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 |
|---|---|---|---|---|---|---|---|---|
[
"\\sqrt{3}(\\pi+3)"
] | [
"skywork"
] | bbca92bdc9b28be2dbaf887370ca5e3f28a07dc649335454d0026e5d963c499a | [
{
"content": "1. A cube with edge $a=\\sqrt{2+\\sqrt{3}}$ is illuminated by a cylindrical beam of light with radius $\\rho=\\sqrt{2}$, directed along the main diagonal of the cube (the axis of the beam contains the main diagonal). Find the area of the illuminated part of the cube's surface.",
"role": "user"... | 1. A cube with edge $a=\sqrt{2+\sqrt{3}}$ is illuminated by a cylindrical beam of light with radius $\rho=\sqrt{2}$, directed along the main diagonal of the cube (the axis of the beam contains the main diagonal). Find the area of the illuminated part of the cube's surface. | "[\"\\\\sqrt{3}(\\\\pi+3)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3757, "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:17674"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"52"
] | [
"skywork"
] | 503af21f2b97a976e2e2a819098826b9b6b1ec1c5d6bd9ccedf8d00417b2c732 | [
{
"content": "Using the numbers 0, 1, 2, 3, 4, 5 to form unique three-digit numbers, determine the total number of even numbers that can be formed.",
"role": "user"
}
] | Using the numbers 0, 1, 2, 3, 4, 5 to form unique three-digit numbers, determine the total number of even numbers that can be formed. | "[\"52\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3763, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "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:17675"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-1"
] | [
"skywork"
] | 93dd478e55175f5118b47453d5fd311105e7cd78033093530f7e2be658651401 | [
{
"content": "An odd function $f(x)$ defined on $R$ satisfies $f(x) = f(2-x)$. When $x \\in [0,1]$, $f(x) = ax^{3} + 2x + a + 1$. Find $f(2023)$.",
"role": "user"
}
] | An odd function $f(x)$ defined on $R$ satisfies $f(x) = f(2-x)$. When $x \in [0,1]$, $f(x) = ax^{3} + 2x + a + 1$. Find $f(2023)$. | "[\"-1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3728, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:17676"}] | {
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} |
[
"30"
] | [
"skywork"
] | e8c941e7067105dc514a70eb8b81cc38b3268379918d6d96e081761b7bc4bede | [
{
"content": "Given that Jackie has $40$ thin rods, one of each integer length from $1 \\text{ cm}$ through $40 \\text{ cm}$, with rods of lengths $5 \\text{ cm}$, $12 \\text{ cm}$, and $20 \\text{ cm}$ already placed on a table, find the number of the remaining rods that she can choose as the fourth rod to for... | Given that Jackie has $40$ thin rods, one of each integer length from $1 \text{ cm}$ through $40 \text{ cm}$, with rods of lengths $5 \text{ cm}$, $12 \text{ cm}$, and $20 \text{ cm}$ already placed on a table, find the number of the remaining rods that she can choose as the fourth rod to form a quadrilateral with posi... | "[\"30\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3738, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17677"}] | {
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} |
[
"0"
] | [
"skywork"
] | e36a37d085bcc071b5e22366fe695c1c74f55595bdfca6c5757bb34b70b92f1a | [
{
"content": "6. Given that the equation $x^{3}+a x^{2}+b x+c=$ 0 has three non-zero real roots forming a geometric sequence. Then $a^{3} c-b^{3}=$ $\\qquad$",
"role": "user"
}
] | 6. Given that the equation $x^{3}+a x^{2}+b x+c=$ 0 has three non-zero real roots forming a geometric sequence. Then $a^{3} c-b^{3}=$ $\qquad$ | "[\"0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3760, "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:17678"}] | {
"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
} |
[
"607"
] | [
"skywork"
] | 3f0907f619bf193ae1f116a52ef43b31a477840c700ac63d4e6dc823a043fa45 | [
{
"content": "A plane contains $40$ lines, no $2$ of which are parallel. Suppose that there are $3$ points where exactly $3$ lines intersect, $4$ points where exactly $4$ lines intersect, $5$ points where exactly $5$ lines intersect, $6$ points where exactly $6$ lines intersect, and no points where more than $6... | A plane contains $40$ lines, no $2$ of which are parallel. Suppose that there are $3$ points where exactly $3$ lines intersect, $4$ points where exactly $4$ lines intersect, $5$ points where exactly $5$ lines intersect, $6$ points where exactly $6$ lines intersect, and no points where more than $6$ lines intersect. Fin... | "[\"607\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3769, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17679"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"e"
] | [
"skywork"
] | a97d792f6cbe734c9258d156489985fb91670ce5ed2ca9e7a85a46eadeada70b | [
{
"content": "6. Find the minimum value of the constant $\\lambda$ such that for all positive integers $n$ and any positive real numbers $x_{k}(1 \\leqslant k \\leqslant n)$ whose sum is 1, we have\n$$\n\\lambda \\prod_{k=1}^{n}\\left(1-x_{k}\\right) \\geqslant 1-\\sum_{k=1}^{n} x_{k}^{2} .\n$$",
"role": "u... | 6. Find the minimum value of the constant $\lambda$ such that for all positive integers $n$ and any positive real numbers $x_{k}(1 \leqslant k \leqslant n)$ whose sum is 1, we have
$$
\lambda \prod_{k=1}^{n}\left(1-x_{k}\right) \geqslant 1-\sum_{k=1}^{n} x_{k}^{2} .
$$ | "[\"e\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3762, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:17680"}] | {
"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{1}{4}"
] | [
"skywork"
] | 4a7399cef86a59557478a73e3d4e3f4e3815a83ce1632cf7548a975de0cef1fc | [
{
"content": "If $x^{2y}=16$ and $x = 16$, what is the value of $y$? Express your answer as a common fraction.",
"role": "user"
}
] | If $x^{2y}=16$ and $x = 16$, what is the value of $y$? Express your answer as a common fraction. | "[\"\\\\frac{1}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3782, "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:17681"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"26"
] | [
"skywork"
] | 6e03aad7af4a27e0795b35de141cedc47f08f189c7f8beebbda05f175dbc5492 | [
{
"content": "Find the arithmetic mean of the prime numbers in this list: 21, 23, 25, 27, 29",
"role": "user"
}
] | Find the arithmetic mean of the prime numbers in this list: 21, 23, 25, 27, 29 | "[\"26\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3777, "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:17682"}] | {
"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
} |
[
"AA_{1}=26,R=5,V=1250"
] | [
"skywork"
] | e3227ef0fbf662954f360d1e27a42e0ca5f76b9956b7ce14d298c37ab2cc271a | [
{
"content": "7. On the edge $B C$ of the parallelepiped $A B C D A_{1} B_{1} C_{1} D_{1}$, a point $M$ is chosen. A sphere constructed on the segment $C_{1} M$ as a diameter touches the planes of four faces of the parallelepiped, and one of them at a point lying on the edge $B_{1} B$. It is known that $B M=1, ... | 7. On the edge $B C$ of the parallelepiped $A B C D A_{1} B_{1} C_{1} D_{1}$, a point $M$ is chosen. A sphere constructed on the segment $C_{1} M$ as a diameter touches the planes of four faces of the parallelepiped, and one of them at a point lying on the edge $B_{1} B$. It is known that $B M=1, C M=24$. Find the leng... | "[\"AA_{1}=26,R=5,V=1250\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3761, "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:17683"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"0 \\leqslant f(P) \\leqslant \\frac{3}{4}"
] | [
"skywork"
] | c0d1dd6fb39780bd33bdce0cd7699a7f69d63c7055970465cd1575a9878cfe00 | [
{
"content": "Example 3 Let $P$ be a point inside (including the boundary) a regular tetrahedron $T$ with volume 1. Draw 4 planes through $P$ parallel to the 4 faces of $T$, dividing $T$ into 14 pieces. Let $f(P)$ be the sum of the volumes of those pieces which are neither tetrahedra nor parallelepipeds. Find t... | Example 3 Let $P$ be a point inside (including the boundary) a regular tetrahedron $T$ with volume 1. Draw 4 planes through $P$ parallel to the 4 faces of $T$, dividing $T$ into 14 pieces. Let $f(P)$ be the sum of the volumes of those pieces which are neither tetrahedra nor parallelepipeds. Find the range of $f(P)$. (3... | "[\"0 \\\\leqslant f(P) \\\\leqslant \\\\frac{3}{4}\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 3744, "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:17684"}] | {
"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
} |
[
"C"
] | [
"skywork"
] | e259f959c2f20780d819375aeeb255fc1df271b2703d7df56685737dfb8d7465 | [
{
"content": "6. The dihedral angle $\\alpha-A B-\\beta$ is $60^{\\circ}, P \\in \\alpha, Q \\in \\beta, P, Q$ are not on $A B$, the angle between $P Q$ and $A B$ is $45^{\\circ}$, and $P Q=$ $7 \\sqrt{2}, Q$ is 3 units away from $A B$. Then the distance from $P$ to $A B$ is ( ).\n(A) 5\n(B) $\\sqrt{37}$\n(C) 8... | 6. The dihedral angle $\alpha-A B-\beta$ is $60^{\circ}, P \in \alpha, Q \in \beta, P, Q$ are not on $A B$, the angle between $P Q$ and $A B$ is $45^{\circ}$, and $P Q=$ $7 \sqrt{2}, Q$ is 3 units away from $A B$. Then the distance from $P$ to $A B$ is ( ).
