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 |
|---|---|---|---|---|---|---|---|---|
[
"n \\geq 512"
] | [
"skywork"
] | e8b6e8f1801d07a92fc39f28afc9b481448e1996208e7d69d4590ca4c6ab8daa | [
{
"content": "In every cell of a table with $n$ rows and ten columns, a digit is written. It is known that for every row $A$ and any two columns, you can always find a row that has different digits from $A$ only when it intersects with two columns. Prove that $n\\geq512$.",
"role": "user"
}
] | In every cell of a table with $n$ rows and ten columns, a digit is written. It is known that for every row $A$ and any two columns, you can always find a row that has different digits from $A$ only when it intersects with two columns. Prove that $n\geq512$. | "[\"n \\\\geq 512\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2468, "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:16428"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1487"
] | [
"skywork"
] | e2dd3f9a7115c1653b3da871b2b36d0d272db391e56ace436c115a03f7af0647 | [
{
"content": "How many positive integers less than 1998 are relatively prime to 1547? (Two integers are relatively prime if they have no common factors besides 1.)",
"role": "user"
}
] | How many positive integers less than 1998 are relatively prime to 1547? (Two integers are relatively prime if they have no common factors besides 1.) | "[\"1487\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2484, "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:16429"}, {"dataset": "skywork", "extra_inf... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"skywork"
] | 7c069cdee490459b38d9f2459226f55ceffbb174e08bcba1e46e47ddf2ab8cd6 | [
{
"content": "13. [9] How many functions $f:\\{0,1\\}^{3} \\rightarrow\\{0,1\\}$ satisfy the property that, for all ordered triples $\\left(a_{1}, a_{2}, a_{3}\\right)$ and $\\left(b_{1}, b_{2}, b_{3}\\right)$ such that $a_{i} \\geq b_{i}$ for all $i, f\\left(a_{1}, a_{2}, a_{3}\\right) \\geq f\\left(b_{1}, b_{... | 13. [9] How many functions $f:\{0,1\}^{3} \rightarrow\{0,1\}$ satisfy the property that, for all ordered triples $\left(a_{1}, a_{2}, a_{3}\right)$ and $\left(b_{1}, b_{2}, b_{3}\right)$ such that $a_{i} \geq b_{i}$ for all $i, f\left(a_{1}, a_{2}, a_{3}\right) \geq f\left(b_{1}, b_{2}, b_{3}\right)$ ? | "[\"20\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2454, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16430"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{7}{4}"
] | [
"skywork"
] | de3fb4a29e58b8f6c381f5f28be972d829f597de3f1bdc3535b4285b1e17ca6d | [
{
"content": "Example 9 If the equation $\\left(x^{2}-1\\right)\\left(x^{2}-4\\right)=k$ has 4 non-zero real roots, and the 4 points corresponding to them on the number line are equally spaced, then $k=$ $\\qquad$",
"role": "user"
}
] | Example 9 If the equation $\left(x^{2}-1\right)\left(x^{2}-4\right)=k$ has 4 non-zero real roots, and the 4 points corresponding to them on the number line are equally spaced, then $k=$ $\qquad$ | "[\"\\\\frac{7}{4}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2474, "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:16431"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"10^7"
] | [
"skywork"
] | facb339fff6242d5d7f40b2fc72e31ebbaca48ce72dd7596889d4ab3dd80fa23 | [
{
"content": "3. Given that $x$ and $y$ are real numbers greater than 10, the characteristic of $\\lg x$ is $a$, and the mantissa is $b$; the characteristic of $\\lg y$ is $c$, and the mantissa is $d$, and $|1-a|+\\sqrt{c-4}=1$, $b+d=1$, then $x y=$ $\\qquad$",
"role": "user"
}
] | 3. Given that $x$ and $y$ are real numbers greater than 10, the characteristic of $\lg x$ is $a$, and the mantissa is $b$; the characteristic of $\lg y$ is $c$, and the mantissa is $d$, and $|1-a|+\sqrt{c-4}=1$, $b+d=1$, then $x y=$ $\qquad$ | "[\"10^7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2456, "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:16432"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"k"
] | [
"skywork"
] | 9ff0d281e9f47168bd9ef2eaaf1fa7ff06b62ec658511a3b8a3fdeab4fecdd04 | [
{
"content": "A and B plays the following game: they choose randomly $k$ integers from $\\{1,2,\\dots,100\\}$; if their sum is even, A wins, else B wins. For what values of $k$ does A and B have the same chance of winning?",
"role": "user"
}
] | A and B plays the following game: they choose randomly $k$ integers from $\{1,2,\dots,100\}$; if their sum is even, A wins, else B wins. For what values of $k$ does A and B have the same chance of winning? | "[\" k \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2472, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16433"}] | {
"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
} |
[
"9999"
] | [
"skywork"
] | af341771fe84a18e90ad17e5531705faad2fff2c34b59db4986224a8bdda45b4 | [
{
"content": "For each positive integer $n$, let $s(n)$ be the sum of the digits of $n$. Find the smallest positive integer $k$ such that\n\\[s(k) = s(2k) = s(3k) = \\cdots = s(2013k) = s(2014k).\\]",
"role": "user"
}
] | For each positive integer $n$, let $s(n)$ be the sum of the digits of $n$. Find the smallest positive integer $k$ such that
\[s(k) = s(2k) = s(3k) = \cdots = s(2013k) = s(2014k).\] | "[\"9999\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2478, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:16434"}] | {
"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"
] | 2a0e185e58d4220e950ce6c4257df0de917ed79195bcd1cfce76a7d6f50e526d | [
{
"content": "30.2. Given that $x+2$ and $x-3$ are factors of $p(x)=a x^{3}+a x^{2}+b x+12$, what is the remainder when $p(x)$ is divided by $x-1$ ?",
"role": "user"
}
] | 30.2. Given that $x+2$ and $x-3$ are factors of $p(x)=a x^{3}+a x^{2}+b x+12$, what is the remainder when $p(x)$ is divided by $x-1$ ? | "[\"18\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2449, "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:16435"}] | {
"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
} |
[
"84"
] | [
"skywork"
] | 6c3a089e885e553cebf0237c247605e283366ad808ff369ada0be406444a4f54 | [
{
"content": "Let $x_{1}=y_{1}=x_{2}=y_{2}=1$, then for $n \\geq 3$ let $x_{n}=x_{n-1} y_{n-2}+x_{n-2} y_{n-1}$ and $y_{n}=y_{n-1} y_{n-2}- x_{n-1} x_{n-2}$. What are the last two digits of $\\left|x_{2012}\\right|$ ?",
"role": "user"
}
] | Let $x_{1}=y_{1}=x_{2}=y_{2}=1$, then for $n \geq 3$ let $x_{n}=x_{n-1} y_{n-2}+x_{n-2} y_{n-1}$ and $y_{n}=y_{n-1} y_{n-2}- x_{n-1} x_{n-2}$. What are the last two digits of $\left|x_{2012}\right|$ ? | "[\"84\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2482, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16436"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"24"
] | [
"skywork"
] | b9a1a036ca85ef49e773d263741a792c7d9ada006c478db05068a0d822f0b42f | [
{
"content": "A circle with center \\( Q \\) and radius 2 rolls around the inside of a right triangle \\( DEF \\) with side lengths 9, 12, and 15, always remaining tangent to at least one side of the triangle. When \\( Q \\) first returns to its original position, through what distance has \\( Q \\) traveled?",... | A circle with center \( Q \) and radius 2 rolls around the inside of a right triangle \( DEF \) with side lengths 9, 12, and 15, always remaining tangent to at least one side of the triangle. When \( Q \) first returns to its original position, through what distance has \( Q \) traveled? | "[\"24\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2479, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16437"}] | {
"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\\sqrt{10}"
] | [
"skywork"
] | d25a6b82469adadfbef6ddc4f987e8984c69adcaed44edd0e36e371dbb7c4fed | [
{
"content": "In triangle \\( \\triangle ABC \\), \\( \\angle BAC = 90^\\circ \\), \\( AC = AB = 4 \\), and point \\( D \\) is inside \\( \\triangle ABC \\) such that \\( AD = \\sqrt{2} \\). Find the minimum value of \\( BD + CD \\).",
"role": "user"
}
