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 |
|---|---|---|---|---|---|---|---|---|
[
"210"
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"content": "In the expansion of the binomial ${({(\\frac{1}{x}}^{\\frac{1}{4}}+{{x}^{2}}^{\\frac{1}{3}})}^{n})$, the coefficient of the third last term is $45$. Find the coefficient of the term containing $x^{3}$.",
"role": "user"
}
] | In the expansion of the binomial ${({(\frac{1}{x}}^{\frac{1}{4}}+{{x}^{2}}^{\frac{1}{3}})}^{n})$, the coefficient of the third last term is $45$. Find the coefficient of the term containing $x^{3}$. | "[\"210\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108166, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:118102"}] | {
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[
"\\frac{5\\sqrt{11}}{4}"
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] | f52c51f0fa8093dc5631f9fb8e79a0bafd8c8f0d93a7dfb3650d1aff26246cf8 | [
{
"content": "What is the area, in square units, of a triangle that has sides of $5, 3,$ and $3$ units? Express your answer in simplest radical form.",
"role": "user"
}
] | What is the area, in square units, of a triangle that has sides of $5, 3,$ and $3$ units? Express your answer in simplest radical form. | "[\"\\\\frac{5\\\\sqrt{11}}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108180, "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:118103"}] | {
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[
"(n, k) \\text{ such that } k = 0 \\text{ or } k = n, \\text{ or both } n \\text{ and } k \\text{ are even, \\text{ or } (n, k) = (2, 1).}"
] | [
"skywork"
] | 7cc8a30e9e48ade45151c619ffe5f7361cac28224352b7bae4de2c1f5213ed40 | [
{
"content": "For integers $n \\ge k \\ge 0$ we define the [i]bibinomial coefficient[/i] $\\left( \\binom{n}{k} \\right)$ by\n\\[ \\left( \\binom{n}{k} \\right) = \\frac{n!!}{k!!(n-k)!!} .\\]\nDetermine all pairs $(n,k)$ of integers with $n \\ge k \\ge 0$ such that the corresponding bibinomial coefficient is ... | For integers $n \ge k \ge 0$ we define the [i]bibinomial coefficient[/i] $\left( \binom{n}{k} \right)$ by
\[ \left( \binom{n}{k} \right) = \frac{n!!}{k!!(n-k)!!} .\]
Determine all pairs $(n,k)$ of integers with $n \ge k \ge 0$ such that the corresponding bibinomial coefficient is an integer. | "[\"(n, k) \\\\text{ such that } k = 0 \\\\text{ or } k = n, \\\\text{ or both } n \\\\text{ and } k \\\\text{ are even, \\\\text{ or } (n, k) = (2, 1).}\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 108160, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118105"}] | {
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[
"6"
] | [
"skywork"
] | b0ff59c24f30072a8cf18d60de3cc1d7f9cb96efe4af0c87ab8d29d9bbba16c8 | [
{
"content": "6. On the table, there are three cones standing on their bases, touching each other. The radii of their bases are 23, 46, and 69. A truncated cone is placed on the table with its smaller base down, and it shares a generatrix with each of the other cones. Find the radius of the smaller base of the ... | 6. On the table, there are three cones standing on their bases, touching each other. The radii of their bases are 23, 46, and 69. A truncated cone is placed on the table with its smaller base down, and it shares a generatrix with each of the other cones. Find the radius of the smaller base of the truncated cone.
# | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108170, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118107"}] | {
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} |
[
"31.5"
] | [
"skywork"
] | d6d8ef659d6fa16709130c33a8ae83b344074fa9a7ab6180864b81ba12584e38 | [
{
"content": "A triangle has vertices at $(-2,3),(7,-3),(4,6)$. Calculate the area of this triangle in square units and express your answer as a decimal to the nearest tenth.",
"role": "user"
}
] | A triangle has vertices at $(-2,3),(7,-3),(4,6)$. Calculate the area of this triangle in square units and express your answer as a decimal to the nearest tenth. | "[\"31.5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108202, "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:118108"}] | {
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} |
[
"(1998, 0), (-2002, 4000)"
] | [
"skywork"
] | b427508e79dc6eb1d92f55a44fcc68772e91fe961d69b0f89d49f1b2ee8fe995 | [
{
"content": "Find all pairs $(p,q)$ of real numbers such that $p+q=1998$ and the solutions of the equation $x^2+px+q=0$ are integers.",
"role": "user"
}
] | Find all pairs $(p,q)$ of real numbers such that $p+q=1998$ and the solutions of the equation $x^2+px+q=0$ are integers. | "[\"(1998, 0), (-2002, 4000)\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108176, "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:118109"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2(2 + \\sqrt{13})"
] | [
"skywork"
] | d7478e7ff7ce7072e00d1772f075839c67c09a02cb0edbff7ea968b5038b333e | [
{
"content": "Points \\( M \\) and \\( N \\) are the midpoints of the sides \\( AC \\) and \\( CB \\) of the isosceles triangle \\( ACB \\). Point \\( L \\) lies on the median \\( BM \\) such that \\( BL : BM = 4 : 9 \\). A circle with center at point \\( L \\) is tangent to the line \\( MN \\) and intersects t... | Points \( M \) and \( N \) are the midpoints of the sides \( AC \) and \( CB \) of the isosceles triangle \( ACB \). Point \( L \) lies on the median \( BM \) such that \( BL : BM = 4 : 9 \). A circle with center at point \( L \) is tangent to the line \( MN \) and intersects the line \( AB \) at points \( Q \) and \( ... | "[\"2(2 + \\\\sqrt{13})\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108151, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118110"}] | {
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} |
[
"4"
] | [
"skywork"
] | 10973c540f713e668968c39a55fdd8c4e12b3ecfb6614a35b0658488155548ea | [
{
"content": "5.18. In parallelogram $A B C D$, point $K$ is the midpoint of side $B C$, and point $M$ is the midpoint of side $C D$. Find $A D$, if $A K=6$ cm, $A M=3$ cm, and $\\angle K A M=60^{\\circ}$.",
"role": "user"
}
] | 5.18. In parallelogram $A B C D$, point $K$ is the midpoint of side $B C$, and point $M$ is the midpoint of side $C D$. Find $A D$, if $A K=6$ cm, $A M=3$ cm, and $\angle K A M=60^{\circ}$. | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108174, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:118111"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{5}{2}"
] | [
"skywork"
] | 0a82b105290d7dc0ec6d403b6dee01cd7a3e581e5b45d32688605cb0d2bb64ba | [
{
"content": "If $x+y=1$ and $x^{2}+y^{2}=2$, calculate $x^{3}+y^{3}$.",
"role": "user"
}
] | If $x+y=1$ and $x^{2}+y^{2}=2$, calculate $x^{3}+y^{3}$. | "[\"\\\\frac{5}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108189, "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:118112"}] | {
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"2\\sqrt{2}"
] | [
"skywork"
] | d176226fb9cace61d3c77c1da3fdfd5d830b11d9ef36c8434e4c02f5ba5bb369 | [
{
"content": "Example 3 In the Cartesian coordinate system $x O y$, $P$ is a moving point not on the $x$-axis, satisfying the condition: Through $P$, two tangent lines can be drawn to the parabola $y^{2}=4 x$, and the line $l_{P}$ connecting the two points of tangency is perpendicular to $P O$. Let the intersec... | Example 3 In the Cartesian coordinate system $x O y$, $P$ is a moving point not on the $x$-axis, satisfying the condition: Through $P$, two tangent lines can be drawn to the parabola $y^{2}=4 x$, and the line $l_{P}$ connecting the two points of tangency is perpendicular to $P O$. Let the intersection points of the lin... | "[\"2\\\\sqrt{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108171, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118113"}] | {
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"reference_components": 1,
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} |
[
"1247"
] | [
"skywork"
] | cfa7ca05f07ec1d3268e5ec7cd5e17b774c6cc557317ecb311adce6d5e7c6ec3 | [
{
"content": "Let $\\mathcal{P}$ be the parabola in the plane determined by the equation $y = x^2.$ Suppose a circle $\\mathcal{C}$ intersects $\\mathcal{P}$ at four distinct points. If three of these points are $(-28,784),$ $(-2,4),$ and $(13,169),$ find the sum of the distances from the focus of $\\mathcal{... | Let $\mathcal{P}$ be the parabola in the plane determined by the equation $y = x^2.$ Suppose a circle $\mathcal{C}$ intersects $\mathcal{P}$ at four distinct points. If three of these points are $(-28,784),$ $(-2,4),$ and $(13,169),$ find the sum of the distances from the focus of $\mathcal{P}$ to all four of the int... | "[\"1247\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108156, "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:118114"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 90f9e07beb9ed8c8ff0657117de0ec6a30a690dcc5976754c41b284636d36a14 | [
{
"content": "2. (17 points) Point $M$ lies inside segment $A B$, the length of which is 40 cm. Points are chosen: $N$ at the midpoint of $A M, P$ at the midpoint of $M B, C$ at the midpoint of $N M, D$ at the midpoint of $M P$. Find the length of segment $C D$ in cm.",
"role": "user"
}
] | 2. (17 points) Point $M$ lies inside segment $A B$, the length of which is 40 cm. Points are chosen: $N$ at the midpoint of $A M, P$ at the midpoint of $M B, C$ at the midpoint of $N M, D$ at the midpoint of $M P$. Find the length of segment $C D$ in cm. | "[\"10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108175, "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:118115"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3333"
] | [
"skywork"
] | 210e848966f543122c21b5c2a1f0b1bae704a17eb6117f048d439e09a77f641d | [
{
"content": "Find the total number of sets of positive integers \\((x, y, z)\\), where \\(x, y\\) and \\(z\\) are positive integers, with \\(x < y < z\\) such that\n$$\nx + y + z = 203.\n$$",
"role": "user"
}
] | Find the total number of sets of positive integers \((x, y, z)\), where \(x, y\) and \(z\) are positive integers, with \(x < y < z\) such that
$$
x + y + z = 203.
