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 |
|---|---|---|---|---|---|---|---|---|
[
"\\text{Bob}"
] | [
"skywork"
] | 6cee3273380897794c97457869bb70967c5eb0c6ff311249757297337d6e0f70 | [
{
"content": "Alice, Bob, Cindy, David, and Emily sit in a circle. Alice refuses to sit to the right of Bob, and Emily sits next to Cindy. If David sits next to two girls, determine who could sit immediately to the right of Alice.",
"role": "user"
}
] | Alice, Bob, Cindy, David, and Emily sit in a circle. Alice refuses to sit to the right of Bob, and Emily sits next to Cindy. If David sits next to two girls, determine who could sit immediately to the right of Alice. | "[\"\\\\text{Bob}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 544, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14578"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"504"
] | [
"skywork"
] | d43250ef58f7bd4137d26dc8be6fe6327619bd7135935bf714d588c85c6725ab | [
{
"content": "5. If 7 is subtracted from the thought three-digit number, the resulting difference will be divisible by 7; if 8 is subtracted, the resulting difference will be divisible by 8; if 9 is subtracted, the resulting difference will be divisible by 9. What is the smallest possible number thought of?",
... | 5. If 7 is subtracted from the thought three-digit number, the resulting difference will be divisible by 7; if 8 is subtracted, the resulting difference will be divisible by 8; if 9 is subtracted, the resulting difference will be divisible by 9. What is the smallest possible number thought of? | "[\"504\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 549, "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:14579"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"110111"
] | [
"skywork"
] | e023cb5e000378543737d4ad6de9b9ff1cf030f87e4b57f5b637aab60710444f | [
{
"content": "Find the product of $1011_2 \\cdot 101_2$. Express your answer in base 2.",
"role": "user"
}
] | Find the product of $1011_2 \cdot 101_2$. Express your answer in base 2. | "[\"110111\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 562, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14580"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"skywork"
] | 28322c8956e03122b70adccc3a07e70215c90ba3db268a0fa7c041b14ce6c52a | [
{
"content": "4. We will call a number greater than 25 semi-prime if it is the sum of some two distinct prime numbers. What is the maximum number of consecutive natural numbers that can be semi-prime?",
"role": "user"
}
] | 4. We will call a number greater than 25 semi-prime if it is the sum of some two distinct prime numbers. What is the maximum number of consecutive natural numbers that can be semi-prime? | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 552, "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:14581"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"32"
] | [
"skywork"
] | bce4e3ba0887d4560ee967ec3dc9672d94b4151933bc313e88d9402fb603a24e | [
{
"content": "The altitudes of an acute-angled triangle $ABC$, drawn from vertices $B$ and $C$, are 7 and 9, respectively, and the median $AM$ is 8. Points $P$ and $Q$ are symmetric to point $M$ with respect to sides $AC$ and $AB$, respectively. Find the perimeter of quadrilateral $APMQ$.\n\n#",
"role": "us... | The altitudes of an acute-angled triangle $ABC$, drawn from vertices $B$ and $C$, are 7 and 9, respectively, and the median $AM$ is 8. Points $P$ and $Q$ are symmetric to point $M$ with respect to sides $AC$ and $AB$, respectively. Find the perimeter of quadrilateral $APMQ$.
# | "[\"32\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 538, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14582"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"8\\sqrt{3}"
] | [
"skywork"
] | 13c31df967c23d4af0a222e044b538636cb4f178924ea21323615b49bf7a5ea7 | [
{
"content": "7. Given a sphere with a radius of 3. Then the maximum volume of the inscribed regular tetrahedron is $\\qquad$ .",
"role": "user"
}
] | 7. Given a sphere with a radius of 3. Then the maximum volume of the inscribed regular tetrahedron is $\qquad$ . | "[\"8\\\\sqrt{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 555, "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:14583"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 4dd2e9ee2b09be049179228d606615664891bae50c770024f9908e21b2612b09 | [
{
"content": "15. Triangle $P Q R$ has been divided into twenty-five congruent right-angled triangles, as shown. The length of $R P$ is $2.4 \\mathrm{~cm}$. What is the length of $P Q$ ?\nA $3 \\mathrm{~cm}$\nB $3.2 \\mathrm{~cm}$\nC $3.6 \\mathrm{~cm}$\nD $4 \\mathrm{~cm}$\nE $4.8 \\mathrm{~cm}$",
"role": ... | 15. Triangle $P Q R$ has been divided into twenty-five congruent right-angled triangles, as shown. The length of $R P$ is $2.4 \mathrm{~cm}$. What is the length of $P Q$ ?
A $3 \mathrm{~cm}$
B $3.2 \mathrm{~cm}$
C $3.6 \mathrm{~cm}$
D $4 \mathrm{~cm}$
E $4.8 \mathrm{~cm}$ | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 548, "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:14584"}] | {
"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
} |
[
"56.20"
] | [
"skywork"
] | daf2d15146f8263a7406f4cf79ccfede08f5ab155da3a36afa061273cf31e0e1 | [
{
"content": "Davi goes to a warehouse that sells a bottle of orange juice for $\\mathrm{R} \\$ 2.80$ and a box with six of these bottles for $\\mathrm{R} \\$ 15.00$. He needs to buy 22 bottles for his birthday. How much will he spend, at a minimum?",
"role": "user"
}
] | Davi goes to a warehouse that sells a bottle of orange juice for $\mathrm{R} \$ 2.80$ and a box with six of these bottles for $\mathrm{R} \$ 15.00$. He needs to buy 22 bottles for his birthday. How much will he spend, at a minimum? | "[\"56.20\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 559, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14585"}] | {
"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
} |
[
"963090"
] | [
"skywork"
] | 1689d0c59ea540d61e217028a4b17a018fc3a755f78e23d7aebd343e8f250b73 | [
{
"content": "19. A bank issues ATM cards to its customers. Each card is associated with a password, which consists of 6 digits with no three consecutive digits being the same. It is known that no two cards have the same password. What is the maximum number of ATM cards the bank has issued?\n\nA bank issues ATM... | 19. A bank issues ATM cards to its customers. Each card is associated with a password, which consists of 6 digits with no three consecutive digits being the same. It is known that no two cards have the same password. What is the maximum number of ATM cards the bank has issued?
A bank issues ATM cards to its customers.... | "[\"963090\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 550, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14586"}] | {
"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
} |
[
"42"
] | [
"skywork"
] | 23d185c8fa983abffb9b2b16e28c6664b265cfe49d03c4a4b73f6c2c310f33ee | [
{
"content": "5. (10 points) 30 students are lined up in ascending order of height, with the height difference between adjacent students being the same. The sum of the heights of the first 10 students is 12.5 meters, and the sum of the heights of the first 20 students is 26.5 meters. What is the sum of the heig... | 5. (10 points) 30 students are lined up in ascending order of height, with the height difference between adjacent students being the same. The sum of the heights of the first 10 students is 12.5 meters, and the sum of the heights of the first 20 students is 26.5 meters. What is the sum of the heights of these 30 studen... | "[\"42\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 569, "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:14587"}] | {
"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
} |
[
"x=\\frac{23}{10}, y=\\frac{23}{6}, z=\\frac{23}{2}"
] | [
"skywork"
] | 244d2cca7a38ab21ff8f5ed8800d8d751ff7cd57cb998b2a61ff0be9b6db7473 | [
{
"content": "Example 12 Solve the system of equations\n$$\n\\left\\{\\begin{array}{l}\n\\frac{1}{x}+\\frac{1}{y+z}=\\frac{1}{2}, \\\\\n\\frac{1}{y}+\\frac{1}{z+x}=\\frac{1}{3}, \\\\\n\\frac{1}{z}+\\frac{1}{x+y}=\\frac{1}{4} .\n\\end{array}\\right.\n$$\n(1996, Beijing Junior High School Mathematics Competition)... | Example 12 Solve the system of equations
$$
\left\{\begin{array}{l}
\frac{1}{x}+\frac{1}{y+z}=\frac{1}{2}, \\
\frac{1}{y}+\frac{1}{z+x}=\frac{1}{3}, \\
\frac{1}{z}+\frac{1}{x+y}=\frac{1}{4} .
