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 |
|---|---|---|---|---|---|---|---|---|
[
"S_{1}=S_{2}"
] | [
"skywork"
] | 7e89f672f8871ee63398382b423af19982f959eec04b7c791414ef5be33cc95f | [
{
"content": "Given $n$ integers $a_{1}=1, a_{2}, a_{3}, \\ldots, a_{n}$, and $a_{i} \\leq a_{i+1} \\leq 2 a_{i}(i=1,2, \\ldots, n-1)$, and the sum of all numbers is even. Can these numbers be divided into two groups such that the sums of the numbers in these groups are equal?",
"role": "user"
}
] | Given $n$ integers $a_{1}=1, a_{2}, a_{3}, \ldots, a_{n}$, and $a_{i} \leq a_{i+1} \leq 2 a_{i}(i=1,2, \ldots, n-1)$, and the sum of all numbers is even. Can these numbers be divided into two groups such that the sums of the numbers in these groups are equal? | "[\"S_{1}=S_{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108397, "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:118328"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"x_i = 0"
] | [
"skywork"
] | f23cc9c77a637d792501f1915f2f70a5b9d69c827366fc93eb3762f4aad5547c | [
{
"content": "Find all integer sequences of the form $ x_i, 1 \\le i \\le 1997$, that satisfy $ \\sum_{k\\equal{}1}^{1997} 2^{k\\minus{}1} x_{k}^{1997}\\equal{}1996\\prod_{k\\equal{}1}^{1997}x_k$.",
"role": "user"
}
] | Find all integer sequences of the form $ x_i, 1 \le i \le 1997$, that satisfy $ \sum_{k\equal{}1}^{1997} 2^{k\minus{}1} x_{k}^{1997}\equal{}1996\prod_{k\equal{}1}^{1997}x_k$. | "[\" x_i = 0 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108403, "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:118329"}] | {
"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
} |
[
"32"
] | [
"skywork"
] | d5d1e1a83b3d8cbe0168251f98b4f504c1b2d3c8a90337c89a1d087b2ff6ae47 | [
{
"content": "2. Given four non-coplanar points $A, B, C, D$, where the distance between any two points is distinct, consider a plane $\\alpha$ with the following property: three of the points $A, B, C, D$ are at the same distance from $\\alpha$, and the fourth point is at a distance that is twice the distance ... | 2. Given four non-coplanar points $A, B, C, D$, where the distance between any two points is distinct, consider a plane $\alpha$ with the following property: three of the points $A, B, C, D$ are at the same distance from $\alpha$, and the fourth point is at a distance that is twice the distance of one of the three poin... | "[\"32\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108391, "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:118330"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | 625d4dec2faf1d7c1cd505a65e5da858aef1221b4595663869ce8f9d769f876f | [
{
"content": "Consider the set of all points $(x,y)$ in the coordinate plane for which one of the coordinates is exactly twice the other. If we were to plot all such points, into how many regions would the resulting graph split up the plane?",
"role": "user"
}
] | Consider the set of all points $(x,y)$ in the coordinate plane for which one of the coordinates is exactly twice the other. If we were to plot all such points, into how many regions would the resulting graph split up the plane? | "[\"4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108407, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118331"}] | {
"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
} |
[
"80"
] | [
"skywork"
] | 4d5f488021cad59a5f7394983b563b08f5694f1141cbb730163fa1e122b015a8 | [
{
"content": "In the diagram, \\( S \\) lies on \\( R T \\), \\( \\angle Q T S = 40^{\\circ} \\), \\( Q S = Q T \\), and \\( \\triangle P R S \\) is equilateral. Find the value of \\( x \\).",
"role": "user"
}
] | In the diagram, \( S \) lies on \( R T \), \( \angle Q T S = 40^{\circ} \), \( Q S = Q T \), and \( \triangle P R S \) is equilateral. Find the value of \( x \). | "[\"80\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108393, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118332"}] | {
"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
} |
[
"500\\mathrm{~}^{2}"
] | [
"skywork"
] | 8335f05be9f1650e48d61974d6343f46fb5303ce9d37587005e337da36723a6d | [
{
"content": "14. A square of side-length $30 \\mathrm{~cm}$ is divided into nine smaller identical squares. The large square contains three circles with radii $5 \\mathrm{~cm}$ (bottom right), $4 \\mathrm{~cm}$ (top left) and $3 \\mathrm{~cm}$ (top right), as shown. What is the total area of the shaded part?\n... | 14. A square of side-length $30 \mathrm{~cm}$ is divided into nine smaller identical squares. The large square contains three circles with radii $5 \mathrm{~cm}$ (bottom right), $4 \mathrm{~cm}$ (top left) and $3 \mathrm{~cm}$ (top right), as shown. What is the total area of the shaded part?
A $400 \mathrm{~cm}^{2}$
B ... | "[\"500\\\\mathrm{~}^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108413, "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:118335"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"x = 1, y = 9, u = 8, v = 6"
] | [
"skywork"
] | 9d7a1b30d55511eb94a912994b61bda2bfa5ba6421d1e3fe50e0245a77747aaa | [
{
"content": "18. (15 points) Let the set $M=\\{n \\in \\mathbf{Z} \\mid 0 \\leqslant n \\leqslant 11\\}$, and the set $F=\\{(a, b, c, d) \\mid a, b, c, d \\in M\\}$. The mapping $f: F \\rightarrow \\mathbf{Z}$ is defined such that $(a, b, c, d)$ corresponds to $a b - c d$. If $(u, v, x, y)$ corresponds to 39, ... | 18. (15 points) Let the set $M=\{n \in \mathbf{Z} \mid 0 \leqslant n \leqslant 11\}$, and the set $F=\{(a, b, c, d) \mid a, b, c, d \in M\}$. The mapping $f: F \rightarrow \mathbf{Z}$ is defined such that $(a, b, c, d)$ corresponds to $a b - c d$. If $(u, v, x, y)$ corresponds to 39, and $(u, y, x, v)$ corresponds to 6... | "[\"x = 1, y = 9, u = 8, v = 6\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108410, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118336"}] | {
"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
} |
[
"\\arcsin \\frac{3\\sqrt{73}}{73}"
] | [
"skywork"
] | 658f9b24cd7d1b3846d3d778333ce41ee066e77ca9f525ab755cfe540b4e4d46 | [
{
"content": "In the right triangular prism $A B O - A_1 B_1 O_1$, $O O_1=4, O A=4, O B=3$, $\\angle A O B=90^{\\circ}$, $D$ is the midpoint of segment $A_1 B_1$, and $P$ is a point on the lateral edge $B B_1$. If $O P \\perp B D$, find the angle between $O P$ and the base $A O B$ (express the result in terms o... | In the right triangular prism $A B O - A_1 B_1 O_1$, $O O_1=4, O A=4, O B=3$, $\angle A O B=90^{\circ}$, $D$ is the midpoint of segment $A_1 B_1$, and $P$ is a point on the lateral edge $B B_1$. If $O P \perp B D$, find the angle between $O P$ and the base $A O B$ (express the result in terms of an inverse trigonometri... | "[\"\\\\arcsin \\\\frac{3\\\\sqrt{73}}{73}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108409, "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:118337"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | 56037b0fe20b1e3b8c0076ee29816d05d9b69cad831ab4ee533537791cad23d7 | [
{
"content": "6. (6 points) Fill in a natural number in each of the $\\square$ and $\\triangle$ to make the equation true.\n$$\n\\square^{2}+12=\\triangle^{2} \\text {, then: } \\square+\\triangle=6 \\text {. }\n$$",
"role": "user"
}
] | 6. (6 points) Fill in a natural number in each of the $\square$ and $\triangle$ to make the equation true.
$$
\square^{2}+12=\triangle^{2} \text {, then: } \square+\triangle=6 \text {. }
$$ | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108418, "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:118338"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2}"
] | [
"skywork"
] | 00b8c5a8699aeee1818a3086052e60b6ab5f53c740b68bcf797bab4fea40880f | [
{
"content": "Given the ellipse $\\Gamma: \\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 (a > b > 0)$, its right focus is $F(3,0)$, and its top and bottom vertices are $A$ and $B$ respectively. The line $AF$ intersects $\\Gamma$ at another point $M$. If the line $BM$ intersects the $x$-axis at point $N(12,0)$, then th... | Given the ellipse $\Gamma: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$, its right focus is $F(3,0)$, and its top and bottom vertices are $A$ and $B$ respectively. The line $AF$ intersects $\Gamma$ at another point $M$. If the line $BM$ intersects the $x$-axis at point $N(12,0)$, then the eccentricity of $\Gamma$... | "[\"\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108412, "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:118339"}] | {
"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
} |
[
"539"
] | [
"skywork"
] | 4e09cecccd98e93bedcca7172160854e88f56c951516bb661c7fddb099843da1 | [
{
"content": "In the diagram below, $ABCD$ is a square. Point $E$ is the midpoint of $\\overline{AD}$. Points $F$ and $G$ lie on $\\overline{CE}$, and $H$ and $J$ lie on $\\overline{AB}$ and $\\overline{BC}$, respectively, so that $FGHJ$ is a square. Points $K$ and $L$ lie on $\\overline{GH}$, and $M$ and $N$ l... | In the diagram below, $ABCD$ is a square. Point $E$ is the midpoint of $\overline{AD}$. Points $F$ and $G$ lie on $\overline{CE}$, and $H$ and $J$ lie on $\overline{AB}$ and $\overline{BC}$, respectively, so that $FGHJ$ is a square. Points $K$ and $L$ lie on $\overline{GH}$, and $M$ and $N$ lie on $\overline{AD}$ and $... | "[\"539\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 108411, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118340"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"42"
] | [
"skywork"
] | 22b2e6e62b05f9cdeb3aaa625924fd68ea60b00743215eed317eab5205d72b58 | [
{
"content": "# Task 7. (14 points)\n\nIn a certain company, no two employees have jobs of the same difficulty, and no two employees receive the same salary. On April 1, each employee made two statements:\n\n(a) There will not be 12 employees with more difficult jobs.\n\n(b) At least 30 employees have a higher ... | # Task 7. (14 points)
In a certain company, no two employees have jobs of the same difficulty, and no two employees receive the same salary. On April 1, each employee made two statements:
(a) There will not be 12 employees with more difficult jobs.