$$ | "[\"3333\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108182, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:118116"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.0236"
] | [
"skywork"
] | 8d25e1c3b27377f844a7d99d606494509ef149c01a9e2297bd38044f7b779971 | [
{
"content": "Example 1. The probability of event $A$ occurring in each of 900 independent trials is $p=0.8$. Find the probability that event $A$ will occur: a) 750 times; b) 710 times.",
"role": "user"
}
] | Example 1. The probability of event $A$ occurring in each of 900 independent trials is $p=0.8$. Find the probability that event $A$ will occur: a) 750 times; b) 710 times. | "[\"0.0236\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108185, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118117"}] | {
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} |
[
"160"
] | [
"skywork"
] | 7e70adba09050e189f07d9e3699b5c9444e4ad1b32e1b33a6cde2d62b77e45bd | [
{
"content": "4. Let $a_{1}, a_{2}, \\cdots, a_{20} \\in\\{1,2, \\cdots, 5\\}, b_{1}, b_{2}, \\cdots, b_{20} \\in\\{1,2, \\cdots, 10\\}$, and the set $X=$ $\\left\\{(i, j) \\mid 1 \\leqslant i<j \\leqslant 20,\\left(a_{i}-a_{j}\\right)\\left(b_{i}-b_{j}\\right)<0\\right\\}$. Find the maximum number of elements ... | 4. Let $a_{1}, a_{2}, \cdots, a_{20} \in\{1,2, \cdots, 5\}, b_{1}, b_{2}, \cdots, b_{20} \in\{1,2, \cdots, 10\}$, and the set $X=$ $\left\{(i, j) \mid 1 \leqslant i<j \leqslant 20,\left(a_{i}-a_{j}\right)\left(b_{i}-b_{j}\right)<0\right\}$. Find the maximum number of elements in $X$. | "[\"160\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108183, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:118118"}] | {
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"reference_present": true
} |
[
"834"
] | [
"skywork"
] | b0ee0d255942534f311eb1eabea79ae53c5193a83a28bcd0b7518e364404ef6b | [
{
"content": "A sequence is defined as follows: $a_1=a_2=a_3=1$, and, for all positive integers $n$, $a_{n+3}=a_{n+2}+a_{n+1}+a_n$. Given that $a_{28}= 6090307$, $a_{29}=11201821$, and $a_{30}=20603361$, find the remainder when $\\displaystyle \\sum_{k=1}^{28}a_k$ is divided by 1000.",
"role": "user"
}
] | A sequence is defined as follows: $a_1=a_2=a_3=1$, and, for all positive integers $n$, $a_{n+3}=a_{n+2}+a_{n+1}+a_n$. Given that $a_{28}= 6090307$, $a_{29}=11201821$, and $a_{30}=20603361$, find the remainder when $\displaystyle \sum_{k=1}^{28}a_k$ is divided by 1000. | "[\"834\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108179, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118119"}] | {
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[
"f(x) = \\begin{cases}\n-(1-x)^c + 1 &\\text{ if $x < 1$} \\\\\n1 &\\text{ if $x = 1$} \\\\\nk(x-1)^c + 1 &\\text{ if $x > 1$}\n\\end{cases}, \\text{ for some real constants }c \\geq 0, k > 0"
] | [
"skywork"
] | 25723f8a513ea5ec727d783f7e342e732ba8e05a6c452e7adee3913791a59970 | [
{
"content": "Let's put down $a = -b$, then we have that $f(b^2) = f(b) + f(-b) - f(b)f(-b)$. If we need that f would be nondecreasing, it must be held that $f(b^2) >= f(b)$, so $f(-b)[1-f(b)] >= 0$ too. From that we have only two possibilities to discuss:\n\nCASE 1: $f(b) = 1$ and $f(-b) = 0$ (this implies tha... | Let's put down $a = -b$, then we have that $f(b^2) = f(b) + f(-b) - f(b)f(-b)$. If we need that f would be nondecreasing, it must be held that $f(b^2) >= f(b)$, so $f(-b)[1-f(b)] >= 0$ too. From that we have only two possibilities to discuss:
CASE 1: $f(b) = 1$ and $f(-b) = 0$ (this implies that for each $a<0: f(a)=0$... | "[\"f(x) = \\\\begin{cases}\\n-(1-x)^c + 1 &\\\\text{ if $x < 1$} \\\\\\\\\\n1 &\\\\text{ if $x = 1$} \\\\\\\\\\nk(x-1)^c + 1 &\\\\text{ if $x > 1$}\\n\\\\end{cases}, \\\\text{ for some real constants }c \\\\geq 0, k > 0\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 108167, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118120"}] | {
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} |
[
"m \\times n"
] | [
"skywork"
] | 72a31e8248c2c7444f279900dd3ab13855140db25ce0bfcd511d8b4cf7805363 | [
{
"content": "In a $ 40 \\times 50$ array of control buttons, each button has two states: on and off\u000b. By touching a button, its state and the states of all buttons in the same row and in the same column are switched. Prove that the array of control buttons may be altered from the all-off\u000b state to th... | In a $ 40 \times 50$ array of control buttons, each button has two states: on and off . By touching a button, its state and the states of all buttons in the same row and in the same column are switched. Prove that the array of control buttons may be altered from the all-off state to the all-on state by touching button... | "[\" m \\\\times n \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108184, "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:118121"}] | {
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} |
[
"\\lambda\\neq2"
] | [
"skywork"
] | 8123f2f563e31ff5e4c76d1d9089921baf3adf5c951ef6ecca33b263c5a6cbaf | [
{
"content": "1. Quadratic equation\n$(1-i) x^{2}+(\\lambda+i) x+(1+i \\lambda)=0 \\quad(i$ is the imaginary unit, $\\lambda \\in R)$ has two imaginary roots if and only if the range of $\\lambda$ is $\\qquad$ .",
"role": "user"
}
] | 1. Quadratic equation
$(1-i) x^{2}+(\lambda+i) x+(1+i \lambda)=0 \quad(i$ is the imaginary unit, $\lambda \in R)$ has two imaginary roots if and only if the range of $\lambda$ is $\qquad$ . | "[\"\\\\lambda\\\\neq2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108181, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118122"}] | {
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} |
[
"\\frac{p-1}{2}"
] | [
"skywork"
] | 451dbb689113934369e9d211cbb67fd2703a92a0ee95ad238eae78457a151603 | [
{
"content": "Example 2 Let $p$ be an odd prime satisfying $p \\equiv 1(\\bmod 4)$, calculate $\\sum_{k=1}^{p-1}\\left\\{\\frac{k^{2}}{p}\\right\\}$, where $\\{x\\}=x-[x],[x]$ is the greatest integer not exceeding $x$.\n\nTranslate the above text into English, please keep the original text's line breaks and for... | Example 2 Let $p$ be an odd prime satisfying $p \equiv 1(\bmod 4)$, calculate $\sum_{k=1}^{p-1}\left\{\frac{k^{2}}{p}\right\}$, where $\{x\}=x-[x],[x]$ is the greatest integer not exceeding $x$.
Translate the above text into English, please keep the original text's line breaks and format, and output the translation re... | "[\"\\\\frac{p-1}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108191, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:118123"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | 964ea71e0909e2fa6735db1a536e06a0b1a89caa874c70df6ef33ec0a85b5ec4 | [
{
"content": "Let $x_1, x_2, \\ldots , x_n$ be a sequence of integers such that\n(i) $-1 \\le x_i \\le 2$ for $i = 1,2, \\ldots n$\n(ii) $x_1 + \\cdots + x_n = 19$; and\n(iii) $x_1^2 + x_2^2 + \\cdots + x_n^2 = 99$.\nLet $m$ and $M$ be the minimal and maximal possible values of $x_1^3 + \\cdots + x_n^3$, respec... | Let $x_1, x_2, \ldots , x_n$ be a sequence of integers such that
(i) $-1 \le x_i \le 2$ for $i = 1,2, \ldots n$
(ii) $x_1 + \cdots + x_n = 19$; and
(iii) $x_1^2 + x_2^2 + \cdots + x_n^2 = 99$.
Let $m$ and $M$ be the minimal and maximal possible values of $x_1^3 + \cdots + x_n^3$, respectively. Then $\frac Mm =$
$\mathr... | "[\"7\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 108190, "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:118124"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"67"
] | [
"skywork"
] | 32b2663286a0d6ff7cfd209b63c3e50c7c72cb9feb938ad6b6f2f84ed66731c0 | [
{
"content": "5. For a set $M$ containing 4 elements, we say it is \"evenly connected\" if for every element $x$ in $M$, at least one of the numbers $x-2$ or $x+2$ also belongs to $M$. Let $S_{n}$ be the number of \"evenly connected\" subsets of $\\{1,2, \\ldots, n\\}$. Determine the smallest number $n$ such th... | 5. For a set $M$ containing 4 elements, we say it is "evenly connected" if for every element $x$ in $M$, at least one of the numbers $x-2$ or $x+2$ also belongs to $M$. Let $S_{n}$ be the number of "evenly connected" subsets of $\{1,2, \ldots, n\}$. Determine the smallest number $n$ such that $S_{n} \geq 2011$. | "[\"67\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108194, "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:118125"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"00\\overline{355446}"
] | [
"skywork"
] | abdc4b8babbf2a0f005aff240b730c89193c39ec065433261e3eac55b13a609b | [
{
"content": "The value of $0 . \\overline{1}+0 . \\overline{12}+0 . \\overline{123}$ is\n(A) $0 . \\overline{343}$\n(B) $0 . \\overline{355}$\n(C) $0.3 \\overline{5}$\n(D) $0 . \\overline{355446}$\n(E) $0 . \\overline{355445}$",
"role": "user"
}
] | The value of $0 . \overline{1}+0 . \overline{12}+0 . \overline{123}$ is
(A) $0 . \overline{343}$
(B) $0 . \overline{355}$
(C) $0.3 \overline{5}$
(D) $0 . \overline{355446}$
(E) $0 . \overline{355445}$ | "[\"00\\\\overline{355446}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108201, "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:118127"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"C"
] | [
"skywork"
] | 9d114ca731dc93b1279b92a7925ba697e9699d21b5ff749b1a909794f8db0983 | [
{
"content": "2. Given the quadratic trinomial in $x$ with integer coefficients $a x^{2}+b x+c$, when $x$ takes the values $1, 3, 6, 8$, a student recorded the values of this quadratic trinomial as $1, 5, 25, 50$. Upon checking, only one of these results is incorrect. The incorrect result is ( ).\n(A) When $x=1... | 2. Given the quadratic trinomial in $x$ with integer coefficients $a x^{2}+b x+c$, when $x$ takes the values $1, 3, 6, 8$, a student recorded the values of this quadratic trinomial as $1, 5, 25, 50$. Upon checking, only one of these results is incorrect. The incorrect result is ( ).