] | In triangle \( \triangle ABC \), \( \angle BAC = 90^\circ \), \( AC = AB = 4 \), and point \( D \) is inside \( \triangle ABC \) such that \( AD = \sqrt{2} \). Find the minimum value of \( BD + CD \). | "[\"2\\\\sqrt{10}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2473, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16438"}] | {
"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
} |
[
"T'"
] | [
"skywork"
] | c65f19d64f532a49d6d555d3a3083d1e28cee388c5fda2b1b8ab896d1e463889 | [
{
"content": "In the plane let $\\,C\\,$ be a circle, $\\,L\\,$ a line tangent to the circle $\\,C,\\,$ and $\\,M\\,$ a point on $\\,L$. Find the locus of all points $\\,P\\,$ with the following property: there exists two points $\\,Q,R\\,$ on $\\,L\\,$ such that $\\,M\\,$ is the midpoint of $\\,QR\\,$ and $\\,... | In the plane let $\,C\,$ be a circle, $\,L\,$ a line tangent to the circle $\,C,\,$ and $\,M\,$ a point on $\,L$. Find the locus of all points $\,P\,$ with the following property: there exists two points $\,Q,R\,$ on $\,L\,$ such that $\,M\,$ is the midpoint of $\,QR\,$ and $\,C\,$ is the inscribed circle of triangle $... | "[\" T' \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2469, "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:16439"}] | {
"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"
] | 89d1241589799be386ff95a11ac73950a4692db3388f046b45e81d1a5dcbce8c | [
{
"content": "1.020. $\\left(\\left(1 \\frac{1}{7}-\\frac{23}{49}\\right): \\frac{22}{147}-\\left(0.6: 3 \\frac{3}{4}\\right) \\cdot 2 \\frac{1}{2}+3.75: 1 \\frac{1}{2}\\right): 2.2$.",
"role": "user"
}
] | 1.020. $\left(\left(1 \frac{1}{7}-\frac{23}{49}\right): \frac{22}{147}-\left(0.6: 3 \frac{3}{4}\right) \cdot 2 \frac{1}{2}+3.75: 1 \frac{1}{2}\right): 2.2$. | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2492, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16440"}] | {
"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
} |
[
"72^{\\circ}"
] | [
"skywork"
] | 4d7d423421f60662a613346565ef4260fd9ff714087c8793ca998c77b4eeaf00 | [
{
"content": "An icosahedron is a regular polyhedron with twenty faces, all of which are equilateral triangles. If an icosahedron is rotated by $\\theta$ degrees around an axis that passes through two opposite vertices so that it occupies exactly the same region of space as before, what is the smallest possible... | An icosahedron is a regular polyhedron with twenty faces, all of which are equilateral triangles. If an icosahedron is rotated by $\theta$ degrees around an axis that passes through two opposite vertices so that it occupies exactly the same region of space as before, what is the smallest possible positive value of $\th... | "[\"72^{\\\\circ}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2481, "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:16442"}] | {
"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
} |
[
"7"
] | [
"skywork"
] | 3241e3deb013c025ec6eba12deed30f47d0ea017250747204c6165f9a24441bb | [
{
"content": "Let $\nf(n) =\n\\begin{cases}\nn^2+1 & \\text{if }n\\text{ is odd} \\\\\n\\dfrac{n}{2} & \\text{if }n\\text{ is even}\n\\end{cases}.\n$\n\nFor how many integers $n$ from 1 to 100, inclusive, does $f ( f (\\dotsb f (n) \\dotsb )) = 1$ for some number of applications of $f$?",
"role": "user"
}... | Let $
f(n) =
\begin{cases}
n^2+1 & \text{if }n\text{ is odd} \\
\dfrac{n}{2} & \text{if }n\text{ is even}
\end{cases}.
$
For how many integers $n$ from 1 to 100, inclusive, does $f ( f (\dotsb f (n) \dotsb )) = 1$ for some number of applications of $f$? | "[\"7\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2491, "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:16443"}] | {
"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;1;1),(7;-3;-1)"
] | [
"skywork"
] | 538b3d575f2303d0049ad72063ebb806ecc5e710e7b611455b4935cdfc90cd37 | [
{
"content": "6.219. $\\left\\{\\begin{array}{l}x+y+z=3, \\\\ x+2 y-z=2, \\\\ x+y z+z x=3 .\\end{array}\\right.$",
"role": "user"
}
] | 6.219. $\left\{\begin{array}{l}x+y+z=3, \\ x+2 y-z=2, \\ x+y z+z x=3 .\end{array}\right.$ | "[\"(1;1;1),(7;-3;-1)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2495, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "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:16444"}] | {
"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
} |
[
"18!"
] | [
"skywork"
] | 6da253cb501a00b8bd53f7144d977f99d970c22891e0f639a773192d8c78915b | [
{
"content": "Rubanov I.S.\n\nThe number 1 is written on the board. If the number $a$ is written on the board, it can be replaced by any number of the form $a+d$, where $d$ is coprime with $a$ and $10 \\leq d \\leq 20$.\n\nIs it possible to obtain the number $18!$ on the board after several such operations?",
... | Rubanov I.S.
The number 1 is written on the board. If the number $a$ is written on the board, it can be replaced by any number of the form $a+d$, where $d$ is coprime with $a$ and $10 \leq d \leq 20$.
Is it possible to obtain the number $18!$ on the board after several such operations? | "[\"18!\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2483, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16445"}] | {
"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
} |
[
"1503"
] | [
"skywork"
] | 45e97e18087fb624d486a720fb6f8325655030cc4b3df2aeffc5ed90f5505211 | [
{
"content": "7. Let $[x]$ denote the greatest integer not exceeding the real number $x$. Find the number of elements in the set $\\left\\{n \\left\\lvert\\, n=\\left[\\frac{k^{2}}{2005}\\right]\\right., 1 \\leqslant k \\leqslant 2004, k \\in \\mathbf{N}\\right\\}$.",
"role": "user"
}
] | 7. Let $[x]$ denote the greatest integer not exceeding the real number $x$. Find the number of elements in the set $\left\{n \left\lvert\, n=\left[\frac{k^{2}}{2005}\right]\right., 1 \leqslant k \leqslant 2004, k \in \mathbf{N}\right\}$. | "[\"1503\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2487, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:16446"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"300"
] | [
"skywork"
] | 406d7796d95498ca9b90a46a884f349a5376b57525df37ad10b9e005fa2bb294 | [
{
"content": "Compute $156 + 44 + 26 + 74$.",
"role": "user"
}
] | Compute $156 + 44 + 26 + 74$. | "[\"300\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2516, "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:16447"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1.9"
] | [
"skywork"
] | 6d61822e03bf858b94c2c3149b667484c3441d555bab1faa29157c3c87bb33ce | [
{
"content": "A quiz has three questions, with each question worth one mark. If $20 \\%$ of the students got 0 questions correct, $5 \\%$ got 1 question correct, $40 \\%$ got 2 questions correct, and $35 \\%$ got all 3 questions correct, then the overall class mean (average) mark was\n(A) 1.8\n(B) 1.9\n(C) 2\n(... | A quiz has three questions, with each question worth one mark. If $20 \%$ of the students got 0 questions correct, $5 \%$ got 1 question correct, $40 \%$ got 2 questions correct, and $35 \%$ got all 3 questions correct, then the overall class mean (average) mark was
(A) 1.8
(B) 1.9
(C) 2
(D) 2.1
(E) 2.35 | "[\"1.9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2498, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16448"}] | {
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"reference_components": 1,
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} |
[
"\\textbf{(D)}"
] | [
"skywork"
] | f98c70dba46992a5f36a3a3e1d0fdc20e50b2eaeb5334451d70073d4c19c8e46 | [
{
"content": "Let $f(x) = \\sin{x} + 2\\cos{x} + 3\\tan{x}$, using radian measure for the variable $x$. In what interval does the smallest positive value of $x$ for which $f(x) = 0$ lie?\n$\\textbf{(A)}\\ (0,1) \\qquad \\textbf{(B)}\\ (1, 2) \\qquad\\textbf{(C)}\\ (2, 3) \\qquad\\textbf{(D)}\\ (3, 4) \\qquad\\... | Let $f(x) = \sin{x} + 2\cos{x} + 3\tan{x}$, using radian measure for the variable $x$. In what interval does the smallest positive value of $x$ for which $f(x) = 0$ lie?