(b) At least 30 employees have a higher salary. How many employees a... | "[\"42\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108408, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118341"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"A=-2, B=4, C=2"
] | [
"skywork"
] | fc8e96bec31498d09bd94a47f70d6ff83ee1969f044d325f9ac37cdd34dc11bb | [
{
"content": "5. Express $M=\\frac{8 x}{(x+1)^{2}(x-1)}$ as partial fractions.",
"role": "user"
}
] | 5. Express $M=\frac{8 x}{(x+1)^{2}(x-1)}$ as partial fractions. | "[\"A=-2, B=4, C=2\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108431, "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:118342"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"x_{1}=0,x_{2}=5,x_{3}=\\frac{38}{11}"
] | [
"skywork"
] | 6a7a0e69e983f9c9c32f40d51ab08d0ebe2622811ba222b81164324cffeb0aed | [
{
"content": "6.015. $\\frac{7(x-2)(x-3)(x-4)}{(2 x-7)(x+2)(x-6)}=-2$.",
"role": "user"
}
] | 6.015. $\frac{7(x-2)(x-3)(x-4)}{(2 x-7)(x+2)(x-6)}=-2$. | "[\"x_{1}=0,x_{2}=5,x_{3}=\\\\frac{38}{11}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108433, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118343"}] | {
"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{31\\sqrt{2}}{25}"
] | [
"skywork"
] | 84e13468adc38c12fb60e30c5b9f8009f073cfeead000263a6f0a2ef29c0b5be | [
{
"content": "Given the function $f(x)=\\sin (x+ \\frac{7\\pi}{4})+\\cos (x- \\frac{3\\pi}{4})$, where $x\\in R$.\n(1) Find the smallest positive period and the minimum value of $f(x)$;\n(2) Given that $f(\\alpha)= \\frac{6}{5}$, where $0 < \\alpha < \\frac{3\\pi}{4}$, find the value of $f(2\\alpha)$.",
"ro... | Given the function $f(x)=\sin (x+ \frac{7\pi}{4})+\cos (x- \frac{3\pi}{4})$, where $x\in R$.
(1) Find the smallest positive period and the minimum value of $f(x)$;
(2) Given that $f(\alpha)= \frac{6}{5}$, where $0 < \alpha < \frac{3\pi}{4}$, find the value of $f(2\alpha)$. | "[\"\\\\frac{31\\\\sqrt{2}}{25}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108415, "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:118344"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"5:11"
] | [
"skywork"
] | adc3dfc3f231459252cbe0bca7b676d4b9a976575e8e20a4d66dffcbf26282bb | [
{
"content": "1. The arithmetic progression $a_{n}$ is such that its difference is not equal to zero, and $a_{10}, a_{13}$, and $a_{19}$ are consecutive terms of some geometric progression. Find the ratio $a_{12}: a_{18}$.",
"role": "user"
}
] | 1. The arithmetic progression $a_{n}$ is such that its difference is not equal to zero, and $a_{10}, a_{13}$, and $a_{19}$ are consecutive terms of some geometric progression. Find the ratio $a_{12}: a_{18}$. | "[\"5:11\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108416, "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:118345"}] | {
"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
} |
[
"30"
] | [
"skywork"
] | 6dbd6e866eec439943f16e909ad3ac3d236377d6ae7f020b3a2a21ab4619f818 | [
{
"content": "At the 2013 Winnebago County Fair a vendor is offering a \"fair special\" on sandals. If you buy one pair of sandals at the regular price of $50, you get a second pair at a 40% discount, and a third pair at half the regular price. Javier took advantage of the \"fair special\" to buy three pairs of... | At the 2013 Winnebago County Fair a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at the regular price of $50, you get a second pair at a 40% discount, and a third pair at half the regular price. Javier took advantage of the "fair special" to buy three pairs of sandals. What percentage ... | "[\"30\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108432, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:118346"}] | {
"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"
] | ea0bb0d2f9379b7b2cafa0b076066e12412874230dbff150aba099d038c36570 | [
{
"content": "Mathematician Wiener, the founder of cybernetics, was asked about his age during his Ph.D. awarding ceremony at Harvard University because he looked very young. Wiener's interesting response was: \"The cube of my age is a four-digit number, and the fourth power of my age is a six-digit number. The... | Mathematician Wiener, the founder of cybernetics, was asked about his age during his Ph.D. awarding ceremony at Harvard University because he looked very young. Wiener's interesting response was: "The cube of my age is a four-digit number, and the fourth power of my age is a six-digit number. These two numbers together... | "[\"18\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108417, "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:118347"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\pi}{4} - \\frac{1}{2}"
] | [
"skywork"
] | 64cbf3020709a38126f48bff316030ae80491875d8cbfac4dcb5645aa0d285d9 | [
{
"content": "Evaluate the integral $\\int_{0}^{\\frac{\\pi}{2}} \\sin^{2} \\frac{x}{2} dx =$ \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | Evaluate the integral $\int_{0}^{\frac{\pi}{2}} \sin^{2} \frac{x}{2} dx =$ \_\_\_\_\_\_. | "[\"\\\\frac{\\\\pi}{4} - \\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108439, "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:118348"}] | {
"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
} |
[
"51,68,84"
] | [
"skywork"
] | 6a0cb0a3933e7ddbe47ee19ac3b15ffcd32b26825456ee3e84575a693e826cc5 | [
{
"content": "3. (7 points) It is known that a two-digit number divides 1477, leaving a remainder of 49. What are all the two-digit numbers that satisfy this condition?",
"role": "user"
}
] | 3. (7 points) It is known that a two-digit number divides 1477, leaving a remainder of 49. What are all the two-digit numbers that satisfy this condition? | "[\"51,68,84\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108429, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:118349"}] | {
"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
} |
[
"59"
] | [
"skywork"
] | 9ec508913ad9ba0102b49a92ab2a7157c8b34492215e3a7623dabd2188bc25e0 | [
{
"content": "For every $m \\geq 2$ , let $Q(m)$ be the least positive integer with the following property: For every $n \\geq Q(m)$ , there is always a perfect cube $k^3$ in the range $n < k^3 \\leq mn$ . Find the remainder when \\[\\sum_{m = 2}^{2017} Q(m)\\] is divided by $1000$ .",
"role": "user"
}
] | For every $m \geq 2$ , let $Q(m)$ be the least positive integer with the following property: For every $n \geq Q(m)$ , there is always a perfect cube $k^3$ in the range $n < k^3 \leq mn$ . Find the remainder when \[\sum_{m = 2}^{2017} Q(m)\] is divided by $1000$ . | "[\"59\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 108419, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118350"}] | {
"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+\\sqrt{3}"
] | [
"skywork"
] | ccc0abc3c428dd4b857e08e3fdd401d77e64b877678d62365e1d1cd255fb5117 | [
{
"content": "Eight spheres of radius 1, one per octant, are each tangent to the coordinate planes. What is the radius of the smallest sphere, centered at the origin, that contains these eight spheres?",
"role": "user"
}
] | Eight spheres of radius 1, one per octant, are each tangent to the coordinate planes. What is the radius of the smallest sphere, centered at the origin, that contains these eight spheres? | "[\"1+\\\\sqrt{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108447, "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:118351"}] | {
"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
} |
[
"50"
] | [
"skywork"
] | 9c2d8b917936f3d3e5c7c30c9f029fface3f18eb3a1af3c6ba2ec741b59ac1dd | [
{
"content": "Find the number of solutions to\n\\[\\sin x = \\left( \\frac{3}{4} \\right)^x\\]\non the interval \\( (0, 50\\pi) \\).",
"role": "user"
}
] | Find the number of solutions to
\[\sin x = \left( \frac{3}{4} \right)^x\]
on the interval \( (0, 50\pi) \). | "[\"50\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108422, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:118352"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"51"
] | [
"skywork"
] | 5afcb6900d62fb2d6d1a3fe30b8a83b69485a1cb1d050611c5dbba5e42825243 | [
{
"content": "$1 \\cdot 109$ Choose 3 numbers from $0,1,2, \\cdots \\cdots, 9$ such that their sum is an even number not less than 10. How many different ways are there to do this?",
"role": "user"
}
] | $1 \cdot 109$ Choose 3 numbers from $0,1,2, \cdots \cdots, 9$ such that their sum is an even number not less than 10. How many different ways are there to do this? | "[\"51\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108425, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118353"}] | {
"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
} |
[
"216"
] | [
"skywork"
] | b2ec991344de45a75593ff4458ccd8626513ce1cf6605a9915d27bba7c768aa9 | [
{
"content": "How many equilateral hexagons of side length $\\sqrt{13}$ have one vertex at $(0,0)$ and the other five vertices at lattice points? (A lattice point is a point whose Cartesian coordinates are both integers. A hexagon may be concave but not self-intersecting.)",
"role": "user"
}
] | How many equilateral hexagons of side length $\sqrt{13}$ have one vertex at $(0,0)$ and the other five vertices at lattice points? (A lattice point is a point whose Cartesian coordinates are both integers. A hexagon may be concave but not self-intersecting.) | "[\"216\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108424, "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:118355"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"8"
] | [
"skywork"
] | 4d9350bf610724fff8791cf305a34941667b0f0fed0dab2e5ad4a5e934269c9b | [
{
"content": "Five first-graders stood in a line and held 37 flags. All those to the right of Tanya had 14 flags, to the right of Yasha - 32, to the right of Vera - 20, and to the right of Maksim - 8. How many flags does Dasha have?\n\n#",
"role": "user"
}
] | Five first-graders stood in a line and held 37 flags. All those to the right of Tanya had 14 flags, to the right of Yasha - 32, to the right of Vera - 20, and to the right of Maksim - 8. How many flags does Dasha have?