(A) 5
(B) $\sqrt{37}$
(C) 8
(D) $\sqrt{79}$ | "[\"C\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3765, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17685"}] | {
"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
} |
[
"510050"
] | [
"skywork"
] | a02f27d0322a5bb66df2849c020baaa0838f31d0df305ba1e612ab21011c7516 | [
{
"content": "7. Problem: Let $a, b, c, d$ be integers such that $a>b>c>d \\geq-2021$ and\n$$\n\\frac{a+b}{b+c}=\\frac{c+d}{d+a}\n$$\n(and $b+c \\neq 0 \\neq d+a)$. What is the maximum possible value of $a c$ ?",
"role": "user"
}
] | 7. Problem: Let $a, b, c, d$ be integers such that $a>b>c>d \geq-2021$ and
$$
\frac{a+b}{b+c}=\frac{c+d}{d+a}
$$
(and $b+c \neq 0 \neq d+a)$. What is the maximum possible value of $a c$ ? | "[\"510050\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3783, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17686"}] | {
"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
} |
[
"5840"
] | [
"skywork"
] | a18d8d1a36aa8293d669b76c08cfed1195846b6e13ad8867da87281b43271b1d | [
{
"content": "In the sequence $\\{{a_{n}}\\}$, the adjacent terms ${a_{n}}$ and ${a_{n+1}}$ are the roots of the equation ${x^{2}}+3nx+{{b_{n}}=0}$. Given that ${{a_{10}}=-17}$, find the value of ${{b_{51}}}$.",
"role": "user"
}
] | In the sequence $\{{a_{n}}\}$, the adjacent terms ${a_{n}}$ and ${a_{n+1}}$ are the roots of the equation ${x^{2}}+3nx+{{b_{n}}=0}$. Given that ${{a_{10}}=-17}$, find the value of ${{b_{51}}}$. | "[\"5840\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3754, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:17687"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"n"
] | [
"skywork"
] | 64c6e4fb29520909f466a4870c39531d5d567b8eded6a92b3875156a3668b701 | [
{
"content": "Let $M \\geq 1$ be a real number. Determine all natural numbers $n$ for which there exist distinct natural numbers $a$, $b$, $c > M$, such that\n$n = (a,b) \\cdot (b,c) + (b,c) \\cdot (c,a) + (c,a) \\cdot (a,b)$\n(where $(x,y)$ denotes the greatest common divisor of natural numbers $x$ and $y$).",... | Let $M \geq 1$ be a real number. Determine all natural numbers $n$ for which there exist distinct natural numbers $a$, $b$, $c > M$, such that
$n = (a,b) \cdot (b,c) + (b,c) \cdot (c,a) + (c,a) \cdot (a,b)$
(where $(x,y)$ denotes the greatest common divisor of natural numbers $x$ and $y$). | "[\" n \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3767, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17688"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2376"
] | [
"skywork"
] | 026e1727703bbe54f3482fb985172ce6bf8ea787469eed28093c37ad8d0683b6 | [
{
"content": "314 black balls, 4 white balls and 2 red balls are arranged in a row. Find the total number of ways this can be done if all the balls of the same colour do not appear in a consecutive block.",
"role": "user"
}
] | 314 black balls, 4 white balls and 2 red balls are arranged in a row. Find the total number of ways this can be done if all the balls of the same colour do not appear in a consecutive block. | "[\"2376\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3779, "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:17689"}] | {
"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
} |
[
"3.6"
] | [
"skywork"
] | 93e19ffdbb46abd3750bdf6a9543dac0b372257706f0feb78764d2524dad52f9 | [
{
"content": "Example 2: By the end of 2001, the number of cars in a city was 300,000. It is expected that each year, 6% of the car stock from the previous year will be scrapped, and the number of new cars added each year will be the same. To protect the urban environment, the city's car stock should not exceed... | Example 2: By the end of 2001, the number of cars in a city was 300,000. It is expected that each year, 6% of the car stock from the previous year will be scrapped, and the number of new cars added each year will be the same. To protect the urban environment, the city's car stock should not exceed 600,000. How many new... | "[\"3.6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3771, "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:17690"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"p^{2}-p"
] | [
"skywork"
] | b8ee1c534bf8f8f926f39a54073c769b8acd77fa927aef5dec240de7deabc95f | [
{
"content": "38 For any given prime $p$, how many integer triples $(a, b, c)$ are there such that\n(1) $1 \\leqslant a, b, c \\leqslant 2 p^{2}$;\n(2) $\\frac{[a, c]+[b, c]}{a+b}=\\frac{p^{2}+1}{p^{2}+2} \\cdot c$.",
"role": "user"
}
] | 38 For any given prime $p$, how many integer triples $(a, b, c)$ are there such that
(1) $1 \leqslant a, b, c \leqslant 2 p^{2}$;
(2) $\frac{[a, c]+[b, c]}{a+b}=\frac{p^{2}+1}{p^{2}+2} \cdot c$. | "[\"p^{2}-p\"]" | train-math-numinamath1.5_number_theory | [{"dataset": "skywork", "extra_info": {"index": 3764, "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:17691"}] | {
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[
"8"
] | [
"skywork"
] | a6468b20ef9475f6b14de79d3626efc87a1d795d0dfb0dc9f1128af586b92f58 | [
{
"content": "Let $n{}$ be a positive integer. What is the smallest sum of digits that $5^n + 6^n + 2022^n$ can take?",
"role": "user"
}
] | Let $n{}$ be a positive integer. What is the smallest sum of digits that $5^n + 6^n + 2022^n$ can take? | "[\"8\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3780, "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:17692"}] | {
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[
"\\frac{2\\sqrt{145}}{3}"
] | [
"skywork"
] | 0934d1aa2110ce076d1ff4f95d85a8b3700d1b06e29974de7afc3f1ee2920611 | [
{
"content": "In triangle $ABC$, the height $BD$ is 6, the median $CE$ is 5, and the distance from point $K$ of intersection of segments $BD$ and $CE$ to side $AC$ is 1.\n\nFind the side $AB$.",
"role": "user"
}
] | In triangle $ABC$, the height $BD$ is 6, the median $CE$ is 5, and the distance from point $K$ of intersection of segments $BD$ and $CE$ to side $AC$ is 1.
Find the side $AB$. | "[\"\\\\frac{2\\\\sqrt{145}}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3773, "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:17693"}] | {
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[
"1 + 2004!"
] | [
"skywork"
] | 7be7e147ed5e8f4acbfbeb7e8dc560e1bb6f3168ac86edf03aadb82c929cef02 | [
{
"content": "Let \\( A = \\{1, 2, \\cdots, 2004\\} \\) and \\( f: A \\rightarrow A \\) be a bijection satisfying \\( f^{[2004]}(x) = f(x) \\), where \\( f^{[2004]}(x) \\) denotes applying \\( f \\) 2004 times to \\( x \\). How many such functions \\( f \\) are there?",
"role": "user"
}
] | Let \( A = \{1, 2, \cdots, 2004\} \) and \( f: A \rightarrow A \) be a bijection satisfying \( f^{[2004]}(x) = f(x) \), where \( f^{[2004]}(x) \) denotes applying \( f \) 2004 times to \( x \). How many such functions \( f \) are there? | "[\"1 + 2004!\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3766, "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:17694"}] | {
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[
"3"
] | [
"skywork"
] | a9f1e33511e0751723965a459e01f8ba9b32b07b0489f720166e0f92c650dc99 | [
{
"content": "10. Freda wants to write a number in each of the nine cells of this figure so that the sum of the three numbers on each diameter is 13 and the sum of the eight numbers on the circumference is 40 .\nWhat number must be written in the central cell?\nA 3\nB 5\nC 8\nD 10\nE 12",
"role": "user"
}... | 10. Freda wants to write a number in each of the nine cells of this figure so that the sum of the three numbers on each diameter is 13 and the sum of the eight numbers on the circumference is 40 .
What number must be written in the central cell?
A 3
B 5
C 8
D 10
E 12 | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3785, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17695"}] | {
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[
"178"
] | [
"skywork"
] | cb6be775f0a361edb5799633a30a46b0cc26b5f41ddd3af447c93968e1e648a9 | [
{
"content": "A [i]short-sighted[/i] rook is a rook that beats all squares in the same column and in the same row for which he can not go more than $60$-steps. \nWhat is the maximal amount of short-sighted rooks that don't beat each other that can be put on a $100\\times 100$ chessboard.",
"role": "user"
... | A [i]short-sighted[/i] rook is a rook that beats all squares in the same column and in the same row for which he can not go more than $60$-steps.