$\textbf{(A)}\ (0,1) \qquad \textbf{(B)}\ (1, 2) \qquad\textbf{(C)}\ (2, 3) \qquad\textbf{(D)}\ (3, 4) \qquad\textbf{(E)}\ (4,5)$ | "[\"\\\\textbf{(D)}\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 2494, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16449"}] | {
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} |
[
"x\\in(0;\\frac{1}{2})\\cup(1;2)\\cup(3;6)"
] | [
"skywork"
] | 912dd3c922a9127e40f515c23e8ef793fd0a4d4ef3ca8b92fd6225db643ba0df | [
{
"content": "9.182. $\\log _{2 x}\\left(x^{2}-5 x+6\\right)<1$.",
"role": "user"
}
] | 9.182. $\log _{2 x}\left(x^{2}-5 x+6\right)<1$. | "[\"x\\\\in(0;\\\\frac{1}{2})\\\\cup(1;2)\\\\cup(3;6)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2489, "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:16450"}] | {
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"reference_components": 1,
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} |
[
"\\frac{1}{4}"
] | [
"skywork"
] | d33e913b2a222900d2b006819a920aafc3b96dc925d4c40602bde411802e5b4e | [
{
"content": "Construct a cylindrical iron barrel with a volume of $V$. The lid of the barrel is made of aluminum alloy, and the price of aluminum alloy per unit area is three times that of iron. To minimize the cost of this container, the ratio of the bottom radius $r$ of the iron barrel to its height $h$ shou... | Construct a cylindrical iron barrel with a volume of $V$. The lid of the barrel is made of aluminum alloy, and the price of aluminum alloy per unit area is three times that of iron. To minimize the cost of this container, the ratio of the bottom radius $r$ of the iron barrel to its height $h$ should be _______. | "[\"\\\\frac{1}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2477, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16451"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{n}{2}"
] | [
"skywork"
] | 50c131fd1645c99003a6c4a229d4bf92d5c915444ba8e09bb3bfe8e66bd84cd6 | [
{
"content": "Let $(v_1, ..., v_{2^n})$ be the vertices of an $n$-dimensional hypercube. Label each vertex $v_i$ with a real number $x_i$. Label each edge of the hypercube with the product of labels of the two vertices it connects. Let $S$ be the sum of the labels of all the edges. Over all possible labelings, ... | Let $(v_1, ..., v_{2^n})$ be the vertices of an $n$-dimensional hypercube. Label each vertex $v_i$ with a real number $x_i$. Label each edge of the hypercube with the product of labels of the two vertices it connects. Let $S$ be the sum of the labels of all the edges. Over all possible labelings, find the minimum possi... | "[\"\\\\frac{n}{2}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2485, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16452"}] | {
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} |
[
"14"
] | [
"skywork"
] | 02de2fe7017b03d08264eabaa2521428dc4fecd187eaa8a84fb90a2b1e26e490 | [
{
"content": "How many one-fourths are there in $\\frac{7}{2}$?",
"role": "user"
}
] | How many one-fourths are there in $\frac{7}{2}$? | "[\"14\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2517, "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:16453"}] | {
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} |
[
"84\\mathrm{~}^{2}"
] | [
"skywork"
] | 635aa2dc8f55823f3a622475764aa05c41b60f3d9e0f7a5215411146f86023f6 | [
{
"content": "10.158. Three circles with radii $R_{1}=6 \\mathrm{~cm}, R_{2}=7 \\mathrm{~cm}, R_{3}=8 \\mathrm{~cm}$ touch each other pairwise. Determine the area of the triangle whose vertices coincide with the centers of these circles.",
"role": "user"
}
] | 10.158. Three circles with radii $R_{1}=6 \mathrm{~cm}, R_{2}=7 \mathrm{~cm}, R_{3}=8 \mathrm{~cm}$ touch each other pairwise. Determine the area of the triangle whose vertices coincide with the centers of these circles. | "[\"84\\\\mathrm{~}^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2501, "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:16454"}] | {
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[
"\\frac{e}{2}"
] | [
"skywork"
] | cb24f34671c5ca20aee8055449de1429004341591a2a715f606197e9d2d70d7a | [
{
"content": "A function is given by\n$$\nf(x)=\\ln (a x+b)+x^{2} \\quad (a \\neq 0).\n$$\n(1) If the tangent line to the curve $y=f(x)$ at the point $(1, f(1))$ is $y=x$, find the values of $a$ and $b$.\n\n(2) If $f(x) \\leqslant x^{2}+x$ always holds, find the maximum value of $ab$.",
"role": "user"
}
] | A function is given by
$$
f(x)=\ln (a x+b)+x^{2} \quad (a \neq 0).
$$
(1) If the tangent line to the curve $y=f(x)$ at the point $(1, f(1))$ is $y=x$, find the values of $a$ and $b$.
(2) If $f(x) \leqslant x^{2}+x$ always holds, find the maximum value of $ab$. | "[\"\\\\frac{e}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2486, "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:16455"}] | {
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} |
[
"43"
] | [
"skywork"
] | 8258f2c20d1e497e7da96d0e03c0e1fa87f6d9dedab387734e966ffd14cdcc9f | [
{
"content": "A cuckoo clock is on the wall. At the beginning of every hour, the cuckoo makes a number of \"cuckoo\" sounds equal to the hour displayed by the hour hand (for example, at 19:00 the cuckoo makes 7 sounds). One morning, Maxim approached the clock when it showed 9:05. He started turning the minute h... | A cuckoo clock is on the wall. At the beginning of every hour, the cuckoo makes a number of "cuckoo" sounds equal to the hour displayed by the hour hand (for example, at 19:00 the cuckoo makes 7 sounds). One morning, Maxim approached the clock when it showed 9:05. He started turning the minute hand until he moved the t... | "[\"43\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2497, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16456"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{3}"
] | [
"skywork"
] | 480f506bc61c5973eb73169309e23b7dfa5d405565d1a6eaa7164107bb337c3b | [
{
"content": "(1) The left and right directrices $l_{1} 、 l_{2}$ of the hyperbola $\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1$ trisect the line segment $F_{1} F_{2}$ (where $F_{1} 、 F_{2}$ are the left and right foci of the hyperbola), then the eccentricity $e$ of the hyperbola is ( ).\n(A) $\\frac{\\sqrt{6}}{... | (1) The left and right directrices $l_{1} 、 l_{2}$ of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ trisect the line segment $F_{1} F_{2}$ (where $F_{1} 、 F_{2}$ are the left and right foci of the hyperbola), then the eccentricity $e$ of the hyperbola is ( ).
(A) $\frac{\sqrt{6}}{2}$
(B) $\sqrt{3}$
(C) $\fr... | "[\"\\\\sqrt{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2493, "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:16457"}] | {
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} |
[
"AD=17,BK=\\frac{240}{17},P_{EBM}=\\frac{552}{17}"
] | [
"skywork"
] | f623237642b7cef25dee0f0957eb91a38c7ef17d4b33867eca6f65d4e47f6a3f | [
{
"content": "5. Given a parallelogram $A B C D$. A circle $\\Omega$ with a diameter of 17 is circumscribed around triangle $A B M$, where $M$ is the point of intersection of the diagonals of the given parallelogram. $\\Omega$ intersects the ray $C B$ and the segment $A D$ again at points $E$ and $K$ respective... | 5. Given a parallelogram $A B C D$. A circle $\Omega$ with a diameter of 17 is circumscribed around triangle $A B M$, where $M$ is the point of intersection of the diagonals of the given parallelogram. $\Omega$ intersects the ray $C B$ and the segment $A D$ again at points $E$ and $K$ respectively. The length of arc $A... | "[\"AD=17,BK=\\\\frac{240}{17},P_{EBM}=\\\\frac{552}{17}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2488, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16458"}] | {
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} |
[
"67"
] | [
"skywork"
] | ab778c1028c17da4e51ab5a43c5d9bb608f44a6e9d33a6b1c1113f1a8ae6a14a | [
{
"content": "What is the largest prime $p$ that makes $\\sqrt{17p+625}$ an integer?\n\n$ \\textbf{(A)}\\ 3\n\\qquad\\textbf{(B)}\\ 67\n\\qquad\\textbf{(C)}\\ 101\n\\qquad\\textbf{(D)}\\ 151\n\\qquad\\textbf{(E)}\\ 211\n$",
"role": "user"
}
] | What is the largest prime $p$ that makes $\sqrt{17p+625}$ an integer?