\end{array}\right.
$$
(1996, Beijing Junior High School Mathematics Competition) | "[\"x=\\\\frac{23}{10}, y=\\\\frac{23}{6}, z=\\\\frac{23}{2}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 557, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14588"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"x_{\\}=x_{\\max}=2"
] | [
"skywork"
] | 15218bc553729d72c9675eaac3ab5455d5f2d70b5389bcb005d232edd52df6c9 | [
{
"content": "3.15. Find all positive solutions ($x_{1}>0, x_{2}>0$, $x_{3}>0, x_{4}>0, x_{5}>0$) of the system of equations\n\n$$\n\\left\\{\\begin{array}{l}\nx_{1}+x_{2}=x_{3}^{2} \\\\\nx_{2}+x_{3}=x_{4}^{2} \\\\\nx_{3}+x_{4}=x_{5}^{2} \\\\\nx_{4}+x_{5}=x_{1}^{2} \\\\\nx_{5}+x_{1}=x_{2}^{2}\n\\end{array}\\rig... | 3.15. Find all positive solutions ($x_{1}>0, x_{2}>0$, $x_{3}>0, x_{4}>0, x_{5}>0$) of the system of equations
$$
\left\{\begin{array}{l}
x_{1}+x_{2}=x_{3}^{2} \\
x_{2}+x_{3}=x_{4}^{2} \\
x_{3}+x_{4}=x_{5}^{2} \\
x_{4}+x_{5}=x_{1}^{2} \\
x_{5}+x_{1}=x_{2}^{2}
\end{array}\right.
$$
## 3.4. The number of solutions of t... | "[\"x_{\\\\}=x_{\\\\max}=2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 546, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14589"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{S}{3}\\sqrt{\\frac{S}{2\\pi}}"
] | [
"skywork"
] | 0e5b77292db8e6039e4d24e85f53ef068671f56d72da30f38eae3439b6e156d7 | [
{
"content": "235. The surface area of a spherical segment is $S$ (the spherical part of the segment is considered). Find the maximum value of the volume of this segment.",
"role": "user"
}
] | 235. The surface area of a spherical segment is $S$ (the spherical part of the segment is considered). Find the maximum value of the volume of this segment. | "[\"\\\\frac{S}{3}\\\\sqrt{\\\\frac{S}{2\\\\pi}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 560, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:14591"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 8cc6c66c668bea1bfc31f4223a59b91e26f01231d96154b8763fb0d44b3c3c87 | [
{
"content": "Let $m=\\underbrace{22222222}_{\\text{8 digits}}$ and $n=\\underbrace{444444444}_{\\text{9 digits}}$.\n\nWhat is $\\gcd(m,n)$?",
"role": "user"
}
] | Let $m=\underbrace{22222222}_{\text{8 digits}}$ and $n=\underbrace{444444444}_{\text{9 digits}}$.
What is $\gcd(m,n)$? | "[\"2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 580, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:14592"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"84"
] | [
"skywork"
] | 61da314c3834ab33e13aba045a8e148ed5c6ec71ae0bafef8a265bd18fef444c | [
{
"content": "Suppose $x$ and $y$ are positive real numbers such that $x^2 - 3xy + 4y^2 = 12$. Find the maximum possible value of $x^2 + 3xy + 4y^2$.",
"role": "user"
}
] | Suppose $x$ and $y$ are positive real numbers such that $x^2 - 3xy + 4y^2 = 12$. Find the maximum possible value of $x^2 + 3xy + 4y^2$. | "[\"84\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 571, "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:14593"}] | {
"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{9\\sqrt{2}}{32}"
] | [
"skywork"
] | 16eac10fa67b743f014ebb5b603e68891e4b235f0f4d81eb4ab5a6900fb2b6c5 | [
{
"content": "Example 10 (47th IMO Problem) Find the smallest real number $M$ such that for all real numbers $a, b, c$, we have\n$$\n\\left|a b\\left(a^{2}-b^{2}\\right)+b c\\left(b^{2}-c^{2}\\right)+c a\\left(c^{2}-a^{2}\\right)\\right| \\leqslant M\\left(a^{2}+b^{2}+c^{2}\\right)^{2} .\n$$",
"role": "user... | Example 10 (47th IMO Problem) Find the smallest real number $M$ such that for all real numbers $a, b, c$, we have
$$
\left|a b\left(a^{2}-b^{2}\right)+b c\left(b^{2}-c^{2}\right)+c a\left(c^{2}-a^{2}\right)\right| \leqslant M\left(a^{2}+b^{2}+c^{2}\right)^{2} .
$$ | "[\"\\\\frac{9\\\\sqrt{2}}{32}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 563, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14594"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2.4"
] | [
"skywork"
] | 1997a4614d0ccb032ade6f83c25c0dfa05013229b169eecfb0701553ebf7728d | [
{
"content": "A store has equal amounts of candies priced at 2 rubles per kilogram and candies priced at 3 rubles per kilogram. At what price should the mixture of these candies be sold?",
"role": "user"
}
] | A store has equal amounts of candies priced at 2 rubles per kilogram and candies priced at 3 rubles per kilogram. At what price should the mixture of these candies be sold? | "[\"2.4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 561, "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:14595"}] | {
"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
} |
[
"x = n \\pm \\sqrt{n^2 - m^2}"
] | [
"skywork"
] | ba0d45e6671c57580b6a360909f2ebce8e9269e48ded9e905ab91306de724c72 | [
{
"content": "Given a rectangle $ABCD$, side $AB$ is longer than side $BC$. Find all the points $P$ of the side line $AB$ from which the sides $AD$ and $DC$ are seen from the point $P$ at an equal angle (i.e. $\\angle APD = \\angle DPC$)",
"role": "user"
}
] | Given a rectangle $ABCD$, side $AB$ is longer than side $BC$. Find all the points $P$ of the side line $AB$ from which the sides $AD$ and $DC$ are seen from the point $P$ at an equal angle (i.e. $\angle APD = \angle DPC$) | "[\" x = n \\\\pm \\\\sqrt{n^2 - m^2} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 575, "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:14596"}] | {
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[
"78,84,96"
] | [
"skywork"
] | 569d13260fc0de18d0977ad4992be28d99b89760164dde3d13d4df1b76d5f5d7 | [
{
"content": "4. When written in ascending order, the nine internal angles from three particular triangles form a sequence where the difference between any adjacent pair of numbers in the sequence is a constant $d$. One of the angles measures $42^{\\circ}$. Find all possible values of the size of the largest of... | 4. When written in ascending order, the nine internal angles from three particular triangles form a sequence where the difference between any adjacent pair of numbers in the sequence is a constant $d$. One of the angles measures $42^{\circ}$. Find all possible values of the size of the largest of the nine angles. | "[\"78,84,96\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 558, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14597"}] | {
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} |
[
"856"
] | [
"skywork"
] | 04bb8b112fb2db34d52d6db04088ccdbd085759e33a1b47a5be48668e3309383 | [
{
"content": "Nine hundred forty-three minus eighty-seven equals what number?",
"role": "user"
}
] | Nine hundred forty-three minus eighty-seven equals what number? | "[\"856\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 595, "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:14598"}] | {
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[
"12"
] | [
"skywork"
] | 60777f554cb2edf0a98764788ebf878867eaa6a2eb469f0777dd8ea6b634c162 | [
{
"content": "Let $P$ be a point outside of circle $O.$ A segment is drawn from $P$ such that it is tangent to circle $O$ at point $T.$ Meanwhile, a secant from $P$ intersects $O$ at $A$ and $B,$ such that $PA < PB.$ If $PA = 3$ and $PT = AB - PA,$ then what is $PB$?",
"role": "user"
}
] | Let $P$ be a point outside of circle $O.$ A segment is drawn from $P$ such that it is tangent to circle $O$ at point $T.$ Meanwhile, a secant from $P$ intersects $O$ at $A$ and $B,$ such that $PA < PB.$ If $PA = 3$ and $PT = AB - PA,$ then what is $PB$? | "[\"12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 564, "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:14599"}] | {
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[
"12"
] | [
"skywork"
] | ae8ce5b7b3e4d70177a1bb222dc5e4ea066708a083af037a2f86c21a80c01c30 | [
{
"content": "Find $x$ such that $\\lceil x \\rceil \\cdot x = 156$. Express $x$ as a decimal.",
"role": "user"
}
] | Find $x$ such that $\lceil x \rceil \cdot x = 156$. Express $x$ as a decimal. | "[\"12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 591, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14600"}] | {
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} |
[
"4\\pi"
] | [
"skywork"
] | 770d66b83247a13127f922aaa75bdae350b98361ef354b5131ac41e97a64df0e | [
{
"content": "(11) The smallest positive period of the function $f(x)=2 \\sin \\frac{x}{2}-\\sqrt{3} \\cos x$ is",
"role": "user"
}
] | (11) The smallest positive period of the function $f(x)=2 \sin \frac{x}{2}-\sqrt{3} \cos x$ is | "[\"4\\\\pi\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 582, "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:14601"}] | {
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} |
[
"703.125"
] | [
"skywork"
] | c2ac65baec0963856cb16f8f26cc54a1833ab99062de6e908859bd6d0acdd175 | [
{
"content": "Find the area of the region enclosed by the graph of \\( |x-75| + |y| = \\left|\\frac{x}{3}\\right| \\).",
"role": "user"
}
] | Find the area of the region enclosed by the graph of \( |x-75| + |y| = \left|\frac{x}{3}\right| \). | "[\"703.125\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 572, "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:14602"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"32"
] | [
"skywork"
] | fb222c4642e5b81e1b7f4a4919b2f71e20e59af3aecdaf6761867fad8c7fcf98 | [
{
"content": "Triangle $ABC$ has side lengths $AB=4$, $BC=5$, and $CA=6$. Points $D$ and $E$ are on ray $AB$ with $AB<AD<AE$. The point $F \\neq C$ is a point of intersection of the circumcircles of $\\triangle ACD$ and $\\triangle EBC$ satisfying $DF=2$ and $EF=7$. Then $BE$ can be expressed as $\\tfrac{a+b\\s... | Triangle $ABC$ has side lengths $AB=4$, $BC=5$, and $CA=6$. Points $D$ and $E$ are on ray $AB$ with $AB<AD<AE$. The point $F \neq C$ is a point of intersection of the circumcircles of $\triangle ACD$ and $\triangle EBC$ satisfying $DF=2$ and $EF=7$. Then $BE$ can be expressed as $\tfrac{a+b\sqrt{c}}{d}$, where $a$, $b$... | "[\"32\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 565, "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:14603"}, {"dataset": "skywork", "extra_i... | {
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[
"101"
] | [
"skywork"
] | d46064c6fcac6e51e5011f689d728fff383e17d0c58a9d01f796c35de19a9e82 | [
{
"content": "Let \\( n \\geq 1 \\) be a positive integer. We say that an integer \\( k \\) is a fan of \\( n \\) if \\( 0 \\leq k \\leq n-1 \\) and there exist integers \\( x, y, z \\in \\mathbb{Z} \\) such that\n\\[ \n\\begin{aligned}\nx^2 + y^2 + z^2 &\\equiv 0 \\pmod{n}; \\\\\nxyz &\\equiv k \\pmod{n}.\n\\e... | Let \( n \geq 1 \) be a positive integer. We say that an integer \( k \) is a fan of \( n \) if \( 0 \leq k \leq n-1 \) and there exist integers \( x, y, z \in \mathbb{Z} \) such that
\[
\begin{aligned}
x^2 + y^2 + z^2 &\equiv 0 \pmod{n}; \\
xyz &\equiv k \pmod{n}.