What is the maximal amount of short-sighted rooks that don't beat each other that can be put on a $100\times 100$ chessboard. | "[\"178\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3781, "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:17696"}] | {
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[
"429"
] | [
"skywork"
] | 692156473cdf448a25cb057675a483d708d93827a09962ed3a281bd9b414d755 | [
{
"content": "A certain function $f$ has the properties that $f(3x) = 3f(x)$ for all positive real values of $x$, and that $f(x) = 1-|x-2|$ for $1\\le x \\le 3$. Find the smallest $x$ for which $f(x) = f(2001)$.",
"role": "user"
}
] | A certain function $f$ has the properties that $f(3x) = 3f(x)$ for all positive real values of $x$, and that $f(x) = 1-|x-2|$ for $1\le x \le 3$. Find the smallest $x$ for which $f(x) = f(2001)$. | "[\"429\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3776, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:17697"}] | {
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[
"\\lambda\\geqslant1"
] | [
"skywork"
] | 1709f5fa37908a8e88f78a175d704fda4d81371d5224d540573571ffbf4d0019 | [
{
"content": "3. If for any rectangular prism $A$, there exists a rectangular prism $B$ of the same height as $A$, such that the ratio of the lateral surface area of $B$ to that of $A$ and the ratio of the volume of $B$ to that of $A$ are both equal to $\\lambda$, then the range of values for $\\lambda$ is\nA. ... | 3. If for any rectangular prism $A$, there exists a rectangular prism $B$ of the same height as $A$, such that the ratio of the lateral surface area of $B$ to that of $A$ and the ratio of the volume of $B$ to that of $A$ are both equal to $\lambda$, then the range of values for $\lambda$ is
A. $\lambda>0$
B. $0<\lambda... | "[\"\\\\lambda\\\\geqslant1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3784, "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:17698"}] | {
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[
"17"
] | [
"skywork"
] | 5744f589d30dfa211329c63126c5f768bc3ba0bd971dd9e067a68eb2b077f1a8 | [
{
"content": "24. A pond filled with water, first put the fish into the pond, 2 liters of water overflow; then take out the fish, put the crab into the pond, another 3 liters of water overflow; take out the crab again, put the turtle into the pond, another 5 liters of water overflow. If the fish, crab, and turt... | 24. A pond filled with water, first put the fish into the pond, 2 liters of water overflow; then take out the fish, put the crab into the pond, another 3 liters of water overflow; take out the crab again, put the turtle into the pond, another 5 liters of water overflow. If the fish, crab, and turtle are put into the po... | "[\"17\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3789, "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:17699"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"30"
] | [
"skywork"
] | a2b8a1e1098a424ec71475ae4e01fca87f66100dc725f60fafcb7a6415d85cee | [
{
"content": "Let $ABC$ be a triangle with $AB=13$ , $BC=14$ , and $CA=15$ . Points $P$ , $Q$ , and $R$ are chosen on segments $BC$ , $CA$ , and $AB$ , respectively, such that triangles $AQR$ , $BPR$ , $CPQ$ have the same perimeter, which is $\\frac{4}{5}$ of the perimeter of $PQR$ . What is ... | Let $ABC$ be a triangle with $AB=13$ , $BC=14$ , and $CA=15$ . Points $P$ , $Q$ , and $R$ are chosen on segments $BC$ , $CA$ , and $AB$ , respectively, such that triangles $AQR$ , $BPR$ , $CPQ$ have the same perimeter, which is $\frac{4}{5}$ of the perimeter of $PQR$ . What is the perimeter of $PQR$... | "[\"30\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3774, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17700"}] | {
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[
"8960"
] | [
"skywork"
] | 1a227803858974d8ce464758f6f7d84151f0b7492ff8f66fca677a8b5b0ce4cb | [
{
"content": "In quadrilateral $ABCD$, $AB \\parallel CD$ and $BC \\perp AB$. Lines $AC$ and $BD$ intersect at $E$. If $AB = 20$, $BC = 2016$, and $CD = 16$, find the area of $\\triangle BCE$.\n\n[i]Proposed by Harrison Wang[/i]",
"role": "user"
}
] | In quadrilateral $ABCD$, $AB \parallel CD$ and $BC \perp AB$. Lines $AC$ and $BD$ intersect at $E$. If $AB = 20$, $BC = 2016$, and $CD = 16$, find the area of $\triangle BCE$.
[i]Proposed by Harrison Wang[/i] | "[\"8960\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3787, "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:17701"}] | {
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[
"6\\sqrt{6}"
] | [
"skywork"
] | e09ae3477352e166b77b130c5d8cddd72f3db92dcf12aa81180101d0ed07c868 | [
{
"content": "Find the positive value of $x$ that satisfies $cd = x-3i$ given $|c|=3$ and $|d|=5$.",
"role": "user"
}
] | Find the positive value of $x$ that satisfies $cd = x-3i$ given $|c|=3$ and $|d|=5$. | "[\"6\\\\sqrt{6}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3792, "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:17702"}] | {
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"reference_components": 1,
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} |
[
"2"
] | [
"skywork"
] | 08ab52506b3719243cc6338f9b0d280b9bf960b1da934e309faaee31d48de696 | [
{
"content": "Let $x_1< x_2 < x_3$ be the three real roots of the equation $\\sqrt{2014} x^3 - 4029x^2 + 2 = 0$ . Find $x_2(x_1+x_3)$ .",
"role": "user"
}
] | Let $x_1< x_2 < x_3$ be the three real roots of the equation $\sqrt{2014} x^3 - 4029x^2 + 2 = 0$ . Find $x_2(x_1+x_3)$ . | "[\"2\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 3786, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17703"}, {"dataset": "skywork", "extra_in... | {
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[
"-3"
] | [
"skywork"
] | 615dbda13525799e7b2051d1cb4b5320635ab75c358713f38862c80814550ee9 | [
{
"content": "The graph of a certain quadratic $y = ax^2 + bx + c$ is a parabola with vertex $(-4,0)$ which passes through the point $(1,-75)$. What is the value of $a$?",
"role": "user"
}
] | The graph of a certain quadratic $y = ax^2 + bx + c$ is a parabola with vertex $(-4,0)$ which passes through the point $(1,-75)$. What is the value of $a$? | "[\"-3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3788, "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:17704"}] | {
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[
"N \\text{ is odd}"
] | [
"skywork"
] | 3d63b520ca90d5373b4c98842c19bf053c38e54d89074edda4da60f5c75b27c7 | [
{
"content": "Let $N$ be the number of ordered quintuples $\\left(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\\right)$ of positive integers for which\n\n$$\n\\frac{1}{a_{1}}+\\frac{1}{a_{2}}+\\frac{1}{a_{3}}+\\frac{1}{a_{4}}+\\frac{1}{a_{5}}=1 .\n$$\n\n(For ordered quintuples, the order matters, so $(2,3,15,15,30)$ and $... | Let $N$ be the number of ordered quintuples $\left(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\right)$ of positive integers for which
$$
\frac{1}{a_{1}}+\frac{1}{a_{2}}+\frac{1}{a_{3}}+\frac{1}{a_{4}}+\frac{1}{a_{5}}=1 .
$$
(For ordered quintuples, the order matters, so $(2,3,15,15,30)$ and $(15,2,15,3,30)$ are different order... | "[\"N \\\\text{ is odd}\"]" | train-math-numinamath1.5_olympiads_ref | [{"dataset": "skywork", "extra_info": {"index": 3801, "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:17705"}] | {
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} |
[
"2\\sqrt{5};5+\\sqrt{5}"
] | [
"skywork"
] | 119b06479eb8c5ab59c6a6c7ba86c12cd5510ed64bdf873b0edd4302deca3326 | [
{
"content": "10.236. In an isosceles triangle, the angle at the vertex is $36^{\\circ}$, and the bisector of the angle at the base is $\\sqrt{20}$. Find the lengths of the sides of the triangle.",
"role": "user"
}
] | 10.236. In an isosceles triangle, the angle at the vertex is $36^{\circ}$, and the bisector of the angle at the base is $\sqrt{20}$. Find the lengths of the sides of the triangle. | "[\"2\\\\sqrt{5};5+\\\\sqrt{5}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3790, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17706"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"33"
] | [
"skywork"
] | 380b95604af0efc1a18d3cffc6857dffd14fb0749f28bfb5c625f3d6466591ff | [
{
"content": "What is the 7th term of an arithmetic sequence of 15 terms where the first term is 3 and the last term is 72?",
"role": "user"
}
] | What is the 7th term of an arithmetic sequence of 15 terms where the first term is 3 and the last term is 72? | "[\"33\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3811, "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:17707"}] | {
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"reference_present": true
} |
[
"\\text{No}"
] | [
"skywork"
] | 4fd237b634bb9b142e4a55ffd82841023ab25d14a0e3cefd0e7593d1f8beb96a | [
{
"content": "Consider an acute non-isosceles triangle. In a single step it is allowed to cut any one of the available triangles into two triangles along its median. Is it possible that after a finite number of cuttings all triangles will be isosceles?",
"role": "user"
}
] | Consider an acute non-isosceles triangle. In a single step it is allowed to cut any one of the available triangles into two triangles along its median. Is it possible that after a finite number of cuttings all triangles will be isosceles? | "[\"\\\\text{No}\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 3793, "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:17708"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{10}"
] | [
"skywork"
] | be336ab750c4fd5a58a52fc805b088f72c2e928ae0a0d917282a2be5d8227cb3 | [
{
"content": "6. Evaluate the three solutions and answers provided below. Identify all errors and shortcomings, and provide the correct solution to this problem.\n\nFrom a deck of cards, six cards were selected - three of black suits and three of red suits. The selected cards were shuffled and stacked. Find the... | 6. Evaluate the three solutions and answers provided below. Identify all errors and shortcomings, and provide the correct solution to this problem.