$ \textbf{(A)}\ 3
\qquad\textbf{(B)}\ 67
\qquad\textbf{(C)}\ 101
\qquad\textbf{(D)}\ 151
\qquad\textbf{(E)}\ 211
$ | "[\"67\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2504, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16459"}] | {
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} |
[
"15625=125^{2}"
] | [
"skywork"
] | 771e5511927ff4e92efed5aec67d0a566b850b38be7fed233477bfeaabc66174 | [
{
"content": "625. A typesetter spilled part of the set - a five-digit number that is a perfect square, written with the digits $1,2,5,5$ and 6. Find all such five-digit numbers.",
"role": "user"
}
] | 625. A typesetter spilled part of the set - a five-digit number that is a perfect square, written with the digits $1,2,5,5$ and 6. Find all such five-digit numbers. | "[\"15625=125^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2506, "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:16460"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\sqrt{145}}{9}"
] | [
"skywork"
] | 4967d89f88f087b3b55cd866bc1e18953aeb5834555f218b507333b43ec4c4b8 | [
{
"content": "Consider triangle $A B C$ where $B C=7, C A=8$, and $A B=9$. $D$ and $E$ are the midpoints of $B C$ and $C A$, respectively, and $A D$ and $B E$ meet at $G$. The reflection of $G$ across $D$ is $G^{\\prime}$, and $G^{\\prime} E$ meets $C G$ at $P$. Find the length $P G$.",
"role": "user"
}
] | Consider triangle $A B C$ where $B C=7, C A=8$, and $A B=9$. $D$ and $E$ are the midpoints of $B C$ and $C A$, respectively, and $A D$ and $B E$ meet at $G$. The reflection of $G$ across $D$ is $G^{\prime}$, and $G^{\prime} E$ meets $C G$ at $P$. Find the length $P G$. | "[\"\\\\frac{\\\\sqrt{145}}{9}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2496, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16461"}] | {
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} |
[
"12"
] | [
"skywork"
] | 8d5ced9ac49b4c6db5792bcbeb15fdca9ca5178b8d2dfadd2304e7849547fc06 | [
{
"content": "Find the positive difference between the two solutions to the equation $\\displaystyle\\sqrt[3]{4 - \\frac{x^2}{3}} = -2$.",
"role": "user"
}
] | Find the positive difference between the two solutions to the equation $\displaystyle\sqrt[3]{4 - \frac{x^2}{3}} = -2$. | "[\"12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2536, "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:16463"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\binom{2n}{n}^{2}"
] | [
"skywork"
] | e6967c2e68d1ed12102d9aff8a8fe024e0e29120d6efd062b35491586c02fdbf | [
{
"content": "(A domino is a $1 \\times 2$ or $2 \\times 1$ rectangle. Determine the number of ways to place $n^{2}$ dominos on a $2 n \\times 2 n$ grid so that every $2 \\times 2$ square of the grid has at least two unoccupied cells in the same row or column.)",
"role": "user"
}
] | (A domino is a $1 \times 2$ or $2 \times 1$ rectangle. Determine the number of ways to place $n^{2}$ dominos on a $2 n \times 2 n$ grid so that every $2 \times 2$ square of the grid has at least two unoccupied cells in the same row or column.) | "[\"\\\\binom{2n}{n}^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2503, "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:16464"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"80^\\circ"
] | [
"skywork"
] | 2ff500596f85846330a0398c5dcdab4042093ba2358886b38471c50111a736a0 | [
{
"content": "Suppose $ABCD$ is a convex quadrilateral satisfying $AB=BC$, $AC=BD$, $\\angle ABD = 80^\\circ$, and $\\angle CBD = 20^\\circ$. What is $\\angle BCD$ in degrees?",
"role": "user"
}
] | Suppose $ABCD$ is a convex quadrilateral satisfying $AB=BC$, $AC=BD$, $\angle ABD = 80^\circ$, and $\angle CBD = 20^\circ$. What is $\angle BCD$ in degrees? | "[\"80^\\\\circ\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2528, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:16465"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | 4d7ed25d1a37f8c2e65f469b5975abc8adb3af7eb6fdc80aafe59928559bac0e | [
{
"content": "3. The function $f(x)$ is defined on $\\mathbf{R}$ as an odd function, and $f(2)=0$. For any $x \\in \\mathbf{R}$, $f(x+4)=f(x)+f(4)$ holds, $f(2002)=$ $\\qquad$ .",
"role": "user"
}
] | 3. The function $f(x)$ is defined on $\mathbf{R}$ as an odd function, and $f(2)=0$. For any $x \in \mathbf{R}$, $f(x+4)=f(x)+f(4)$ holds, $f(2002)=$ $\qquad$ . | "[\"0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2455, "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:16467"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"3072"
] | [
"skywork"
] | f92a352449a45295b7abd58c9e5e0ece01e0147ad78ef93ba927d7398125f8d5 | [
{
"content": "A club has $4$ members from each of $4$ different schools, for a total of $16$ members. How many possible ways are there to arrange a presidency and vice-presidency meeting under the following conditions:\n\ni. The club must choose one of the $4$ schools at which to host the meeting,\n\nii. The ho... | A club has $4$ members from each of $4$ different schools, for a total of $16$ members. How many possible ways are there to arrange a presidency and vice-presidency meeting under the following conditions:
i. The club must choose one of the $4$ schools at which to host the meeting,
ii. The host school sends $3$ repres... | "[\"3072\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2511, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16468"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"23"
] | [
"skywork"
] | 9e6fc7645ac3f03f09564d5acbdcf34e1c539e9c99ea85af3a6343785d0de1e0 | [
{
"content": "44. Shown on your answer sheet is a $20 \\times 20$ grid. Place as many queens as you can so that each of them attacks at most one other queen. (A queen is a chess piece that can move any number of squares horizontally, vertically, or diagonally.) It's not very hard to get 20 queens, so you get no... | 44. Shown on your answer sheet is a $20 \times 20$ grid. Place as many queens as you can so that each of them attacks at most one other queen. (A queen is a chess piece that can move any number of squares horizontally, vertically, or diagonally.) It's not very hard to get 20 queens, so you get no points for that, but y... | "[\"23\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2505, "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:16469"}] | {
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"reference_components": 1,
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} |
[
"f(x) = x"
] | [
"skywork"
] | 3b9c6c20e9bc5867dccb02b078275c2e1994d2ff6c96c055c279e01d34797e8c | [
{
"content": "Find all functions $f : R \\to R$ satisfying the conditions:\n1. $f (x + 1) \\ge f (x) + 1$ for all $x \\in R$ \n2. $f (x y) \\ge f (x)f (y)$ for all $x, y \\in R$",
"role": "user"
}
] | Find all functions $f : R \to R$ satisfying the conditions:
1. $f (x + 1) \ge f (x) + 1$ for all $x \in R$
2. $f (x y) \ge f (x)f (y)$ for all $x, y \in R$ | "[\"f(x) = x\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2502, "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:16470"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"32"
] | [
"skywork"
] | 1f2190c16d81ce9764512b7406adac444c199cdc64eeb75b40747f05e7d90545 | [
{
"content": "Let $BE$ and $CF$ be altitudes in triangle $ABC$. If $AE = 24$, $EC = 60$, and $BF = 31$, determine $AF$.",
"role": "user"
}
] | Let $BE$ and $CF$ be altitudes in triangle $ABC$. If $AE = 24$, $EC = 60$, and $BF = 31$, determine $AF$. | "[\"32\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2509, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16471"}] | {
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"reference_components": 1,
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} |
[
"\\frac{1000}{1001}"
] | [
"skywork"
] | b988bc8dd8643d720a9f946dab654f32a14d5aaf30b59a81c321a0c3d8aae0dd | [
{
"content": "Compute \\[\\sum_{n=1}^{1000} \\frac{1}{n^2 + n}.\\]",
"role": "user"
}
] | Compute \[\sum_{n=1}^{1000} \frac{1}{n^2 + n}.\] | "[\"\\\\frac{1000}{1001}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2535, "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:16472"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"37.5"
] | [
"skywork"
] | 8e1fb3a0794e7505a89c311ff88ac19b2d57be11990a46969ea84784fb7ed2a2 | [
{
"content": "What is the area, in square units, of a trapezoid bounded by the lines $y = x$, $y = 10$, $y = 5$ and the $y$-axis? Express your answer as a decimal to the nearest tenth.",
"role": "user"
}
] | What is the area, in square units, of a trapezoid bounded by the lines $y = x$, $y = 10$, $y = 5$ and the $y$-axis? Express your answer as a decimal to the nearest tenth. | "[\"37.5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2523, "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:16473"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"346"
] | [
"skywork"
] | 1a2f977482aa0c614f1456e8babc6b3e1b7be42e79c4b12e28b7d718abbe8c97 | [
{
"content": "Suppose tetrahedron $PABC$ has volume $420$ and satisfies $AB = 13$, $BC = 14$, and $CA = 15$. The minimum possible surface area of $PABC$ can be written as $m+n\\sqrt{k}$, where $m,n,k$ are positive integers and $k$ is not divisible by the square of any prime. Compute $m+n+k$.\n\n[i]Ray Li[/i]",
... | Suppose tetrahedron $PABC$ has volume $420$ and satisfies $AB = 13$, $BC = 14$, and $CA = 15$. The minimum possible surface area of $PABC$ can be written as $m+n\sqrt{k}$, where $m,n,k$ are positive integers and $k$ is not divisible by the square of any prime. Compute $m+n+k$.