(A) When $x=1$, $a x^{2}+b x+c=1$
(B... | "[\"C\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108187, "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:118128"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2 \\sqrt{2}-2"
] | [
"skywork"
] | f87c9de5b8cd1b6c1e4428f730d6a2f145c55b4a73a1084ddc1da84880ceccf7 | [
{
"content": "Let $x$ be a positive real number. Find the maximum possible value of $$\\frac{x^{2}+2-\\sqrt{x^{4}+4}}{x}$$",
"role": "user"
}
] | Let $x$ be a positive real number. Find the maximum possible value of $$\frac{x^{2}+2-\sqrt{x^{4}+4}}{x}$$ | "[\"2 \\\\sqrt{2}-2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108209, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:118129"}] | {
"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"
] | 04e7afb3d1792d2985daed5b168028264a3c72c05466fbbfd1bcdc96658f2e99 | [
{
"content": "Write either $1$ or $-1$ in each of the cells of a $(2n) \\times (2n)$-table, in such a way that there are exactly $2n^2$ entries of each kind. Let the minimum of the absolute values of all row sums and all column sums be $M$. Determine the largest possible value of $M$.",
"role": "user"
}
] | Write either $1$ or $-1$ in each of the cells of a $(2n) \times (2n)$-table, in such a way that there are exactly $2n^2$ entries of each kind. Let the minimum of the absolute values of all row sums and all column sums be $M$. Determine the largest possible value of $M$. | "[\"2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108199, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118131"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\dfrac{3}{5}"
] | [
"skywork"
] | d7a34873e859626ef0bfebbab2c37d29faa3973385b1b3d51c1f7207731edc11 | [
{
"content": "From six balls numbered respectively $1$, $2$, $3$, $4$, $5$, $6$, which are all of the same size, three balls are randomly drawn. Find the probability that exactly two of the balls have consecutive numbers.",
"role": "user"
}
] | From six balls numbered respectively $1$, $2$, $3$, $4$, $5$, $6$, which are all of the same size, three balls are randomly drawn. Find the probability that exactly two of the balls have consecutive numbers. | "[\"\\\\dfrac{3}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108198, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118132"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3}{7}\\bar{i}-\\frac{4}{7}\\bar{j}+\\frac{6}{7}\\bar{k}"
] | [
"skywork"
] | 3c4b2cff4ff387707a7d6f1d10c54df6f66df78178788b826bf5ee4a5622d1f9 | [
{
"content": "315. Express through the orths $\\bar{i}, \\bar{j}, \\bar{k}$ the orth $\\overline{a^{0}}$ of the vector\n\n$$\n\\bar{a}=\\overline{3 i}-4 \\bar{j}+6 \\bar{k}\n$$",
"role": "user"
}
] | 315. Express through the orths $\bar{i}, \bar{j}, \bar{k}$ the orth $\overline{a^{0}}$ of the vector
$$
\bar{a}=\overline{3 i}-4 \bar{j}+6 \bar{k}
$$ | "[\"\\\\frac{3}{7}\\\\bar{i}-\\\\frac{4}{7}\\\\bar{j}+\\\\frac{6}{7}\\\\bar{k}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108192, "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:118133"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"41"
] | [
"skywork"
] | 4a6b4d0e0737f79db44a22c7d74c1bd43c5735eea0f28f0e8c0b40bfa2198217 | [
{
"content": "$1 \\cdot 27$ Find the smallest prime $p$ that cannot be expressed as $\\left|3^{a}-2^{b}\\right|$, where $a$ and $b$ are non-negative integers.",
"role": "user"
}
] | $1 \cdot 27$ Find the smallest prime $p$ that cannot be expressed as $\left|3^{a}-2^{b}\right|$, where $a$ and $b$ are non-negative integers. | "[\"41\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108205, "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:118134"}] | {
"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
} |
[
"210"
] | [
"skywork"
] | 2c64793843b595b9b7781047a87ab94f263622bb4a3cffa77195055b3e8b2d37 | [
{
"content": "First, factorize 42 and 30 into prime factors, then answer the following questions: \n(1) 42= , 30= . \n(2) The common prime factors of 42 and 30 are . \n(3) The unique prime factors of 42 and 30 are . \n(4) The greatest common divisor (GCD) of 42 and 30 is . \n(5) The least... | First, factorize 42 and 30 into prime factors, then answer the following questions:
(1) 42= , 30= .
(2) The common prime factors of 42 and 30 are .
(3) The unique prime factors of 42 and 30 are .
(4) The greatest common divisor (GCD) of 42 and 30 is .
(5) The least common multiple (LCM) of 4... | "[\"210\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108178, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118135"}] | {
"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
} |
[
"A^{2}-B"
] | [
"skywork"
] | 84a45381dfb4593748e1138a4a2fc59a5486cef325136b88cd457dc7a94776e7 | [
{
"content": "163*. Find the condition under which the expression $\\sqrt{A \\pm \\sqrt{\\bar{B}}}$ can be represented in the form of a binomial $\\sqrt{x} \\pm \\sqrt{y}$, where $x$ and $y$ are rational numbers.",
"role": "user"
}
] | 163*. Find the condition under which the expression $\sqrt{A \pm \sqrt{\bar{B}}}$ can be represented in the form of a binomial $\sqrt{x} \pm \sqrt{y}$, where $x$ and $y$ are rational numbers. | "[\"A^{2}-B\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108196, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "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:118136"}] | {
"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
} |
[
"33"
] | [
"skywork"
] | 202d28474ee01ba567c13296760118a71e995a6daaac6acfba6d7230db1fba4a | [
{
"content": "The number 119 has the following properties:\n\n(a) division by 2 leaves a remainder of 1;\n\n(b) division by 3 leaves a remainder of 2;\n\n(c) division by 4 leaves a remainder of 3;\n\n(d) division by 5 leaves a remainder of 4;\n\n(e) division by 6 leaves a remainder of 5.\n\nHow many positive in... | The number 119 has the following properties:
(a) division by 2 leaves a remainder of 1;
(b) division by 3 leaves a remainder of 2;
(c) division by 4 leaves a remainder of 3;
(d) division by 5 leaves a remainder of 4;
(e) division by 6 leaves a remainder of 5.
How many positive integers less than 2007 satisfy thes... | "[\"33\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108210, "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:118137"}] | {
"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
} |
[
"1154"
] | [
"skywork"
] | 126ea1660d93958deff26a39091f94b6ad2827b30c5bea01779debd943ce3f51 | [
{
"content": "Let $[x]$ represent the greatest integer less than or equal to the real number $x$. Define the sets\n$$\n\\begin{array}{l}\nA=\\{y \\mid y=[x]+[2x]+[4x], x \\in \\mathbf{R}\\}, \\\\\nB=\\{1,2, \\cdots, 2019\\}.\n\\end{array}\n$$\n\nFind the number of elements in the intersection $A \\cap B$.",
... | Let $[x]$ represent the greatest integer less than or equal to the real number $x$. Define the sets
$$
\begin{array}{l}
A=\{y \mid y=[x]+[2x]+[4x], x \in \mathbf{R}\}, \\
B=\{1,2, \cdots, 2019\}.