# | "[\"8\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108421, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118356"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{8}"
] | [
"skywork"
] | e85ea5c2088429b5b1d1e683f1e323364f6607d1bfac8dddb40b7f204981d9d5 | [
{
"content": "Compute\n\\[\\left( 1 + \\cos \\frac {\\pi}{8} \\right) \\left( 1 + \\cos \\frac {3 \\pi}{8} \\right) \\left( 1 + \\cos \\frac {5 \\pi}{8} \\right) \\left( 1 + \\cos \\frac {7 \\pi}{8} \\right).\\]",
"role": "user"
}
] | Compute
\[\left( 1 + \cos \frac {\pi}{8} \right) \left( 1 + \cos \frac {3 \pi}{8} \right) \left( 1 + \cos \frac {5 \pi}{8} \right) \left( 1 + \cos \frac {7 \pi}{8} \right).\] | "[\"\\\\frac{1}{8}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108428, "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:118357"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3}{10}"
] | [
"skywork"
] | 552993597f0db5df55185997df2740a02a36ce2c48e642d5476673b9c6c764a3 | [
{
"content": "A five-digit integer is chosen at random from all possible positive five-digit integers. What is the probability that the number's units digit is an even number and less than 6? Express your answer as a common fraction.",
"role": "user"
}
] | A five-digit integer is chosen at random from all possible positive five-digit integers. What is the probability that the number's units digit is an even number and less than 6? Express your answer as a common fraction. | "[\"\\\\frac{3}{10}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108443, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118358"}] | {
"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
} |
[
"559"
] | [
"skywork"
] | 0c2d13725f8bf42eb62be291f32c59dee8b95c0ec0bcf43b231bba87edaf9735 | [
{
"content": "4. Let non-negative real numbers $x_{1}, x_{2}, \\cdots, x_{6}$ satisfy\n$$\n\\begin{array}{c}\nx_{1}+x_{2}+\\cdots+x_{6}=1, x_{1} x_{3} x_{5}+x_{2} x_{4} x_{6} \\geqslant \\frac{1}{540} . \\\\\n\\text { If } \\max \\left\\{x_{1} x_{2} x_{3}+x_{2} x_{3} x_{4}+x_{3} x_{4} x_{5}+x_{4} x_{5} x_{6}+\\... | 4. Let non-negative real numbers $x_{1}, x_{2}, \cdots, x_{6}$ satisfy
$$
\begin{array}{c}
x_{1}+x_{2}+\cdots+x_{6}=1, x_{1} x_{3} x_{5}+x_{2} x_{4} x_{6} \geqslant \frac{1}{540} . \\
\text { If } \max \left\{x_{1} x_{2} x_{3}+x_{2} x_{3} x_{4}+x_{3} x_{4} x_{5}+x_{4} x_{5} x_{6}+\right. \\
\left.x_{5} x_{6} x_{1}+x_{6... | "[\"559\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108420, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118359"}] | {
"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{3\\sqrt{21}}{38416}"
] | [
"skywork"
] | c1f86daa8216d5cd48081b3619fceff6ca5bda2bbc500fdc98b026295f386688 | [
{
"content": "11. (20 points) For any real numbers $a_{1}, a_{2}, \\cdots, a_{5}$ $\\in[0,1]$, find the maximum value of $\\prod_{1 \\leq i<j \\leq 5}\\left|a_{i}-a_{j}\\right|$.",
"role": "user"
}
] | 11. (20 points) For any real numbers $a_{1}, a_{2}, \cdots, a_{5}$ $\in[0,1]$, find the maximum value of $\prod_{1 \leq i<j \leq 5}\left|a_{i}-a_{j}\right|$. | "[\"\\\\frac{3\\\\sqrt{21}}{38416}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108438, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118360"}] | {
"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
} |
[
"-\\sqrt{\\frac{x-2}{x+2}}"
] | [
"skywork"
] | 9485c0134d674429850677f212502d866421b9f0f5358e029e094be75dd11960 | [
{
"content": "2.245. $\\frac{\\left((x+2)^{-1 / 2}+(x-2)^{-1 / 2}\\right)^{-1}+\\left((x+2)^{-1 / 2}-(x-2)^{-1 / 2}\\right)^{-1}}{\\left((x+2)^{-1 / 2}+(x-2)^{-1 / 2}\\right)^{-1}-\\left((x+2)^{-1 / 2}-(x-2)^{-1 / 2}\\right)^{-1}}$.",
"role": "user"
}
] | 2.245. $\frac{\left((x+2)^{-1 / 2}+(x-2)^{-1 / 2}\right)^{-1}+\left((x+2)^{-1 / 2}-(x-2)^{-1 / 2}\right)^{-1}}{\left((x+2)^{-1 / 2}+(x-2)^{-1 / 2}\right)^{-1}-\left((x+2)^{-1 / 2}-(x-2)^{-1 / 2}\right)^{-1}}$. | "[\"-\\\\sqrt{\\\\frac{x-2}{x+2}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108441, "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:118361"}] | {
"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
} |
[
"45"
] | [
"skywork"
] | df0e18a3c51236b0e6630382a54b4eebd68152735d963739b24cb98f0b372bcd | [
{
"content": "If $3^{x}=5$, the value of $3^{x+2}$ is\n(A) 10\n(B) 25\n(C) 2187\n(D) 14\n(E) 45",
"role": "user"
}
] | If $3^{x}=5$, the value of $3^{x+2}$ is
(A) 10
(B) 25
(C) 2187
(D) 14
(E) 45 | "[\"45\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108450, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118362"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"{4}^{{2017}}+3"
] | [
"skywork"
] | b68fe1347ac878a6956d3081cc0665eb10690a89f0440b0059347d1ee4bc2ffa | [
{
"content": "Given an arithmetic sequence $\\\\{ {a_{n}} \\\\}$ with the sum of its first 5 terms equal to 50, and its 7th term ${a_{7}}=22$. Another sequence $\\\\{ {b_{n}} \\\\}$ has the sum of its first $n$ terms denoted as ${{S_{n}}}$, with ${{b_{1}}=1}$, and ${{b_{n+1}}=3{{S_{n}}+1}}$.\n\n(1) Find the gen... | Given an arithmetic sequence $\\{ {a_{n}} \\}$ with the sum of its first 5 terms equal to 50, and its 7th term ${a_{7}}=22$. Another sequence $\\{ {b_{n}} \\}$ has the sum of its first $n$ terms denoted as ${{S_{n}}}$, with ${{b_{1}}=1}$, and ${{b_{n+1}}=3{{S_{n}}+1}}$.
(1) Find the general term formulas for both sequ... | "[\"{4}^{{2017}}+3\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108390, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118363"}] | {
"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
} |
[
"f(n) = n"
] | [
"skywork"
] | 426e2d8389a3362384c3a10217e8c499cfb000480a10b3d3615e9eb83f056e0d | [
{
"content": "Find all functions $f:\\mathbb{N} \\rightarrow \\mathbb{N}$, such that $af(a)^3+2abf(a)+bf(b)$ is a perfect square for all positive integers $a,b$.",
"role": "user"
}
] | Find all functions $f:\mathbb{N} \rightarrow \mathbb{N}$, such that $af(a)^3+2abf(a)+bf(b)$ is a perfect square for all positive integers $a,b$. | "[\" f(n) = n \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108435, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118365"}] | {
"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
} |
[
"54"
] | [
"skywork"
] | 211db3053120032285629bb00691d304ab02c0a125ab7101fc757e6256e8b665 | [
{
"content": "Calculate\n\n(1) Use a simplified method to calculate $2017^{2}-2016 \\times 2018$;\n\n(2) Given $a+b=7$ and $ab=-1$, find the values of $(a+b)^{2}$ and $a^{2}-3ab+b^{2}$.",
"role": "user"
}
] | Calculate
(1) Use a simplified method to calculate $2017^{2}-2016 \times 2018$;
(2) Given $a+b=7$ and $ab=-1$, find the values of $(a+b)^{2}$ and $a^{2}-3ab+b^{2}$. | "[\"54\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108436, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118366"}] | {
"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
} |
[
"1010"
] | [
"skywork"
] | ae4c7b2c0fd7de7bab05d4525aa078fdd6e17aa018726734c7f7d49c0553f795 | [
{
"content": "Given $0 \\leq a_k \\leq 1$ for $k=1,2,\\ldots,2020$, and defining $a_{2021}=a_1, a_{2022}=a_2$, find the maximum value of $\\sum_{k=1}^{2020}\\left(a_{k}-a_{k+1} a_{k+2}\\right)$.",
"role": "user"
}
] | Given $0 \leq a_k \leq 1$ for $k=1,2,\ldots,2020$, and defining $a_{2021}=a_1, a_{2022}=a_2$, find the maximum value of $\sum_{k=1}^{2020}\left(a_{k}-a_{k+1} a_{k+2}\right)$. | "[\"1010\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108423, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:118367"}] | {
"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{4}{3}"
] | [
"skywork"
] | 95ab57983666ced0f1d335354b6f13bc7e2a0b1548ecc55c3ac74ca7c7106335 | [
{
"content": "3. (9th \"Hope Cup\" Invitational Competition Question) If $0<a, b, c<1$, and $a+b+c=2$, then the minimum value of $a^{2}+b^{2}+c^{2}$ is\n\n保留源文本的换行和格式，直接输出翻译结果。",
"role": "user"
}
] | 3. (9th "Hope Cup" Invitational Competition Question) If $0<a, b, c<1$, and $a+b+c=2$, then the minimum value of $a^{2}+b^{2}+c^{2}$ is
保留源文本的换行和格式，直接输出翻译结果。 | "[\"\\\\frac{4}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108466, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118368"}] | {
"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
} |
[
"1680"
] | [
"skywork"
] | 0cb8e7847c5443545cbca4876a3eae0b58fa4385a47d87cf71917acb6f5467b1 | [
{
"content": "Find the number of 8-digit numbers where the product of the digits equals 9261. Present the answer as an integer.",