[i]Ray Li[/i] | "[\"346\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2507, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16474"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"32"
] | [
"skywork"
] | 8c3989db8f2b04e25095468d2f433f2310c56c2c9ea0e2d3fb471fbcd39900e2 | [
{
"content": "17. In a group of 48 children, the ratio of boys to girls is $3: 5$.\nHow many boys must join the group to make the ratio of boys to girls $5: 3$ ?\nA 48\nB 40\nC 32\nD 24\nE 8",
"role": "user"
}
] | 17. In a group of 48 children, the ratio of boys to girls is $3: 5$.
How many boys must join the group to make the ratio of boys to girls $5: 3$ ?
A 48
B 40
C 32
D 24
E 8 | "[\"32\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2518, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16475"}] | {
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} |
[
"2400"
] | [
"skywork"
] | 7a694bf36d762ff43975625afdd940481b94289b931e7cfb4deaeb5b8aa1c958 | [
{
"content": "How many ways are there to arrange three indistinguishable rooks on a $6 \\times 6$ board such that no two rooks are attacking each other?",
"role": "user"
}
] | How many ways are there to arrange three indistinguishable rooks on a $6 \times 6$ board such that no two rooks are attacking each other? | "[\"2400\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2525, "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:16476"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"107"
] | [
"skywork"
] | a71aaef7f7044645698a3b173ec955a2c56c0b8cc32383bf3ecae935feba791c | [
{
"content": "The real function $f$ is defined for $\\forall$ $x\\in \\mathbb{R}$ and $f(0)=0$. Also $f(9+x)=f(9-x)$ and $f(x-10)=f(-x-10)$ for $\\forall$ $x\\in \\mathbb{R}$. What’s the least number of zeros $f$ can have in the interval $[0;2014]$? Does this change, if $f$ is also continuous?",
"role": "us... | The real function $f$ is defined for $\forall$ $x\in \mathbb{R}$ and $f(0)=0$. Also $f(9+x)=f(9-x)$ and $f(x-10)=f(-x-10)$ for $\forall$ $x\in \mathbb{R}$. What’s the least number of zeros $f$ can have in the interval $[0;2014]$? Does this change, if $f$ is also continuous? | "[\"107\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2499, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:16477"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9:4"
] | [
"skywork"
] | a60516dda8b199dff32e8ea1608bccb647d8da319879a1d4607db287a0b39e23 | [
{
"content": "A sphere with radius $r$ is inside a cone, the cross section of which is an equilateral triangle inscribed in a circle. Find the ratio of the total surface area of the cone to the surface area of the sphere.",
"role": "user"
}
] | A sphere with radius $r$ is inside a cone, the cross section of which is an equilateral triangle inscribed in a circle. Find the ratio of the total surface area of the cone to the surface area of the sphere. | "[\"9:4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2508, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:16478"}] | {
"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
} |
[
"27"
] | [
"skywork"
] | 8824b45cd1a315b8f462ac182c9a04512683047544be8c9241e6aaeafc273833 | [
{
"content": "Given that the central angle of a sector is $\\frac{3}{2}$ radians, and its radius is 6 cm, then the arc length of the sector is \\_\\_\\_\\_\\_\\_ cm, and the area of the sector is \\_\\_\\_\\_\\_\\_ cm<sup>2</sup>.",
"role": "user"
}
] | Given that the central angle of a sector is $\frac{3}{2}$ radians, and its radius is 6 cm, then the arc length of the sector is \_\_\_\_\_\_ cm, and the area of the sector is \_\_\_\_\_\_ cm<sup>2</sup>. | "[\"27\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2515, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "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:16479"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 60496518907a52dd5341388cdf0b075c667f1092414d8fce06d75d41a80b1f94 | [
{
"content": "Example 5 Let $n$ be a natural number, $a, b$ be positive real numbers, and satisfy $a+b=2$. Then the minimum value of $\\frac{1}{1+a^{n}}+\\frac{1}{1+b^{n}}$ is $\\qquad$\n(1990, National High School Mathematics Competition)",
"role": "user"
}
] | Example 5 Let $n$ be a natural number, $a, b$ be positive real numbers, and satisfy $a+b=2$. Then the minimum value of $\frac{1}{1+a^{n}}+\frac{1}{1+b^{n}}$ is $\qquad$
(1990, National High School Mathematics Competition) | "[\"1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2531, "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:16480"}] | {
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} |
[
"2017"
] | [
"skywork"
] | 0429bef4e2d91872dbfa26f2839e83bca4a45a629ccf79f2c1ed4c2677127842 | [
{
"content": "A function $f$ is defined recursively by $f(1)=f(2)=1$ and \\[f(n)=f(n-1)-f(n-2)+n\\]for all integers $n \\geq 3$. What is $f(2018)$?",
"role": "user"
}
] | A function $f$ is defined recursively by $f(1)=f(2)=1$ and \[f(n)=f(n-1)-f(n-2)+n\]for all integers $n \geq 3$. What is $f(2018)$? | "[\"2017\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2522, "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:16481"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"12"
] | [
"skywork"
] | 4dff2fa793c53eaea3fc77f703eb3793511d38fdf1cdc314cff4bc4c02e3e72f | [
{
"content": "A cricket can jump two distances: 9 and 8 meters. It competes in a 100-meter race to the edge of a cliff. How many jumps must the cricket make to reach the end of the race without going past the finish line and falling off the cliff?\n\n#",
"role": "user"
}
] | A cricket can jump two distances: 9 and 8 meters. It competes in a 100-meter race to the edge of a cliff. How many jumps must the cricket make to reach the end of the race without going past the finish line and falling off the cliff?
# | "[\"12\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2521, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:16482"}] | {
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"reference_present": true
} |
[
"6/11"
] | [
"skywork"
] | a63bf41e5463356d8cc44e1781f11aeb85cac3e88e896c6c700483c656fa8a8c | [
{
"content": "There are 4 spheres in space with radii 2, 2, 3, and 3, respectively. Each sphere is externally tangent to the other 3 spheres. Additionally, there is a small sphere that is externally tangent to all 4 of these spheres. Find the radius of the small sphere.",
"role": "user"
}
] | There are 4 spheres in space with radii 2, 2, 3, and 3, respectively. Each sphere is externally tangent to the other 3 spheres. Additionally, there is a small sphere that is externally tangent to all 4 of these spheres. Find the radius of the small sphere. | "[\"6/11\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2532, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16483"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"22.5"
] | [
"skywork"
] | 301bcb2f19a5996386538bcb3caf951b1204b90e522bdc29b48a6710c8d1f25d | [
{
"content": "Two lines with slopes $-\\frac{1}{3}$ and $3$ intersect at $(3,3)$. Find the area of the triangle enclosed by these two lines and the line $x+y=12$.",
"role": "user"
}
] | Two lines with slopes $-\frac{1}{3}$ and $3$ intersect at $(3,3)$. Find the area of the triangle enclosed by these two lines and the line $x+y=12$. | "[\"22.5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2539, "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:16484"}] | {
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"reference_components": 1,
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} |
[
"1002"
] | [
"skywork"
] | a8e56877fab97ebd372b8cbe68819b3bf3f109d23ed4523dd14c114283e39331 | [
{
"content": "Positive integers $ a$, $ b$, and $ c$ are chosen so that $ a<b<c$, and the system of equations\r\n\\[ 2x\\plus{}y\\equal{}2003\\text{ and }y\\equal{}|x\\minus{}a|\\plus{}|x\\minus{}b|\\plus{}|x\\minus{}c|\r\n\\]has exactly one solution. What is the minimum value of $ c$?\r\n\r\n$ \\textbf{(A)}\... | Positive integers $ a$, $ b$, and $ c$ are chosen so that $ a<b<c$, and the system of equations
\[ 2x\plus{}y\equal{}2003\text{ and }y\equal{}|x\minus{}a|\plus{}|x\minus{}b|\plus{}|x\minus{}c|
\]has exactly one solution. What is the minimum value of $ c$?