\end{array}
$$
Find the number of elements in the intersection $A \cap B$. | "[\"1154\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108188, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118138"}] | {
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[
"\\frac{6\\sqrt{2}+4}{15}"
] | [
"skywork"
] | 22d7319f8f69725cfe9bcb4cf8d254d573c296b142abfdeb9cbfeb76f62cb88c | [
{
"content": "Given that $a\\in (\\frac{\\pi }{2},\\pi )$ and $\\sin \\alpha =\\frac{1}{3}$,\n\n(1) Find the value of $\\sin 2\\alpha$;\n\n(2) If $\\sin (\\alpha +\\beta )=-\\frac{3}{5}$, $\\beta \\in (0,\\frac{\\pi }{2})$, find the value of $\\sin \\beta$.",
"role": "user"
}
] | Given that $a\in (\frac{\pi }{2},\pi )$ and $\sin \alpha =\frac{1}{3}$,
(1) Find the value of $\sin 2\alpha$;
(2) If $\sin (\alpha +\beta )=-\frac{3}{5}$, $\beta \in (0,\frac{\pi }{2})$, find the value of $\sin \beta$. | "[\"\\\\frac{6\\\\sqrt{2}+4}{15}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108186, "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:118139"}] | {
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[
"5-4\\cdot3:2+1=0"
] | [
"skywork"
] | f5d50b552af56566897065fee642dba045846a2f827cfc7b2202771f3b07d1df | [
{
"content": "7.1. In the expression $5 * 4 * 3 * 2 * 1=0$, replace the asterisks with the four arithmetic operation signs (using each sign exactly once) to make the equation true. No other signs, including parentheses, can be used.",
"role": "user"
}
] | 7.1. In the expression $5 * 4 * 3 * 2 * 1=0$, replace the asterisks with the four arithmetic operation signs (using each sign exactly once) to make the equation true. No other signs, including parentheses, can be used. | "[\"5-4\\\\cdot3:2+1=0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108195, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118140"}] | {
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} |
[
"20"
] | [
"skywork"
] | a551dcdb6f012db668d7ab607197e11414b541e2189194b77b439b434f1a5859 | [
{
"content": "A postman has to deliver five letters to five different houses. Mischievously, he posts one letter through each door without looking to see if it is the correct address. In how many different ways could he do this so that exactly two of the five houses receive the correct letters?",
"role": "u... | A postman has to deliver five letters to five different houses. Mischievously, he posts one letter through each door without looking to see if it is the correct address. In how many different ways could he do this so that exactly two of the five houses receive the correct letters? | "[\"20\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108213, "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:118141"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{25}{16}"
] | [
"skywork"
] | 19ee2ec43263fd268d1c583918c8ec631d68ac726f34ceeb919ce37df8bff896 | [
{
"content": "\\section*{Problem 6 - 071046}\n\nDetermine all real \\(x\\) that satisfy the following equation:\n\n\\[\n\\sqrt{x+\\sqrt{x}}-\\sqrt{x-\\sqrt{x}}=\\frac{3}{2} \\sqrt{\\frac{x}{x+\\sqrt{x}}}\n\\]",
"role": "user"
}
] | \section*{Problem 6 - 071046}
Determine all real \(x\) that satisfy the following equation:
\[
\sqrt{x+\sqrt{x}}-\sqrt{x-\sqrt{x}}=\frac{3}{2} \sqrt{\frac{x}{x+\sqrt{x}}}
\] | "[\"\\\\frac{25}{16}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108193, "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:118142"}] | {
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[
"63"
] | [
"skywork"
] | 6a9498c82213a9b6a766a3551230d9b33bd2ec8376e576e0552d6a6693b86508 | [
{
"content": "5. Group the positive integers $1,2, \\cdots, n, \\cdots$ such that the $k$-th group contains $k+1$ numbers:\n$$\n\\begin{array}{l}\n\\underbrace{(1,2)}_{\\text {1st group }}, \\underbrace{(3,4)}_{\\text {2nd, } 2,5}, \\underbrace{(6,7,8,9)}_{\\text {3rd, group }}, \\\\\n\\underbrace{(10,11,12,13,... | 5. Group the positive integers $1,2, \cdots, n, \cdots$ such that the $k$-th group contains $k+1$ numbers:
$$
\begin{array}{l}
\underbrace{(1,2)}_{\text {1st group }}, \underbrace{(3,4)}_{\text {2nd, } 2,5}, \underbrace{(6,7,8,9)}_{\text {3rd, group }}, \\
\underbrace{(10,11,12,13,14)}_{\text {4th group }}, \cdots
\end... | "[\"63\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108215, "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:118144"}] | {
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"reference_components": 1,
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} |
[
"7000"
] | [
"skywork"
] | 0e8e7fa9babd609b32bda6aa4767f3de963aa5b578d48526fd2f259317a4e247 | [
{
"content": "Find the maximum number of cells that can be coloured from a $4\\times 3000$ board such that no tetromino is formed.\n\n[i]Proposed by Arian Zamani, Matin Yousefi[/i] [b]Rated 5[/b]",
"role": "user"
}
] | Find the maximum number of cells that can be coloured from a $4\times 3000$ board such that no tetromino is formed.
[i]Proposed by Arian Zamani, Matin Yousefi[/i] [b]Rated 5[/b] | "[\"7000\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108212, "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:118145"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | aa9a388d784c060f887c4e10396253fdf55ffdf15ba86f7e5282bcbf4a6eb7f3 | [
{
"content": "Evaluate the expression $2^{3}-2+3$.",
"role": "user"
}
] | Evaluate the expression $2^{3}-2+3$. | "[\"9\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108224, "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:118146"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | 6d6bc915118e608ba175ec6ceb5bc1e2883258a739dcd46d50627ebdac9513d2 | [
{
"content": "12. Satisfy:\n$$\nx+y^{2}=z^{3}, x^{2}+y^{3}=z^{4}, x^{3}+y^{4}=z^{5}\n$$\n\nthe number of ordered triples of real numbers $(x, y, z)$ is $\\qquad$.",
"role": "user"
}
] | 12. Satisfy:
$$
x+y^{2}=z^{3}, x^{2}+y^{3}=z^{4}, x^{3}+y^{4}=z^{5}
$$
the number of ordered triples of real numbers $(x, y, z)$ is $\qquad$. | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108214, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118147"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"560"
] | [
"skywork"
] | f7b948a4a86ec83046824d3a803b85333d00ed879cf5019f38d0c8ebb713abf0 | [
{
"content": "9. (15 points) At a party one day, Kung Fu Panda exchanged all the buns he had for Garfield's spaghetti, with 3 buns for 2 servings of spaghetti. Winnie the Pooh also exchanged all the honey he had for Garfield's spaghetti, with 4 jars of honey for 5 servings of spaghetti. It is known that Kung Fu... | 9. (15 points) At a party one day, Kung Fu Panda exchanged all the buns he had for Garfield's spaghetti, with 3 buns for 2 servings of spaghetti. Winnie the Pooh also exchanged all the honey he had for Garfield's spaghetti, with 4 jars of honey for 5 servings of spaghetti. It is known that Kung Fu Panda and Winnie the ... | "[\"560\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108204, "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:118148"}] | {
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"reference_components": 1,
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} |
[
"[\\frac{5}{2},+\\infty)"
] | [
"skywork"
] | 1746f921eb9e0dac6f97fc9f110cbc8ff6c8e9428b43cabf223a60057f57cbc7 | [
{
"content": "7. Given the function $f(x)=\\sqrt{x^{2}+1}-\\frac{2}{5} a x$, where $a>0$, is a monotonic function on the interval $[0,+\\infty)$, then the range of values for $a$ is $\\qquad$ .",
"role": "user"
}
] | 7. Given the function $f(x)=\sqrt{x^{2}+1}-\frac{2}{5} a x$, where $a>0$, is a monotonic function on the interval $[0,+\infty)$, then the range of values for $a$ is $\qquad$ . | "[\"[\\\\frac{5}{2},+\\\\infty)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108217, "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:118149"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 9f720938acf4fca8c71e256b99661e68e0274ab43ad1113bc536c27047fdee5d | [
{
"content": "11 Given that $x_{1}$ is a root of the equation $x+\\lg x=3$, and $x_{2}$ is a root of the equation $x+10^{x}=3$, then the value of $x_{1}+x_{2}$ is ( ).\n(A) 3\n(B) 6\n(C) 2\n(D) 1",
"role": "user"
}
] | 11 Given that $x_{1}$ is a root of the equation $x+\lg x=3$, and $x_{2}$ is a root of the equation $x+10^{x}=3$, then the value of $x_{1}+x_{2}$ is ( ).
(A) 3
(B) 6
(C) 2
(D) 1 | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108197, "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:118150"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"-4"
] | [
"skywork"
] | 44ee603df30f5b6a79762d7c436539fb91ecdc4bfbed9afd4c711ab261c9842a | [
{
"content": "Consider the points $P(0,0), Q(4,0)$ and $R(1,2)$. The line with equation $y=m x+b$ is parallel to $P R$ and passes through the midpoint of $Q R$. What is the value of $b$ ?",
"role": "user"
}
] | Consider the points $P(0,0), Q(4,0)$ and $R(1,2)$. The line with equation $y=m x+b$ is parallel to $P R$ and passes through the midpoint of $Q R$. What is the value of $b$ ? | "[\"-4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108221, "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:118151"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"50"
] | [
"skywork"
] | 1d5ce0f3930c13c05940acda13c52c5d8ebb5345e38dfa5d7957b2f3427ad62b | [
{
"content": "Let the set \\( P = \\{1, 2, \\ldots, 2014\\} \\) and \\( A \\subseteq P \\). If the difference between any two numbers in the set \\( A \\) is not a multiple of 99, and the sum of any two numbers in the set \\( A \\) is also not a multiple of 99, then the set \\( A \\) can contain at most how man... | Let the set \( P = \{1, 2, \ldots, 2014\} \) and \( A \subseteq P \). If the difference between any two numbers in the set \( A \) is not a multiple of 99, and the sum of any two numbers in the set \( A \) is also not a multiple of 99, then the set \( A \) can contain at most how many elements? | "[\"50\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108227, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118152"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | 2da739caabd4bd87be19ecedb0ef7393918c254a7eacc7a9528046b28113902f | [
{
"content": "9.2 Points A, B, C, D are consecutive vertices of a regular n-gon. What is n if $\\angle \\mathrm{ACD}=120^{\\circ}$?",
"role": "user"
}
] | 9.2 Points A, B, C, D are consecutive vertices of a regular n-gon. What is n if $\angle \mathrm{ACD}=120^{\circ}$? | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108220, "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:118153"}] | {
"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
} |
[
"128"
] | [
"skywork"
] | afbcdc13a3d1fd18aa59479fd1ac019e445a1424a0fd4828588ba7122ba6de92 | [
{
"content": "13. A sequence is given by $x_{1}=2, x_{n+1}=\\frac{x_{n} x_{n}}{32^{n-1}}$. What is $\\frac{x_{4}}{128}$ ?",
"role": "user"
}
] | 13. A sequence is given by $x_{1}=2, x_{n+1}=\frac{x_{n} x_{n}}{32^{n-1}}$. What is $\frac{x_{4}}{128}$ ? | "[\"128\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108207, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118154"}] | {
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"reference_present": true
} |
[
"\\sqrt[3]{4}"
] | [
"skywork"
] | ea02a27a03ddbaaea75f034a3bdf06842673cb1483d7224ee9432f825f2a7610 | [
{
"content": "Given $a$ and $b$ are positive numbers such that $a^b = b^a$ and $b = 4a$, solve for the value of $a$.",
"role": "user"
}
] | Given $a$ and $b$ are positive numbers such that $a^b = b^a$ and $b = 4a$, solve for the value of $a$. | "[\"\\\\sqrt[3]{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108232, "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:118155"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"119"
] | [
"skywork"
] | adf5fa5a39a074ade0e3fa99b5798b1e63adc9d9e2c9b0628b2292e83bab7cad | [
{
"content": "9. The equation $9 x^{3}-3 x^{2}-3 x-1=0$ has a real root of the form $\\frac{\\sqrt[3]{a}+\\sqrt[3]{b}+1}{c}$, where $a, b, c$ are positive integers. Find the value of $a+b+c$.\n(1 mark)\n方程 $9 x^{3}-3 x^{2}-3 x-1=0$ 有一個形如 $\\frac{\\sqrt[3]{a}+\\sqrt[3]{b}+1}{c}$ （其中 $a \\cdot b \\cdot c$ 為正整數）的實... | 9. The equation $9 x^{3}-3 x^{2}-3 x-1=0$ has a real root of the form $\frac{\sqrt[3]{a}+\sqrt[3]{b}+1}{c}$, where $a, b, c$ are positive integers. Find the value of $a+b+c$.