"role": "user"
}
] | Find the number of 8-digit numbers where the product of the digits equals 9261. Present the answer as an integer. | "[\"1680\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108453, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118369"}] | {
"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{8}{3}"
] | [
"skywork"
] | d339e0d94b41a016b283ad714e398e8aa755898a7352a5a420b2c3dc4cf6edcf | [
{
"content": "1. The infantry column stretched out to 1 km. Sergeant Kim, riding out on a gyro-scooter from the end of the column, reached its beginning and returned to the end. The infantrymen walked $4 / 3$ km during this time. How far did the sergeant travel during this time?",
"role": "user"
}
] | 1. The infantry column stretched out to 1 km. Sergeant Kim, riding out on a gyro-scooter from the end of the column, reached its beginning and returned to the end. The infantrymen walked $4 / 3$ km during this time. How far did the sergeant travel during this time? | "[\"\\\\frac{8}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108444, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118370"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"33"
] | [
"skywork"
] | 9816276b3f36c374df7884bb057317ef2f44fe5560726d467186157aea71a7a7 | [
{
"content": "6. (10 points) Doudou's family has 4 people. This year, Doudou's brother is 3 years older than Doudou, and Doudou's mother is 2 years younger than Doudou's father. 5 years ago, the total age of the family was 59 years, and 5 years later, the total age of the family will be 97 years. Doudou's mothe... | 6. (10 points) Doudou's family has 4 people. This year, Doudou's brother is 3 years older than Doudou, and Doudou's mother is 2 years younger than Doudou's father. 5 years ago, the total age of the family was 59 years, and 5 years later, the total age of the family will be 97 years. Doudou's mother is $\qquad$ years ol... | "[\"33\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108440, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118371"}] | {
"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
} |
[
"7"
] | [
"skywork"
] | 74af30c2eefcb5a55dcfb8106820e001bbcd14ae2f011f661ba8f7d890891f82 | [
{
"content": "28.2.9 * Find the smallest positive integer $n(n \\geqslant 3)$, such that in any set of $n$ points in the plane with no three points collinear, there are two points that are vertices of a non-isosceles triangle.",
"role": "user"
}
] | 28.2.9 * Find the smallest positive integer $n(n \geqslant 3)$, such that in any set of $n$ points in the plane with no three points collinear, there are two points that are vertices of a non-isosceles triangle. | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108442, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118372"}] | {
"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{16\\sqrt{37}}{37}"
] | [
"skywork"
] | b9b5df0d31cac4943c85e2ebe630042e3230c905d0321af9b4a352cf80dcba5a | [
{
"content": "The complex numbers corresponding to the vertices $O$, $A$, and $C$ of the parallelogram $OABC$ are $0$, $3+2i$, and $-2+4i$, respectively.<br/>$(1)$ Find the complex number corresponding to point $B$;<br/>$(2)$ In triangle $OAB$, find the height $h$ on side $OB$.",
"role": "user"
}
] | The complex numbers corresponding to the vertices $O$, $A$, and $C$ of the parallelogram $OABC$ are $0$, $3+2i$, and $-2+4i$, respectively.<br/>$(1)$ Find the complex number corresponding to point $B$;<br/>$(2)$ In triangle $OAB$, find the height $h$ on side $OB$. | "[\"\\\\frac{16\\\\sqrt{37}}{37}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108427, "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:118373"}] | {
"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{4}{9}"
] | [
"skywork"
] | 88172a3e80a05506bf436c17ba0be8958aec13925f427d7a7f9f6c18f863d50e | [
{
"content": "## Zadatak B-2.3.\n\nNa stranici $\\overline{A B}$ trokuta $A B C$ dana je točka $E$ takva da je $|A E|=1$ i $|E B|=2$. Neka je točka $D$ na stranici $\\overline{A C}$ takva da je dužina $\\overline{D E}$ paralelna $\\mathrm{s}$ dužinom $\\overline{B C}$, a točka $F$ na stranici $\\overline{B C}$ ... | ## Zadatak B-2.3.
Na stranici $\overline{A B}$ trokuta $A B C$ dana je točka $E$ takva da je $|A E|=1$ i $|E B|=2$. Neka je točka $D$ na stranici $\overline{A C}$ takva da je dužina $\overline{D E}$ paralelna $\mathrm{s}$ dužinom $\overline{B C}$, a točka $F$ na stranici $\overline{B C}$ takva da je dužina $\overline{... | "[\"\\\\frac{4}{9}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108448, "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:118374"}] | {
"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
} |
[
"B"
] | [
"skywork"
] | ae5de5b24ee0b14af60c1cf5c859a711b4a6a167991da4a327e000bd0741b5d4 | [
{
"content": "1. The base edge length of a regular quadrilateral pyramid is 2017, and the side edge length is 2000. Then, the absolute value of the difference between the angle formed by the side edge and the base and the angle on the front face is the smallest for which of the following angles.\nA. $30^{\\circ... | 1. The base edge length of a regular quadrilateral pyramid is 2017, and the side edge length is 2000. Then, the absolute value of the difference between the angle formed by the side edge and the base and the angle on the front face is the smallest for which of the following angles.
A. $30^{\circ}$
B. $40^{\circ}$
C. $5... | "[\"B\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108445, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118375"}] | {
"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
} |
[
"164"
] | [
"skywork"
] | e4910b9b80e3cb0ad163f2a5b1dbc23096613ee81829d2379e46ef3afe0b3067 | [
{
"content": "Let $\\sigma(n)$ be the number of positive divisors of $n$, and let $\\operatorname{rad} n$ be the product of the distinct prime divisors of $n$. By convention, $\\operatorname{rad} 1 = 1$. Find the greatest integer not exceeding \\[ 100\\left(\\sum_{n=1}^{\\infty}\\frac{\\sigma(n)\\sigma(n \\ope... | Let $\sigma(n)$ be the number of positive divisors of $n$, and let $\operatorname{rad} n$ be the product of the distinct prime divisors of $n$. By convention, $\operatorname{rad} 1 = 1$. Find the greatest integer not exceeding \[ 100\left(\sum_{n=1}^{\infty}\frac{\sigma(n)\sigma(n \operatorname{rad} n)}{n^2\sigma(\ope... | "[\"164\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108446, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118376"}] | {
"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
} |
[
"n \\leq 12"
] | [
"skywork"
] | 6029d900123ce21880b9937549c152fff1e01e3e6cccadcba3f3788272bde2e2 | [
{
"content": "$11$ students take a test. For any two question in a test, there are at least $6$ students who solved exactly one of those two questions. Prove that there are no more than $12$ questions in this test. Showing the equality case is not needed.",
"role": "user"
}
] | $11$ students take a test. For any two question in a test, there are at least $6$ students who solved exactly one of those two questions. Prove that there are no more than $12$ questions in this test. Showing the equality case is not needed. | "[\" n \\\\leq 12 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108451, "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:118377"}] | {
"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
} |
[
"-(1+\\sqrt[4]{2})(1+\\sqrt{2})"
] | [
"skywork"
] | ba47b56c42d7a79d5f94d2d7916b3005fd77b30eebafd9b0cc08828a174c3444 | [
{
"content": "Given that $t = \\frac{1}{1 - \\sqrt[4]{2}}$, find the value of $t$.",
"role": "user"
}
] | Given that $t = \frac{1}{1 - \sqrt[4]{2}}$, find the value of $t$. | "[\"-(1+\\\\sqrt[4]{2})(1+\\\\sqrt{2})\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108468, "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:118378"}] | {
"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
} |
[
"21"
] | [
"skywork"
] | 4e856ee1d72863da08f2d3b45a4fb4b06c0dee773030e11d73d8bda849a7ee5c | [
{
"content": "Each of the integers 334 and 419 has digits whose product is 36 . How many 3-digit positive integers have digits whose product is 36 ?\n(A) 21\n(B) 15\n(C) 18\n(D) 24\n(E) 12",
"role": "user"
}
] | Each of the integers 334 and 419 has digits whose product is 36 . How many 3-digit positive integers have digits whose product is 36 ?