$ \textbf{(A)}\ 668 \qquad
\textbf{(B)}\ 669 \qquad
\te... | "[\"1002\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2526, "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:16485"}] | {
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} |
[
"7"
] | [
"skywork"
] | 0c9f918c5d06f8b598651fc45496951d62166e33f6ade85e7152cc7d76f4fccc | [
{
"content": "A regular octagon has sides alternating between 1 and $\\sqrt{2}$. What is the area of the octagon?",
"role": "user"
}
] | A regular octagon has sides alternating between 1 and $\sqrt{2}$. What is the area of the octagon? | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2542, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:16486"}] | {
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} |
[
"f(x)=a^{x}"
] | [
"skywork"
] | f36dfe90643b25ae168b902b37c59cd31b994ded8d6f7220b8d128c50421c97c | [
{
"content": "Five. (20 points) Try to find all functions $f(x)$ that satisfy the following conditions:\n(1) $f(x)$ is a monotonic function defined on $\\mathbf{R}$;\n(2) For any real numbers $x, y$,\n$$\nf(x+y)=f(x) f(y) \\text{; }\n$$\n(3) $f(1)=a(0<a \\neq 1)$.",
"role": "user"
}
] | Five. (20 points) Try to find all functions $f(x)$ that satisfy the following conditions:
(1) $f(x)$ is a monotonic function defined on $\mathbf{R}$;
(2) For any real numbers $x, y$,
$$
f(x+y)=f(x) f(y) \text{; }
$$
(3) $f(1)=a(0<a \neq 1)$. | "[\"f(x)=a^{x}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2512, "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:16487"}] | {
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} |
[
"-7x+\\frac{28}{5}"
] | [
"skywork"
] | 46081454a7685cb15780ad5eb225788c608cdf846affb3212e27eab5ade93f86 | [
{
"content": "10. A line intersects the $y$-axis, the line $y=2 x+2$, and the $x$-axis at the points $A, B$, and $C$, respectively. If segment $A C$ has a length of $4 \\sqrt{2}$ units and $B$ lies in the first quadrant and is the midpoint of segment $A C$, find the equation of the line in slope-intercept form.... | 10. A line intersects the $y$-axis, the line $y=2 x+2$, and the $x$-axis at the points $A, B$, and $C$, respectively. If segment $A C$ has a length of $4 \sqrt{2}$ units and $B$ lies in the first quadrant and is the midpoint of segment $A C$, find the equation of the line in slope-intercept form. | "[\"-7x+\\\\frac{28}{5}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2514, "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:16488"}] | {
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} |
[
"6"
] | [
"skywork"
] | aac5be43ab76046bbd85a2cae533d8f5aa189dcf71bf38f65b3d517a8e2a9681 | [
{
"content": "13. Find the smallest positive integer $n$ such that: if for any finite set of points $A$ in the plane, any $n$ points can be covered by two lines, then there exist two lines that can cover all points in $A$.",
"role": "user"
}
] | 13. Find the smallest positive integer $n$ such that: if for any finite set of points $A$ in the plane, any $n$ points can be covered by two lines, then there exist two lines that can cover all points in $A$. | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2533, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:16489"}] | {
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} |
[
"6,16,26"
] | [
"skywork"
] | f7bbb1d951ecae5b956f809792cb8fe963dfd3154adbc449daa0e22aa9c1bea9 | [
{
"content": "12. There are 48 students participating in three sports activities, each person only participates in one activity, the number of participants in each activity is different, and the number of people in each activity has the digit \"6\". How many people are there in each of the three sports activiti... | 12. There are 48 students participating in three sports activities, each person only participates in one activity, the number of participants in each activity is different, and the number of people in each activity has the digit "6". How many people are there in each of the three sports activities? | "[\"6,16,26\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2520, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16490"}] | {
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} |
[
"3"
] | [
"skywork"
] | ba2b0b50cf23b2d637052fbe52acd4a3e980608021b996b6476934c91014d989 | [
{
"content": "8. Let \"学\" and \"习\" represent two different digits. The product of the four-digit numbers \"学学学学\" and \"习习习习\" is a seven-digit number, and its unit and millionth digits are the same as the digit represented by \"学\". How many two-digit numbers can \"学习\" represent? $\\qquad$",
"role": "us... | 8. Let "学" and "习" represent two different digits. The product of the four-digit numbers "学学学学" and "习习习习" is a seven-digit number, and its unit and millionth digits are the same as the digit represented by "学". How many two-digit numbers can "学习" represent? $\qquad$ | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2534, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16491"}] | {
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} |
[
"936"
] | [
"skywork"
] | 27e38add9826991c29f705a7171bc669efb7455b124e0c37677200a6bd889082 | [
{
"content": "Find the largest three-digit integer that is divisible by each of its distinct, non-zero digits.",
"role": "user"
}
] | Find the largest three-digit integer that is divisible by each of its distinct, non-zero digits. | "[\"936\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2553, "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:16492"}] | {
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"reference_components": 1,
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} |
[
"\\frac{1}{2}"
] | [
"skywork"
] | 0338e8d871561293b710c02ba0d1f97fb05b84b307b2aa3fb3d5220e3efe1129 | [
{
"content": "6. Given the sequence $\\left\\{a_{n}\\right\\}$ satisfies\n$$\na_{1}=6, a_{2}=20, a_{n}\\left(a_{n}-8\\right)=a_{n-1} a_{n+1}-12(n \\geqslant 2) \\text {. }\n$$\n\nLet $\\{x\\}=x-[x]$, where $[x]$ denotes the greatest integer not exceeding the real number $x$. Then $\\lim _{n \\rightarrow \\infty... | 6. Given the sequence $\left\{a_{n}\right\}$ satisfies
$$
a_{1}=6, a_{2}=20, a_{n}\left(a_{n}-8\right)=a_{n-1} a_{n+1}-12(n \geqslant 2) \text {. }
$$
Let $\{x\}=x-[x]$, where $[x]$ denotes the greatest integer not exceeding the real number $x$. Then $\lim _{n \rightarrow \infty}\left\{\sqrt{a_{n}}\right\}=$ $\qquad$ | "[\"\\\\frac{1}{2}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2545, "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:16493"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"-5"
] | [
"skywork"
] | 2bbc6ba60cadd19b900b24866c5bb049a2e51b85e3de8dbbde2e7f991651737c | [
{
"content": "Given two complex numbers $z_1$ and $z_2$ whose corresponding points in the complex plane are symmetrical about the imaginary axis, and $z_1 = 1 + 2i$ where $i$ is the imaginary unit, calculate the product of $z_1$ and $z_2$.",
"role": "user"
}
] | Given two complex numbers $z_1$ and $z_2$ whose corresponding points in the complex plane are symmetrical about the imaginary axis, and $z_1 = 1 + 2i$ where $i$ is the imaginary unit, calculate the product of $z_1$ and $z_2$. | "[\"-5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2519, "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:16494"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.78"
] | [
"skywork"
] | 4f05e6994a1aab03237f24fe12c218efcc218c1f9f4a7215a7de318681ad715c | [
{
"content": "Rounded to 2 decimal places, what is $\\frac{7}{9}$?",
"role": "user"
}
] | Rounded to 2 decimal places, what is $\frac{7}{9}$? | "[\"0.78\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2564, "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:16495"}] | {
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"reference_present": true
} |
[
"5787"
] | [
"skywork"
] | 901528385be8d0a1f6237aac60e9c973b2e1310639745c75bd05f99cedf54f3b | [
{
"content": "Compute the number of digits is $2015!$. Your score will be given by $\\max\\{\\lfloor125(\\min\\{\\tfrac{A}{C},\\tfrac{C}{A}\\}-\\tfrac{1}{5})\\rfloor,0\\}$, where $A$ is your answer and $C$ is the actual answer.",
"role": "user"
}
] | Compute the number of digits is $2015!$. Your score will be given by $\max\{\lfloor125(\min\{\tfrac{A}{C},\tfrac{C}{A}\}-\tfrac{1}{5})\rfloor,0\}$, where $A$ is your answer and $C$ is the actual answer. | "[\"5787\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2530, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16496"}, {"dataset": "skywork", "extra_... | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"99"