(1 mark)
方程 $9 x^{3}-3 x^{2}-3 x-1=0$ 有一個形如 $\frac{\sqrt[3]{a}+\sqrt[3]{b}+1}{c}$ （其中 $a \cdot b \cdot c$ 為正整數）的實根。求 $a+b+c$ 的值。
(1 分) | "[\"119\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108223, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118156"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"143\\mathrm{~}^{2}"
] | [
"skywork"
] | 77c0949fe1344f424bcaf391619f53ef91253e7d9d29484d1cb4a9460a0c4f12 | [
{
"content": "5. Instead of the asterisks, place such digits so that the correct equation is obtained $5^{*}+* * 3=* * 01$.\n\n将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。",
"role": "user"
}
] | 5. Instead of the asterisks, place such digits so that the correct equation is obtained $5^{*}+* * 3=* * 01$.
将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。 | "[\"143\\\\mathrm{~}^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108136, "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:118157"}] | {
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[
"998"
] | [
"skywork"
] | 5f756c896a20277ca2e266c40f2c7f0bb631e1e54e3be56a95538096e02691b3 | [
{
"content": "Given a finite sequence $D$: $a\\_1$, $a\\_2$, ..., $a\\_n$, where $S\\_n$ represents the sum of the first $n$ terms of the sequence $D$, define $\\frac{S\\_1 + S\\_2 + ... + S\\_n}{n}$ as the \"De-Guang sum\" of $D$. If a 99-term sequence $a\\_1$, $a\\_2$, ..., $a\\_99$ has a \"De-Guang sum\" of ... | Given a finite sequence $D$: $a\_1$, $a\_2$, ..., $a\_n$, where $S\_n$ represents the sum of the first $n$ terms of the sequence $D$, define $\frac{S\_1 + S\_2 + ... + S\_n}{n}$ as the "De-Guang sum" of $D$. If a 99-term sequence $a\_1$, $a\_2$, ..., $a\_99$ has a "De-Guang sum" of $1000$, find the "De-Guang sum" of th... | "[\"998\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108219, "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:118158"}] | {
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} |
[
"5"
] | [
"skywork"
] | 0e8090f80f99434a81e782200399fa28d305b7251ffb046355cfce9cb7602aee | [
{
"content": "In the Pascal family, each child has at least 2 brothers and at least 1 sister. What is the smallest possible number of children in this family?\n(A) 3\n(B) 4\n(C) 5\n(D) 6\n(E) 7",
"role": "user"
}
] | In the Pascal family, each child has at least 2 brothers and at least 1 sister. What is the smallest possible number of children in this family?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7 | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108229, "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:118159"}] | {
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} |
[
"N = 9"
] | [
"skywork"
] | d36e18c260eaa537a35adab85b8c8ee4cd7a0335745838f8685977fcd92647c0 | [
{
"content": "$N\\geq9$ distinct real numbers are written on a blackboard. All these numbers are nonnegative, and all are less than $1$. It happens that for very $8$ distinct numbers on the board, the board contains the ninth number distinct from eight such that the sum of all these nine numbers is integer. Fin... | $N\geq9$ distinct real numbers are written on a blackboard. All these numbers are nonnegative, and all are less than $1$. It happens that for very $8$ distinct numbers on the board, the board contains the ninth number distinct from eight such that the sum of all these nine numbers is integer. Find all values $N$ for wh... | "[\" N = 9 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108218, "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:118160"}] | {
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[
"\\text{The first player has a winning strategy by following the symmetric approach.}"
] | [
"skywork"
] | 531893ea3735946d540c6e0cab462ef11c8685958e35b4c98b8ff1437819e4d9 | [
{
"content": "There are 2008 bags numbered from 1 to 2008, with 2008 frogs in each one of them. Two people play in turns. A play consists in selecting a bag and taking out of it any number of frongs (at least one), leaving $ x$ frogs in it ($ x\\geq 0$). After each play, from each bag with a number higher than... | There are 2008 bags numbered from 1 to 2008, with 2008 frogs in each one of them. Two people play in turns. A play consists in selecting a bag and taking out of it any number of frongs (at least one), leaving $ x$ frogs in it ($ x\geq 0$). After each play, from each bag with a number higher than the selected one and h... | "[\"\\\\text{The first player has a winning strategy by following the symmetric approach.}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108206, "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:118161"}] | {
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} |
[
"32\\mathrm{~}"
] | [
"skywork"
] | 262252a5da7f221c313a4504b378b626d7bd0bd6cb7d365896813c4fa6371c10 | [
{
"content": "Each of two cylinders sits on one of their circular faces on a flat surface. Cylinder A, with radius $6 \\mathrm{~cm}$ and height $50 \\mathrm{~cm}$, is empty. Cylinder B, with radius $8 \\mathrm{~cm}$ and height $50 \\mathrm{~cm}$, is full of water. After pouring some water from Cylinder B into C... | Each of two cylinders sits on one of their circular faces on a flat surface. Cylinder A, with radius $6 \mathrm{~cm}$ and height $50 \mathrm{~cm}$, is empty. Cylinder B, with radius $8 \mathrm{~cm}$ and height $50 \mathrm{~cm}$, is full of water. After pouring some water from Cylinder B into Cylinder A, the height of t... | "[\"32\\\\mathrm{~}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108233, "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:118162"}] | {
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} |
[
"x_{1}=1,x_{2}=0.25"
] | [
"skywork"
] | 4c3c0b19ba24855fa55093d193fdc3b56da4e3c68ed6d8574cedafb87f16dfaf | [
{
"content": "$7.1 \\quad \\sqrt{5} \\cdot 0.2^{\\frac{1}{2 x}}-0.04^{1-x}=0$.",
"role": "user"
}
] | $7.1 \quad \sqrt{5} \cdot 0.2^{\frac{1}{2 x}}-0.04^{1-x}=0$. | "[\"x_{1}=1,x_{2}=0.25\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108222, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118163"}] | {
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} |
[
"2+\\log_{2}3"
] | [
"skywork"
] | 09c0317992bfdb95771598aa465c50f6ea91995248af4f00ba57fd25f05248aa | [
{
"content": "17. (10 points) Let the function\n$$\nf(x)=\\log _{2}\\left(a^{x}-b^{x}\\right),\n$$\n\nand $f(1)=1, f(2)=\\log _{2} 12$.\n(1) Find the values of $a, b$;\n(2) When $x \\in[1,2]$, find the maximum value of $f(x)$.",
"role": "user"
}
] | 17. (10 points) Let the function
$$
f(x)=\log _{2}\left(a^{x}-b^{x}\right),
$$
and $f(1)=1, f(2)=\log _{2} 12$.
(1) Find the values of $a, b$;
(2) When $x \in[1,2]$, find the maximum value of $f(x)$. | "[\"2+\\\\log_{2}3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108208, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118164"}] | {
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} |
[
"\\binom{19}{10} - 1"
] | [
"skywork"
] | 3a73c2a791bc7a3ee2fba3d0f618509a144c54f5fec82324a30c9727b7686ab7 | [
{
"content": "Let $S$ be a set of positive integers, each of them having exactly $100$ digits in base $10$ representation. An element of $S$ is called [i]atom[/i] if it is not divisible by the sum of any two (not necessarily distinct) elements of $S$. If $S$ contains at most $10$ atoms, at most how many element... | Let $S$ be a set of positive integers, each of them having exactly $100$ digits in base $10$ representation. An element of $S$ is called [i]atom[/i] if it is not divisible by the sum of any two (not necessarily distinct) elements of $S$. If $S$ contains at most $10$ atoms, at most how many elements can $S$ have? | "[\"\\\\binom{19}{10} - 1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108231, "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:118165"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 8585b671308e25a9be54270ca7b1e5bd9061a8de301fe10080d91314a4a0e0e3 | [
{
"content": "Given that $a, b, c$ are positive real numbers and $\\log _{a} b+\\log _{b} c+\\log _{c} a=0$, find the value of $\\left(\\log _{a} b\\right)^{3}+\\left(\\log _{b} c\\right)^{3}+\\left(\\log _{c} a\\right)^{3}$.",
"role": "user"
}
] | Given that $a, b, c$ are positive real numbers and $\log _{a} b+\log _{b} c+\log _{c} a=0$, find the value of $\left(\log _{a} b\right)^{3}+\left(\log _{b} c\right)^{3}+\left(\log _{c} a\right)^{3}$. | "[\"3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108230, "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:118166"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 90ae7c37a1d70b55c09e0455d79475d1432e92e903b5129b68b043596c490d72 | [
{
"content": "A2. Six standard, fair dice are rolled once. The total of the scores rolled is 32 .\nWhat is the smallest possible score that could have appeared on any of the dice?",
"role": "user"
}
] | A2. Six standard, fair dice are rolled once. The total of the scores rolled is 32 .