(A) 21
(B) 15
(C) 18
(D) 24
(E) 12 | "[\"21\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108459, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118379"}] | {
"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
} |
[
"96327"
] | [
"skywork"
] | b8be5129422193a5c1673d45ce5b140e499d01022732a3b45a63783939ef6f09 | [
{
"content": "70. A five-digit number $\\overline{A B C D E}$ is composed of five different non-zero digits, $\\overline{A B} 、 \\overline{B C} 、 \\overline{C D} 、 \\overline{D E}$ are multiples of $6 、 7 、 8 、 9$ respectively, and $\\overline{A B C D E}$ is divisible by two of $6 、 7 、 8 、 9$, then the value o... | 70. A five-digit number $\overline{A B C D E}$ is composed of five different non-zero digits, $\overline{A B} 、 \overline{B C} 、 \overline{C D} 、 \overline{D E}$ are multiples of $6 、 7 、 8 、 9$ respectively, and $\overline{A B C D E}$ is divisible by two of $6 、 7 、 8 、 9$, then the value of $\overline{A B C D E}$ is ... | "[\"96327\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108426, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118380"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"48"
] | [
"skywork"
] | 688bc0685bf6ce6d7ace45643f5899c085142908e184d13020c0f185196c236a | [
{
"content": "1. Vasya's dad is good at math, but on the way to the garage, he forgot the code for the digital lock on the garage. In his memory, he recalls that all the digits of the code are different and their sum is 28. How many different codes does dad need to try to definitely open the garage, if the open... | 1. Vasya's dad is good at math, but on the way to the garage, he forgot the code for the digital lock on the garage. In his memory, he recalls that all the digits of the code are different and their sum is 28. How many different codes does dad need to try to definitely open the garage, if the opening mechanism of the l... | "[\"48\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108455, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118381"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.872"
] | [
"skywork"
] | 89d5ce0836db5dba909cbe62cbeb0da6068c7750413944bfac93fa0c1b20eb1c | [
{
"content": "Task 1. The probability of event $A$ occurring in each of 484 independent trials is 0.75. Find the probability that the relative frequency of event $A$ deviates from its probability in absolute value by no more than 0.03.",
"role": "user"
}
] | Task 1. The probability of event $A$ occurring in each of 484 independent trials is 0.75. Find the probability that the relative frequency of event $A$ deviates from its probability in absolute value by no more than 0.03. | "[\"0.872\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108470, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118382"}] | {
"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
} |
[
"78"
] | [
"skywork"
] | 7049617b2f7d286833deb0ec1327c58bbca205ba1218e6ea7fb3745ddd86cef9 | [
{
"content": "Three boys and two girls are to stand in a row according to the following requirements. How many different arrangements are there? (Answer with numbers) \n(Ⅰ) The two girls stand next to each other; \n(Ⅱ) Girls cannot stand at the ends; \n(Ⅲ) Girls are arranged from left to right from tallest t... | Three boys and two girls are to stand in a row according to the following requirements. How many different arrangements are there? (Answer with numbers)
(Ⅰ) The two girls stand next to each other;
(Ⅱ) Girls cannot stand at the ends;
(Ⅲ) Girls are arranged from left to right from tallest to shortest;
(Ⅳ) Girl A ... | "[\"78\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108434, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118383"}] | {
"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"
] | ccd3b4c2e961fc38aa1cc652218c5c35e5a83aad2938a20ee7592fcee236f5df | [
{
"content": "Find the units digit of $9^{8^7}$.",
"role": "user"
}
] | Find the units digit of $9^{8^7}$. | "[\"1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108473, "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:118384"}] | {
"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{1011}{2021}"
] | [
"skywork"
] | fe1d6b23cd04f866f6577c9d5125ffb6ce7af1d986db41778cb26e0f5a6af79e | [
{
"content": "3. Calculate the value of the product $\\left(1-\\frac{1}{4}\\right) \\cdot\\left(1-\\frac{1}{9}\\right) \\cdot\\left(1-\\frac{1}{16}\\right) \\cdot \\ldots \\cdot\\left(1-\\frac{1}{2021^{2}}\\right)$.",
"role": "user"
}
] | 3. Calculate the value of the product $\left(1-\frac{1}{4}\right) \cdot\left(1-\frac{1}{9}\right) \cdot\left(1-\frac{1}{16}\right) \cdot \ldots \cdot\left(1-\frac{1}{2021^{2}}\right)$. | "[\"\\\\frac{1011}{2021}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108458, "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:118385"}] | {
"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
} |
[
"36"
] | [
"skywork"
] | 1546067f00e6834be5f94b0ab61c5aa82d5471417c00bfc11665f541c4e2eebc | [
{
"content": "20. Xiaoming sets off from home to his grandmother's house, cycling at a speed of 12 kilometers per hour. 2.5 hours after he leaves, his father realizes that Xiaoming has forgotten his homework, so he sets off on a motorcycle at a speed of 36 kilometers per hour to catch up. As a result, half an h... | 20. Xiaoming sets off from home to his grandmother's house, cycling at a speed of 12 kilometers per hour. 2.5 hours after he leaves, his father realizes that Xiaoming has forgotten his homework, so he sets off on a motorcycle at a speed of 36 kilometers per hour to catch up. As a result, half an hour after Xiaoming arr... | "[\"36\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108457, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118386"}] | {
"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
} |
[
"22"
] | [
"skywork"
] | 52de2be8b4f1065388187241b298093ccb85d4b80ec8e472f80c99a0ff716ee0 | [
{
"content": "13. The diagram shows a quadrilateral $P Q R S$ made from two similar right-angled triangles, $P Q R$ and $P R S$. The length of $P Q$ is 3 , the length of $Q R$ is 4 and $\\angle P R Q=\\angle P S R$.\nWhat is the perimeter of $P Q R S$ ?\nA 22\nB $22 \\frac{5}{6}$\nC 27\nD 32\nE $\\quad 45 \\fra... | 13. The diagram shows a quadrilateral $P Q R S$ made from two similar right-angled triangles, $P Q R$ and $P R S$. The length of $P Q$ is 3 , the length of $Q R$ is 4 and $\angle P R Q=\angle P S R$.
What is the perimeter of $P Q R S$ ?
A 22
B $22 \frac{5}{6}$
C 27
D 32
E $\quad 45 \frac{1}{3}$ | "[\"22\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108465, "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:118387"}] | {
"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
} |
[
"71"
] | [
"skywork"
] | 76557a5eeccafb4453fff3f63013030a31dc08339c4c2ac0d4ef45aefd2ef273 | [
{
"content": "For all real numbers $r$ and $s$, define the mathematical operation $\\#$ such that the following conditions apply: $r\\ \\#\\ 0 = r, r\\ \\#\\ s = s\\ \\#\\ r$, and $(r + 1)\\ \\#\\ s = (r\\ \\#\\ s) + s + 1$. What is the value of $11\\ \\#\\ 5$?",
"role": "user"
}
] | For all real numbers $r$ and $s$, define the mathematical operation $\#$ such that the following conditions apply: $r\ \#\ 0 = r, r\ \#\ s = s\ \#\ r$, and $(r + 1)\ \#\ s = (r\ \#\ s) + s + 1$. What is the value of $11\ \#\ 5$? | "[\"71\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108460, "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:118388"}] | {
"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
} |
[
"16"
] | [
"skywork"
] | d0620735093260b625875401e7bee9217827bb92a5b318f3e5ef6e9cfe5caf4f | [
{
"content": "Folklore\n\nOn a chessboard, $n$ white and $n$ black rooks are placed such that rooks of different colors do not attack each other. Find the maximum possible value of $n$.\n\n#",
"role": "user"
}
] | Folklore
On a chessboard, $n$ white and $n$ black rooks are placed such that rooks of different colors do not attack each other. Find the maximum possible value of $n$.
# | "[\"16\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108469, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118389"}] | {
"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"
] | d28373b86316fb1917d1efc488977fc568554670f4eea3ebd20c2d6eb96009fa | [
{
"content": "18. Four different prime numbers $\\mathrm{a}, \\mathrm{~b}, \\mathrm{c}, \\mathrm{~d}$ satisfy the following properties:\n(1) $a+b+c+d$ is also a prime number; (2) The sum of two of $\\mathrm{a}, \\mathrm{~b}, \\mathrm{c}, \\mathrm{~d}$ is also a prime number; (3) The sum of three of $\\mathrm{a}... | 18. Four different prime numbers $\mathrm{a}, \mathrm{~b}, \mathrm{c}, \mathrm{~d}$ satisfy the following properties:
(1) $a+b+c+d$ is also a prime number; (2) The sum of two of $\mathrm{a}, \mathrm{~b}, \mathrm{c}, \mathrm{~d}$ is also a prime number; (3) The sum of three of $\mathrm{a}, \mathrm{~b}, \mathrm{c}, \math... | "[\"31\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108464, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118390"}] | {
"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
} |
[
"28\\mathrm{~}^{2}"
] | [
"skywork"
] | 37dfe4faa4936f4bb673a71b482a3eb05be50337aea000673f4d17c2de1a44d8 | [
{
"content": "7.2. If the width of a rectangle is increased by 3 cm and the height is decreased by 3 cm, its area will not change. How will the area change if, instead, the width of the original rectangle is decreased by 4 cm and the height is increased by 4 cm?",
"role": "user"
}
] | 7.2. If the width of a rectangle is increased by 3 cm and the height is decreased by 3 cm, its area will not change. How will the area change if, instead, the width of the original rectangle is decreased by 4 cm and the height is increased by 4 cm? | "[\"28\\\\mathrm{~}^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108461, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118391"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"90 \\text{ minutes}"
] | [
"skywork"
] | 56c4834f64efb2b136e0ffa721e7063b91cda3b0e6e23e526c2108cb9885b6d9 | [
{
"content": "Roy is starting a baking company and decides that he will sell cupcakes. He sells $n$ cupcakes for $(n + 20)(n + 15)$ cents. A man walks in and buys $\\$10.50$ worth of cupcakes. Roy bakes cupcakes at a rate of $10$ cupcakes an hour. How many minutes will it take Roy to complete the order?",
"... | Roy is starting a baking company and decides that he will sell cupcakes. He sells $n$ cupcakes for $(n + 20)(n + 15)$ cents. A man walks in and buys $\$10.50$ worth of cupcakes. Roy bakes cupcakes at a rate of $10$ cupcakes an hour. How many minutes will it take Roy to complete the order? | "[\"90 \\\\text{ minutes}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108456, "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:118392"}] | {
"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
} |
[
"a=-\\sqrt{6}"
] | [
"skywork"
] | 5b41250d9073decf4e11c9f951e16c4b6c2518a5959baa50159a3169b6ab2662 | [
{
"content": "Example 5 Let the quadratic function $y=x^{2}+2 a x+\\frac{a^{2}}{2}(a<0)$ have its vertex at $A$, and intersect the $x$-axis at points $B$ and $C$. When $\\triangle A B C$ is an equilateral triangle, the value of $a$ is $\\qquad$",
"role": "user"
}
] | Example 5 Let the quadratic function $y=x^{2}+2 a x+\frac{a^{2}}{2}(a<0)$ have its vertex at $A$, and intersect the $x$-axis at points $B$ and $C$. When $\triangle A B C$ is an equilateral triangle, the value of $a$ is $\qquad$ | "[\"a=-\\\\sqrt{6}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108463, "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:118393"}] | {