From a deck of cards, six cards were selected - three of black suits and three of red suits. The selected cards were shuffled and stacked. Find the probability that the th... | "[\"\\\\frac{1}{10}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3770, "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:17709"}] | {
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"reference_components": 1,
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} |
[
"1010"
] | [
"skywork"
] | 7265fd2b80a915cbe04213ffa92183e8eb03bc9dabc5dff8d5050b926b17312d | [
{
"content": "Find the largest real $C$ such that for all pairwise distinct positive real $a_{1}, a_{2}, \\ldots, a_{2019}$ the following inequality holds $$\\frac{a_{1}}{\\left|a_{2}-a_{3}\\right|}+\\frac{a_{2}}{\\left|a_{3}-a_{4}\\right|}+\\ldots+\\frac{a_{2018}}{\\left|a_{2019}-a_{1}\\right|}+\\frac{a_{2019}... | Find the largest real $C$ such that for all pairwise distinct positive real $a_{1}, a_{2}, \ldots, a_{2019}$ the following inequality holds $$\frac{a_{1}}{\left|a_{2}-a_{3}\right|}+\frac{a_{2}}{\left|a_{3}-a_{4}\right|}+\ldots+\frac{a_{2018}}{\left|a_{2019}-a_{1}\right|}+\frac{a_{2019}}{\left|a_{1}-a_{2}\right|}>C$$ | "[\"1010\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3799, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:17710"}] | {
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} |
[
"24"
] | [
"skywork"
] | 1bee848bd91afa5fd7be58b785c6d41fab5ddb417b22ddf4d52fd4a055637d65 | [
{
"content": "Two cross sections of a right hexagonal pyramid are obtained by cutting the pyramid with planes parallel to the hexagonal base. The areas of the cross sections are $216\\sqrt{3}$ square feet and $486\\sqrt{3}$ square feet. The two planes are $8$ feet apart. How far from the apex of the pyramid is ... | Two cross sections of a right hexagonal pyramid are obtained by cutting the pyramid with planes parallel to the hexagonal base. The areas of the cross sections are $216\sqrt{3}$ square feet and $486\sqrt{3}$ square feet. The two planes are $8$ feet apart. How far from the apex of the pyramid is the larger cross section... | "[\"24\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3807, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17711"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | 202e454cb108d5b0c417f4297f56a049cbfbcd1cc58660f22be48f02294a9ba9 | [
{
"content": "A regular polygon has interior angles of 120 degrees. How many sides does the polygon have?",
"role": "user"
}
] | A regular polygon has interior angles of 120 degrees. How many sides does the polygon have? | "[\"6\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3819, "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:17712"}] | {
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} |
[
"\\frac{8a}{3}"
] | [
"skywork"
] | 9a547e554f6ae53fe6b328749e198c8d98479545e5f352be49298b7d83d3d982 | [
{
"content": "3.13. From vertex $C$ of the rhombus $A B C D$, whose side is equal to $a$, two segments $C E$ and $C F$ are drawn, dividing the rhombus into three equal-area figures. It is known that $\\cos C=\\frac{1}{4}$. Find the sum $C E+C F$.",
"role": "user"
}
] | 3.13. From vertex $C$ of the rhombus $A B C D$, whose side is equal to $a$, two segments $C E$ and $C F$ are drawn, dividing the rhombus into three equal-area figures. It is known that $\cos C=\frac{1}{4}$. Find the sum $C E+C F$. | "[\"\\\\frac{8a}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3797, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17713"}] | {
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} |
[
"2002"
] | [
"skywork"
] | c487f107f748b1211be16140afbbcd11399630c4a2067245dea625aa4c823d77 | [
{
"content": "Suppose $ n$ is a product of four distinct primes $ a,b,c,d$ such that:\r\n$ (i)$ $ a\\plus{}c\\equal{}d;$\r\n$ (ii)$ $ a(a\\plus{}b\\plus{}c\\plus{}d)\\equal{}c(d\\minus{}b);$\r\n$ (iii)$ $ 1\\plus{}bc\\plus{}d\\equal{}bd$.\r\nDetermine $ n$.",
"role": "user"
}
] | Suppose $ n$ is a product of four distinct primes $ a,b,c,d$ such that:
$ (i)$ $ a\plus{}c\equal{}d;$
$ (ii)$ $ a(a\plus{}b\plus{}c\plus{}d)\equal{}c(d\minus{}b);$
$ (iii)$ $ 1\plus{}bc\plus{}d\equal{}bd$.
Determine $ n$. | "[\"2002\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3795, "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:17714"}, {"dataset": "skywork", "extra_inf... | {
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[
"3349"
] | [
"skywork"
] | 91f3ae65174ecbaa12433f992f50ce62e867266fc55fed65a9efeb0b8f5c43b2 | [
{
"content": "11. From the sequence of positive integers $1,2,3,4,5, \\cdots$, remove the multiples of 3 and 4, but retain all multiples of 5 (for example, 15 and 120 are retained). After removing, the remaining numbers form a new sequence: $1,2,5,7,10, \\cdots$. Find the 2010th term of the new sequence.",
... | 11. From the sequence of positive integers $1,2,3,4,5, \cdots$, remove the multiples of 3 and 4, but retain all multiples of 5 (for example, 15 and 120 are retained). After removing, the remaining numbers form a new sequence: $1,2,5,7,10, \cdots$. Find the 2010th term of the new sequence. | "[\"3349\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3796, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17715"}] | {
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} |
[
"\\frac{1}{3}"
] | [
"skywork"
] | 048054b45438f8f4bcb71e0758a42bb75d5c14e85c98ed1934311d4ff8481921 | [
{
"content": "There is a moving point \\( P \\) on the \\( x \\)-axis. Given the fixed points \\( A(0,2) \\) and \\( B(0,4) \\), what is the maximum value of \\( \\sin \\angle APB \\) when \\( P \\) moves along the entire \\( x \\)-axis?",
"role": "user"
}
] | There is a moving point \( P \) on the \( x \)-axis. Given the fixed points \( A(0,2) \) and \( B(0,4) \), what is the maximum value of \( \sin \angle APB \) when \( P \) moves along the entire \( x \)-axis? | "[\"\\\\frac{1}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3794, "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:17716"}] | {
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} |
[
"2037"
] | [
"skywork"
] | e71a27ef405d87d3db47da83681184f7185358dc572a5645206312a1891d3ff2 | [
{
"content": "Joey wrote a system of equations on a blackboard, where each of the equations was of the form $a + b = c$ or $a \\cdot b = c$ for some variables or integers $a, b, c$ . Then Sean came to the board and erased all of the plus signs and multiplication signs, so that the board reads: $x\\,\\,\\,\... | Joey wrote a system of equations on a blackboard, where each of the equations was of the form $a + b = c$ or $a \cdot b = c$ for some variables or integers $a, b, c$ . Then Sean came to the board and erased all of the plus signs and multiplication signs, so that the board reads: $x\,\,\,\, z = 15$ $x\,\,\,\, y = ... | "[\"2037\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 3803, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:17717"}] | {
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} |
[
"\\ln |e^x + 1| + C"
] | [
"skywork"
] | f4047645efe548fcbc45f961872a202294e75720809c157bc076bb74ecb572c2 | [
{
"content": "Calculate the following indefinite integrals.\r\n\r\n[1] $\\int \\sin x\\sin 2x dx$\r\n\r\n[2] $\\int \\frac{e^{2x}}{e^x-1}dx$\r\n\r\n[3] $\\int \\frac{\\tan ^2 x}{\\cos ^2 x}dx$\r\n\r\n[4] $\\int \\frac{e^x+e^{-x}}{e^x-e^{-x}}dx$\r\n\r\n[5] $\\int \\frac{e^x}{e^x+1}dx$",
"role": "user"
}
] | Calculate the following indefinite integrals.
[1] $\int \sin x\sin 2x dx$
[2] $\int \frac{e^{2x}}{e^x-1}dx$
[3] $\int \frac{\tan ^2 x}{\cos ^2 x}dx$
[4] $\int \frac{e^x+e^{-x}}{e^x-e^{-x}}dx$
[5] $\int \frac{e^x}{e^x+1}dx$ | "[\"\\\\ln |e^x + 1| + C\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3798, "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:17718"}] | {
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"reference_present": true
} |
[
"8"
] | [
"skywork"
] | 0580e4db3258805715960796c1a007730eb5ac4073a53707f99c0138895e2357 | [
{
"content": "If $x=2$ and $v=3 x$, then the value of $(2 v-5)-(2 x-5)$ is\n(A) 2\n(B) 8\n(C) -2\n(D) -7\n(E) 6",
"role": "user"
}
] | If $x=2$ and $v=3 x$, then the value of $(2 v-5)-(2 x-5)$ is
(A) 2
(B) 8
(C) -2
(D) -7
(E) 6 | "[\"8\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3831, "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:17719"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\sqrt{11}}{2}"
] | [
"skywork"
] | 956f51ed3c5e59c1934df52ece3a8a1739dd78dfc3c2f51b7a5ed0dead5471ba | [
{
"content": "8. Let $D$ be a point inside $\\triangle A B C$ such that $\\angle B A D=$ $\\angle B C D$, and $\\angle B D C=90^{\\circ}$. Given $A B=5, B C=$ $6, M$ is the midpoint of $A C$. Then $D M=$ $\\qquad$",
"role": "user"
}
] | 8. Let $D$ be a point inside $\triangle A B C$ such that $\angle B A D=$ $\angle B C D$, and $\angle B D C=90^{\circ}$. Given $A B=5, B C=$ $6, M$ is the midpoint of $A C$. Then $D M=$ $\qquad$ | "[\"\\\\frac{\\\\sqrt{11}}{2}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3805, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17720"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"\\frac{1}{4}"
] | [
"skywork"
] | e562981c55ccd4b013652ba1d0d75a4a0a9a1bf3ace86556b2c7eb2cb4cebd36 | [
{
"content": "Regular octagon $ABCDEFGH$ is divided into eight smaller equilateral triangles, such as $\\triangle ABJ$, where $J$ is the center of the octagon. By connecting every second vertex starting from $A$, we obtain a larger equilateral triangle $\\triangle ACE$. Compute the ratio of the area of $\\trian... | Regular octagon $ABCDEFGH$ is divided into eight smaller equilateral triangles, such as $\triangle ABJ$, where $J$ is the center of the octagon. By connecting every second vertex starting from $A$, we obtain a larger equilateral triangle $\triangle ACE$. Compute the ratio of the area of $\triangle ABJ$ to the area of $... | "[\"\\\\frac{1}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3800, "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:17721"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"13"
] | [
"skywork"
] | abd6abe289034d3bff9541830da960803969dfafac5182c134dea502d2e3fd6a | [
{
"content": "The least positive angle $\\alpha$ for which $$\\left(\\frac34-\\sin^2(\\alpha)\\right)\\left(\\frac34-\\sin^2(3\\alpha)\\right)\\left(\\frac34-\\sin^2(3^2\\alpha)\\right)\\left(\\frac34-\\sin^2(3^3\\alpha)\\right)=\\frac1{256}$$ has a degree measure of $\\tfrac{m}{n}$, where $m$ and $n$ are relat... | The least positive angle $\alpha$ for which $$\left(\frac34-\sin^2(\alpha)\right)\left(\frac34-\sin^2(3\alpha)\right)\left(\frac34-\sin^2(3^2\alpha)\right)\left(\frac34-\sin^2(3^3\alpha)\right)=\frac1{256}$$ has a degree measure of $\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. | "[\"13\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3817, "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:17722"}, {"dataset": "skywork", "extra_... | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\sqrt{2}}{2}"
] | [
"skywork"
] | b386775c72756e6a5322a03316f4801dba63074fc3a3d273b433c5753c5fba5d | [
{
"content": "Let $a_1\\in (0,1)$ and $(a_n)_{n\\ge 1}$ a sequence of real numbers defined by $a_{n+1}=a_n(1-a_n^2),\\ (\\forall)n\\ge 1$. Evaluate $\\lim_{n\\to \\infty} a_n\\sqrt{n}$.",
"role": "user"
}
] | Let $a_1\in (0,1)$ and $(a_n)_{n\ge 1}$ a sequence of real numbers defined by $a_{n+1}=a_n(1-a_n^2),\ (\forall)n\ge 1$. Evaluate $\lim_{n\to \infty} a_n\sqrt{n}$. | "[\"\\\\frac{\\\\sqrt{2}}{2}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3815, "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:17723"}] | {
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} |
[
"11"
] | [
"skywork"
] | 82d378f9b95590eac63d8457edc5492d51d641721d33a52a62f22564d6bba8ae | [
{
"content": "How many three-digit multiples of 9 consist only of odd digits?",
"role": "user"
}