What is the smallest possible score that could have appeared on any of the dice? | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108243, "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:118167"}] | {
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} |
[
"73"
] | [
"skywork"
] | fff5fe43aa1ac4d8a0c979b7f4d2555b6618f721c6ef9ad267d55213713ba079 | [
{
"content": "1. (6 points) Calculate: $121 \\times \\frac{13}{25}+12 \\times \\frac{21}{25}$.",
"role": "user"
}
] | 1. (6 points) Calculate: $121 \times \frac{13}{25}+12 \times \frac{21}{25}$. | "[\"73\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108249, "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:118169"}] | {
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"reference_components": 1,
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} |
[
"432 \\mathrm{~cm}^{2}"
] | [
"skywork"
] | 71001ffac80e61254e79c785c376a914491f8c077f083da83251a95fd86164c0 | [
{
"content": "Example 1 As shown in Figure 1, in hexagon $A B C D E F$, $A B \\cong$ $E D$, $A F \\cong C D$, $B C \\xlongequal[=]{=}$ $F E$, diagonal $F D \\perp$ $B D$. It is known that $F D=24 \\mathrm{~cm}$, $B D=18 \\mathrm{~cm}$. What is the area of hexagon $A B C D E F$ in square centimeters?",
"role... | Example 1 As shown in Figure 1, in hexagon $A B C D E F$, $A B \cong$ $E D$, $A F \cong C D$, $B C \xlongequal[=]{=}$ $F E$, diagonal $F D \perp$ $B D$. It is known that $F D=24 \mathrm{~cm}$, $B D=18 \mathrm{~cm}$. What is the area of hexagon $A B C D E F$ in square centimeters? | "[\"432 \\\\mathrm{~cm}^{2}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108225, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118170"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{\\sqrt[2^{n-1}]{2} - 1}"
] | [
"skywork"
] | b2e7f66027bf60f8a14372a7e8b8d25673a3fdcbfef82599c0b79bc5de334b32 | [
{
"content": "Sequence {$x_n$} satisfies: $x_1=1$ , ${x_n=\\sqrt{x_{n-1}^2+x_{n-1}}+x_{n-1}}$ ( ${n>=2}$ )\nFind the general term of {$x_n$}",
"role": "user"
}
] | Sequence {$x_n$} satisfies: $x_1=1$ , ${x_n=\sqrt{x_{n-1}^2+x_{n-1}}+x_{n-1}}$ ( ${n>=2}$ )
Find the general term of {$x_n$} | "[\"\\\\frac{1}{\\\\sqrt[2^{n-1}]{2} - 1}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108237, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118171"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"65"
] | [
"skywork"
] | 15604e5a6db1abf36a78fcaf3b1a23e49eede670e7b4c7449397b936dd1080ba | [
{
"content": "In a triangle with integer side lengths, one side is twice as long as a second side, and the length of the third side is 17. What is the greatest possible perimeter of the triangle?",
"role": "user"
}
] | In a triangle with integer side lengths, one side is twice as long as a second side, and the length of the third side is 17. What is the greatest possible perimeter of the triangle? | "[\"65\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108238, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118172"}] | {
"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
} |
[
"3120"
] | [
"skywork"
] | f1ebd0576a9833cb5188eb3c309129a56f323a388b960dd8b67825e502310191 | [
{
"content": "Each vertex of convex pentagon $ABCDE$ is to be assigned a color. There are $6$ colors to choose from, and the ends of each diagonal must have different colors. How many different colorings are possible?\n$\\textbf{(A)}\\ 2520\\qquad\\textbf{(B)}\\ 2880\\qquad\\textbf{(C)}\\ 3120\\qquad\\textbf{(D... | Each vertex of convex pentagon $ABCDE$ is to be assigned a color. There are $6$ colors to choose from, and the ends of each diagonal must have different colors. How many different colorings are possible?
$\textbf{(A)}\ 2520\qquad\textbf{(B)}\ 2880\qquad\textbf{(C)}\ 3120\qquad\textbf{(D)}\ 3250\qquad\textbf{(E)}\ 3750$ | "[\"3120\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 108234, "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:118173"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"skywork"
] | 1d2b9460554cd81fe778598a8a18127f4b717c0953989c02659ef6e49bb181b7 | [
{
"content": "$10 \\cdot 771^{2}, 2^{2}, 3^{2}, \\cdots, 123456789^{2}$ What is the digit in the units place of the sum? \n(China Junior High School Mathematics League, 1990)",
"role": "user"
}
] | $10 \cdot 771^{2}, 2^{2}, 3^{2}, \cdots, 123456789^{2}$ What is the digit in the units place of the sum?
(China Junior High School Mathematics League, 1990) | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108235, "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:118174"}] | {
"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
} |
[
"u_{n}=\\frac{n(n+1)}{2}+1"
] | [
"skywork"
] | 8e1a93b0bfc689e7cf7b557c4088d90a3b38a90b7f2073a2b85727f0affeaded | [
{
"content": "We trace $n$ lines in the plane, no two parallel, no three concurrent. Into how many parts is the plane divided?",
"role": "user"
}
] | We trace $n$ lines in the plane, no two parallel, no three concurrent. Into how many parts is the plane divided? | "[\"u_{n}=\\\\frac{n(n+1)}{2}+1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108247, "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:118175"}] | {
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[
"-\\frac{8}{3}"
] | [
"skywork"
] | 0824b670f616d0572d073e65fd4443f4099976bf88ece58e15cc34e84d183fb4 | [
{
"content": "3. Let $x, y$, and $z$ be real numbers that satisfy the following system:\n$$\n\\begin{aligned}\nx+3 y+6 z & =1 \\\\\nx y+2 x z+6 y z & =-8 \\\\\nx y z & =2\n\\end{aligned}\n$$\n\nFind the smallest possible value of $x+y+z$.",
"role": "user"
}
] | 3. Let $x, y$, and $z$ be real numbers that satisfy the following system:
$$
\begin{aligned}
x+3 y+6 z & =1 \\
x y+2 x z+6 y z & =-8 \\
x y z & =2
\end{aligned}
$$
Find the smallest possible value of $x+y+z$. | "[\"-\\\\frac{8}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108242, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118176"}] | {
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[
"\\text{box 3}"
] | [
"skywork"
] | 64910b774a7d7f56b4fce2eaee44805cd9b8a3aee9fbb6c914040b5352f7fb37 | [
{
"content": "There are $ 7$ boxes arranged in a row and numbered $1$ through $7$. You have a stack of $2015$ cards, which you place one by one in the boxes. The first card is placed in box #$1$, the second in box #$2$, and so forth up to the seventh card which is placed in box #$7$. You then start working bac... | There are $ 7$ boxes arranged in a row and numbered $1$ through $7$. You have a stack of $2015$ cards, which you place one by one in the boxes. The first card is placed in box #$1$, the second in box #$2$, and so forth up to the seventh card which is placed in box #$7$. You then start working back in the other directi... | "[\"\\\\text{box 3}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108241, "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:118177"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"22"
] | [
"skywork"
] | e4a523d516c489bb37ea08255f413092fecf1584724f18f022c57029c285ce08 | [
{
"content": "A three-dimensional rectangular box with dimensions $X$, $Y$, and $Z$ has faces whose surface areas are $24$, $24$, $48$, $48$, $72$, and $72$ square units. What is $X$ + $Y$ + $Z$?",
"role": "user"
}
] | A three-dimensional rectangular box with dimensions $X$, $Y$, and $Z$ has faces whose surface areas are $24$, $24$, $48$, $48$, $72$, and $72$ square units. What is $X$ + $Y$ + $Z$? | "[\"22\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108239, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118178"}] | {
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} |
[
"2004"
] | [
"skywork"
] | c14caf9e670963057144a420bfb93f7a99b8b00dbe89d7d612837b6658d53455 | [
{
"content": "Let $(x,y,z)$ be an ordered triplet of real numbers that satisfies the following system of equations: \\begin{align*}x+y^2+z^4&=0,\\\\y+z^2+x^4&=0,\\\\z+x^2+y^4&=0.\\end{align*} If $m$ is the minimum possible value of $\\lfloor x^3+y^3+z^3\\rfloor$, find the modulo $2007$ residue of $m$.",
"ro... | Let $(x,y,z)$ be an ordered triplet of real numbers that satisfies the following system of equations: \begin{align*}x+y^2+z^4&=0,\\y+z^2+x^4&=0,\\z+x^2+y^4&=0.\end{align*} If $m$ is the minimum possible value of $\lfloor x^3+y^3+z^3\rfloor$, find the modulo $2007$ residue of $m$. | "[\"2004\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108236, "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:118179"}] | {
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} |
[
"288"
] | [
"skywork"
] | 36b3b2ca3483620b81576acee30cfb9fda35cb315349db202db7fda28fadbac6 | [
{
"content": "How many ways are there to arrange the numbers $1$ through $8$ into a $2$ by $4$ grid such that the sum of the numbers in each of the two rows are all multiples of $6,$ and the sum of the numbers in each of the four columns are all multiples of $3$?",
"role": "user"
}
] | How many ways are there to arrange the numbers $1$ through $8$ into a $2$ by $4$ grid such that the sum of the numbers in each of the two rows are all multiples of $6,$ and the sum of the numbers in each of the four columns are all multiples of $3$? | "[\"288\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108240, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118180"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"121"
] | [
"skywork"
] | 27afee5411cd7afb7c646fa2b69f3a48c7cffa3c60bcbfd5461fba8e69925718 | [
{
"content": "[ Divisibility of numbers. General properties ]\n\nFind the smallest natural $n$ for which $(n+1)(n+2)(n+3)(n+4)$ is divisible by 1000.",
"role": "user"
}
] | [ Divisibility of numbers. General properties ]
Find the smallest natural $n$ for which $(n+1)(n+2)(n+3)(n+4)$ is divisible by 1000. | "[\"121\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108257, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118181"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 596139a21035e949a7ee5d69f456e60ed9d04c0e08665fa9c54686656f3d8fdf | [