"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
} |
[
"8748"
] | [
"skywork"
] | 6448eb76dcde3b10142fa362418ecda81c0d41ccd91837792cc825d2b8c4803c | [
{
"content": "The number 25 is expressed as the sum of positive integers \\(x_{1}, x_{2}, \\cdots, x_{k}\\), where \\(k \\leq 25\\). What is the maximum value of the product of \\(x_{1}, x_{2}, x_{3}, \\cdots\\), and \\(x_{k}\\)?",
"role": "user"
}
] | The number 25 is expressed as the sum of positive integers \(x_{1}, x_{2}, \cdots, x_{k}\), where \(k \leq 25\). What is the maximum value of the product of \(x_{1}, x_{2}, x_{3}, \cdots\), and \(x_{k}\)? | "[\"8748\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108471, "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:118394"}] | {
"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
} |
[
"32"
] | [
"skywork"
] | 7f78895b9037a20bdf8b084fa0f0578f735b6c3f95b31a17b3517ed23d64a931 | [
{
"content": "What is the value of $\\frac12\\cdot\\frac41\\cdot\\frac18\\cdot\\frac{16}{1} \\dotsm \\frac{1}{512}\\cdot\\frac{1024}{1}$?",
"role": "user"
}
] | What is the value of $\frac12\cdot\frac41\cdot\frac18\cdot\frac{16}{1} \dotsm \frac{1}{512}\cdot\frac{1024}{1}$? | "[\"32\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108477, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118395"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | 45c2f8fd369868f8ebcd5099083976a6b6048c77c3bbd97b28884d0e69c421a3 | [
{
"content": "4. Alana, Beatrix, Celine, and Deanna played 6 games of tennis together. In each game, the four of them split into two teams of two and one of the teams won the game. If Alana was on the winning team for 5 games, Beatrix for 2 games, and Celine for 1 game, for how many games was Deanna on the winn... | 4. Alana, Beatrix, Celine, and Deanna played 6 games of tennis together. In each game, the four of them split into two teams of two and one of the teams won the game. If Alana was on the winning team for 5 games, Beatrix for 2 games, and Celine for 1 game, for how many games was Deanna on the winning team? | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108476, "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:118397"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\pi}{4}"
] | [
"skywork"
] | e475225ecc7a6436d2ba280e12cdbfba45c36a80ec1f7c237c67f58dcc4e139c | [
{
"content": "Given that \\(\\sin (x + \\sin x) = \\cos (x - \\cos x)\\), where \\(x \\in [0, \\pi]\\). Find \\(x\\).",
"role": "user"
}
] | Given that \(\sin (x + \sin x) = \cos (x - \cos x)\), where \(x \in [0, \pi]\). Find \(x\). | "[\"\\\\frac{\\\\pi}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108474, "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:118398"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{5\\pi}{12}"
] | [
"skywork"
] | a5d857154239b0d3e5f54186c41acd13b292e7c901e376746fd1bfa528d9c355 | [
{
"content": "Find an axis of symmetry for the function $f(x) = \\cos(2x + \\frac{\\pi}{6})$.",
"role": "user"
}
] | Find an axis of symmetry for the function $f(x) = \cos(2x + \frac{\pi}{6})$. | "[\"\\\\frac{5\\\\pi}{12}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108489, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118399"}] | {
"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
} |
[
"840"
] | [
"skywork"
] | 1b1d28e3133973a214f4a1bdf48eb4ac063e2f066f235f2a6fdf1442109e61a3 | [
{
"content": "Given that $x$ is a multiple of $12600$, what is the greatest common divisor of $g(x) = (5x + 7)(11x + 3)(17x + 8)(4x + 5)$ and $x$?",
"role": "user"
}
] | Given that $x$ is a multiple of $12600$, what is the greatest common divisor of $g(x) = (5x + 7)(11x + 3)(17x + 8)(4x + 5)$ and $x$? | "[\"840\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108479, "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:118400"}] | {
"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{All initial numbers } q \\text{ such that } (r, s) \\text{ with } \\gcd(r, s) = 1 \\text{ and not both odd}"
] | [
"skywork"
] | 6faf40721d3559a0124c39e566561ca77ea87730115a290ce38fead3bf786620 | [
{
"content": "Azambuja writes a rational number $q$ on a blackboard. One operation is to delete $q$ and replace it by $q+1$; or by $q-1$; or by $\\frac{q-1}{2q-1}$ if $q \\neq \\frac{1}{2}$. The final goal of Azambuja is to write the number $\\frac{1}{2018}$ after performing a finite number of operations.\n[b]a... | Azambuja writes a rational number $q$ on a blackboard. One operation is to delete $q$ and replace it by $q+1$; or by $q-1$; or by $\frac{q-1}{2q-1}$ if $q \neq \frac{1}{2}$. The final goal of Azambuja is to write the number $\frac{1}{2018}$ after performing a finite number of operations.
[b]a)[/b] Show that if the init... | "[\"\\\\text{All initial numbers } q \\\\text{ such that } (r, s) \\\\text{ with } \\\\gcd(r, s) = 1 \\\\text{ and not both odd}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108462, "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:118401"}] | {
"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
} |
[
"n \\leqslant 998 \\text{ or } n \\geqslant 3991"
] | [
"skywork"
] | e09d1c2bb171a9abd665cbb9d2b790a146f1a373e4a31825e2dde19ed28a5ee3 | [
{
"content": "58. 09. For any natural number $k$, we call a rectangle of size $1 \\times k$ a \"strip\". Try to determine for which natural numbers $n$, a rectangle of size $1995 \\times n$ can be divided into distinct \"strips\"?",
"role": "user"
}
] | 58. 09. For any natural number $k$, we call a rectangle of size $1 \times k$ a "strip". Try to determine for which natural numbers $n$, a rectangle of size $1995 \times n$ can be divided into distinct "strips"? | "[\"n \\\\leqslant 998 \\\\text{ or } n \\\\geqslant 3991\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108475, "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:118402"}] | {
"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
} |
[
"B"
] | [
"skywork"
] | 0e3adc480b221fbc582164665777cb4b593e42722de1677df2d045178c85114c | [
{
"content": "$30 \\cdot 4$ has 99 natural numbers greater than 1, their sum is 300. If 9 of these numbers are each decreased by 2, and the remaining 90 numbers are each increased by 1. Then the product of the resulting 99 numbers must be\n(A) odd.\n(B) even.\n(C) prime.\n(D) a perfect square.\n(2nd \"Five Shee... | $30 \cdot 4$ has 99 natural numbers greater than 1, their sum is 300. If 9 of these numbers are each decreased by 2, and the remaining 90 numbers are each increased by 1. Then the product of the resulting 99 numbers must be
(A) odd.
(B) even.
(C) prime.
(D) a perfect square.
(2nd "Five Sheep Cup" Junior High School Mat... | "[\"B\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108472, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118403"}] | {
"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
} |
[
"53_4"
] | [
"skywork"
] | 13506ccfabb1576c0c439a0d8d4acb1cd31714a07de123eade3c964e990fc442 | [
{
"content": "Express the quotient $2213_4 \\div 13_4$ in base 4.",
"role": "user"
}
] | Express the quotient $2213_4 \div 13_4$ in base 4. | "[\"53_4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108490, "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:118404"}] | {
"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}{7}"
] | [
"skywork"
] | f4fe82f8f5e65749a57a649fa7c40572cd973287d3b1375ec4a2a52d5feb2937 | [
{
"content": "Solve for $r$: $$\\frac{r+3}{r-2} = \\frac{r-1}{r+1}.$$Express your answer as a fraction.",
"role": "user"
}
] | Solve for $r$: $$\frac{r+3}{r-2} = \frac{r-1}{r+1}.$$Express your answer as a fraction. | "[\"-\\\\frac{1}{7}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108508, "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:118405"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | c5c47c742945e32f1fb332240f02be6a0c4add9e30f047636ca821550d4e23ea | [
{
"content": "40. Given that $a$ is a positive integer, the solution to the system of equations $\\left\\{\\begin{array}{l}a x+y=-4 \\\\ 2 x+y=-2\\end{array}\\right.$ satisfies $x>0$, then $a=$",
"role": "user"
}
] | 40. Given that $a$ is a positive integer, the solution to the system of equations $\left\{\begin{array}{l}a x+y=-4 \\ 2 x+y=-2\end{array}\right.$ satisfies $x>0$, then $a=$ | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108485, "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:118407"}] | {
"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{4 \\sqrt{2}}{3}"
] | [
"skywork"
] | 1c9e0edc397bff19f8d743ac7a19827b1e738fc6e46bfcf2cd1baf2b79c21ab2 | [
{
"content": "In trapezoid \\(ABCD\\), \\(\\overrightarrow{AB} = 2 \\overrightarrow{DC}\\), \\(|\\overrightarrow{BC}| = 6\\). Point \\(P\\) is a point in the plane of trapezoid \\(ABCD\\) and satisfies \\(\\overrightarrow{AP} + \\overrightarrow{BP} + 4 \\overrightarrow{DP} = 0\\). Additionally, \\(\\overrightar... | In trapezoid \(ABCD\), \(\overrightarrow{AB} = 2 \overrightarrow{DC}\), \(|\overrightarrow{BC}| = 6\). Point \(P\) is a point in the plane of trapezoid \(ABCD\) and satisfies \(\overrightarrow{AP} + \overrightarrow{BP} + 4 \overrightarrow{DP} = 0\). Additionally, \(\overrightarrow{DA} \cdot \overrightarrow{CB} = |\over... | "[\"\\\\frac{4 \\\\sqrt{2}}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108449, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118408"}] | {
"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
} |
[
"25"
] | [
"skywork"
] | 850cecf55b1a05a979af087cbc0faf056761a4b791e994df7cb1f59feb54a223 | [
{
"content": "Petya wants to color some cells of a $6 \\times 6$ square so that there are as many vertices as possible that belong to exactly three colored squares. What is the maximum number of such vertices he can achieve?",
"role": "user"
}
] | Petya wants to color some cells of a $6 \times 6$ square so that there are as many vertices as possible that belong to exactly three colored squares. What is the maximum number of such vertices he can achieve? | "[\"25\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108488, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:118409"}] | {
"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
} |
[
"7"
] | [
"skywork"
] | b361473aebb8bfea50d92d8dc8f38ec0a09a6f3ba1ec96404cf96a3025793440 | [
{
"content": "Exercise 10. I have socks of two different colors: 6 blue socks and 6 red socks. I take several socks at random. How many should I take, at a minimum, to be sure of having two socks of different colors?",
"role": "user"
}
] | Exercise 10. I have socks of two different colors: 6 blue socks and 6 red socks. I take several socks at random. How many should I take, at a minimum, to be sure of having two socks of different colors? | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108503, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118410"}] | {
"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
} |
[
"905"
] | [
"skywork"
] | 83dc636ebe6a9cd7258d7907eb1ba1359ee056205739acdbc0c5464aade5a841 | [
{
"content": "Sequence $(a_n)$ is defined as $a_{n+1}-2a_n+a_{n-1}=7$ for every $n\\geq 2$, where $a_1 = 1, a_2=5$. What is $a_{17}$?\n\n$ \n\\textbf{(A)}\\ 895\n\\qquad\\textbf{(B)}\\ 900\n\\qquad\\textbf{(C)}\\ 905\n\\qquad\\textbf{(D)}\\ 910\n\\qquad\\textbf{(E)}\\ \\text{None of the above}\n$",
"role": ... | Sequence $(a_n)$ is defined as $a_{n+1}-2a_n+a_{n-1}=7$ for every $n\geq 2$, where $a_1 = 1, a_2=5$. What is $a_{17}$?