\end{aligned}
\]
Let \( f(n) \) be the number of fans... | "[\"101\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 566, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14604"}] | {
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[
"20"
] | [
"skywork"
] | 32be5b5e642bb71340c9161b24f63d213c70ed5d8587266f84d67de0a574d566 | [
{
"content": "Determine the number of positive integers $a \\le 250$ for which the set $\\{a+1, a+2, \\dots, a+1000\\}$ contains\n\n$\\bullet$ Exactly $333$ multiples of $3$,\n$\\bullet$ Exactly $142$ multiples of $7$, and\n$\\bullet$ Exactly $91$ multiples of $11$.\n\n[i]Based on a proposal by Rajiv Movva[/i]"... | Determine the number of positive integers $a \le 250$ for which the set $\{a+1, a+2, \dots, a+1000\}$ contains
$\bullet$ Exactly $333$ multiples of $3$,
$\bullet$ Exactly $142$ multiples of $7$, and
$\bullet$ Exactly $91$ multiples of $11$.
[i]Based on a proposal by Rajiv Movva[/i] | "[\"20\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 574, "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:14605"}] | {
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} |
[
"1010"
] | [
"skywork"
] | 2b3eac61a1c799bce58af2e8ebdcb5b7b7184f85324f514e0a42db272c8cfa81 | [
{
"content": "We write the following equation: \\((x-1) \\ldots (x-2020) = (x-1) \\ldots (x-2020)\\). What is the minimal number of factors that need to be erased so that there are no real solutions?",
"role": "user"
}
] | We write the following equation: \((x-1) \ldots (x-2020) = (x-1) \ldots (x-2020)\). What is the minimal number of factors that need to be erased so that there are no real solutions? | "[\"1010\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 545, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:14606"}] | {
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[
"13"
] | [
"skywork"
] | 1cdeba5313c358fca19882cf3231fec831c945985b6af5706c7d33e1563f78b4 | [
{
"content": "Task 2. Find all integers $n$ for which $\\frac{4 n-2}{n+5}$ is the square of a rational number. (A rational number is a number in $\\mathbb{Q}$.)",
"role": "user"
}
] | Task 2. Find all integers $n$ for which $\frac{4 n-2}{n+5}$ is the square of a rational number. (A rational number is a number in $\mathbb{Q}$.) | "[\"13\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 584, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14607"}] | {
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} |
[
"S_{n}=\\frac{n(n+1)(n+2)}{3}+\\frac{(-1)^{n}-1}{2}"
] | [
"skywork"
] | 528f58ed3bcd3f488acfed11f65187e59b57aa48d4609ed91c4502df36630034 | [
{
"content": "Let's determine the sum of the first $n$ terms of the following sequence:\n\n$$\n1+7+11+21+\\cdots+\\left[n(n+1)+(-1)^{n}\\right]\n$$",
"role": "user"
}
] | Let's determine the sum of the first $n$ terms of the following sequence:
$$
1+7+11+21+\cdots+\left[n(n+1)+(-1)^{n}\right]
$$ | "[\"S_{n}=\\\\frac{n(n+1)(n+2)}{3}+\\\\frac{(-1)^{n}-1}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 577, "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:14608"}] | {
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} |
[
"7"
] | [
"skywork"
] | 381b4fd9823ef8aa94cfcc625fd7f9e2fe0eca32cabd57ea93a6f07d9df1ae30 | [
{
"content": "9.5. Let $M$ - be a finite set of numbers (distinct). It is known that among any three of its elements, there will be two whose sum belongs to $M$. What is the maximum number of elements that can be in $M$?",
"role": "user"
}
] | 9.5. Let $M$ - be a finite set of numbers (distinct). It is known that among any three of its elements, there will be two whose sum belongs to $M$. What is the maximum number of elements that can be in $M$? | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 578, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14609"}] | {
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} |
[
"\\frac{5}{3}"
] | [
"skywork"
] | 5ae224bf2012bf9a975e1ce16cf5508ec42062acec72490feaeb8df450770ff8 | [
{
"content": "What is the value of $\\frac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}}$?",
"role": "user"
}
] | What is the value of $\frac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}}$? | "[\"\\\\frac{5}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 600, "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:14610"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2^3"
] | [
"skywork"
] | eb1e97cae3e631cabc178cac3b5cd199bf61bd1b75956542227d67bebd59c92e | [
{
"content": "What is the value of \\( \\sqrt{16 \\times \\sqrt{16}} \\)?",
"role": "user"
}
] | What is the value of \( \sqrt{16 \times \sqrt{16}} \)? | "[\"2^3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 598, "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:14611"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"8"
] | [
"skywork"
] | 9d7e2803484f329100968302a03c6e1e3dc62e8ebf1782cd173e65f32c311431 | [
{
"content": "Each cell of an $100\\times 100$ board is divided into two triangles by drawing some diagonal. What is the smallest number of colors in which it is always possible to paint these triangles so that any two triangles having a common side or vertex have different colors?",
"role": "user"
}
] | Each cell of an $100\times 100$ board is divided into two triangles by drawing some diagonal. What is the smallest number of colors in which it is always possible to paint these triangles so that any two triangles having a common side or vertex have different colors? | "[\"8\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 589, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14612"}] | {
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"reference_present": true
} |
[
"(2,-2),(-2,2)"
] | [
"skywork"
] | 763c1c0feb8bb6e0ffc5a549485b009e68a5057285517dade3ab5b6ffe5bb1be | [
{
"content": "2. Find all integer solutions $(x, y)$ of the following equation:\n$$\n7 x^{2}-40 x y+7 y^{2}=(|x-y|+2)^{3} \\text {. }\n$$",
"role": "user"
}
] | 2. Find all integer solutions $(x, y)$ of the following equation:
$$
7 x^{2}-40 x y+7 y^{2}=(|x-y|+2)^{3} \text {. }
$$ | "[\"(2,-2),(-2,2)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 590, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14613"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2+ \\sqrt {2}"
] | [
"skywork"
] | ddf35fa688adff8d430d80a8d071bbd5eaf3a0d0e10973d8d1951371a1d7062c | [
{
"content": "In the rectangular coordinate system xOy, the parametric equation of line l is $$\\begin{cases} \\overset{x=t}{y=1+t}\\end{cases}$$ (t is the parameter), line m is parallel to line l and passes through the coordinate origin, and the parametric equation of circle C is $$\\begin{cases} \\overset{x=1... | In the rectangular coordinate system xOy, the parametric equation of line l is $$\begin{cases} \overset{x=t}{y=1+t}\end{cases}$$ (t is the parameter), line m is parallel to line l and passes through the coordinate origin, and the parametric equation of circle C is $$\begin{cases} \overset{x=1+cos\phi }{y=2+sin\phi }\en... | "[\"2+ \\\\sqrt {2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 551, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14614"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"(2, 5)"
] | [
"skywork"
] | e006fda04997767ea299d0685ffae2317332a0c092637860f82557d375778b0b | [
{
"content": "Determine all pairs $(p, q)$ of prime numbers such that $p^p + q^q + 1$ is divisible by $pq.$",
"role": "user"
}
] | Determine all pairs $(p, q)$ of prime numbers such that $p^p + q^q + 1$ is divisible by $pq.$ | "[\" (2, 5) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 579, "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:14615"}] | {
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[
"13"
] | [
"skywork"
] | 1d63da394c667d8e7b6e23d47bdad11f58f005d1f6232b28c17aeca9b8d3809d | [
{
"content": "How many integers $-15 \\leq n \\leq 15$ satisfy $(n-3)(n+5)(n+9) < 0$?",
"role": "user"
}
] | How many integers $-15 \leq n \leq 15$ satisfy $(n-3)(n+5)(n+9) < 0$? | "[\"13\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 604, "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:14616"}] | {
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"-2"
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"skywork"
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{
"content": "Given triangle $ABC$ with midpoint $D$ on side $BC$, and point $G$ satisfies $\\overrightarrow{GA}+ \\overrightarrow{BG}+ \\overrightarrow{CG}= \\overrightarrow{0}$, and $\\overrightarrow{AG}=\\lambda \\overrightarrow{GD}$, determine the value of $\\lambda$.",
"role": "user"
}
] | Given triangle $ABC$ with midpoint $D$ on side $BC$, and point $G$ satisfies $\overrightarrow{GA}+ \overrightarrow{BG}+ \overrightarrow{CG}= \overrightarrow{0}$, and $\overrightarrow{AG}=\lambda \overrightarrow{GD}$, determine the value of $\lambda$. | "[\"-2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 588, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14617"}] | {
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"skywork"
] | 02bbfc291a87bdf7bc7088d7edb8ba94a23b502500a632a2cac88c16d7e1b0a9 | [
{
"content": "A teacher drew a rectangle $ABCD$ on the board. A student named Petya divided this rectangle into two rectangles with a line parallel to side $AB$. It turned out that the areas of these parts are in the ratio 1:2, and their perimeters are in the ratio 3:5 (in the same order). Another student named... | A teacher drew a rectangle $ABCD$ on the board. A student named Petya divided this rectangle into two rectangles with a line parallel to side $AB$. It turned out that the areas of these parts are in the ratio 1:2, and their perimeters are in the ratio 3:5 (in the same order). Another student named Vasya divided this re... | "[\"20/19\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 567, "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:14618"}] | {
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[
"6"
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{
"content": "\\section*{Problem 19}\n\nA polygonal line connects two opposite vertices of a cube with side 2 . Each segment of the line has length 3 and each vertex lies on the faces (or edges) of the cube. What is the smallest number of segments the line can have?\n\n\\section*{Answer \\(\\quad 6\\)}",
"r... | \section*{Problem 19}
A polygonal line connects two opposite vertices of a cube with side 2 . Each segment of the line has length 3 and each vertex lies on the faces (or edges) of the cube. What is the smallest number of segments the line can have?