{
"content": "Evaluate $\\lfloor0.999\\rfloor+\\lceil2.001\\rceil$.",
"role": "user"
}
] | Evaluate $\lfloor0.999\rfloor+\lceil2.001\rceil$. | "[\"3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108277, "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:118182"}] | {
"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
} |
[
"48"
] | [
"skywork"
] | d731be54c24fa6939fa3e49ccee7874b672ffde57790905e89863e2c43c5e6b2 | [
{
"content": "A certain organism begins as three cells. Each cell splits and becomes two cells at the end of two days. At the end of another two days, every cell of the organism splits and becomes two cells. This process lasts for a total of 8 days, and no cells die during this time. How many cells are there at... | A certain organism begins as three cells. Each cell splits and becomes two cells at the end of two days. At the end of another two days, every cell of the organism splits and becomes two cells. This process lasts for a total of 8 days, and no cells die during this time. How many cells are there at the end of the $8^\te... | "[\"48\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108267, "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:118183"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"13/20"
] | [
"skywork"
] | ef2ebc19c0022660db3727491b628b265ac9d171e472d5520c12667fbffe5fb9 | [
{
"content": "Points \\( M \\) and \\( N \\) are located on side \\( BC \\) of triangle \\( ABC \\), and point \\( K \\) is on side \\( AC \\), with \\( BM : MN : NC = 1 : 1 : 2 \\) and \\( CK : AK = 1 : 4 \\). Given that the area of triangle \\( ABC \\) is 1, find the area of quadrilateral \\( AMNK \\).",
... | Points \( M \) and \( N \) are located on side \( BC \) of triangle \( ABC \), and point \( K \) is on side \( AC \), with \( BM : MN : NC = 1 : 1 : 2 \) and \( CK : AK = 1 : 4 \). Given that the area of triangle \( ABC \) is 1, find the area of quadrilateral \( AMNK \). | "[\"13/20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108253, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118186"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"855"
] | [
"skywork"
] | 5c0702e650b779f065ecdd75c8a3438b03d5d6a09ec64be8c1bda6eed8caa5d5 | [
{
"content": "Given that Jennifer plans to build a fence around her garden in the shape of a rectangle, with $24$ fence posts, and evenly distributing the remaining along the edges, with $6$ yards between each post, and with the longer side of the garden, including corners, having three times as many posts as t... | Given that Jennifer plans to build a fence around her garden in the shape of a rectangle, with $24$ fence posts, and evenly distributing the remaining along the edges, with $6$ yards between each post, and with the longer side of the garden, including corners, having three times as many posts as the shorter side, calcu... | "[\"855\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108255, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:118187"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 34dd4809205ce0c6ccac877f72d806a7caf53cf82c22e00015efc538cda13789 | [
{
"content": "A sphere with a radius of 1 is inscribed in a cone, the height of which is twice the diameter of the sphere. Find the ratio of the total surface area of the cone to the surface area of the sphere.",
"role": "user"
}
] | A sphere with a radius of 1 is inscribed in a cone, the height of which is twice the diameter of the sphere. Find the ratio of the total surface area of the cone to the surface area of the sphere. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108270, "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:118188"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"31"
] | [
"skywork"
] | 405329b1ebacad6ac855af3f2f22eadd58301d7e5e0cf22cba8f7faf3c0e8009 | [
{
"content": "Determine for how many positive integers $n\\in\\{1, 2, \\ldots, 2022\\}$ it holds that $402$ divides at least one of\n\\[n^2-1, n^3-1, n^4-1\\]",
"role": "user"
}
] | Determine for how many positive integers $n\in\{1, 2, \ldots, 2022\}$ it holds that $402$ divides at least one of
\[n^2-1, n^3-1, n^4-1\] | "[\"31\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108266, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118189"}] | {
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"reference_components": 1,
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} |
[
"\\frac{27\\sqrt{2}}{8}"
] | [
"skywork"
] | eedc76e8bb1a51265f4c21c9cf216d20b49b7141d6aa6c0268718a09c80c5e6b | [
{
"content": "11.172. The angle between the generatrix of the cone and the plane of the base is $30^{\\circ}$. The lateral surface area of the cone is $3 \\pi \\sqrt{3}$ square units. Determine the volume of a regular hexagonal pyramid inscribed in the cone.",
"role": "user"
}
] | 11.172. The angle between the generatrix of the cone and the plane of the base is $30^{\circ}$. The lateral surface area of the cone is $3 \pi \sqrt{3}$ square units. Determine the volume of a regular hexagonal pyramid inscribed in the cone. | "[\"\\\\frac{27\\\\sqrt{2}}{8}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108275, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118190"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"0.367879"
] | [
"skywork"
] | 8eda1927b937e241bfdc1a2c07f9fd137c134e314d249a7b84d511f679f5cb15 | [
{
"content": "A radio system consisting of 1000 components (each with a failure rate of $\\lambda_{i} = 10^{-6}$ failures/hour) has been tested and accepted by the customer. Determine the probability of the system operating without failure over the interval $t_{1} < (t = t_{1} + \\Delta t) < t_{2}$, where $\\De... | A radio system consisting of 1000 components (each with a failure rate of $\lambda_{i} = 10^{-6}$ failures/hour) has been tested and accepted by the customer. Determine the probability of the system operating without failure over the interval $t_{1} < (t = t_{1} + \Delta t) < t_{2}$, where $\Delta t = 1000$ hours. | "[\"0.367879\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108269, "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:118192"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"14580"
] | [
"skywork"
] | 1ff5785d0273a318dbf85f677cb510b7110538829bf1c9dcb409b4a86493b5b1 | [
{
"content": "8. Andrey likes all numbers that are not divisible by 3, and Tanya likes all numbers that do not contain digits that are divisible by 3.\n\na) How many four-digit numbers are liked by both Andrey and Tanya?\n\nb) Find the total sum of the digits of all such four-digit numbers.",
"role": "user"... | 8. Andrey likes all numbers that are not divisible by 3, and Tanya likes all numbers that do not contain digits that are divisible by 3.
a) How many four-digit numbers are liked by both Andrey and Tanya?
b) Find the total sum of the digits of all such four-digit numbers. | "[\"14580\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108256, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118193"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"17"
] | [
"skywork"
] | f34773ffb9897074f70ec0c3031f48b09aec64bea99c4628f5a4b204cb667ebf | [
{
"content": "Suppose the graph of $y=f(x)$ includes the points $(1,5),$ $(2,3),$ and $(3,1)$.\n\nBased only on this information, there are two points that must be on the graph of $y=f(f(x))$. If we call those points $(a,b)$ and $(c,d),$ what is $ab+cd$?",
"role": "user"
}
] | Suppose the graph of $y=f(x)$ includes the points $(1,5),$ $(2,3),$ and $(3,1)$.
Based only on this information, there are two points that must be on the graph of $y=f(f(x))$. If we call those points $(a,b)$ and $(c,d),$ what is $ab+cd$? | "[\"17\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108271, "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:118194"}] | {
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"reference_components": 1,
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} |
[
"-1"
] | [
"skywork"
] | db371d9024269e3a5725611647acfc3f5f99cff55232bf974b20c23133125ffc | [
{
"content": "Given that $\\sin x - \\cos x < 0$, determine the range of the function $y = \\frac{\\sin x}{|\\sin x|} + \\frac{\\cos x}{|\\cos x|} + \\frac{\\tan x}{|\\tan x|}$.",
"role": "user"
}
] | Given that $\sin x - \cos x < 0$, determine the range of the function $y = \frac{\sin x}{|\sin x|} + \frac{\cos x}{|\cos x|} + \frac{\tan x}{|\tan x|}$. | "[\"-1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108254, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118195"}] | {
"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
} |
[
"194"
] | [
"skywork"
] | d1c7c58fff866e12957f0d5e3537105176e034df455801266d7235f6f5023899 | [
{
"content": "7. Given an increasing sequence of positive integers $a_{1}, a_{2}, \\cdots$ satisfying $a_{7}=120$, for any positive integer $n$, we have\n$$\na_{n+2}=a_{n+1}+a_{n} \\text {. }\n$$\n\nThen $a_{8}=$ $\\qquad$",
"role": "user"
}
] | 7. Given an increasing sequence of positive integers $a_{1}, a_{2}, \cdots$ satisfying $a_{7}=120$, for any positive integer $n$, we have
$$
a_{n+2}=a_{n+1}+a_{n} \text {. }
$$
Then $a_{8}=$ $\qquad$ | "[\"194\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108263, "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:118196"}] | {
"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
} |
[
"841"
] | [
"skywork"
] | 7efee6bf2a778d8ff9aa6d83aaf79360dd086b9986f10f33e9ad0f9558123f89 | [
{
"content": "20. Each cell in this cross-number can be filled with a non-zero digit so that all of the conditions in the clues are satisfied.\nThe digits used are not necessarily distinct.\nACROSS\n1. Four less than a factor of 105 .\n3. One more than a palindrome.\n5. The square-root of the answer to this Kan... | 20. Each cell in this cross-number can be filled with a non-zero digit so that all of the conditions in the clues are satisfied.
The digits used are not necessarily distinct.
