightarrow{b})\\bot \\overrightarrow{b}$, calculate the angle between $\\overrightarrow{a}$ and $\\overrightarrow{b}$.",
"role": "user"... | Given non-zero vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfy $|\overrightarrow{a}|=2|\overrightarrow{b}|$, and $(\overrightarrow{a}-\overrightarrow{b})\bot \overrightarrow{b}$, calculate the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$. | "[\"\\\\frac{\\\\pi}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 407, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14437"}] | {
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} |
[
"\\frac{49}{128}"
] | [
"skywork"
] | e260fc43bbcaebd50bbcf69d3126c2861863e1f258ed1d19b5bd6a835a44fbbe | [
{
"content": "Given the function $g(x)=x-1$, and the function $f(x)$ satisfies $f(x+1)=-2f(x)-1$. When $x \\in (0,1]$, $f(x)=x^{2}-x$. For any $x_1 \\in (1,2]$ and $x_2 \\in R$, determine the minimum value of $(x_1-x_2)^2+(f(x_1)-g(x_2))^2$.",
"role": "user"
}
] | Given the function $g(x)=x-1$, and the function $f(x)$ satisfies $f(x+1)=-2f(x)-1$. When $x \in (0,1]$, $f(x)=x^{2}-x$. For any $x_1 \in (1,2]$ and $x_2 \in R$, determine the minimum value of $(x_1-x_2)^2+(f(x_1)-g(x_2))^2$. | "[\"\\\\frac{49}{128}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 383, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:14438"}] | {
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} |
[
"794598996"
] | [
"skywork"
] | 131ff41d24220e09959f5730865d59455e35d00fb7b4aed04722bd44be7406da | [
{
"content": "10. (20 points) Find\n$$\nf(x)=|x-1|+2|x-2|+\\cdots+2011|x-2011|\n$$\n\nthe minimum value.",
"role": "user"
}
] | 10. (20 points) Find
$$
f(x)=|x-1|+2|x-2|+\cdots+2011|x-2011|
$$
the minimum value. | "[\"794598996\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 392, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14439"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1792"
] | [
"skywork"
] | 127c96b2f249474b58bc122db744f65ef6aed44e5b9764f73e10276b635c0fb4 | [
{
"content": "11. (10 points) The cinema is screening four animated films: \"Toy Story\", \"Ice Age\", \"Shrek\", and \"The Monkey King\", with ticket prices of 50 yuan, 55 yuan, 60 yuan, and 65 yuan, respectively. Each audience member can watch at least one and at most two films. Due to time constraints, \"Ice... | 11. (10 points) The cinema is screening four animated films: "Toy Story", "Ice Age", "Shrek", and "The Monkey King", with ticket prices of 50 yuan, 55 yuan, 60 yuan, and 65 yuan, respectively. Each audience member can watch at least one and at most two films. Due to time constraints, "Ice Age" and "Shrek" cannot both b... | "[\"1792\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 395, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14440"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{4}"
] | [
"skywork"
] | 7449752761ea3b464f66509b285f0217d67cbed9bfa309b7d9db803897463973 | [
{
"content": "Determine the maximum of the expression\n\n$$\nx^{2} y+y^{2} z+z^{2} x-x^{2} z-y^{2} x-z^{2} y\n$$\n\nfor $0 \\leqslant x \\leqslant 1,0 \\leqslant y \\leqslant 1,0 \\leqslant z \\leqslant 1$.",
"role": "user"
}
] | Determine the maximum of the expression
$$
x^{2} y+y^{2} z+z^{2} x-x^{2} z-y^{2} x-z^{2} y
$$
for $0 \leqslant x \leqslant 1,0 \leqslant y \leqslant 1,0 \leqslant z \leqslant 1$. | "[\"\\\\frac{1}{4}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 403, "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:14441"}] | {
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[
"1"
] | [
"skywork"
] | 75ce49a1a9b880cf6d0c048afce43d64d182c183f18702a3893f744da4078037 | [
{
"content": "1. Let set $A=\\{-1,0,2\\}$, set $B=\\{-x \\mid x \\in A$, and $2-x \\notin A\\}$. Then $B=(\\quad$.\n(A) $\\{1\\}$\n(B) $\\{-2\\}$\n(C) $\\{-1,-2\\}$\n(D) $\\{-1,0\\}$",
"role": "user"
}
] | 1. Let set $A=\{-1,0,2\}$, set $B=\{-x \mid x \in A$, and $2-x \notin A\}$. Then $B=(\quad$.