\section*{Answer \(\quad 6\)} | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 586, "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:14619"}] | {
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[
"57"
] | [
"skywork"
] | bcdf837c01aa26be238ee22b4621c7cc986e036e339e324dba891df3c268b9c6 | [
{
"content": "If the integers \\( a, b, \\) and \\( c \\) satisfy:\n\\[\na + b + c = 3, \\quad a^3 + b^3 + c^3 = 3,\n\\]\nthen what is the maximum value of \\( a^2 + b^2 + c^2 \\)?",
"role": "user"
}
] | If the integers \( a, b, \) and \( c \) satisfy:
\[
a + b + c = 3, \quad a^3 + b^3 + c^3 = 3,
\]
then what is the maximum value of \( a^2 + b^2 + c^2 \)? | "[\"57\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 592, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "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:14620"}] | {
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[
"18"
] | [
"skywork"
] | 8462b77f590288d819933d37b4a8f171095dbe61e5009b4f9dfa72d00fdc5106 | [
{
"content": "A circle with a radius of 3 units has its center at $(0, 0)$. Another circle with a radius of 5 units has its center at $(12, 0)$. A line tangent to both these circles intersects the $x$-axis at $(x, 0)$ to the right of the origin. Determine the value of $x$. Express your answer as a common fracti... | A circle with a radius of 3 units has its center at $(0, 0)$. Another circle with a radius of 5 units has its center at $(12, 0)$. A line tangent to both these circles intersects the $x$-axis at $(x, 0)$ to the right of the origin. Determine the value of $x$. Express your answer as a common fraction. | "[\"18\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 596, "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:14621"}] | {
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"32"
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"skywork"
] | b34dfc8d379d17b530df67042b21ba79ed219cc2c59525f6594f78224e8494fa | [
{
"content": "One, (40 points) Let $S$ be a set of positive integers with the property: for any $x \\in S$, the arithmetic mean of the remaining numbers in $S$ after removing $x$ is a positive integer, and it satisfies $1 \\in S$, 2016 is the maximum element of $S$. Find the maximum value of $|S|$.",
"role"... | One, (40 points) Let $S$ be a set of positive integers with the property: for any $x \in S$, the arithmetic mean of the remaining numbers in $S$ after removing $x$ is a positive integer, and it satisfies $1 \in S$, 2016 is the maximum element of $S$. Find the maximum value of $|S|$. | "[\"32\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 594, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:14622"}] | {
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"\\sqrt{3}"
] | [
"skywork"
] | 3c5a42bb3690553fbd7b8b5da3ec156b822556b2f6519dd97e3ee08a87715122 | [
{
"content": "2. In rectangle $A B C D$, points $E$ and $F$ lie on sides $A B$ and $C D$ respectively such that both $A F$ and $C E$ are perpendicular to diagonal $B D$. Given that $B F$ and $D E$ separate $A B C D$ into three polygons with equal area, and that $E F=1$, find the length of $B D$.",
"role": "... | 2. In rectangle $A B C D$, points $E$ and $F$ lie on sides $A B$ and $C D$ respectively such that both $A F$ and $C E$ are perpendicular to diagonal $B D$. Given that $B F$ and $D E$ separate $A B C D$ into three polygons with equal area, and that $E F=1$, find the length of $B D$. | "[\"\\\\sqrt{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 581, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14623"}] | {
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"skywork"
] | 0a11eb2c1e425e735d7be15962a142c1dbf02686acbaf0f6d498605d6b0ca041 | [
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"content": "13. An ant crawls along the edges of a cube with side length 1 unit. Starting from one of the vertices, in each minute the ant travels from one vertex to an adjacent vertex. After crawling for 7 minutes, the ant is at a distance of $\\sqrt{3}$ units from the starting point. Find the number of poss... | 13. An ant crawls along the edges of a cube with side length 1 unit. Starting from one of the vertices, in each minute the ant travels from one vertex to an adjacent vertex. After crawling for 7 minutes, the ant is at a distance of $\sqrt{3}$ units from the starting point. Find the number of possible routes the ant has... | "[\"546\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 576, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14624"}] | {
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[
"90"
] | [
"skywork"
] | 71172fbebc548a3bbab1c6360e44f52e965a3f44cebdf540172752bc7debe24c | [
{
"content": "Obukhov B B.\n\nGiven a convex pentagon $A B C D E$, all sides of which are equal. It is known that angle $A$ is $120^{\\circ}$, angle $C$ is $135^{\\circ}$, and angle $D$ is $n^{\\circ}$.\n\nFind all possible integer values of $n$.\n\n#",
"role": "user"
}
] | Obukhov B B.
Given a convex pentagon $A B C D E$, all sides of which are equal. It is known that angle $A$ is $120^{\circ}$, angle $C$ is $135^{\circ}$, and angle $D$ is $n^{\circ}$.
Find all possible integer values of $n$.
# | "[\"90\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 570, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14625"}] | {
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[
"16 \\sqrt{2.2 \\cdot (\\sqrt{2}-1)}"
] | [
"skywork"
] | 4cc5d9ff742411b5fe33cd74857116e13634f7ea90cb177680570287ece94e9b | [
{
"content": "The volume of a regular octagonal prism is $8 \\, \\mathrm{m}^{3}$, and its height is $2.2 \\, \\mathrm{m}$. Find the lateral surface area of the prism.",
"role": "user"
}
] | The volume of a regular octagonal prism is $8 \, \mathrm{m}^{3}$, and its height is $2.2 \, \mathrm{m}$. Find the lateral surface area of the prism. | "[\"16 \\\\sqrt{2.2 \\\\cdot (\\\\sqrt{2}-1)}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 587, "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:14626"}] | {
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[
"-\\frac{5}{2}\\leqslantx<2"
] | [
"skywork"
] | 4bb861289b4e8559266713de84fe43bb798d643a2a8a89c53bd25e9b683f23d7 | [
{
"content": "7. The solution set of the inequality $\\sqrt{2 x+5}>x+1$ is",
"role": "user"
}
] | 7. The solution set of the inequality $\sqrt{2 x+5}>x+1$ is | "[\"-\\\\frac{5}{2}\\\\leqslantx<2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 603, "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:14627"}] | {
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[
"15"
] | [
"skywork"
] | 7fa90947bdf57e67c44756b3bf5ffeab625505315a57bca211b27cf2dd39ed70 | [
{
"content": "Problem 2. We have two hourglasses that measure 7 minutes and 11 minutes. An egg needs to boil for 15 minutes. How can we measure this time using the two sand hourglasses?",
"role": "user"
}
] | Problem 2. We have two hourglasses that measure 7 minutes and 11 minutes. An egg needs to boil for 15 minutes. How can we measure this time using the two sand hourglasses? | "[\"15\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 601, "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:14628"}] | {
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} |
[
"{(9;8;4),(-3;-2;2),(9;4;8),(-3;2;-2)}"
] | [
"skywork"
] | 7e4dac676fc42f8fa430d99e07bfd4b039c24475436ba2df2b7b6231c5e10581 | [
{
"content": "Example 3. Solve the system of equations in integers:\n\n$$\n\\left\\{\\begin{array}{l}\nx^{2}-y^{2}-z^{2}=1 \\\\\ny+z-x=3\n\\end{array}\\right.\n$$",
"role": "user"
}
] | Example 3. Solve the system of equations in integers:
$$
\left\{\begin{array}{l}
x^{2}-y^{2}-z^{2}=1 \\
y+z-x=3
\end{array}\right.