$
\textbf{(A)}\ 895
\qquad\textbf{(B)}\ 900
\qquad\textbf{(C)}\ 905
\qquad\textbf{(D)}\ 910
\qquad\textbf{(E)}\ \text{None of the above}
$ | "[\"905\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108487, "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:118411"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"(2,2,2,2),(1,2,3,5),(2,1,3,5),(1,2,5,3),(2,1,5,3),(3,5,1,2),(5,3,1,2),(3,5,2,1),(5,3,2,1)"
] | [
"skywork"
] | 6c1aabbf6caf264cbdcbee4bc388daefd4127bcab78b54509faa87ccac713057 | [
{
"content": "# Problem 4. (Kuyanov 9.)\n\nFind all quadruples of natural numbers $a, b, c, d$ for which the following equations are satisfied:\n\n\\[\n\\left\\{\n\\begin{array}{l}\na+b=c d \\\\\nc+d=a b\n\\end{array}\n\\right.\n\\]",
"role": "user"
}
] | # Problem 4. (Kuyanov 9.)
Find all quadruples of natural numbers $a, b, c, d$ for which the following equations are satisfied:
\[
\left\{
\begin{array}{l}
a+b=c d \\
c+d=a b
\end{array}
\right.
\] | "[\"(2,2,2,2),(1,2,3,5),(2,1,3,5),(1,2,5,3),(2,1,5,3),(3,5,1,2),(5,3,1,2),(3,5,2,1),(5,3,2,1)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108495, "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:118412"}] | {
"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
} |
[
"214"
] | [
"skywork"
] | acc1abac4401df79b86a49b6cc2c2bab13bffd6e841dcd53fbe4f7937df09444 | [
{
"content": "4. (20 points) Before the math lesson, the teacher wrote nine consecutive numbers on the board, but the duty students accidentally erased one of them. When the lesson began, it turned out that the sum of the remaining eight numbers is 1703. Which number did the duty students erase?",
"role": "... | 4. (20 points) Before the math lesson, the teacher wrote nine consecutive numbers on the board, but the duty students accidentally erased one of them. When the lesson began, it turned out that the sum of the remaining eight numbers is 1703. Which number did the duty students erase? | "[\"214\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108499, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118414"}] | {
"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
} |
[
"14"
] | [
"skywork"
] | b6a6e3181b3b5ef87a135072b23c69f7971b3155f579f21f1ae570ded2dccefb | [
{
"content": "On a blackboard, Kiara wrote 20 integers, all of them different from zero. Then, for each pair of numbers written by Kiara, Yndira wrote on the same blackboard the respective product between them (including, if the result of some product was already written, Yndira repeated it).\n\nFor example, if... | On a blackboard, Kiara wrote 20 integers, all of them different from zero. Then, for each pair of numbers written by Kiara, Yndira wrote on the same blackboard the respective product between them (including, if the result of some product was already written, Yndira repeated it).
For example, if the numbers 2, 3, 4, an... | "[\"14\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108481, "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:118415"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{3}-1"
] | [
"skywork"
] | 82c591998efb9314e7812d4cb2edd0e156e16c1479c1f0b5422d00394ea5a496 | [
{
"content": "6. Six unit disks $C_{1}, C_{2}, C_{3}, C_{4}, C_{5}, C_{6}$ are in the plane such that they don't intersect each other and $C_{i}$ is tangent to $C_{i+1}$ for $1 \\leq i \\leq 6$ (where $C_{7}=C_{1}$ ). Let $C$ be the smallest circle that contains all six disks. Let $r$ be the smallest possible r... | 6. Six unit disks $C_{1}, C_{2}, C_{3}, C_{4}, C_{5}, C_{6}$ are in the plane such that they don't intersect each other and $C_{i}$ is tangent to $C_{i+1}$ for $1 \leq i \leq 6$ (where $C_{7}=C_{1}$ ). Let $C$ be the smallest circle that contains all six disks. Let $r$ be the smallest possible radius of $C$, and $R$ th... | "[\"\\\\sqrt{3}-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108486, "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:118416"}] | {
"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{11\\sqrt{3}}{10}"
] | [
"skywork"
] | 989fdb9e3d6d4a09cd13ad19d2ceb5dc01a9e8719a54d21ec204653a192e8e93 | [
{
"content": "6. The base of the pyramid $TABC$ is the triangle $ABC$, all sides of which are equal to 3, and the height of the pyramid, equal to $\\sqrt{3}$, coincides with the lateral edge $TA$. Find the area of the section of the pyramid by a plane that passes through the center of the sphere circumscribed a... | 6. The base of the pyramid $TABC$ is the triangle $ABC$, all sides of which are equal to 3, and the height of the pyramid, equal to $\sqrt{3}$, coincides with the lateral edge $TA$. Find the area of the section of the pyramid by a plane that passes through the center of the sphere circumscribed around the pyramid, is p... | "[\"\\\\frac{11\\\\sqrt{3}}{10}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108478, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118417"}] | {
"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
} |
[
"28"
] | [
"skywork"
] | 92208eb0edd422a416a5d8817a85effe4688a0647f12b335537e991c5b97bce7 | [
{
"content": "Five consecutive two-digit positive integers, each less than 30, are not prime. What is the largest of these five integers?",
"role": "user"
}
] | Five consecutive two-digit positive integers, each less than 30, are not prime. What is the largest of these five integers? | "[\"28\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108513, "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:118418"}] | {
"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
} |
[
"D"
] | [
"skywork"
] | 318b9e4d9c77d10e92aeaace3fbc4aa36fe3c43fdb1d01379cf7264bfd28dbae | [
{
"content": "1.96 If $N=\\sqrt{1985 \\cdot 1985 \\cdots \\cdots \\cdot 1985-7^{n+1}}$, then $N$ must be\n(A) an irrational number.\n(B) a positive integer whose last digit is 1.\n(C) a number whose first digit is 5.\n(D) none of the above.\n(China Beijing High School Mathematics Competition, 1985)",
"role"... | 1.96 If $N=\sqrt{1985 \cdot 1985 \cdots \cdots \cdot 1985-7^{n+1}}$, then $N$ must be
(A) an irrational number.
(B) a positive integer whose last digit is 1.
(C) a number whose first digit is 5.
(D) none of the above.
(China Beijing High School Mathematics Competition, 1985) | "[\"D\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108500, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118419"}] | {
"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
} |
[
"273"
] | [
"skywork"
] | 240d962f2ea1af76fda8a010cf00b4ceb546b07c2cbf41f930f12000e1391246 | [
{
"content": "Let $x$ and $y$ be two distinct positive real numbers. We define three sequences $(A_n),$ $(G_n),$ and $(H_n)$ as follows. First, $A_1,$ $G_1,$ and $H_1$ are the arithmetic mean, geometric mean, and harmonic mean of $x$ and $y,$ respectively. Then for $n \\ge 2,$ $A_n,$ $G_n,$ $H_n$ are the ari... | Let $x$ and $y$ be two distinct positive real numbers. We define three sequences $(A_n),$ $(G_n),$ and $(H_n)$ as follows. First, $A_1,$ $G_1,$ and $H_1$ are the arithmetic mean, geometric mean, and harmonic mean of $x$ and $y,$ respectively. Then for $n \ge 2,$ $A_n,$ $G_n,$ $H_n$ are the arithmetic mean, geometric... | "[\"273\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108496, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118420"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt[4]{20}"
] | [
"skywork"
] | fb6ce5846f912b986158accfb02bd339789e6ba615e0e882ce43341f8b874884 | [
{
"content": "Three, (50 points) Find the smallest real number $\\lambda$, such that for any positive integer $n$, we have $(n,[n \\sqrt{5}])<\\lambda \\sqrt{n}$, where $(a, b)$ denotes the greatest common divisor of the positive integers $a$ and $b$, and $[x]$ denotes the greatest integer not exceeding the rea... | Three, (50 points) Find the smallest real number $\lambda$, such that for any positive integer $n$, we have $(n,[n \sqrt{5}])<\lambda \sqrt{n}$, where $(a, b)$ denotes the greatest common divisor of the positive integers $a$ and $b$, and $[x]$ denotes the greatest integer not exceeding the real number $x$.
将上面的文本翻译成英文... | "[\"\\\\sqrt[4]{20}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108406, "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:118421"}] | {
"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
} |
[
"54"
] | [
"skywork"
] | 167b08781098275d2b157568261f8a3352364bde6431fb62a685e79cf9f5ed7c | [
{
"content": "A2. Polona wants to draw three lines that intersect at the same point (see figure), such that the angles between them satisfy $\\beta=2 \\alpha$ and $\\alpha=3 \\gamma$. How many degrees must the angle $\\alpha$ be?\n(A) 18\n(B) 36\n(C) 50\n(D) 54\n(E) 60",
"role": "user"
}
] | A2. Polona wants to draw three lines that intersect at the same point (see figure), such that the angles between them satisfy $\beta=2 \alpha$ and $\alpha=3 \gamma$. How many degrees must the angle $\alpha$ be?