(A) $\{1\}$
(B) $\{-2\}$
(C) $\{-1,-2\}$
(D) $\{-1,0\}$ | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 401, "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:14442"}] | {
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[
"4\\sqrt{e}-2"
] | [
"skywork"
] | 33d4eb6f2367ff4d6760a6af1b5170c87da47932106e4fd7308d87303b709ce3 | [
{
"content": "Given functions $f(x)=-2x$ for $x<0$ and $g(x)=\\frac{x}{\\ln x}+x-2$. If $f(x_{1})=g(x_{2})$, find the minimum value of $x_{2}-2x_{1}$.",
"role": "user"
}
] | Given functions $f(x)=-2x$ for $x<0$ and $g(x)=\frac{x}{\ln x}+x-2$. If $f(x_{1})=g(x_{2})$, find the minimum value of $x_{2}-2x_{1}$. | "[\"4\\\\sqrt{e}-2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 387, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14443"}] | {
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} |
[
"\\frac{1}{8}"
] | [
"skywork"
] | 5125b0e2c6eb0f09cca20ed859a90ed138165d6664feeb567984225f20b31942 | [
{
"content": "Four teams, including Quixajuba, are competing in a volleyball tournament where:\n\n- Each team plays against every other team exactly once;\n- Any match ends with one team winning;\n- In any match, the teams have an equal probability of winning;\n- At the end of the tournament, the teams are rank... | Four teams, including Quixajuba, are competing in a volleyball tournament where:
- Each team plays against every other team exactly once;
- Any match ends with one team winning;
- In any match, the teams have an equal probability of winning;
- At the end of the tournament, the teams are ranked by the number of victori... | "[\"\\\\frac{1}{8}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 397, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14444"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"18"
] | [
"skywork"
] | b7a5e7ab3e0b16aa753c40c836245daae1b571736e9ccf48028b492158703e5f | [
{
"content": "Find, with explanation, the maximum value of $f(x)=x^3-3x$ on the set of all real numbers $x$ satisfying $x^4+36\\leq 13x^2$.",
"role": "user"
}
] | Find, with explanation, the maximum value of $f(x)=x^3-3x$ on the set of all real numbers $x$ satisfying $x^4+36\leq 13x^2$. | "[\"18\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 398, "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:14445"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.467"
] | [
"skywork"
] | 7fded1086a30f5e56e1e3ba7eced554314d25e38385b409762c80fabb444539f | [
{
"content": "Example 10. Two positive numbers, each not greater than one, are taken at random. What is the probability that their sum does not exceed one and their product is no more than $2 / 9?$",
"role": "user"
}
] | Example 10. Two positive numbers, each not greater than one, are taken at random. What is the probability that their sum does not exceed one and their product is no more than $2 / 9?$ | "[\"0.467\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 413, "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:14446"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"{-1,2,0,3}"
] | [
"skywork"
] | ff15373efe733b06e5da973940dca1a7734f87cb882e12baca72c20678ffad82 | [
{
"content": "Example 2 If $x \\in\\left\\{-1,1,2, x^{2}-2 x\\right\\}$, then the set of real numbers $x$ is",
"role": "user"
}
] | Example 2 If $x \in\left\{-1,1,2, x^{2}-2 x\right\}$, then the set of real numbers $x$ is | "[\"{-1,2,0,3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 389, "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:14447"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"22"
] | [
"skywork"
] | 742a73be2a488bf913c3bfedbfe986a3cb26a0eac0ada49c96a7030bbe16786e | [
{
"content": "In response to the call of the commander, 55 soldiers came: archers and swordsmen. All of them were dressed either in golden or black armor. It is known that swordsmen tell the truth when wearing black armor and lie when wearing golden armor, while archers do the opposite.\n\n- To the question \"A... | In response to the call of the commander, 55 soldiers came: archers and swordsmen. All of them were dressed either in golden or black armor. It is known that swordsmen tell the truth when wearing black armor and lie when wearing golden armor, while archers do the opposite.