$$ | "[\"{(9;8;4),(-3;-2;2),(9;4;8),(-3;2;-2)}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 593, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14629"}] | {
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[
"31"
] | [
"skywork"
] | ab40552414c72e770d2f43d1c45f936fc978237337abf3c56d88f8c647ee82aa | [
{
"content": "The base $9$ representation of a positive integer is $AB$ and its base $7$ representation is $BA$. What is the integer expressed in base $10$?",
"role": "user"
}
] | The base $9$ representation of a positive integer is $AB$ and its base $7$ representation is $BA$. What is the integer expressed in base $10$? | "[\"31\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 599, "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:14630"}] | {
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[
"80"
] | [
"skywork"
] | 1e4f70b6e130f3b798cb346462d90ded8521d0e96c4350a0566351998acffc76 | [
{
"content": "A person named Jia and their four colleagues each own a car with license plates ending in 9, 0, 2, 1, and 5, respectively. To comply with the local traffic restriction rules from the 5th to the 9th day of a certain month (allowing cars with odd-ending numbers on odd days and even-ending numbers on... | A person named Jia and their four colleagues each own a car with license plates ending in 9, 0, 2, 1, and 5, respectively. To comply with the local traffic restriction rules from the 5th to the 9th day of a certain month (allowing cars with odd-ending numbers on odd days and even-ending numbers on even days), they agre... | "[\"80\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 602, "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:14631"}] | {
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} |
[
"\\textbf{(A)}0"
] | [
"skywork"
] | ff30e7bde3accc409ddeb70abf6d26b19735ff564ce0067f237686ebc9a50305 | [
{
"content": "In a given plane, points $A$ and $B$ are $10$ units apart. How many points $C$ are there in the plane such that the perimeter of $\\triangle ABC$ is $50$ units and the area of $\\triangle ABC$ is $100$ square units?\n$\\textbf{(A) }0\\qquad\\textbf{(B) }2\\qquad\\textbf{(C) }4\\qquad\\textbf{(D) }... | In a given plane, points $A$ and $B$ are $10$ units apart. How many points $C$ are there in the plane such that the perimeter of $\triangle ABC$ is $50$ units and the area of $\triangle ABC$ is $100$ square units?
$\textbf{(A) }0\qquad\textbf{(B) }2\qquad\textbf{(C) }4\qquad\textbf{(D) }8\qquad\textbf{(E) }\text{infini... | "[\"\\\\textbf{(A)}0\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 611, "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:14632"}] | {
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} |
[
"468321"
] | [
"skywork"
] | da1a2c30f31d3eb73391c59aa245fe691157116f2e2c8888f383fc505def5a4b | [
{
"content": "The six-digit number $M=\\overline{abc321}$, where $a, b, c$ are three different numbers, and all are greater than 3. If $M$ is a multiple of 7, what is the smallest value of $M$?",
"role": "user"
}
] | The six-digit number $M=\overline{abc321}$, where $a, b, c$ are three different numbers, and all are greater than 3. If $M$ is a multiple of 7, what is the smallest value of $M$? | "[\"468321\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 608, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14633"}] | {
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[
"\\frac{3\\sqrt{15}}{4}"
] | [
"skywork"
] | 64dda5e7ace03f8930f4d526f86d701185f55d4a0b30acbd7ee29c40b83f0330 | [
{
"content": "$\\left[\\begin{array}{c}\\text { [Ratio of areas of triangles with a common angle] } \\\\ {[\\underline{\\text { Heron's Formula }}]}\\end{array}\\right.$\n\nGiven a triangle $ABC$ with sides $AB=6$, $AC=4$, and $BC=8$. Point $D$ lies on side $AB$, and point $E$ lies on side $AC$, such that $AD=2... | $\left[\begin{array}{c}\text { [Ratio of areas of triangles with a common angle] } \\ {[\underline{\text { Heron's Formula }}]}\end{array}\right.$
Given a triangle $ABC$ with sides $AB=6$, $AC=4$, and $BC=8$. Point $D$ lies on side $AB$, and point $E$ lies on side $AC$, such that $AD=2$ and $AE=3$. Find the area of tr... | "[\"\\\\frac{3\\\\sqrt{15}}{4}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 585, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:14634"}] | {
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[
"109"
] | [
"skywork"
] | 9caa6e2e23cbb53f8dfaf105738417536d9b31a8e67d33b016bcb6b9f5df9f57 | [
{
"content": "Find the remainder when $9 \\times 99 \\times 999 \\times \\cdots \\times \\underbrace{99\\cdots9}_{\\text{999 9's}}$ is divided by $1000$ .",
"role": "user"
}
] | Find the remainder when $9 \times 99 \times 999 \times \cdots \times \underbrace{99\cdots9}_{\text{999 9's}}$ is divided by $1000$ . | "[\"109\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 612, "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:14635"}, {"dataset": "skywork", "extra_info... | {
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} |
[
"499"
] | [
"skywork"
] | 711aeaa9112dcde058489aebca4caf04bc01da30c052072bd7b21291798b2442 | [
{
"content": "9.2. All natural numbers from 1 to 1000 inclusive are divided into two groups: even and odd. In which group is the sum of all digits used to write the numbers greater, and by how much?",
"role": "user"
}
] | 9.2. All natural numbers from 1 to 1000 inclusive are divided into two groups: even and odd. In which group is the sum of all digits used to write the numbers greater, and by how much? | "[\"499\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 610, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14636"}] | {
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[
"(2.8, 1.8), (-1.4, -2.4), (1.8, 2.8), (-2.4, -1.4)"
] | [
"skywork"
] | 253aa88c73a6ac6aaccbc526a4d17a3a4970a5499565757d35fe3b15c0a21099 | [
{
"content": "Find all the pairs of real numbers $(x,y)$ that are solutions of the system:\n$(x^{2}+y^{2})^{2}-xy(x+y)^{2}=19 $ \n$| x - y | = 1$",
"role": "user"
}
] | Find all the pairs of real numbers $(x,y)$ that are solutions of the system:
$(x^{2}+y^{2})^{2}-xy(x+y)^{2}=19 $
$| x - y | = 1$ | "[\"(2.8, 1.8), (-1.4, -2.4), (1.8, 2.8), (-2.4, -1.4)\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 606, "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:14637"}] | {
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"reference_components": 1,
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} |
[
"23"
] | [
"skywork"
] | 0807672cd530e2bf078b2e65b52dc2e7ffa3ca3a69cc32830a4fc66b3a8a5d75 | [
{
"content": "Task 2. Find the number of all three-digit numbers that are divisible by 15 and whose sum of digits is less than or equal to 9.",
"role": "user"
}
] | Task 2. Find the number of all three-digit numbers that are divisible by 15 and whose sum of digits is less than or equal to 9. | "[\"23\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 605, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:14638"}] | {
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} |
[
"39"
] | [
"skywork"
] | c31cc44a19e4e0769a719a8d146f8d4fa12aeddad7e43a74797a1d9bfce8c15d | [
{
"content": "2. (10 points) Xiao Long's mother is 3 years younger than his father, his mother's age this year is 9 times Xiao Long's age this year, and his father's age next year will be 8 times Xiao Long's age next year. What is the father's age this year?",
"role": "user"
}
] | 2. (10 points) Xiao Long's mother is 3 years younger than his father, his mother's age this year is 9 times Xiao Long's age this year, and his father's age next year will be 8 times Xiao Long's age next year. What is the father's age this year? | "[\"39\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 617, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:14639"}] | {
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} |
[
"1"
] | [
"skywork"
] | caff7f24d32e90360a44e7fd2bbfb2c5e56767cb287bcfc943925a58fffc8d59 | [
{
"content": "Example! Given that $f(x)$ is a function defined on $\\mathbf{R}$, $f(1)=1$, and for any $x \\in \\mathbf{R}$, $f(x+5) \\geqslant f(x)+5$, $f(x+1) \\leqslant f(x)+1$. If $g(x)=f(x)+1-x$, find the value of $g(2002)$.",
"role": "user"
}
] | Example! Given that $f(x)$ is a function defined on $\mathbf{R}$, $f(1)=1$, and for any $x \in \mathbf{R}$, $f(x+5) \geqslant f(x)+5$, $f(x+1) \leqslant f(x)+1$. If $g(x)=f(x)+1-x$, find the value of $g(2002)$. | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 573, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "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:14640"}] | {
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[
"\\begin{pmatrix} -5 \\\\ 9 \\\\ -8 \\end{pmatrix}"
] | [
"skywork"
] | be94f8ee24a91ef603dc5eaec6b75d9318cc8aa9a3d13b36e7420d7331ecc9d7 | [
{
"content": "Find $\\begin{pmatrix} -5 \\\\ 1 \\\\ -4 \\end{pmatrix} + \\begin{pmatrix} 0 \\\\ 8 \\\\ -4 \\end{pmatrix}.$",
"role": "user"
}
] | Find $\begin{pmatrix} -5 \\ 1 \\ -4 \end{pmatrix} + \begin{pmatrix} 0 \\ 8 \\ -4 \end{pmatrix}.$ | "[\"\\\\begin{pmatrix} -5 \\\\\\\\ 9 \\\\\\\\ -8 \\\\end{pmatrix}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 627, "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:14641"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"504"
] | [
"skywork"
] | 47b57620cad2c7fbf8889a8141e7c0782623ec9c156b7de4ce94621060cdf1ae | [
{
"content": "5. Vasya is coming up with a 4-digit password for a code lock. He doesn't like the digit 2, so he doesn't use it. Additionally, he doesn't like when two identical digits are next to each other. He also wants the first digit to match the last digit. How many options need to be tried to guarantee gu... | 5. Vasya is coming up with a 4-digit password for a code lock. He doesn't like the digit 2, so he doesn't use it. Additionally, he doesn't like when two identical digits are next to each other. He also wants the first digit to match the last digit. How many options need to be tried to guarantee guessing Vasya's passwor... | "[\"504\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 618, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14642"}, {"dataset": "skywork", "extra_info... | {
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"reference_components": 1,
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} |
[
"2003"
] | [
"skywork"
] | 3699d0e8ddb25122da16e742e448c037e1b717287dbc53e1adc6603600d08711 | [
{
"content": "At most, how many interior angles greater than $180^\\circ$ can a 2006-sided polygon have?",
"role": "user"
}