ACROSS
1. Four less than a factor of 105 .
3. One more than a palindrome.
5. The square-root of the answer to this Kangaroo question.
DOWN
1. Two... | "[\"841\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108245, "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:118197"}] | {
"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
} |
[
"39"
] | [
"skywork"
] | 70a92ab5f3aa6eec5abdf1ec63308a01521ca87ec2827d0a679cd5a8af73b7ab | [
{
"content": "Example 7 (CMO-11 Test) Let $S=\\{1,2, \\cdots, 50\\}$, find the smallest natural number $k$, such that in any $-k$ element subset of $S$ there exist two distinct numbers $a$ and $b$, satisfying $(a+b) \\mid a b$.",
"role": "user"
}
] | Example 7 (CMO-11 Test) Let $S=\{1,2, \cdots, 50\}$, find the smallest natural number $k$, such that in any $-k$ element subset of $S$ there exist two distinct numbers $a$ and $b$, satisfying $(a+b) \mid a b$. | "[\"39\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108258, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118198"}] | {
"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
} |
[
"30.67"
] | [
"skywork"
] | fd193c099c9d8ca18536b08ff2f434fd7c8caaa1a5741c860bf42ec764c62e59 | [
{
"content": "Marla has a large white cube that has an edge of 8 feet. She also has enough green paint to cover 200 square feet. Marla uses all the paint to create a white circle centered on each face, surrounded by a green border. What is the area of one of the white circles, in square feet?\nA) $15.34$ sq ft\... | Marla has a large white cube that has an edge of 8 feet. She also has enough green paint to cover 200 square feet. Marla uses all the paint to create a white circle centered on each face, surrounded by a green border. What is the area of one of the white circles, in square feet?
A) $15.34$ sq ft
B) $30.67$ sq ft
C) $45... | "[\"30.67\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108273, "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:118199"}] | {
"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
} |
[
"2600"
] | [
"skywork"
] | dfb3a979f02d137cc19ac7c9acaabb2b65e20ddc23f2adcbf2d241b219570661 | [
{
"content": "Find the number of ordered pairs of integers $(a,b)$ with $1 \\leq a \\leq 100$ and $b \\geq 0$ such that the polynomial $x^2+ax+b$ can be factored into the product of two (not necessarily distinct) linear factors with integer coefficients.",
"role": "user"
}
] | Find the number of ordered pairs of integers $(a,b)$ with $1 \leq a \leq 100$ and $b \geq 0$ such that the polynomial $x^2+ax+b$ can be factored into the product of two (not necessarily distinct) linear factors with integer coefficients. | "[\"2600\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108250, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:118200"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"12:30"
] | [
"skywork"
] | 739754f1dc337916db54f50ce44ea5b6ab4d4cb1ca1c3094f5424bdfc915ff2e | [
{
"content": "Theo's watch is 10 minutes slow, but he believes it is 5 minutes fast. Leo's watch is 5 minutes fast, but he believes it is 10 minutes slow. At the same moment, each of them looks at his own watch. Theo thinks it is 12:00. What time does Leo think it is?\n\nA) 11:30 \nB) 11:45 \nC) 12:00 \nD) 1... | Theo's watch is 10 minutes slow, but he believes it is 5 minutes fast. Leo's watch is 5 minutes fast, but he believes it is 10 minutes slow. At the same moment, each of them looks at his own watch. Theo thinks it is 12:00. What time does Leo think it is?
A) 11:30
B) 11:45
C) 12:00
D) 12:30
E) 12:45 | "[\"12:30\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108280, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118201"}] | {
"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
} |
[
"72"
] | [
"skywork"
] | 7482b0b0309205df34c10d30b086e8df23f4ba84140c264afae84dca77b92f5c | [
{
"content": "3.5 On the first day of the sports competition, $\\frac{1}{6}$ of the boys' team and $\\frac{1}{7}$ of the girls' team did not meet the qualifying standards and were eliminated from further competition. Over the remaining period of the competition, an equal number of athletes from both teams were ... | 3.5 On the first day of the sports competition, $\frac{1}{6}$ of the boys' team and $\frac{1}{7}$ of the girls' team did not meet the qualifying standards and were eliminated from further competition. Over the remaining period of the competition, an equal number of athletes from both teams were eliminated due to non-co... | "[\"72\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108260, "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:118202"}] | {
"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}{3} \\leqslant x \\leqslant \\frac{2}{3}"
] | [
"skywork"
] | 6d5415713363909fb99abecb0e4c6efb24d872e98fd7003eaa639955526fbbe1 | [
{
"content": "4. 34 Find the range of real values of $x$ that satisfy the following relation:\n$$|3 x-2|+|3 x+1|=3$$",
"role": "user"
}
] | 4. 34 Find the range of real values of $x$ that satisfy the following relation:
$$|3 x-2|+|3 x+1|=3$$ | "[\"-\\\\frac{1}{3} \\\\leqslant x \\\\leqslant \\\\frac{2}{3}\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 108289, "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:118203"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3}{5}"
] | [
"skywork"
] | a989705aea46ccb103727db7ed04357c50964382543a24edecf1065ca0a41f2b | [
{
"content": "An unfair coin has the property that when flipped four times, it has the same probability of turning up 2 heads and 2 tails (in any order) as 3 heads and 1 tail (in any order). What is the probability of getting a head in any one flip?",
"role": "user"
}
] | An unfair coin has the property that when flipped four times, it has the same probability of turning up 2 heads and 2 tails (in any order) as 3 heads and 1 tail (in any order). What is the probability of getting a head in any one flip? | "[\"\\\\frac{3}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108286, "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:118204"}] | {
"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,-1,0,1,3"
] | [
"skywork"
] | 2bc21580d766388c55c6c914878f371be7727a5305203e3f8016754afa9873cc | [
{
"content": "Example 9 (2002 Australian National Mathematics Competition) Given the polynomial $P(n)=n^{3}-n^{2}-5 n+2$, find all integers $n$ such that $P^{2}(n)$ is the square of a prime number.",
"role": "user"
}
] | Example 9 (2002 Australian National Mathematics Competition) Given the polynomial $P(n)=n^{3}-n^{2}-5 n+2$, find all integers $n$ such that $P^{2}(n)$ is the square of a prime number. | "[\"-3,-1,0,1,3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108282, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118206"}] | {
"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
} |
[
"k = \\left\\lceil \\frac{n-3}{2} \\right\\rceil - 1"
] | [
"skywork"
] | 1f3f2d9e53a0a84e84b1499932241bd63ffc13ec81bb14d0268bb3e4d53a0b80 | [
{
"content": "There are n cups arranged on the circle. Under one of cups is hiden a coin. For every move, it is allowed to choose 4 cups and verify if the coin lies under these cups. After that, the cups are returned into its former places and the coin moves to one of two neigbor cups. What is the minimal numbe... | There are n cups arranged on the circle. Under one of cups is hiden a coin. For every move, it is allowed to choose 4 cups and verify if the coin lies under these cups. After that, the cups are returned into its former places and the coin moves to one of two neigbor cups. What is the minimal number of moves we need in ... | "[\" k = \\\\left\\\\lceil \\\\frac{n-3}{2} \\\\right\\\\rceil - 1 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108246, "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:118207"}] | {
"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
} |
[
"63"
] | [
"skywork"
] | bc23e147a916035d38a40bedc2e40d29fcd098e9b4e6a4ebf29688ac28651ff6 | [
{
"content": "8・ 78 The increasing sequence of integers that are divisible by 3 and are 1 less than a perfect square is $3,15,24,48, \\cdots$ What is the remainder when the 1994th term of this sequence is divided by 1000?",
"role": "user"
}
] | 8・ 78 The increasing sequence of integers that are divisible by 3 and are 1 less than a perfect square is $3,15,24,48, \cdots$ What is the remainder when the 1994th term of this sequence is divided by 1000? | "[\"63\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 108285, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118208"}] | {
"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
} |
[
"9"
] | [
"skywork"
] | 6ba884dd1662ec16022c117cdd6e92f16e846985bbe316b116776edbdee8bf47 | [
{
"content": "1. Let real numbers $a, b, c$ satisfy\n$$\n\\begin{array}{l}\na+b+c=3, a^{2}+b^{2}+c^{2}=4 . \\\\\n\\text { Then } \\frac{a^{2}+b^{2}}{2-c}+\\frac{b^{2}+c^{2}}{2-a}+\\frac{c^{2}+a^{2}}{2-b}=(\\quad) \\text {. }\n\\end{array}\n$$\n(A) 0\n(B) 3\n(C) 6\n(D) 9",
"role": "user"
}
] | 1. Let real numbers $a, b, c$ satisfy
$$
\begin{array}{l}
a+b+c=3, a^{2}+b^{2}+c^{2}=4 . \\
\text { Then } \frac{a^{2}+b^{2}}{2-c}+\frac{b^{2}+c^{2}}{2-a}+\frac{c^{2}+a^{2}}{2-b}=(\quad) \text {. }
\end{array}
$$
(A) 0
(B) 3
(C) 6
(D) 9 | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108281, "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:118210"}] | {
"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
} |
[
"3\\sqrt{6}"
] | [
"skywork"
] | 15f2fa3fce0006b6f8ab431715374686c348ce09825ca7e5f6ec002926a96764 | [
{
"content": "A balloon that inflates into the shape of a perfect cube is being blown up at a rate such that at time \\( t \\) (in fortnights), it has a surface area of \\( 6t \\) square furlongs. At what rate, in cubic furlongs per fortnight, is the air being pumped in when the surface area is 144 square furlo... | A balloon that inflates into the shape of a perfect cube is being blown up at a rate such that at time \( t \) (in fortnights), it has a surface area of \( 6t \) square furlongs. At what rate, in cubic furlongs per fortnight, is the air being pumped in when the surface area is 144 square furlongs? | "[\"3\\\\sqrt{6}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108265, "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:118211"}] | {
"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
} |
[
"p=-1,p=\\frac{15}{8}"
] | [
"skywork"
] | edb214144bf1e956005f66538dc5250c6a817e76bec1f81bbf88b9a3972aac68 | [
{
"content": "1. Find all values of $p$, for each of which the numbers $4 p+5, 2 p$ and $|p-3|$ are respectively the first, second, and third terms of some geometric progression.",
"role": "user"
}
] | 1. Find all values of $p$, for each of which the numbers $4 p+5, 2 p$ and $|p-3|$ are respectively the first, second, and third terms of some geometric progression. | "[\"p=-1,p=\\\\frac{15}{8}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108272, "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:118212"}] | {
"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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