- To the question "Are you wearing golden arm... | "[\"22\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 399, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14448"}] | {
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"2a^2"
] | [
"skywork"
] | 2a020b337731ea4248d4f2b9999e6634f2640d5d3487550aa55e8324e47bcdaf | [
{
"content": "3. An equilateral triangle with side $a$ is inscribed in a circle. A point $M$ is chosen on the circle. Determine the sum of the squares of the distances from point $M$ to the vertices of the triangle.",
"role": "user"
}
] | 3. An equilateral triangle with side $a$ is inscribed in a circle. A point $M$ is chosen on the circle. Determine the sum of the squares of the distances from point $M$ to the vertices of the triangle. | "[\"2a^2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 417, "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:14449"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"35"
] | [
"skywork"
] | 9051eae7628349914823a98fcb8252762c11e67ce93f410b891a9bddf7fb5b57 | [
{
"content": "Alice and the Cheshire Cat play a game. At each step, Alice either (1) gives the cat a penny, which causes the cat to change the number of (magic) beans that Alice has from $n$ to $5n$ or (2) gives the cat a nickel, which causes the cat to give Alice another bean. Alice wins (and the cat disappear... | Alice and the Cheshire Cat play a game. At each step, Alice either (1) gives the cat a penny, which causes the cat to change the number of (magic) beans that Alice has from $n$ to $5n$ or (2) gives the cat a nickel, which causes the cat to give Alice another bean. Alice wins (and the cat disappears) as soon as the numb... | "[\"35\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 410, "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:14450"}] | {
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"reference_components": 1,
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} |
[
"75^{\\circ}"
] | [
"skywork"
] | 2c659ae3cb1a9f8a8663af846768e6df62185fde93cffb44f5b345908a2f94f2 | [
{
"content": "What is the measure of $\\angle X Z Y$ if $M$ is the midpoint of $Y Z$, $\\angle X M Z=30^{\\circ}$, and $\\angle X Y Z=15^{\\circ}$?",
"role": "user"
}
] | What is the measure of $\angle X Z Y$ if $M$ is the midpoint of $Y Z$, $\angle X M Z=30^{\circ}$, and $\angle X Y Z=15^{\circ}$? | "[\"75^{\\\\circ}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 416, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:14451"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | c1955dc31dd0ba48568eb6731e9ce2ac1e579c87b8928298769f2261e40c476d | [
{
"content": "1. Solve the equation $x^{2}+3+\\log _{2}\\left(x^{2}-4 x+6\\right)=4 x$.",
"role": "user"
}
] | 1. Solve the equation $x^{2}+3+\log _{2}\left(x^{2}-4 x+6\right)=4 x$. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 409, "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:14453"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | dcb1b40844c1917d764e6fdb33a4b363f4a0a780ccd330203aae44406d743059 | [
{
"content": "6. If $\\sin \\alpha+\\sin \\beta=1, \\cos \\alpha+\\cos \\beta=0$, then $\\cos 2 \\alpha+\\cos 2 \\beta=$",
"role": "user"
}
] | 6. If $\sin \alpha+\sin \beta=1, \cos \alpha+\cos \beta=0$, then $\cos 2 \alpha+\cos 2 \beta=$ | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 423, "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:14454"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"43"
] | [
"skywork"
] | c47eae4b559bde329f86b214c932b3908ad0cacbe3aed30d4b4165a349f073c2 | [
{
"content": "The number $m$ is a prime number between 30 and 50. If you divide $m$ by 12, the remainder is 7. What is the value of $m$?",
"role": "user"
}