] | At most, how many interior angles greater than $180^\circ$ can a 2006-sided polygon have? | "[\"2003\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 630, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14643"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"580"
] | [
"skywork"
] | c386bd15412dbee01eba21098da1cc6ed9de51cb8204dbd5e1c00e9364899b36 | [
{
"content": "During a recent campaign for office, a candidate made a tour of a country which we assume lies in a plane. On the first day of the tour he went east, on the second day he went north, on the third day west, on the fourth day south, on the fifth day east, etc. If the candidate went $\\frac{n^{2}}{2}... | During a recent campaign for office, a candidate made a tour of a country which we assume lies in a plane. On the first day of the tour he went east, on the second day he went north, on the third day west, on the fourth day south, on the fifth day east, etc. If the candidate went $\frac{n^{2}}{2}$ miles on the $n^{\mbo... | "[\"580\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 614, "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:14644"}] | {
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[
"18750"
] | [
"skywork"
] | e9bac1c297f66ede65bf8d03de32ebbff949e2d71ab72e569c4fca7cde9fe1af | [
{
"content": "A truck has new tires fitted on all four wheels. A tire is considered completely worn out if it has traveled $15000 \\mathrm{~km}$ on the rear wheel or $25000 \\mathrm{~km}$ on the front wheel. How far can the truck travel before all four tires are completely worn out if the front and rear pairs o... | A truck has new tires fitted on all four wheels. A tire is considered completely worn out if it has traveled $15000 \mathrm{~km}$ on the rear wheel or $25000 \mathrm{~km}$ on the front wheel. How far can the truck travel before all four tires are completely worn out if the front and rear pairs of tires are swapped at s... | "[\"18750\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 597, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14645"}] | {
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[
"2n - 6"
] | [
"skywork"
] | 1c3d21a2603af227adc7174b55242f1ac1614d348876b3bf12904a93eda084b9 | [
{
"content": "A convex 2011-gon is drawn on the board. Peter keeps drawing its diagonals in such a way, that each newly drawn diagonal intersected no more than one of the already drawn diagonals. What is the greatest number of diagonals that Peter can draw?",
"role": "user"
}
] | A convex 2011-gon is drawn on the board. Peter keeps drawing its diagonals in such a way, that each newly drawn diagonal intersected no more than one of the already drawn diagonals. What is the greatest number of diagonals that Peter can draw? | "[\"2n - 6\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 620, "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:14646"}] | {
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[
"0.333"
] | [
"skywork"
] | 065d9488b2bf31c53d716b2dbade3ce66fa46e6f74fc90ea618f91b991c7ae64 | [
{
"content": "The expression \\(\\frac{3}{10}+\\frac{3}{100}+\\frac{3}{1000}\\) can be simplified by converting each fraction to a decimal, and then calculating the sum.",
"role": "user"
}
] | The expression \(\frac{3}{10}+\frac{3}{100}+\frac{3}{1000}\) can be simplified by converting each fraction to a decimal, and then calculating the sum. | "[\"0.333\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 613, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:14647"}] | {
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[
"x^{2}-y^{2}=R^{2}"
] | [
"skywork"
] | d98361b193610b057660f1af6813ed5b3c4c3c3f144e98b733086037dda02ad0 | [
{
"content": "Example 9. As shown in Figure $9, \\mathrm{AB}$ is the diameter of a fixed circle $\\mathrm{O}$, and the moving chord $M N \\perp A B$. Find the equation of the locus of the intersection point $P$ of the lines $A N$ and $M B$.",
"role": "user"
}
] | Example 9. As shown in Figure $9, \mathrm{AB}$ is the diameter of a fixed circle $\mathrm{O}$, and the moving chord $M N \perp A B$. Find the equation of the locus of the intersection point $P$ of the lines $A N$ and $M B$. | "[\"x^{2}-y^{2}=R^{2}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 615, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14648"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{5}{7}"
] | [
"skywork"
] | 67e31ed0b58a3b0304c3d6587ac72a55a42498a7d9e7f367a4a81267bf9ad3bf | [
{
"content": "Given three different numbers are randomly selected from the set $\\{-2, -1, 0, 0, 3, 4, 5\\}$ and multiplied together, calculate the probability that the product is $0$.",
"role": "user"
}
] | Given three different numbers are randomly selected from the set $\{-2, -1, 0, 0, 3, 4, 5\}$ and multiplied together, calculate the probability that the product is $0$. | "[\"\\\\frac{5}{7}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 607, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14649"}] | {
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[
"\\frac{\\sqrt{15}}{4}"
] | [
"skywork"
] | 6d20ee202f76371b1a2bac8eefb8e22a2086ddc4d61141522d5daab24b4530d9 | [
{
"content": "Given vectors $\\overrightarrow{a}=(\\sin x, \\sqrt{3}\\cos x)$, $\\overrightarrow{b}=(-1,1)$, and $\\overrightarrow{c}=(1,1)$, where $x \\in [0, \\pi]$.\n\n(1) If $(\\overrightarrow{a} + \\overrightarrow{b}) \\parallel \\overrightarrow{c}$, find the value of $x$;\n\n(2) If $\\overrightarrow{a} \\... | Given vectors $\overrightarrow{a}=(\sin x, \sqrt{3}\cos x)$, $\overrightarrow{b}=(-1,1)$, and $\overrightarrow{c}=(1,1)$, where $x \in [0, \pi]$.
(1) If $(\overrightarrow{a} + \overrightarrow{b}) \parallel \overrightarrow{c}$, find the value of $x$;
(2) If $\overrightarrow{a} \cdot \overrightarrow{b} = \frac{1}{2}$, ... | "[\"\\\\frac{\\\\sqrt{15}}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 616, "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:14652"}] | {
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[
"20"
] | [
"skywork"
] | 07500e655122abe15cae71c0682d7cf9a33ba0a1a057bc14f1bf7250ecc7a71f | [
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"content": "Start with an angle of \\(60^\\circ\\) and bisect it, then bisect the lower \\(30^\\circ\\) angle, then the upper \\(15^\\circ\\) angle, and so on, always alternating between the upper and lower of the previous two angles constructed. This process approaches a limiting line that divides the origin... | Start with an angle of \(60^\circ\) and bisect it, then bisect the lower \(30^\circ\) angle, then the upper \(15^\circ\) angle, and so on, always alternating between the upper and lower of the previous two angles constructed. This process approaches a limiting line that divides the original \(60^\circ\) angle into two ... | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 621, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14653"}] | {
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[
"100"
] | [
"skywork"
] | 8c722e8be8cfa0df2bdafa4201baa9f20834604e44d443063a24cb3a774f04cc | [
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"content": "Three. (50 points)\nThere are 21 points on a circle. Among all the arcs with these 21 points as endpoints, what is the minimum number of arcs that do not exceed $120^{\\circ}$?",
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}
] | Three. (50 points)
There are 21 points on a circle. Among all the arcs with these 21 points as endpoints, what is the minimum number of arcs that do not exceed $120^{\circ}$? | "[\"100\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 631, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14654"}] | {
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[
"511566"
] | [
"skywork"
] | fe8be0059955b02a0bce6b11c407881a1ccabb9ac75dbfc1aa0a746e34c95996 | [
{
"content": "Problem 5. The numbers from 1 to 2021 are written on a board. Denis wants to choose 1010 of them such that the sum of any two does not equal 2021 or 2022. How many ways are there to do this?",
"role": "user"
}
] | Problem 5. The numbers from 1 to 2021 are written on a board. Denis wants to choose 1010 of them such that the sum of any two does not equal 2021 or 2022. How many ways are there to do this? | "[\"511566\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 634, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14655"}, {"dataset": "skywork", "extra_in... | {
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[
"1009"
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"skywork"
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"content": "On an island, there are knights, liars, and followers; each person knows who is who. All 2018 island residents were lined up and each was asked to answer \"Yes\" or \"No\" to the question: \"Are there more knights than liars on the island?\" The residents responded one by one in such a way that th... | On an island, there are knights, liars, and followers; each person knows who is who. All 2018 island residents were lined up and each was asked to answer "Yes" or "No" to the question: "Are there more knights than liars on the island?" The residents responded one by one in such a way that the others could hear. Knights... | "[\"1009\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 609, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14656"}] | {
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"194"
] | [
"skywork"
] | 68b736532b33b37e188dc9c31c8d7724767f489cdc50a1a6036f43b2bbe9ef85 | [
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"content": "Given that $ 2^{2004}$ is a $ 604$ -digit number whose first digit is $ 1$ , how many elements of the set $ S \\equal{} \\{2^0,2^1,2^2, \\ldots,2^{2003}\\}$ have a first digit of $ 4$ ?",
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] | Given that $ 2^{2004}$ is a $ 604$ -digit number whose first digit is $ 1$ , how many elements of the set $ S \equal{} \{2^0,2^1,2^2, \ldots,2^{2003}\}$ have a first digit of $ 4$ ? | "[\"194\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 619, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14657"}] | {
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[
"54"
] | [
"skywork"
] | 1ad235646f7a94d207573653fbdcc8e833e5e1cabbb4fd36e2e1ecf0a9b2bc41 | [
{
"content": "In three-dimensional space, find the number of lattice points that have a distance of 5 from the origin.\n\nNote: A point is a lattice point if all its coordinates are integers.",
"role": "user"
}
] | In three-dimensional space, find the number of lattice points that have a distance of 5 from the origin.