] | How many three-digit multiples of 9 consist only of odd digits? | "[\"11\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3818, "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:17724"}] | {
"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
} |
[
"182"
] | [
"skywork"
] | 223faec98a5719527667c74f5144c1eff36e75339f6ccb361405adb08fda65d8 | [
{
"content": "By a proper divisor of a natural number we mean a positive integral divisor other than 1 and the number itself. A natural number greater than 1 will be called nice if it is equal to the product of its distinct proper divisors. What is the sum of the first ten nice numbers?",
"role": "user"
}... | By a proper divisor of a natural number we mean a positive integral divisor other than 1 and the number itself. A natural number greater than 1 will be called nice if it is equal to the product of its distinct proper divisors. What is the sum of the first ten nice numbers? | "[\"182\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3808, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17725"}, {"dataset": "skywork", "extra_in... | {
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"reference_components": 1,
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} |
[
"\\frac{\\alpha}{\\beta}"
] | [
"skywork"
] | c7a49887e9ba14b5129ccd298d388c85eceb9d60d1a71b989e2d3f8edbac9c38 | [
{
"content": "Example 1. Find $\\lim _{x \\rightarrow 0} \\frac{\\ln (1+\\alpha x)}{\\sin \\beta x}$.",
"role": "user"
}
] | Example 1. Find $\lim _{x \rightarrow 0} \frac{\ln (1+\alpha x)}{\sin \beta x}$. | "[\"\\\\frac{\\\\alpha}{\\\\beta}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3816, "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:17726"}] | {
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[
"\\arccos\\left(\\frac{2}{3}\\right)"
] | [
"skywork"
] | dfe225655788f4d779adc4529573e7744bd862b56c29b01c95aa0fd61f316bef | [
{
"content": "In a tetrahedron $A B C D$ where all edges are of equal length, points $E$ and $F$ are the midpoints of edges $A D$ and $B C$ respectively. Connect $A$ to $F$ and $C$ to $E$. Find the angle between the skew lines $A F$ and $C E$.",
"role": "user"
}
] | In a tetrahedron $A B C D$ where all edges are of equal length, points $E$ and $F$ are the midpoints of edges $A D$ and $B C$ respectively. Connect $A$ to $F$ and $C$ to $E$. Find the angle between the skew lines $A F$ and $C E$. | "[\"\\\\arccos\\\\left(\\\\frac{2}{3}\\\\right)\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 3809, "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:17727"}] | {
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[
"303369"
] | [
"skywork"
] | bf564805f441df4cd10a7ed447b99eb072ef97f363eda74d859afdafb7cd49a1 | [
{
"content": "[ [Decimal numeral system ]\n\nFind the largest six-digit number, in which each digit, starting from the third, is equal to the sum of the two preceding digits.\n\n#",
"role": "user"
}
] | [ [Decimal numeral system ]
Find the largest six-digit number, in which each digit, starting from the third, is equal to the sum of the two preceding digits.
# | "[\"303369\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3814, "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:17728"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2519"
] | [
"skywork"
] | 4a357695adfe00567a5e2c60e760ddafda4832693ce6d5e7e5a4642274be68cc | [
{
"content": "A number which when divided by $10$ leaves a remainder of $9$, when divided by $9$ leaves a remainder of $8$, by $8$ leaves a remainder of $7$, etc., down to where, when divided by $2$, it leaves a remainder of $1$, is:",
"role": "user"
}
] | A number which when divided by $10$ leaves a remainder of $9$, when divided by $9$ leaves a remainder of $8$, by $8$ leaves a remainder of $7$, etc., down to where, when divided by $2$, it leaves a remainder of $1$, is: | "[\"2519\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3821, "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:17729"}] | {
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"reference_components": 1,
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} |
[
"2079"
] | [
"skywork"
] | 4226d041a5bc67d8541998dce2711a848d46f916a970d15ab6f5a92fe29a801b | [
{
"content": "5. (20 points) Alexei came up with the following game. First, he chooses a number $x$ such that $2017 \\leqslant x \\leqslant 2117$. Then he checks if $x$ is divisible by 3, 5, 7, 9, and 11 without a remainder. If $x$ is divisible by 3, Alexei awards the number 3 points, if by 5 - then 5 points, .... | 5. (20 points) Alexei came up with the following game. First, he chooses a number $x$ such that $2017 \leqslant x \leqslant 2117$. Then he checks if $x$ is divisible by 3, 5, 7, 9, and 11 without a remainder. If $x$ is divisible by 3, Alexei awards the number 3 points, if by 5 - then 5 points, ..., if by 11 - then 11 p... | "[\"2079\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3810, "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:17731"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"608"
] | [
"skywork"
] | 2794084e0b78863eda66b09292a2623ca4a403b84573e088debd2ef148de624e | [
{
"content": "The arithmetic sequence $a, a+d$, $a+2 d, a+3 d, \\ldots, a+(n-1) d$ has the following properties:\n\n- When the first, third, and fifth, and so on terms are added, up to and including the last term, the sum is 320 .\n- When the first, fourth, seventh, and so on, terms are added, up to and includi... | The arithmetic sequence $a, a+d$, $a+2 d, a+3 d, \ldots, a+(n-1) d$ has the following properties:
- When the first, third, and fifth, and so on terms are added, up to and including the last term, the sum is 320 .
- When the first, fourth, seventh, and so on, terms are added, up to and including the last term, the sum ... | "[\"608\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3813, "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:17732"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"m(n-1)"
] | [
"skywork"
] | 92fc9c31b26064b44512fbe47db0528d34402a0429749bdaa5126db627026754 | [
{
"content": "1. An exam consists of $m$ questions, with $n$ students participating, where $m, n \\geqslant 2$ are given integers. The scoring rule for each question is: if exactly $x$ students fail to answer the question correctly, then each student who answers the question correctly gets $x$ points, and those... | 1. An exam consists of $m$ questions, with $n$ students participating, where $m, n \geqslant 2$ are given integers. The scoring rule for each question is: if exactly $x$ students fail to answer the question correctly, then each student who answers the question correctly gets $x$ points, and those who fail to answer cor... | "[\"m(n-1)\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3802, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17733"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"1"
] | [
"skywork"
] | 03ce726e603be46eb7faef62350ca41d64d2c7562a1e13d42f2ba4b06de4e9cd | [
{
"content": "4. Given $n(n \\geqslant 3)$ real numbers $x_{1}, x_{2}, \\cdots, x_{n}$ satisfying $\\left\\{\\begin{array}{l}x_{1}+x_{2}+\\cdots+x_{n}=n \\\\ x_{1}^{2}+x_{2}^{2}+\\cdots+x_{n}^{2}=n\\end{array}\\right.$, then\n$$\n\\frac{x_{1} x_{2}+x_{2} x_{3}+\\cdots+x_{n-1} x_{n}+x_{n} x_{1}}{\\frac{1}{x_{1}}... | 4. Given $n(n \geqslant 3)$ real numbers $x_{1}, x_{2}, \cdots, x_{n}$ satisfying $\left\{\begin{array}{l}x_{1}+x_{2}+\cdots+x_{n}=n \\ x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}=n\end{array}\right.$, then
$$
\frac{x_{1} x_{2}+x_{2} x_{3}+\cdots+x_{n-1} x_{n}+x_{n} x_{1}}{\frac{1}{x_{1}}+\frac{1}{x_{2}}+\cdots+\frac{1}{x_{n}... | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3823, "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:17734"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"394"
] | [
"skywork"
] | 9c5223abf59f34dc41f12c92992628f5f9ebabfb04174f8070dbb0ed98f4fc95 | [
{
"content": "A solitaire game is played as follows. Six distinct pairs of matched tiles are placed in a bag. The player randomly draws tiles one at a time from the bag and retains them, except that matching tiles are put aside as soon as they appear in the player's hand. The game ends if the player ever holds ... | A solitaire game is played as follows. Six distinct pairs of matched tiles are placed in a bag. The player randomly draws tiles one at a time from the bag and retains them, except that matching tiles are put aside as soon as they appear in the player's hand. The game ends if the player ever holds three tiles, no two of... | "[\"394\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3825, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17735"}, {"dataset": "skywork", "extra_i... | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"\\frac{2\\sqrt{3}}{3}"
] | [
"skywork"
] | 209b9bc65200ef9c009fbe6faed4ac2ee8408d63dea0c6d58902c8d4cdd874aa | [
{
"content": "Given the hyperbola $\\frac{x^{2}}{a^{2}} - \\frac{y^{2}}{b^{2}} = 1 (a > 0, b > 0)$ with its right focus $F$, draw a line perpendicular to the $x$-axis passing through $F$, intersecting the two asymptotes at points $A$ and $B$, and intersecting the hyperbola at point $P$ in the first quadrant. De... | Given the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 (a > 0, b > 0)$ with its right focus $F$, draw a line perpendicular to the $x$-axis passing through $F$, intersecting the two asymptotes at points $A$ and $B$, and intersecting the hyperbola at point $P$ in the first quadrant. Denote $O$ as the origin. ... | "[\"\\\\frac{2\\\\sqrt{3}}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3806, "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:17736"}] | {
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"label_correctness_independently_verified": false,
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} |
[
"32"
] | [
"skywork"
] | 5a336c06c9007a2ce2b0fd740a8db9952533ce6413d3b7674dad27c7acb14d1c | [
{
"content": "A square of $3 \\times 3$ is subdivided into 9 small squares of $1 \\times 1$. It is desired to distribute the nine digits $1, 2, . . . , 9$ in each small square of $1 \\times 1$, a number in each small square. Find the number of different distributions that can be formed in such a way that the di... | A square of $3 \times 3$ is subdivided into 9 small squares of $1 \times 1$. It is desired to distribute the nine digits $1, 2, . . . , 9$ in each small square of $1 \times 1$, a number in each small square. Find the number of different distributions that can be formed in such a way that the difference of the digits in... | "[\"32\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3827, "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:17737"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"657"
] | [
"skywork"
] | 81cf2b92d84cc51d5f8ef49aa21329651485278fe7d90fbd0f73fbc8ba1d0149 | [
{
"content": "How many three-digit numbers remain if we exclude all three-digit numbers where there are exactly two adjacent identical digits?",
"role": "user"
}
] | How many three-digit numbers remain if we exclude all three-digit numbers where there are exactly two adjacent identical digits? | "[\"657\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 3835, "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:17738"}] | {
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"reference_components": 1,
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} |
[
"405"
] | [
"skywork"
] | 0dc8253a51b9e5196b09c1c16745973763c02c83ce1f3f0889889848d32b5598 | [
{
"content": "How many non- empty subsets $S$ of $\\{1,2,3,\\ldots ,15\\}$ have the following two properties?\n$(1)$ No two consecutive integers belong to $S$.\n$(2)$ If $S$ contains $k$ elements, then $S$ contains no number less than $k$.\n$\\mathrm{(A) \\ } 277\\qquad \\mathrm{(B) \\ } 311\\qquad \\mathrm{(C)... | How many non- empty subsets $S$ of $\{1,2,3,\ldots ,15\}$ have the following two properties?