] | The number $m$ is a prime number between 30 and 50. If you divide $m$ by 12, the remainder is 7. What is the value of $m$? | "[\"43\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 429, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14455"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-2"
] | [
"skywork"
] | 102b8e4ffbef741afd11b611d8859d8a7ff81f5235d7a30fc69a1cb2ae2ccbc2 | [
{
"content": "1. For what values of $a$ do the equations\n\n$$\nx^{2}+a x+1=0 \\quad \\text { and } \\quad x^{2}+x+a=0\n$$\n\nhave at least one common root?",
"role": "user"
}
] | 1. For what values of $a$ do the equations
$$
x^{2}+a x+1=0 \quad \text { and } \quad x^{2}+x+a=0
$$
have at least one common root? | "[\"-2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 431, "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:14456"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2028"
] | [
"skywork"
] | 86857375becc701643c889d50c2751617f574353d3e4f336bec46d8a2b6425ab | [
{
"content": "Let \\( p, q, r, s \\) be distinct real numbers such that the roots of \\( x^2 - 12px - 13q = 0 \\) are \\( r \\) and \\( s \\), and the roots of \\( x^2 - 12rx - 13s = 0 \\) are \\( p \\) and \\( q \\). Find the value of \\( p + q + r + s \\).",
"role": "user"
}
] | Let \( p, q, r, s \) be distinct real numbers such that the roots of \( x^2 - 12px - 13q = 0 \) are \( r \) and \( s \), and the roots of \( x^2 - 12rx - 13s = 0 \) are \( p \) and \( q \). Find the value of \( p + q + r + s \). | "[\"2028\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 412, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14457"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"3789"
] | [
"skywork"
] | e598245539a3632ca0cc7201eeb44a66274ebd52267556b486a40d0c1824b6fc | [
{
"content": "Example 12 The function $f: \\mathrm{N}^{+} \\rightarrow \\mathrm{N}^{+}$ satisfies\n(1) $f(n+1)>f(n)$,\n(2) $f[f(n)]=3 n$.\n\nFind $f(1992)$.",
"role": "user"
}
] | Example 12 The function $f: \mathrm{N}^{+} \rightarrow \mathrm{N}^{+}$ satisfies
(1) $f(n+1)>f(n)$,
(2) $f[f(n)]=3 n$.
Find $f(1992)$. | "[\"3789\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 422, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14458"}] | {
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"reference_present": true
} |
[
"1:4"
] | [
"skywork"
] | 2f254cb532798009a34bb6f8cf97ac8767e49d7db36116db59ac575411e9f0d8 | [
{
"content": "Given parallelogram ABCD with E the midpoint of diagonal BD. Point E is connected to a point F on DA such that DF = (2/5)DA. What is the ratio of the area of triangle DFE to the area of quadrilateral ABEF?",
"role": "user"
}
] | Given parallelogram ABCD with E the midpoint of diagonal BD. Point E is connected to a point F on DA such that DF = (2/5)DA. What is the ratio of the area of triangle DFE to the area of quadrilateral ABEF? | "[\"1:4\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 424, "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:14459"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"9\\pi-14\\arccos\\frac{1}{3}-4\\sqrt{2}"
] | [
"skywork"
] | 9dcb5977eb639717a68d2fbb8898749738e188a8aba828b68502623a27fd57c1 | [
{
"content": "5. The center of a circle with radius 2 lies on the circumference of a circle with radius 3. Find the area of the intersection of the circles bounded by these circumferences.",
"role": "user"
}
] | 5. The center of a circle with radius 2 lies on the circumference of a circle with radius 3. Find the area of the intersection of the circles bounded by these circumferences. | "[\"9\\\\pi-14\\\\arccos\\\\frac{1}{3}-4\\\\sqrt{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 419, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14460"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"45"
] | [
"skywork"
] | d5e2ef4cbd2090503c90b0d17272738a0325c128af0d4bbe31e14d32994a283f | [
{