] | [
"skywork"
] | 0bdb3038742152d168cadc585ab234a46f6b4ca7e9308235f5a00ea79fc4d527 | [
{
"content": ". We have a checkerboard with a side length of 99. There is a fly on each square. In one step, each fly must move exactly one square diagonally (several flies can then end up on the same square). After one step, what is the minimum number of empty squares?",
"role": "user"
}
] | . We have a checkerboard with a side length of 99. There is a fly on each square. In one step, each fly must move exactly one square diagonally (several flies can then end up on the same square). After one step, what is the minimum number of empty squares? | "[\"99\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2547, "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:16497"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"72"
] | [
"skywork"
] | 656ec288bc429505507e62e99cae928a74b18823dcc0b943c15d3a738fa6f9d7 | [
{
"content": "3、A and B are 36 kilometers apart. Supermen A and B start walking from $\\mathbf{A}$ to $\\mathbf{B}$ at the same time. Once they reach $\\mathbf{B}$, they immediately walk back to $\\mathbf{A}$, and upon reaching $\\mathbf{A}$, they immediately walk back to $\\mathbf{B}$...... They keep moving ba... | 3、A and B are 36 kilometers apart. Supermen A and B start walking from $\mathbf{A}$ to $\mathbf{B}$ at the same time. Once they reach $\mathbf{B}$, they immediately walk back to $\mathbf{A}$, and upon reaching $\mathbf{A}$, they immediately walk back to $\mathbf{B}$...... They keep moving back and forth between $\mathb... | "[\"72\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2541, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16498"}] | {
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"reference_components": 1,
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} |
[
"115440"
] | [
"skywork"
] | 419986988f9b2e490b51929282fb24c4fbbcfbb9a5e13184a1f638a97e44db5b | [
{
"content": "Consider pairs $(f,g)$ of functions from the set of nonnegative integers to itself such that \n[list]\n[*]$f(0) \\geq f(1) \\geq f(2) \\geq \\dots \\geq f(300) \\geq 0$\n[*]$f(0)+f(1)+f(2)+\\dots+f(300) \\leq 300$\n[*]for any 20 nonnegative integers $n_1, n_2, \\dots, n_{20}$, not necessarily dist... | Consider pairs $(f,g)$ of functions from the set of nonnegative integers to itself such that
[list]
[*]$f(0) \geq f(1) \geq f(2) \geq \dots \geq f(300) \geq 0$
[*]$f(0)+f(1)+f(2)+\dots+f(300) \leq 300$
[*]for any 20 nonnegative integers $n_1, n_2, \dots, n_{20}$, not necessarily distinct, we have $$g(n_1+n_2+\dots+n_{... | "[\"115440\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2543, "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:16499"}] | {
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} |
[
"90"
] | [
"skywork"
] | 3ec81f0e7b9ecd08a338f3ab5ff4642fc35d23c5c7decaa61fc79d837d6fae2e | [
{
"content": "3. A circle is circumscribed around an acute-angled triangle $A B C$. Point $K$ is the midpoint of the smaller arc $A C$ of this circle, and point $L$ is the midpoint of the smaller arc $A K$ of this circle. Segments $B K$ and $A C$ intersect at point $P$. Find the angle between the lines $B C$ an... | 3. A circle is circumscribed around an acute-angled triangle $A B C$. Point $K$ is the midpoint of the smaller arc $A C$ of this circle, and point $L$ is the midpoint of the smaller arc $A K$ of this circle. Segments $B K$ and $A C$ intersect at point $P$. Find the angle between the lines $B C$ and $L P$, given that $B... | "[\"90\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2527, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:16500"}] | {
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"reference_components": 1,
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} |
[
"g_{\\max}(x)=\\frac{1}{25},g_{\\}(x)=4-\\sqrt{34}"
] | [
"skywork"
] | f293c6774f9692c86a88916623b05c8962f3593864ba5064e93133bfb162dc96 | [
{
"content": "For example, let $\\mathrm{R} \\mathbf{R}$ be the set of real numbers, and $f: \\mathbf{R} \\rightarrow \\mathbf{R}$ be a function satisfying $f(\\cot x)=\\cos 2 x+\\sin 2 x$ for all $0<x<\\pi$. Define $g(x)=f(x) \\cdot f(1-x)$ for $-1 \\leqslant x \\leqslant 1$. Find the maximum and minimum value... | For example, let $\mathrm{R} \mathbf{R}$ be the set of real numbers, and $f: \mathbf{R} \rightarrow \mathbf{R}$ be a function satisfying $f(\cot x)=\cos 2 x+\sin 2 x$ for all $0<x<\pi$. Define $g(x)=f(x) \cdot f(1-x)$ for $-1 \leqslant x \leqslant 1$. Find the maximum and minimum values of $g(x)$ on $[-1,1]$.
(2003 Vie... | "[\"g_{\\\\max}(x)=\\\\frac{1}{25},g_{\\\\}(x)=4-\\\\sqrt{34}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2540, "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:16501"}] | {
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} |
[
"7295"
] | [
"skywork"
] | caab9921e55537023b23569696a6efb05c574dcde71fb0b3de05a68c862d85e1 | [
{
"content": "Let $A B C D E F$ be a convex hexagon with the following properties. (a) $\\overline{A C}$ and $\\overline{A E}$ trisect $\\angle B A F$. (b) $\\overline{B E} \\| \\overline{C D}$ and $\\overline{C F} \\| \\overline{D E}$. (c) $A B=2 A C=4 A E=8 A F$. Suppose that quadrilaterals $A C D E$ and $A D... | Let $A B C D E F$ be a convex hexagon with the following properties. (a) $\overline{A C}$ and $\overline{A E}$ trisect $\angle B A F$. (b) $\overline{B E} \| \overline{C D}$ and $\overline{C F} \| \overline{D E}$. (c) $A B=2 A C=4 A E=8 A F$. Suppose that quadrilaterals $A C D E$ and $A D E F$ have area 2014 and 1400, ... | "[\"7295\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2537, "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:16502"}] | {
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"reference_components": 1,
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} |
[
"45"
] | [
"skywork"
] | c26aeb397cf5ab2f7cf1acd05e8ee5633014639c79ead7bf3187cff147d4f226 | [
{
"content": "7.3. Masha and Sasha take turns (starting with Masha) writing 10 digits on the board from left to right to form a ten-digit number. Moreover, it is not allowed to write two consecutive identical digits. If the resulting number is divisible by 9, then Sasha wins; otherwise, Masha wins. Who will win... | 7.3. Masha and Sasha take turns (starting with Masha) writing 10 digits on the board from left to right to form a ten-digit number. Moreover, it is not allowed to write two consecutive identical digits. If the resulting number is divisible by 9, then Sasha wins; otherwise, Masha wins. Who will win with correct play fro... | "[\"45\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2557, "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:16503"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1,2"
] | [
"skywork"
] | b17d6c36d90aad21c55507da077c3c3419e647282d5c8cf69dd849774b56d145 | [
{
"content": "2. Solve the equation in natural numbers: $1+x+x^{2}+x^{3}=2^{y}$.",
"role": "user"
}
] | 2. Solve the equation in natural numbers: $1+x+x^{2}+x^{3}=2^{y}$. | "[\"1,2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2548, "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:16504"}] | {
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} |
[
"a < \\frac{1}{4}"
] | [
"skywork"
] | 5ca26e39903dbe0bc2a9b1d3b9232f99afb665b063729525c66031971003981f | [
{
"content": "Find all $a\\in\\mathbb{R}$ for which there exists a non-constant function $f: (0,1]\\rightarrow\\mathbb{R}$ such that \\[a+f(x+y-xy)+f(x)f(y)\\leq f(x)+f(y)\\] for all $x,y\\in(0,1].$",
"role": "user"
}
] | Find all $a\in\mathbb{R}$ for which there exists a non-constant function $f: (0,1]\rightarrow\mathbb{R}$ such that \[a+f(x+y-xy)+f(x)f(y)\leq f(x)+f(y)\] for all $x,y\in(0,1].$ | "[\"a < \\\\frac{1}{4}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2544, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16505"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1998, 3834"
] | [
"skywork"
] | ccf5e4e413225de6658cca2c60228ec6941643a885b0493e3f7d19a0a2874c71 | [
{
"content": "Find all positive integers $ n$ having exactly $ 16$ divisors $ 1\\equal{}d_1<d_2<...<d_{16}\\equal{}n$ such that $ d_6\\equal{}18$ and $ d_9\\minus{}d_8\\equal{}17.$",