$(1)$ No two consecutive integers belong to $S$.
$(2)$ If $S$ contains $k$ elements, then $S$ contains no number less than $k$.
$\mathrm{(A) \ } 277\qquad \mathrm{(B) \ } 311\qquad \mathrm{(C) \ } 376\qquad \mathrm{(D) \ } 377\... | "[\"405\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3822, "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:17739"}] | {
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} |
[
"16"
] | [
"skywork"
] | 435281f8a7fa1cfab64eab9acc56823685557cd4924003ba265d09bcd836a7e4 | [
{
"content": "34. Each person silently remembers two numbers that are not equal to 0. Calculate the square of the sum of these two numbers, and record the result as “共”. Calculate the square of the difference of these two numbers, and record the result as “迎”. Then calculate the product of these two numbers, an... | 34. Each person silently remembers two numbers that are not equal to 0. Calculate the square of the sum of these two numbers, and record the result as “共”. Calculate the square of the difference of these two numbers, and record the result as “迎”. Then calculate the product of these two numbers, and record it as “接”. Us... | "[\"16\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3824, "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:17740"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"31"
] | [
"skywork"
] | d65b4a4a2628d85452f040a5159d28b3ef137e21bb9a664989468884fb8be28c | [
{
"content": "14. (6 points) The average of six numbers is 24, and the average after adding one more number is 25, the number added is",
"role": "user"
}
] | 14. (6 points) The average of six numbers is 24, and the average after adding one more number is 25, the number added is | "[\"31\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3833, "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:17741"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | 3de928075f7f33211ffe733390e1ff0cfbe0dc3be95b82c9f078fa5091b9cf0d | [
{
"content": "Problem 1. (Option 1)\n\nCalculate $x^{3}+3 x$, where $x=\\sqrt[3]{2+\\sqrt{5}}-\\frac{1}{\\sqrt[3]{2+\\sqrt{5}}}$.",
"role": "user"
}
] | Problem 1. (Option 1)
Calculate $x^{3}+3 x$, where $x=\sqrt[3]{2+\sqrt{5}}-\frac{1}{\sqrt[3]{2+\sqrt{5}}}$. | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3841, "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:17742"}] | {
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} |
[
"(m, n)=\\left(\\frac{\\sqrt{3}}{2}, \\frac{1}{2}\\right)"
] | [
"skywork"
] | d3be13acf6e189a2e528287c8c6adfbd12ee0113465f0a41a54d92ce1a24211a | [
{
"content": "8. If for any $\\alpha, \\beta$ satisfying $\\alpha \\pm \\beta \\neq k \\cdot 360^{\\circ}$, we have\n$$\n\\begin{array}{l}\n\\frac{\\sin \\left(\\alpha+30^{\\circ}\\right)+\\sin \\left(\\beta-30^{\\circ}\\right)}{\\cos \\alpha-\\cos \\beta} \\\\\n=m \\cot \\frac{\\beta-\\alpha}{2}+n,\n\\end{arra... | 8. If for any $\alpha, \beta$ satisfying $\alpha \pm \beta \neq k \cdot 360^{\circ}$, we have
$$
\begin{array}{l}
\frac{\sin \left(\alpha+30^{\circ}\right)+\sin \left(\beta-30^{\circ}\right)}{\cos \alpha-\cos \beta} \\
=m \cot \frac{\beta-\alpha}{2}+n,
\end{array}
$$
then the array $(m, n)=$ $\qquad$ | "[\"(m, n)=\\\\left(\\\\frac{\\\\sqrt{3}}{2}, \\\\frac{1}{2}\\\\right)\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3804, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17743"}] | {
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"reference_present": true
} |
[
"8"
] | [
"skywork"
] | 8180dd520e99b840bf9d4b6910af93b11f7455e20b3bae188637e44e4b05c131 | [
{
"content": "In a gumball machine containing 13 red, 5 blue, 1 white, and 9 green gumballs, what is the least number of gumballs that must be bought to guarantee receiving 3 gumballs of the same color?",
"role": "user"
}
] | In a gumball machine containing 13 red, 5 blue, 1 white, and 9 green gumballs, what is the least number of gumballs that must be bought to guarantee receiving 3 gumballs of the same color? | "[\"8\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3847, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17744"}] | {
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} |
[
"(10,121)"
] | [
"skywork"
] | d86b065ebfd581f8610c758ce4301c9399a01654ff4ca4e722a773391116a3cb | [
{
"content": "9. (16 points) Given the quadratic function\n$$\ny=f(x)=x^{2}+b x+c \\text {. }\n$$\n\nthe graph passes through the point $(1,13)$, and\n$$\ny=f\\left(x-\\frac{1}{2}\\right)\n$$\n\nis an even function.\n(1) Find the analytical expression of $f(x)$.\n(2) Does the graph of the function $y=f(x)$ have... | 9. (16 points) Given the quadratic function
$$
y=f(x)=x^{2}+b x+c \text {. }
$$
the graph passes through the point $(1,13)$, and
$$
y=f\left(x-\frac{1}{2}\right)
$$
is an even function.
(1) Find the analytical expression of $f(x)$.
(2) Does the graph of the function $y=f(x)$ have any points where the x-coordinate is ... | "[\"(10,121)\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3820, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "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:17745"}] | {
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[
"15,75,105,165"
] | [
"skywork"
] | e4d76049dd2130c219dd51535286f0b93314673ed4c45901801d9424fc9a6a3c | [
{
"content": "11.5. Find all values that angle $B$ of triangle $ABC$ can take if it is known that the distance between the bases of the altitudes dropped from vertices $A$ and $C$ is half the radius of the circumscribed circle around this triangle.",
"role": "user"
}
] | 11.5. Find all values that angle $B$ of triangle $ABC$ can take if it is known that the distance between the bases of the altitudes dropped from vertices $A$ and $C$ is half the radius of the circumscribed circle around this triangle. | "[\"15,75,105,165\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3839, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17746"}] | {
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} |
[
"n(k+1)"
] | [
"skywork"
] | 6a2282ab5f6a2faa9fc544546ab91c04514be975455ce2bf88726d67adacec8a | [
{
"content": "How many rooks can be placed in an $n\\times n$ chessboard such that each rook is threatened by at most $2k$ rooks?\n(15 points)\n[i]Proposed by Mostafa Einollah zadeh[/i]",
"role": "user"
}
] | How many rooks can be placed in an $n\times n$ chessboard such that each rook is threatened by at most $2k$ rooks?