"content": "3. In quadrilateral $A B C D$, side $A B$ is equal to diagonal $A C$ and is perpendicular to side $A D$, and diagonal $A C$ is perpendicular to side $C D$. A point $K$ is taken on side $A D$ such that $A C=A K$. The bisector of angle $A D C$ intersects $B K$ at point $M$. Find the angle $A C M$. (... | 3. In quadrilateral $A B C D$, side $A B$ is equal to diagonal $A C$ and is perpendicular to side $A D$, and diagonal $A C$ is perpendicular to side $C D$. A point $K$ is taken on side $A D$ such that $A C=A K$. The bisector of angle $A D C$ intersects $B K$ at point $M$. Find the angle $A C M$. (R. Zhenodarov) | "[\"45\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 415, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:14461"}] | {
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"any_reference_component_parses": true,
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} |
[
"\\sqrt{10}"
] | [
"skywork"
] | fb6b47ec2835f3d242d7593bb0be33ff43563bcf141a73c1ee974bcf520a2fb7 | [
{
"content": "Suppose $A B C$ is a triangle with circumcenter $O$ and orthocenter $H$ such that $A, B, C, O$, and $H$ are all on distinct points with integer coordinates. What is the second smallest possible value of the circumradius of $A B C$ ?",
"role": "user"
}
] | Suppose $A B C$ is a triangle with circumcenter $O$ and orthocenter $H$ such that $A, B, C, O$, and $H$ are all on distinct points with integer coordinates. What is the second smallest possible value of the circumradius of $A B C$ ? | "[\"\\\\sqrt{10}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 414, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14462"}] | {
"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
} |
[
"264"
] | [
"skywork"
] | 92c80b5873d775205976b47981cd52bf8c60906d65783ed99ee2f40658d86689 | [
{
"content": "For any real number $x$, $\\lfloor x \\rfloor$ represents the largest integer not exceeding $x$, for example: $\\lfloor 2 \\rfloor = 2$, $\\lfloor 3.2 \\rfloor = 3$. Then $\\lfloor \\log_{2}1 \\rfloor + \\lfloor \\log_{2}2 \\rfloor + \\lfloor \\log_{2}3 \\rfloor + \\ldots + \\lfloor \\log_{2}64 \\... | For any real number $x$, $\lfloor x \rfloor$ represents the largest integer not exceeding $x$, for example: $\lfloor 2 \rfloor = 2$, $\lfloor 3.2 \rfloor = 3$. Then $\lfloor \log_{2}1 \rfloor + \lfloor \log_{2}2 \rfloor + \lfloor \log_{2}3 \rfloor + \ldots + \lfloor \log_{2}64 \rfloor =$ ? | "[\"264\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 428, "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:14464"}] | {
"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"
] | a40328b2f730dd8e01351236ce228acbc96267948f69a1673e9bcb6251b6b9b2 | [
{
"content": "Suppose that $m$ and $n$ are integers with $1 \\leq m \\leq 49$ and $n \\geq 0$ such that $m$ divides $n^{n+1}+1$. What is the number of possible values of $m$ ?",
"role": "user"
}
] | Suppose that $m$ and $n$ are integers with $1 \leq m \leq 49$ and $n \geq 0$ such that $m$ divides $n^{n+1}+1$. What is the number of possible values of $m$ ? | "[\"29\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 434, "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:14465"}] | {
"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{57}{20}"
] | [
"skywork"
] | 73082916eb392964e4bb2ef3a08b9af31aebe49fba608895080d5beedb16ac54 | [
{
"content": "II. (50 points) Given the sequence $\\left\\{a_{n}\\right\\}$ defined by\n$$\na_{1}=\\frac{2}{3}, a_{n+1}=a_{n}^{2}+a_{n-1}^{2}+\\cdots+a_{1}^{2}\\left(n \\in \\mathbf{N}_{+}\\right)\n$$\n\nDetermine. If for any $n\\left(n \\in \\mathbf{N}_{+}\\right)$,\n$$\n\\frac{1}{a_{1}+1}+\\frac{1}{a_{2}+1}+\... | II. (50 points) Given the sequence $\left\{a_{n}\right\}$ defined by
$$
a_{1}=\frac{2}{3}, a_{n+1}=a_{n}^{2}+a_{n-1}^{2}+\cdots+a_{1}^{2}\left(n \in \mathbf{N}_{+}\right)
$$
Determine. If for any $n\left(n \in \mathbf{N}_{+}\right)$,
$$
\frac{1}{a_{1}+1}+\frac{1}{a_{2}+1}+\cdots+\frac{1}{a_{n}+1}<M
$$