(A) 18
(B) 36
(C) 50
(D) 54
(E) 60 | "[\"54\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108512, "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:118422"}] | {
"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
} |
[
"2016"
] | [
"skywork"
] | 5dbb4fe05f6168df81d4f9f50e40dc6a49ad9fdf1fa5ad31dd324a2edcb04398 | [
{
"content": "6. (15 points) For a natural number $N$, if at least six numbers in the nine natural numbers from $1 \\sim 9$ can be factors of $N$, then $N$ is called a “Six-Union Number”. Among the natural numbers greater than 2000, the smallest “Six-Union Number” is $\\qquad$",
"role": "user"
}
] | 6. (15 points) For a natural number $N$, if at least six numbers in the nine natural numbers from $1 \sim 9$ can be factors of $N$, then $N$ is called a “Six-Union Number”. Among the natural numbers greater than 2000, the smallest “Six-Union Number” is $\qquad$ | "[\"2016\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108505, "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:118423"}] | {
"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
} |
[
"4462"
] | [
"skywork"
] | a95e1ead156fc8cc0d6bc21636da75680bea0209ac7b2d04be68446fe76d3e7b | [
{
"content": "18. (6 points) Given the four-digit number $\\overline{\\mathrm{ABCD}}$, the conclusions of three people, Jia, Yi, and Bing, are as follows:\n\nJia: “The unit digit is half of the hundred digit”;\nYi: “The tens digit is 1.5 times the hundred digit”;\nBing: “The average of the four digits is 4”.\nA... | 18. (6 points) Given the four-digit number $\overline{\mathrm{ABCD}}$, the conclusions of three people, Jia, Yi, and Bing, are as follows:
Jia: “The unit digit is half of the hundred digit”;
Yi: “The tens digit is 1.5 times the hundred digit”;
Bing: “The average of the four digits is 4”.
According to the above informa... | "[\"4462\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108492, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118424"}] | {
"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{a^2}{a - b}"
] | [
"skywork"
] | 05594d681d29746557bb350bff676aa71b92855be28a88d50d5f1772ab6c8dec | [
{
"content": "Given distinct straight lines $ OA$ and $ OB$. From a point in $ OA$ a perpendicular is drawn to $ OB$; from the foot of this perpendicular a line is drawn perpendicular to $ OA$. From the foot of this second perpendicular a line is drawn perpendicular to $ OB$; and so on indefinitely. The leng... | Given distinct straight lines $ OA$ and $ OB$. From a point in $ OA$ a perpendicular is drawn to $ OB$; from the foot of this perpendicular a line is drawn perpendicular to $ OA$. From the foot of this second perpendicular a line is drawn perpendicular to $ OB$; and so on indefinitely. The lengths of the first and s... | "[\"\\\\frac{a^2}{a - b}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108510, "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:118425"}] | {
"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
} |
[
"4913"
] | [
"skywork"
] | cd8477675952ae7044cede0c3fc1e66f57ce5f3c727a4dd08c1f4897f4f68d82 | [
{
"content": "2. Determine the four-digit number $\\overline{x y z t}$ whose sum of digits is 17, if all digits are different and satisfy the equations\n\n$$\n2 x=y-z \\quad \\text { and } \\quad y=t^{2}\n$$",
"role": "user"
}
] | 2. Determine the four-digit number $\overline{x y z t}$ whose sum of digits is 17, if all digits are different and satisfy the equations
$$
2 x=y-z \quad \text { and } \quad y=t^{2}
$$ | "[\"4913\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108497, "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:118426"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"42"
] | [
"skywork"
] | c412211166b6064e91aabd9d386a2cbc2c92e72956190603eb57e369af930924 | [
{
"content": "If real numbers \\(x\\) and \\(y\\) satisfy \\(x^2 + y^2 = 20\\), what is the maximum value of \\(xy + 8x + y\\)?",
"role": "user"
}
] | If real numbers \(x\) and \(y\) satisfy \(x^2 + y^2 = 20\), what is the maximum value of \(xy + 8x + y\)? | "[\"42\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108498, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118427"}] | {
"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"
] | fec3ab3ce0d337eb07e2d010cd0e6572fcebbc1559b5db1e40c6f7a402272c0e | [
{
"content": "5. Given distinct complex numbers $m, n$ satisfying $m n \\neq 0$, the set $\\left\\{m^{2}, n^{2}\\right\\}=\\{m, n\\}$, then $m+n=$\n\n untranslated portion:\n将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。 \n\nNote: The last sentence is a note about the translation request and is not part of the text to be t... | 5. Given distinct complex numbers $m, n$ satisfying $m n \neq 0$, the set $\left\{m^{2}, n^{2}\right\}=\{m, n\}$, then $m+n=$
untranslated portion:
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。
Note: The last sentence is a note about the translation request and is not part of the text to be translated. Here is the translation... | "[\"-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108501, "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:118428"}] | {
"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
} |
[
"38"
] | [
"skywork"
] | 9cbfe5770cdea41f90329f08a988b6c9bd3a697697f681eb8803fcaed931199e | [
{
"content": "Yatsenko I.v.\n\nFrom the volcano station to the summit of Stromboli, it takes 4 hours to walk along the road, and then another 4 hours along the path. At the summit, there are two craters. The first crater erupts for 1 hour, then remains silent for 17 hours, then erupts again for 1 hour, and so o... | Yatsenko I.v.
From the volcano station to the summit of Stromboli, it takes 4 hours to walk along the road, and then another 4 hours along the path. At the summit, there are two craters. The first crater erupts for 1 hour, then remains silent for 17 hours, then erupts again for 1 hour, and so on. The second crater eru... | "[\"38\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108493, "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:118429"}] | {
"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
} |
[
"20"
] | [
"skywork"
] | f93c7d3929edc274458870938848f4d79ed5832cc593b2c0cdb263d14af92075 | [
{
"content": "For positive integers $a$ and $b$, let $M(a, b)=\\frac{\\operatorname{lcm}(a, b)}{\\operatorname{gcd}(a, b)}$, and for each positive integer $n \\geq 2$, define $$x_{n}=M(1, M(2, M(3, \\ldots, M(n-2, M(n-1, n)) \\ldots)))$$ Compute the number of positive integers $n$ such that $2 \\leq n \\leq 202... | For positive integers $a$ and $b$, let $M(a, b)=\frac{\operatorname{lcm}(a, b)}{\operatorname{gcd}(a, b)}$, and for each positive integer $n \geq 2$, define $$x_{n}=M(1, M(2, M(3, \ldots, M(n-2, M(n-1, n)) \ldots)))$$ Compute the number of positive integers $n$ such that $2 \leq n \leq 2021$ and $5 x_{n}^{2}+5 x_{n+1}^... | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108504, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118430"}] | {
"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
} |
[
"e^{nx} \\sum_{i=0}^{n-1} n^i"
] | [
"skywork"
] | 74756d0f4faf02d1bf42061f6b7c0d7f5cac1d3c5efde30597542efe35b369ed | [
{
"content": "Find the $n$-th derivative with respect to $x$ of\n$$\\int_{0}^{x} \\left(1+\\frac{x-t}{1!}+\\frac{(x-t)^{2}}{2!}+\\ldots+\\frac{(x-t)^{n-1}}{(n-1)!}\\right)e^{nt} dt.$$",
"role": "user"
}
] | Find the $n$-th derivative with respect to $x$ of
$$\int_{0}^{x} \left(1+\frac{x-t}{1!}+\frac{(x-t)^{2}}{2!}+\ldots+\frac{(x-t)^{n-1}}{(n-1)!}\right)e^{nt} dt.$$ | "[\" e^{nx} \\\\sum_{i=0}^{n-1} n^i \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108506, "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:118431"}] | {
"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
} |
[
"57.14\\%"
] | [
"skywork"
] | b8921affc5fccfc2f800ff8f0e54d24aca5a810deb90e86846bccf63a9d96fcf | [
{
"content": "A rectangular box has interior dimensions 8-inches by 7-inches by 12-inches. The box is filled with as many solid 4-inch cubes as possible, with all of the cubes entirely inside the rectangular box. What percent of the volume of the box is taken up by the cubes?",
"role": "user"
}
] | A rectangular box has interior dimensions 8-inches by 7-inches by 12-inches. The box is filled with as many solid 4-inch cubes as possible, with all of the cubes entirely inside the rectangular box. What percent of the volume of the box is taken up by the cubes? | "[\"57.14\\\\%\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108517, "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:118432"}] | {
"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
} |
[
"36"
] | [
"skywork"
] | 24aeec2790dc0e88f0e8a1f4efb56f360d38f05eb62614f729bd53c25226dede | [
{
"content": "You can arrange 15 balls in the shape of a triangle, but you cannot arrange 96 balls in the shape of a square (missing one ball). Out of how many balls, not exceeding 50, can you arrange them both in the shape of a triangle and a square?",
"role": "user"
}
] | You can arrange 15 balls in the shape of a triangle, but you cannot arrange 96 balls in the shape of a square (missing one ball). Out of how many balls, not exceeding 50, can you arrange them both in the shape of a triangle and a square? | "[\"36\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108502, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118433"}] | {
"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
} |
[
"1003"
] | [
"skywork"
] | 0c963fef1a242e59191b84525a434f63012d4714cd55a8a36aafc1b99a561df0 | [
{
"content": "Let \\( P \\) be a regular 2006-sided polygon. A diagonal of \\( P \\) is called a \"good edge\" if its endpoints divide the polygon into two parts, each containing an odd number of the polygon's sides. Each side of \\( P \\) is also considered a \"good edge\".\n\nGiven that 2003 non-intersecting ... | Let \( P \) be a regular 2006-sided polygon. A diagonal of \( P \) is called a "good edge" if its endpoints divide the polygon into two parts, each containing an odd number of the polygon's sides. Each side of \( P \) is also considered a "good edge".
Given that 2003 non-intersecting diagonals divide \( P \) into seve... | "[\"1003\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108491, "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:118434"}] | {
"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
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.