(15 points)
[i]Proposed by Mostafa Einollah zadeh[/i] | "[\" n(k+1) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3812, "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:17747"}] | {
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} |
[
"\\dfrac{3\\sqrt{5}}{5}"
] | [
"skywork"
] | d0fcfe09348dd962f9552f1ac6078aa45545d1ec4c11aa42d281eac2e668c763 | [
{
"content": "The hyperbola C: $\\dfrac{x^{2}}{a^{2}} - \\dfrac{y^{2}}{b^{2}} = 1$ ($a > 0, b > 0$) has one focus that is also the focus of the parabola $y^{2} = 4x$. Line $l$ is an asymptote of $C$ and intersects the circle $(x-1)^{2} + y^{2} = a^{2}$ at points $A$ and $B$. If $|AB| = b$, determine the eccentr... | The hyperbola C: $\dfrac{x^{2}}{a^{2}} - \dfrac{y^{2}}{b^{2}} = 1$ ($a > 0, b > 0$) has one focus that is also the focus of the parabola $y^{2} = 4x$. Line $l$ is an asymptote of $C$ and intersects the circle $(x-1)^{2} + y^{2} = a^{2}$ at points $A$ and $B$. If $|AB| = b$, determine the eccentricity of the hyperbola $... | "[\"\\\\dfrac{3\\\\sqrt{5}}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3829, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17748"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"2-\\sqrt{3}"
] | [
"skywork"
] | 1a17a081f5163d024ed6aac799e9cf7cf9e3ce6b40d1f6b861bdf0eb27f1df38 | [
{
"content": "Solve the equations: \n(1) $(x-3)^2+2x(x-3)=0$ \n(2) $x^2-4x+1=0$.",
"role": "user"
}
] | Solve the equations:
(1) $(x-3)^2+2x(x-3)=0$
(2) $x^2-4x+1=0$. | "[\"2-\\\\sqrt{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3845, "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:17749"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"125"
] | [
"skywork"
] | 68f02f3efc920b688ab4cdceb34590b96ab395c05a27de8c0d10f144fe5c7002 | [
{
"content": "For how many integers $n$ between 1 and 500 inclusive is $$(\\sin t + i\\cos t)^n = \\sin(2nt) + i\\cos(2nt)$$ true for all real $t$?",
"role": "user"
}
] | For how many integers $n$ between 1 and 500 inclusive is $$(\sin t + i\cos t)^n = \sin(2nt) + i\cos(2nt)$$ true for all real $t$? | "[\"125\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3828, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17750"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1/16"
] | [
"skywork"
] | 94f57f836e05008d03066bcc9bc7eb43f7f977cfe55df5f5bbd7b8fc9df50e9a | [
{
"content": "Calculate the limit of the function:\n\n$$\\lim _{x \\rightarrow 0}\\left(\\frac{\\arcsin ^{2} x}{\\arcsin ^{2} 4 x}\\right)^{2 x+1}$$",
"role": "user"
}
] | Calculate the limit of the function:
$$\lim _{x \rightarrow 0}\left(\frac{\arcsin ^{2} x}{\arcsin ^{2} 4 x}\right)^{2 x+1}$$ | "[\"1/16\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3840, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17751"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{6}{7}"
] | [
"skywork"
] | c23e36c949f4142a58bd5cf9419631906001b44d809d18f52d587129f27592d0 | [
{
"content": "What is $\\frac{3}{4}$ divided by $\\frac{7}{8}$?",
"role": "user"
}
] | What is $\frac{3}{4}$ divided by $\frac{7}{8}$? | "[\"\\\\frac{6}{7}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3867, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17752"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"e^{\\alpha + \\beta}"
] | [
"skywork"
] | 597a9b7694c4a1afe61679ce156c70c4192956388eb9056e1eca28bd8467ce16 | [
{
"content": "Let $D:=\\{(x, y)\\mid x,y\\in\\mathbb R_+,x \\ne y,x^y=y^x\\}$. (Obvious that $x\\ne1$ and $y\\ne1$). And let $\\alpha\\le\\beta$ be positive real numbers. Find\n$$\\inf_{(x,y)\\in D}x^\\alpha y^\\beta.$$\n\n[i]Proposed by Arkady Alt[/i]",
"role": "user"
}
] | Let $D:=\{(x, y)\mid x,y\in\mathbb R_+,x \ne y,x^y=y^x\}$. (Obvious that $x\ne1$ and $y\ne1$). And let $\alpha\le\beta$ be positive real numbers. Find
$$\inf_{(x,y)\in D}x^\alpha y^\beta.$$
[i]Proposed by Arkady Alt[/i] | "[\" e^{\\\\alpha + \\\\beta} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3832, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17753"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1080"
] | [
"skywork"
] | 76d7855e01235e3fade4e09c6798c88919c4f322aede05f9ebf41049d302f4a1 | [
{
"content": "If four departments A, B, C, and D select from six tourist destinations, calculate the total number of ways in which at least three departments have different destinations.",
"role": "user"
}
] | If four departments A, B, C, and D select from six tourist destinations, calculate the total number of ways in which at least three departments have different destinations. | "[\"1080\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3834, "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:17754"}] | {
"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
} |
[
"\\tan^{-1}\\left(\\frac{1009}{1005}\\right)"
] | [
"skywork"
] | e6c77079309001b4444af556e455f60d303db88b78bcd7dadcf034027dc5c480 | [
{
"content": "Find the angle of reflection $\\theta$ such that a ball bounces 2012 times inside a $1 \\times 1$ square before returning to its starting point.",
"role": "user"
}
] | Find the angle of reflection $\theta$ such that a ball bounces 2012 times inside a $1 \times 1$ square before returning to its starting point. | "[\"\\\\tan^{-1}\\\\left(\\\\frac{1009}{1005}\\\\right)\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 3843, "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:17755"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-2"
] | [
"skywork"
] | 1b3ba104673ba867addb3eccda550bfb994ed3233caa68bb365f31f0df8243a0 | [
{
"content": "Let $d_1$, $d_2$, $d_3$, $d_4$, $e_1$, $e_2$, $e_3$, and $e_4$ be real numbers such that for every real number $x$, we have\n\\[\n x^8 - 2x^7 + 2x^6 - 2x^5 + 2x^4 - 2x^3 + 2x^2 - 2x + 1 = (x^2 + d_1 x + e_1)(x^2 + d_2 x + e_2)(x^2 + d_3 x + e_3)(x^2 + d_4 x + e_4). \n\\]\nCompute $d_1 e_1 + d_2 e... | Let $d_1$, $d_2$, $d_3$, $d_4$, $e_1$, $e_2$, $e_3$, and $e_4$ be real numbers such that for every real number $x$, we have
\[
x^8 - 2x^7 + 2x^6 - 2x^5 + 2x^4 - 2x^3 + 2x^2 - 2x + 1 = (x^2 + d_1 x + e_1)(x^2 + d_2 x + e_2)(x^2 + d_3 x + e_3)(x^2 + d_4 x + e_4).
\]
Compute $d_1 e_1 + d_2 e_2 + d_3 e_3 + d_4 e_4$. | "[\"-2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3842, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17756"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"F(0;-\\frac{2}{3})"
] | [
"skywork"
] | 40c6c7dab32f85ba45b465cc19584a50acc35388f8d157d94f686689f51217fc | [
{
"content": "113. Given a triangle with vertices $A(4 ; 6), B(-3 ; 0)$, $C(2 ;-3)$. Find the angles of the triangle, the equation of the bisector $A D$, the equation of the altitude $C E$, and the point of their intersection.",
"role": "user"
}
] | 113. Given a triangle with vertices $A(4 ; 6), B(-3 ; 0)$, $C(2 ;-3)$. Find the angles of the triangle, the equation of the bisector $A D$, the equation of the altitude $C E$, and the point of their intersection. | "[\"F(0;-\\\\frac{2}{3})\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3830, "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:17757"}] | {
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} |
[
"8634"
] | [
"skywork"
] | dac3c57514315c72eeb91b3443ef37e397b6daccd0bb91040d0e9d84b70ffb38 | [
{
"content": "$O$ is the center of square $A B C D$, and $M$ and $N$ are the midpoints of $\\overline{B C}$ and $\\overline{A D}$, respectively. Points $A^{\\prime}, B^{\\prime}, C^{\\prime}, D^{\\prime}$ are chosen on $\\overline{A O}, \\overline{B O}, \\overline{C O}, \\overline{D O}$, respectively, so that $... | $O$ is the center of square $A B C D$, and $M$ and $N$ are the midpoints of $\overline{B C}$ and $\overline{A D}$, respectively. Points $A^{\prime}, B^{\prime}, C^{\prime}, D^{\prime}$ are chosen on $\overline{A O}, \overline{B O}, \overline{C O}, \overline{D O}$, respectively, so that $A^{\prime} B^{\prime} M C^{\prim... | "[\"8634\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3826, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:17758"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"80"
] | [
"skywork"
] | d82e13440c60552b74a6709c6054f02ddceb6637e0b6d0ba95da54f6aff80f28 | [
{
"content": "17. How many three-digit numbers are increased by 99 when their digits are reversed?\nA 4\nB 8\nC 10\nD 80\nE 90",
"role": "user"
}
] | 17. How many three-digit numbers are increased by 99 when their digits are reversed?