holds true. Fin... | "[\"\\\\frac{57}{20}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 406, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14466"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"64"
] | [
"skywork"
] | 9d017ee5edd12682a2daadb0de5caf5ac505188b311cd6e293c211d7368dd8ec | [
{
"content": "16. (6 points) If a rectangular prism has a length that is twice its width, and a width that is twice its height, and the sum of all its edges is 56, then the volume of this rectangular prism is $\\qquad$ .",
"role": "user"
}
] | 16. (6 points) If a rectangular prism has a length that is twice its width, and a width that is twice its height, and the sum of all its edges is 56, then the volume of this rectangular prism is $\qquad$ . | "[\"64\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 418, "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:14467"}] | {
"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
} |
[
"421"
] | [
"skywork"
] | 9d494846f58e8a16fe93a5dffb33c26448ece3828bcab332a87e4094ef882131 | [
{
"content": "19. Erin lists all three-digit primes that are 21 less than a square. What is the mean of the numbers in Erin's list?",
"role": "user"
}
] | 19. Erin lists all three-digit primes that are 21 less than a square. What is the mean of the numbers in Erin's list? | "[\"421\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 425, "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:14468"}] | {
"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"
] | 1b6ccb99076b9ab76c14ca785ad56aa6370992662552345b6dbb2cdde72ad835 | [
{
"content": "8. Given $(\\sqrt{2}+1)^{21}=a+b \\sqrt{2}$, where $a, b$ are positive integers. Then $(b, 27)=$ $\\qquad$",
"role": "user"
}
] | 8. Given $(\sqrt{2}+1)^{21}=a+b \sqrt{2}$, where $a, b$ are positive integers. Then $(b, 27)=$ $\qquad$ | "[\"1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 421, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:14469"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"36"
] | [
"skywork"
] | 7ebdfcb287554ddd9cc774239b71a8bf908af88bd19ce09c149a3b7e7f41b241 | [
{
"content": "9. The ancient Greek mathematicians associated natural numbers with polygons in the following way,\nTriangular numbers: $1,3,6,10,15$, $\\qquad$\nSquare numbers: $1,4,9,16,25$, $\\qquad$\nPentagonal numbers: 1, 5, 12, 22, 35, $\\qquad$\nHexagonal numbers: $1,6,15,28,45$, $\\qquad$\nAccording to th... | 9. The ancient Greek mathematicians associated natural numbers with polygons in the following way,
Triangular numbers: $1,3,6,10,15$, $\qquad$
Square numbers: $1,4,9,16,25$, $\qquad$
Pentagonal numbers: 1, 5, 12, 22, 35, $\qquad$
Hexagonal numbers: $1,6,15,28,45$, $\qquad$
According to the above sequence, the 8th trian... | "[\"36\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 426, "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:14470"}] | {
"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
} |
[
"133"
] | [
"skywork"
] | 4f258dda650f8d5efb56ec892b6909afebd6e500a0dc2f813374a764f8c16aee | [
{
"content": "The first term of a sequence is 2005. Each succeeding term is the sum of the cubes of the digits of the previous terms. What is the 2005th term of the sequence?\r\n\r\n$ \\textbf{(A)}\\ 29\\qquad\r\n\\textbf{(B)}\\ 55\\qquad\r\n\\textbf{(C)}\\ 85\\qquad\r\n\\textbf{(D)}\\ 133\\qquad\r\n\\textbf{(E... | The first term of a sequence is 2005. Each succeeding term is the sum of the cubes of the digits of the previous terms. What is the 2005th term of the sequence?
$ \textbf{(A)}\ 29\qquad
\textbf{(B)}\ 55\qquad
\textbf{(C)}\ 85\qquad
\textbf{(D)}\ 133\qquad
\textbf{(E)}\ 250$ | "[\"133\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 430, "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:14471"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
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