Note: A point is a lattice point if all its coordinates are integers. | "[\"54\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 638, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14658"}] | {
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[
"1006"
] | [
"skywork"
] | 0f63056d9cefc3321d611ac5140b67a3fdbf119075f72f55ed499e9f0318ac40 | [
{
"content": "Determine, with proof, the smallest positive integer \\( n \\) with the following property: For every choice of \\( n \\) integers, there exist at least two whose sum or difference is divisible by 2009.",
"role": "user"
}
] | Determine, with proof, the smallest positive integer \( n \) with the following property: For every choice of \( n \) integers, there exist at least two whose sum or difference is divisible by 2009. | "[\"1006\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 629, "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:14659"}] | {
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[
"1"
] | [
"skywork"
] | 25c1e56a0692c532fe061ff8014143aeabe5b9b008910f749aea67e2629e4855 | [
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"content": "The expression $\\frac{x^2-3x+2}{x^2-5x+6} \\div \\frac{x^2-5x+4}{x^2-7x+12}$, when simplified is:",
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}
] | The expression $\frac{x^2-3x+2}{x^2-5x+6} \div \frac{x^2-5x+4}{x^2-7x+12}$, when simplified is: | "[\"1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 644, "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:14660"}] | {
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[
"\\frac{(\\sqrt{a l}+\\sqrt{b m}+\\sqrt{c n})^{2}}{\\delta}"
] | [
"skywork"
] | 20cf5627e01f84b931a99b0df9ac06e5c443f579820ab11a873b98bd92dafc25 | [
{
"content": "Example 7 Let $x \\geqslant 0, y \\geqslant 0, z \\geqslant 0, a, b, c, l, m, n$ be given positive numbers, and $a x+b y+c z=\\delta$ be a constant, find\n$$w=\\frac{l}{x}+\\frac{m}{y}+\\frac{n}{z}$$\n\nthe minimum value.",
"role": "user"
}
] | Example 7 Let $x \geqslant 0, y \geqslant 0, z \geqslant 0, a, b, c, l, m, n$ be given positive numbers, and $a x+b y+c z=\delta$ be a constant, find
$$w=\frac{l}{x}+\frac{m}{y}+\frac{n}{z}$$
the minimum value. | "[\"\\\\frac{(\\\\sqrt{a l}+\\\\sqrt{b m}+\\\\sqrt{c n})^{2}}{\\\\delta}\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 626, "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:14661"}] | {
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[
"\\frac{9}{4}"
] | [
"skywork"
] | ef1dab00f3444b0af851ab64d8edc8247e7c8367e784f1f1c785a40a1d397ee2 | [
{
"content": "2. Let planar vectors $\\boldsymbol{a} 、 \\boldsymbol{b}$ satisfy $|\\boldsymbol{a}+\\boldsymbol{b}|=3$. Then the maximum value of $a \\cdot b$ is $\\qquad$",
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}
] | 2. Let planar vectors $\boldsymbol{a} 、 \boldsymbol{b}$ satisfy $|\boldsymbol{a}+\boldsymbol{b}|=3$. Then the maximum value of $a \cdot b$ is $\qquad$ | "[\"\\\\frac{9}{4}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 624, "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:14662"}] | {
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[
"100"
] | [
"skywork"
] | 3ef72277a530b721932ed24666f14a7716907a1f8a7ac94a38d52cf02354ee47 | [
{
"content": "Let $w$ and $z$ be complex numbers such that $|w| = 1$ and $|z| = 10$ . Let $\\theta = \\arg \\left(\\tfrac{w-z}{z}\\right)$ . The maximum possible value of $\\tan^2 \\theta$ can be written as $\\tfrac{p}{q}$ , where $p$ and $q$ are relatively prime positive integers. Find $p+q$ . (Note that $\\ar... | Let $w$ and $z$ be complex numbers such that $|w| = 1$ and $|z| = 10$ . Let $\theta = \arg \left(\tfrac{w-z}{z}\right)$ . The maximum possible value of $\tan^2 \theta$ can be written as $\tfrac{p}{q}$ , where $p$ and $q$ are relatively prime positive integers. Find $p+q$ . (Note that $\arg(w)$ , for $w \neq 0$ , denote... | "[\"100\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 632, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14663"}, {"dataset": "skywork", "extra_info... | {
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[
"2520"
] | [
"skywork"
] | c1cfcf9d00cd17248bb397c4a3cfdc859914e7e629739771a59e7c70fcdc3b9a | [
{
"content": "What is the least common multiple of 105 and 360?",
"role": "user"
}
] | What is the least common multiple of 105 and 360? | "[\"2520\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 666, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14664"}] | {
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[
"(n-1)! \\times \\binom{n}{m} \\times m!"
] | [
"skywork"
] | 2a072321294098cc98bba7ff04ad876724b2b02d1ac434b9aff08b76c991455c | [
{
"content": "Bangladesh National Mathematical Olympiad 2016 Higher Secondary\n\n[b][u]Problem 5:[/u][/b]\nSuppose there are $m$ Martians and $n$ Earthlings at an intergalactic peace conference. To ensure the Martians stay peaceful at the conference, we must make sure that no two Martians sit together, such tha... | Bangladesh National Mathematical Olympiad 2016 Higher Secondary
[b][u]Problem 5:[/u][/b]
Suppose there are $m$ Martians and $n$ Earthlings at an intergalactic peace conference. To ensure the Martians stay peaceful at the conference, we must make sure that no two Martians sit together, such that between any two Martian... | "[\"(n-1)! \\\\times \\\\binom{n}{m} \\\\times m!\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 628, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14665"}] | {
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[
"9"
] | [
"skywork"
] | 4a68ec73db69cd582553b63c04ecbeed658670e97cbf898aebffb369e616e8f5 | [
{
"content": "1. Which of these is the sum of the cubes of two consecutive integers?\nA 4\nB 9\nC 16\nD 25\nE 36",
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}
] | 1. Which of these is the sum of the cubes of two consecutive integers?