A 4
B 8
C 10
D 80
E 90 | "[\"80\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3854, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17759"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"18"
] | [
"skywork"
] | 8ee8d795bcd19c031b3ea01af497d01c886a94b755a05788209a427e1d8b425c | [
{
"content": "# Task 8.2\n\nA team consisting of Petya, Vasya, and a one-person scooter is participating in a race. The distance is divided into segments of equal length, the number of which is 42, with a checkpoint at the beginning of each. Petya runs a segment in 9 minutes, Vasya in 11 minutes, and on the sco... | # Task 8.2
A team consisting of Petya, Vasya, and a one-person scooter is participating in a race. The distance is divided into segments of equal length, the number of which is 42, with a checkpoint at the beginning of each. Petya runs a segment in 9 minutes, Vasya in 11 minutes, and on the scooter, either of them can... | "[\"18\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3846, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17760"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"87"
] | [
"skywork"
] | 267505f25b2201e47b5641bd82615ba23ccda0b82d78a942916bf0fe68da04b5 | [
{
"content": "Two mathematicians take a morning coffee break each day. They arrive at the cafeteria independently, at random times between 9 a.m. and 10 a.m., and stay for exactly $m$ minutes. The probability that either one arrives while the other is in the cafeteria is $40 \\%,$ and $m = a - b\\sqrt {c},$ whe... | Two mathematicians take a morning coffee break each day. They arrive at the cafeteria independently, at random times between 9 a.m. and 10 a.m., and stay for exactly $m$ minutes. The probability that either one arrives while the other is in the cafeteria is $40 \%,$ and $m = a - b\sqrt {c},$ where $a, b,$ and $c$ are p... | "[\"87\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3837, "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:17761"}, {"dataset": "skywork", "extra_inf... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-\\frac{7}{8}"
] | [
"skywork"
] | 9c181a9a552ee110aa216c940034fc41afccb5ae03ecacf7297437e5bf7439fc | [
{
"content": "Given $sin(x+\\frac{π}{12})=-\\frac{1}{4}$, find the value of $cos(\\frac{5π}{6}-2x)$.",
"role": "user"
}
] | Given $sin(x+\frac{π}{12})=-\frac{1}{4}$, find the value of $cos(\frac{5π}{6}-2x)$. | "[\"-\\\\frac{7}{8}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3862, "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:17763"}] | {
"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
} |
[
"10"
] | [
"skywork"
] | 4949f84244a804b4f27f0786cdae3638ed236e97bb91e70184e82d998e03462f | [
{
"content": "The number of distinct even numbers that can be formed using the digits 0, 1, 2, and 3.",
"role": "user"
}
] | The number of distinct even numbers that can be formed using the digits 0, 1, 2, and 3. | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3855, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17764"}] | {
"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
} |
[
"734"
] | [
"skywork"
] | 3d4ec5fd805e9562328df69795000d70168782f47901dcb82b6ccccf42c52078 | [
{
"content": "5. The function $f(x)=[x]+[2 x]+\\left[\\frac{5 x}{3}\\right]+[3 x]+[4 x], x \\in[0,100]$, then the number of elements in the range of $f(x)$ is ().\nA. 734\nB. 733\nC. 701\nD. 700",
"role": "user"
}
] | 5. The function $f(x)=[x]+[2 x]+\left[\frac{5 x}{3}\right]+[3 x]+[4 x], x \in[0,100]$, then the number of elements in the range of $f(x)$ is ().
A. 734
B. 733
C. 701
D. 700 | "[\"734\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3848, "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:17765"}] | {
"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
} |
[
"1563"
] | [
"skywork"
] | 74b218351df8eeb7ac9a1afba1b025de20072577feba871d9be5f3998a8e89a0 | [
{
"content": "11. (12 points) In the equation $\\overline{\\mathrm{ABCD}}+E \\times F \\times G \\times H=2011$, $A, B, C, D, E, F, G, H$ represent different digits from $1 \\sim 8$ (different letters represent different digits), then the four-digit number $\\overline{\\mathrm{ABCD}}=$ $\\qquad$\n\n将上面的文本翻译成英文，... | 11. (12 points) In the equation $\overline{\mathrm{ABCD}}+E \times F \times G \times H=2011$, $A, B, C, D, E, F, G, H$ represent different digits from $1 \sim 8$ (different letters represent different digits), then the four-digit number $\overline{\mathrm{ABCD}}=$ $\qquad$
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。 | "[\"1563\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3759, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17766"}] | {
"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
} |
[
"18"
] | [
"skywork"
] | 94eb0af72d828c92768383e8e588d35b5f8b51976b6b2dc7955d02d99d1302dc | [
{
"content": "In the diagram, each of the three identical circles touch the other two. The circumference of each circle is 36. What is the perimeter of the shaded region?",
"role": "user"
}
] | In the diagram, each of the three identical circles touch the other two. The circumference of each circle is 36. What is the perimeter of the shaded region? | "[\"18\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3866, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17767"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 89ca5d568fb5d5146111099169643ffff1e6a8570dd8c2c176eee7fd9501298c | [
{
"content": "Find the sum $$\\frac{2^{1}}{4^{1}-1}+\\frac{2^{2}}{4^{2}-1}+\\frac{2^{4}}{4^{4}-1}+\\frac{2^{8}}{4^{8}-1}+\\cdots$$",
"role": "user"
}
] | Find the sum $$\frac{2^{1}}{4^{1}-1}+\frac{2^{2}}{4^{2}-1}+\frac{2^{4}}{4^{4}-1}+\frac{2^{8}}{4^{8}-1}+\cdots$$ | "[\"1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3849, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17768"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"21"
] | [
"skywork"
] | 151c412efbe92eecc881ddab3b7c26013073d6074d15240a39a3eb722984edcd | [
{
"content": "The sum of two numbers is $45$. Their difference is $3$. What is the lesser of the two numbers?",
"role": "user"
}
] | The sum of two numbers is $45$. Their difference is $3$. What is the lesser of the two numbers? | "[\"21\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3879, "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:17769"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | c5ea32ec7ea342f627e4d04ba19b2d50d2c57a98c56d2a452b84d111ec433703 | [
{
"content": "12. (12 points) Given\n$$\n\\begin{array}{l}\nf(x, y) \\\\\n=x^{3}+y^{3}+x^{2} y+x y^{2}-3\\left(x^{2}+y^{2}+x y\\right)+3(x+y),\n\\end{array}\n$$\n\nand $x, y \\geqslant \\frac{1}{2}$. Find the minimum value of $f(x, y)$.",
"role": "user"
}
] | 12. (12 points) Given
$$
\begin{array}{l}
f(x, y) \\
=x^{3}+y^{3}+x^{2} y+x y^{2}-3\left(x^{2}+y^{2}+x y\right)+3(x+y),
\end{array}
$$
and $x, y \geqslant \frac{1}{2}$. Find the minimum value of $f(x, y)$. | "[\"1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3868, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:17770"}] | {
"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
} |
[
"31"
] | [
"skywork"
] | 3674eaa700b4faaa18636e09b304cd88cf50fdabb27245d4d231979113311f1f | [
{
"content": "Katelyn is building an integer (in base $10$). She begins with $9$. Each step, she appends a randomly chosen digit from $0$ to $9$ inclusive to the right end of her current integer. She stops immediately when the current integer is $0$ or $1$ (mod $11$). The probability that the final integer ends... | Katelyn is building an integer (in base $10$). She begins with $9$. Each step, she appends a randomly chosen digit from $0$ to $9$ inclusive to the right end of her current integer. She stops immediately when the current integer is $0$ or $1$ (mod $11$). The probability that the final integer ends up being $0$ (mod $11... | "[\"31\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3853, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17771"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-1"
] | [
"skywork"
] | 83da40e4a5c96e434be564c6a943249527e89e260954cb5ebc0efadc3b4377ea | [
{
"content": "Task B-2.3. Without solving the quadratic equation $x^{2}+2 x+2=0$, calculate the value of the expression $\\frac{x_{1}^{3}+x_{2}^{3}}{\\left(x_{1}-x_{2}\\right)^{2}}$, where $x_{1}, x_{2}$ are the solutions of the given equation.",
"role": "user"
}
] | Task B-2.3. Without solving the quadratic equation $x^{2}+2 x+2=0$, calculate the value of the expression $\frac{x_{1}^{3}+x_{2}^{3}}{\left(x_{1}-x_{2}\right)^{2}}$, where $x_{1}, x_{2}$ are the solutions of the given equation. | "[\"-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3865, "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:17772"}] | {
"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
} |
[
"\\text{m is not squarefree}"
] | [
"skywork"
] | f44da53966d86e5a92ab3f38ee0ec388502f8a052ae39f72bc3557fda75b3179 | [
{
"content": "For which positive integers $m$ does there exist an infinite arithmetic sequence of integers $a_1, a_2, . . .$ and an infinite geometric sequence of integers $g_1, g_2, . . .$ satisfying the following properties?\n[list]\n[*] $a_n - g_n$ is divisible by $m$ for all integers $n \\ge 1$;\n[*] $a_2 -... | For which positive integers $m$ does there exist an infinite arithmetic sequence of integers $a_1, a_2, . . .$ and an infinite geometric sequence of integers $g_1, g_2, . . .$ satisfying the following properties?
[list]
[*] $a_n - g_n$ is divisible by $m$ for all integers $n \ge 1$;
[*] $a_2 - a_1$ is not divisible by ... | "[\"\\\\text{m is not squarefree}\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 3858, "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:17773"}] | {
"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
} |
[
"100"
] | [
"skywork"
] | f6a21f61742a6915d4178bc1863e446d0b9f99f437d75412f5005cebf17f9cb3 | [
{
"content": "## Task $1 / 84$\n\nSolve the equation $1984^{\\lg x}=2 \\cdot 1984^{2}-x^{\\lg 1984}$ in real numbers $x$.",
"role": "user"
}
] | ## Task $1 / 84$
Solve the equation $1984^{\lg x}=2 \cdot 1984^{2}-x^{\lg 1984}$ in real numbers $x$. | "[\"100\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3875, "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:17774"}] | {
"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
} |
[
"344"
] | [
"skywork"
] | 1d1ebb2e0cd2189111026f6abddaaef5d5bda27053e48a0fce600058cbcdb8b3 | [
{
"content": "Start with a three-digit positive integer $A$ . Obtain $B$ by interchanging the two leftmost digits of $A$ . Obtain $C$ by doubling $B$ . Obtain $D$ by subtracting $500$ from $C$ . Given that $A + B + C + D = 2014$ , fi\fnd $A$ .",
"role": "user"
}
] | Start with a three-digit positive integer $A$ . Obtain $B$ by interchanging the two leftmost digits of $A$ . Obtain $C$ by doubling $B$ . Obtain $D$ by subtracting $500$ from $C$ . Given that $A + B + C + D = 2014$ , fi nd $A$ . | "[\"344\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3852, "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:17775"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
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