A 4
B 9
C 16
D 25
E 36 | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 654, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14666"}] | {
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[
"15"
] | [
"skywork"
] | eab439636f52e296e3811c265d8a39da0b778b02cfc1e46356797b629081e84e | [
{
"content": "38. There are 2 bowls of noodles, 4 bowls of rice, and 6 bowls of dumplings on the table. Baobao eats 6 bowls of them at random. The number of possible combinations of the remaining food is $\\qquad$ kinds.",
"role": "user"
}
] | 38. There are 2 bowls of noodles, 4 bowls of rice, and 6 bowls of dumplings on the table. Baobao eats 6 bowls of them at random. The number of possible combinations of the remaining food is $\qquad$ kinds. | "[\"15\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 622, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14667"}] | {
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"reference_components": 1,
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} |
[
"\\frac{2\\pi}{3}"
] | [
"skywork"
] | 9624e675230cc69155f766f50bea7af5bc68a5f38c2169e764bb26322eaaa544 | [
{
"content": "Given that the coordinates of a direction vector of line $l$ are $({-1,\\sqrt{3}})$, the inclination angle of line $l$ is ____.",
"role": "user"
}
] | Given that the coordinates of a direction vector of line $l$ are $({-1,\sqrt{3}})$, the inclination angle of line $l$ is ____. | "[\"\\\\frac{2\\\\pi}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 639, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14668"}] | {
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} |
[
"60"
] | [
"skywork"
] | 7530b0cccaa7542978254bececc4938f200745f6a75a0dae2cb0e80a56033ce3 | [
{
"content": "Two students, A and B, each choose 2 out of 6 extracurricular reading materials. Calculate the number of ways in which the two students choose extracurricular reading materials such that they have exactly 1 material in common.",
"role": "user"
}
] | Two students, A and B, each choose 2 out of 6 extracurricular reading materials. Calculate the number of ways in which the two students choose extracurricular reading materials such that they have exactly 1 material in common. | "[\"60\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 650, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:14669"}] | {
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[
"-1"
] | [
"skywork"
] | 19f3f07f52d715a1c91e0ae830bf529ac5af19e2eb8cb234a2f7a10ddbb445fe | [
{
"content": "Example 1 Given $x^{2}+x+1=0$, try to find the value of the rational expression $x^{14}+\\frac{1}{x^{14}}$.",
"role": "user"
}
] | Example 1 Given $x^{2}+x+1=0$, try to find the value of the rational expression $x^{14}+\frac{1}{x^{14}}$. | "[\"-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 652, "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:14670"}] | {
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[
"1/4"
] | [
"skywork"
] | 5322df3eaf6cff7f59b0ef4d1f1cca66a83b085c8534208234b06b25b27f12b7 | [
{
"content": "Let $ABC$ be an equilateral triangle. $A $ point $P$ is chosen at random within this triangle. What is the probability that the sum of the distances from point $P$ to the sides of triangle $ABC$ are measures of the sides of a triangle?",
"role": "user"
}
] | Let $ABC$ be an equilateral triangle. $A $ point $P$ is chosen at random within this triangle. What is the probability that the sum of the distances from point $P$ to the sides of triangle $ABC$ are measures of the sides of a triangle? | "[\"1/4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 637, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:14671"}, {"dataset": "skywork", "extra_info... | {
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[
"19"
] | [
"skywork"
] | 7e792ed3655698df9a7ca1211fb53e628a40dbe3b59bff798378846855546949 | [
{
"content": "Problem 9.5. Buratino has many coins of 5 and 6 soldi, more than 10 of each type. Coming to the store and buying a book for $N$ soldi, he realized that he could not pay for it without receiving change. What is the greatest value that the natural number $N$ can take if it is no more than 50?",
... | Problem 9.5. Buratino has many coins of 5 and 6 soldi, more than 10 of each type. Coming to the store and buying a book for $N$ soldi, he realized that he could not pay for it without receiving change. What is the greatest value that the natural number $N$ can take if it is no more than 50? | "[\"19\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 633, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "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:14672"}] | {
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[
"5"
] | [
"skywork"
] | 057426431a33cba70d77620617d88ab5eab15fd22804a7fe2c706b505d50b6c6 | [
{
"content": "16. Anna and Bonnie are racing on a 400-meter oval track. They start at the same time, but Anna is ahead because she is 25% faster than Bonnie. Then Anna will have run ( ) laps when she first overtakes Bonnie.\n(A) $\\frac{5}{4}$\n(B) $\\frac{10}{3}$\n(C) 4\n(D) 5\n(E) 25",
"role": "user"
}
... | 16. Anna and Bonnie are racing on a 400-meter oval track. They start at the same time, but Anna is ahead because she is 25% faster than Bonnie. Then Anna will have run ( ) laps when she first overtakes Bonnie.
(A) $\frac{5}{4}$
(B) $\frac{10}{3}$
(C) 4
(D) 5
(E) 25 | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 636, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14673"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1995"
] | [
"skywork"
] | dd5927a24f3dc58252aa9e9d402b7aab230a3027190489bc2d12aae1fe51f5f0 | [
{
"content": "Three. (50 points) If a positive integer is regular itself and it is the sum of different regular numbers, then this number is called \"valid\". Question: How many \"valid\" numbers are there in the set $\\{1,2,3, \\cdots, 2001\\}$? (\"Regular\" numbers are $a_{1}, a_{2}, \\cdots, a_{1}$, $\\cdots... | Three. (50 points) If a positive integer is regular itself and it is the sum of different regular numbers, then this number is called "valid". Question: How many "valid" numbers are there in the set $\{1,2,3, \cdots, 2001\}$? ("Regular" numbers are $a_{1}, a_{2}, \cdots, a_{1}$, $\cdots$, where $a_{1}=1, a_{k}=k+a_{k-1... | "[\"1995\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 643, "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:14674"}] | {
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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{11}{6}\\sqrt{3}"
] | [
"skywork"
] | e8986fa54f8fcd51d1375c4776f3a42e4046997ff0429a037e00718f76a5ddd2 | [
{
"content": "Example 4 (2003 National High School Mathematics Competition) If $x \\in\\left[-\\frac{5}{12} \\pi,-\\frac{\\pi}{3}\\right]$, then what is the maximum value of $y=\\tan \\left(x+\\frac{2}{3} \\pi\\right)-$ $\\tan \\left(x+\\frac{\\pi}{6}\\right)+\\cos \\left(x+\\frac{\\pi}{6}\\right)$?",
"role... | Example 4 (2003 National High School Mathematics Competition) If $x \in\left[-\frac{5}{12} \pi,-\frac{\pi}{3}\right]$, then what is the maximum value of $y=\tan \left(x+\frac{2}{3} \pi\right)-$ $\tan \left(x+\frac{\pi}{6}\right)+\cos \left(x+\frac{\pi}{6}\right)$? | "[\"\\\\frac{11}{6}\\\\sqrt{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 656, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14675"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | e61908a69b7a890a0931a16c823bdd4187047ae6e9c481c98976da5f614b2515 | [
{
"content": "7. There is a sequence of numbers: $1,2,2,3,3,3,1,2,2,3,3,3, \\cdots \\cdots$ Starting from the first number and adding them sequentially, if the total sum is 358, then the last number added is $\\qquad$ _.",
"role": "user"
}
] | 7. There is a sequence of numbers: $1,2,2,3,3,3,1,2,2,3,3,3, \cdots \cdots$ Starting from the first number and adding them sequentially, if the total sum is 358, then the last number added is $\qquad$ _. | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 647, "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:14676"}] | {
"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
} |
[
"24"
] | [
"skywork"
] | 2974fd6a06dee46fb4fca23342abeb48689309f94d647afabb4bd4fd3d7fb65e | [
{
"content": "For a nonnegative integer $n$, let $r_7(n)$ denote the remainder when $n$ is divided by $7.$ Determine the $15^{\\text{th}}$ entry in an ordered list of all nonnegative integers $n$ that satisfy $$r_7(3n)\\le 3.$$",
"role": "user"
}
] | For a nonnegative integer $n$, let $r_7(n)$ denote the remainder when $n$ is divided by $7.$ Determine the $15^{\text{th}}$ entry in an ordered list of all nonnegative integers $n$ that satisfy $$r_7(3n)\le 3.$$ | "[\"24\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 641, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:14677"}] | {
"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{28}{3}"
] | [
"skywork"
] | 41256cb19906ed4ad02902bc5a4d835628a33f6db758ebd2ff4f63c89930b5a3 | [
{
"content": "Calculate the monotonic intervals of $F(x)=\\int_{0}^{x}{(t^{2}+2t-8)dt}$ for $x > 0$.\n\n(1) Determine the monotonic intervals of $F(x)$.\n\n(2) Find the maximum and minimum values of the function $F(x)$ on the interval $[1,2]$.",
"role": "user"
}
] | Calculate the monotonic intervals of $F(x)=\int_{0}^{x}{(t^{2}+2t-8)dt}$ for $x > 0$.
(1) Determine the monotonic intervals of $F(x)$.
(2) Find the maximum and minimum values of the function $F(x)$ on the interval $[1,2]$. | "[\"-\\\\frac{28}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 640, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "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:14678"}] | {
"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
} |
[
"4"
] | [
"skywork"
] | 61f735b995012be8269ffb8026422af0628912e9ce9168acfe6e246932a3303e | [
{
"content": "Let $\\mathbb{N}$ denote the set of positive integers, and let $S$ be a set. There exists a function $f :\\mathbb{N} \\rightarrow S$ such that if $x$ and $y$ are a pair of positive integers with their difference being a prime number, then $f(x) \\neq f(y)$. Determine the minimum number of elements... | Let $\mathbb{N}$ denote the set of positive integers, and let $S$ be a set. There exists a function $f :\mathbb{N} \rightarrow S$ such that if $x$ and $y$ are a pair of positive integers with their difference being a prime number, then $f(x) \neq f(y)$. Determine the minimum number of elements in $S$. | "[\"4\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 635, "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:14679"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-\\frac{1}{2}"
] | [
"skywork"
] | fd549e9689f13e2bb16df4509ca9bbd3b612d414d884c41043b0d9e15ecd1d55 | [
{
"content": "Let \\( n = 1990 \\), then what is \\( \\frac{1}{2^{n}}\\left(1-3 \\mathrm{C}_{n}^{2}+3^{2} \\mathrm{C}_{n}^{4}-3^{3} \\mathrm{C}_{n}^{6}+\\cdots+3^{994} \\mathrm{C}_{n}^{1988}-3^{9995} \\mathrm{C}_{n}^{1990}\\right) \\)?",
"role": "user"
}
] | Let \( n = 1990 \), then what is \( \frac{1}{2^{n}}\left(1-3 \mathrm{C}_{n}^{2}+3^{2} \mathrm{C}_{n}^{4}-3^{3} \mathrm{C}_{n}^{6}+\cdots+3^{994} \mathrm{C}_{n}^{1988}-3^{9995} \mathrm{C}_{n}^{1990}\right) \)? | "[\"-\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 648, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14680"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
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