"role": "user"
}
] | Find all positive integers $ n$ having exactly $ 16$ divisors $ 1\equal{}d_1<d_2<...<d_{16}\equal{}n$ such that $ d_6\equal{}18$ and $ d_9\minus{}d_8\equal{}17.$ | "[\"1998, 3834\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2559, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16506"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | ef78cc4191737d9b8777f3b8a9693561c66421942485339fec9c577f35ffa94f | [
{
"content": "Problem 1. A group of schoolchildren decided to buy pizza. Each pizza is cut into 12 pieces. They calculated that if each boy eats 7 pieces and each girl eats 2 pieces, then three pizzas would not be enough. If they buy four pizzas, then each boy can have 8 pieces and each girl can have 4 pieces, ... | Problem 1. A group of schoolchildren decided to buy pizza. Each pizza is cut into 12 pieces. They calculated that if each boy eats 7 pieces and each girl eats 2 pieces, then three pizzas would not be enough. If they buy four pizzas, then each boy can have 8 pieces and each girl can have 4 pieces, and there will still b... | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2538, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16507"}] | {
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} |
[
"0.25"
] | [
"skywork"
] | 45126b2e4f674ccefea4a1115e7cc0de8ee59c599af1cda6bb42a70e1e723dfa | [
{
"content": "The sum of non-negative numbers $x_{1}, x_{2}, \\ldots, x_{10}$ is 1. Find the maximum possible value of the sum $x_{1} x_{2}+$ $x_{2} x_{3}+\\ldots+x_{9} x_{10}$",
"role": "user"
}
] | The sum of non-negative numbers $x_{1}, x_{2}, \ldots, x_{10}$ is 1. Find the maximum possible value of the sum $x_{1} x_{2}+$ $x_{2} x_{3}+\ldots+x_{9} x_{10}$ | "[\"0.25\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2556, "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:16508"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"55"
] | [
"skywork"
] | ed4830bde46f9e2afe98d0986059858b01098932e64561e7731f8ab4f3dd5d4a | [
{
"content": "$2 \\cdot 35$ subset $X$ of the set $\\{00,01, \\cdots, 98,99\\}$ satisfies: in any infinite sequence of digits, there are two adjacent digits that form an element of $X$. What is the minimum number of elements that $X$ should contain?",
"role": "user"
}
] | $2 \cdot 35$ subset $X$ of the set $\{00,01, \cdots, 98,99\}$ satisfies: in any infinite sequence of digits, there are two adjacent digits that form an element of $X$. What is the minimum number of elements that $X$ should contain? | "[\"55\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2552, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16509"}] | {
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"plain_numeric_reference": true,
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} |
[
"x_{1}=x_{2}=\\cdots=x_{n}=1"
] | [
"skywork"
] | 46e5d1334ad8327ab1a9042b49f12f32f1defa92fa29983d364355ec141ce9d2 | [
{
"content": "2. Solve the system of equations\n$$\n\\left\\{\\begin{array}{l}\nx_{1}+x_{2}+\\cdots+x_{n}=n \\\\\nx_{1}^{2}+x_{2}^{2}+\\cdots+x_{n}^{2}=n \\\\\n\\cdots \\cdots \\\\\nx_{1}^{n}+x_{2}^{n}+\\cdots+x_{n}^{n}=n\n\\end{array}\\right.\n$$",
"role": "user"
}
] | 2. Solve the system of equations
$$
\left\{\begin{array}{l}
x_{1}+x_{2}+\cdots+x_{n}=n \\
x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}=n \\
\cdots \cdots \\
x_{1}^{n}+x_{2}^{n}+\cdots+x_{n}^{n}=n
\end{array}\right.
$$ | "[\"x_{1}=x_{2}=\\\\cdots=x_{n}=1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2555, "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:16510"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"0.8664"
] | [
"skywork"
] | 9e3e0259ab3766b0b917783c190e9e30ba7ceea2ce32ea3c772546b5face4474 | [
{
"content": "331. The measurement of the shaft diameter is being performed without systematic (one-sided) errors. Random measurement errors $X$ follow a normal distribution with a root mean square deviation $\\sigma=10$ mm. Find the probability that the measurement will be performed with an error not exceeding... | 331. The measurement of the shaft diameter is being performed without systematic (one-sided) errors. Random measurement errors $X$ follow a normal distribution with a root mean square deviation $\sigma=10$ mm. Find the probability that the measurement will be performed with an error not exceeding $15 \mathrm{mm}$ in ab... | "[\"0.8664\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2566, "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:16511"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"12"
] | [
"skywork"
] | dbb6ec6e169bab0a7f59d9fa278deed8e1312ef02ed905f02d1ea6802e7efead | [
{
"content": "# Task № 2.3\n\n## Condition:\n\nDmitry has socks in his wardrobe: 14 pairs of blue socks, 24 pairs of black socks, and 10 pairs of white socks. Dmitry bought some more pairs of black socks and found that now the black socks make up 3/5 of the total number of socks. How many pairs of black socks d... | # Task № 2.3
## Condition:
Dmitry has socks in his wardrobe: 14 pairs of blue socks, 24 pairs of black socks, and 10 pairs of white socks. Dmitry bought some more pairs of black socks and found that now the black socks make up 3/5 of the total number of socks. How many pairs of black socks did Dmitry buy? | "[\"12\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2561, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16512"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1:3"
] | [
"skywork"
] | 73d8b35ce8828f9ed060ef7d0342ca8f5d2f8523600b9f33bd267ef30376649b | [
{
"content": "The lengths of the sides of a triangle are $\\sqrt{3}, \\sqrt{4}(=2), \\sqrt{5}$. \n\nIn what ratio does the altitude perpendicular to the middle side divide it?",
"role": "user"
}
] | The lengths of the sides of a triangle are $\sqrt{3}, \sqrt{4}(=2), \sqrt{5}$.
In what ratio does the altitude perpendicular to the middle side divide it? | "[\"1:3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2524, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16513"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4\\sqrt{6}"
] | [
"skywork"
] | b04efbe5ef4ae23413169e892a57b3fab5e32a7799a31cd4276c99aa670dcc10 | [
{
"content": "Find the volume of the tetrahedron $ABCD$ with edges $AB=3$, $AC=5$, and $BD=7$, if the distance between the midpoints $M$ and $N$ of its edges $AB$ and $CD$ is 2, and the line $AB$ forms equal angles with the lines $AC$, $BD$, and $MN$.",
"role": "user"
}
] | Find the volume of the tetrahedron $ABCD$ with edges $AB=3$, $AC=5$, and $BD=7$, if the distance between the midpoints $M$ and $N$ of its edges $AB$ and $CD$ is 2, and the line $AB$ forms equal angles with the lines $AC$, $BD$, and $MN$. | "[\"4\\\\sqrt{6}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2546, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16514"}] | {
"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}{3}"
] | [
"skywork"
] | 1bbe264f36d84dcd81ae94cc6f666041f7780f8445c7d586a2d5686a799bdeac | [
{
"content": "A recipe calls for $\\frac{1}{3}$ cup of sugar. If you already have $\\frac{1}{6}$ cup, how much more sugar is required to reach the initial quantity? Once you find this quantity, if you need a double amount for another recipe, how much sugar would that be in total?",
"role": "user"
}
] | A recipe calls for $\frac{1}{3}$ cup of sugar. If you already have $\frac{1}{6}$ cup, how much more sugar is required to reach the initial quantity? Once you find this quantity, if you need a double amount for another recipe, how much sugar would that be in total? | "[\"\\\\frac{1}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2562, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16515"}] | {
"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
} |
[
"242"
] | [
"skywork"
] | 1fb381ef0bf6bdf0be76bc7c2656dc1dccf50fceb20dc4a75b52412f14a84cb0 | [
{
"content": "Let $ f(n)$ be the number of times you have to hit the $ \\sqrt {\\ }$ key on a calculator to get a number less than $ 2$ starting from $ n$ . For instance, $ f(2) \\equal{} 1$ , $ f(5) \\equal{} 2$ . For how many $ 1 < m < 2008$ is $ f(m)$ odd?",
"role": "user"
}
] | Let $ f(n)$ be the number of times you have to hit the $ \sqrt {\ }$ key on a calculator to get a number less than $ 2$ starting from $ n$ . For instance, $ f(2) \equal{} 1$ , $ f(5) \equal{} 2$ . For how many $ 1 < m < 2008$ is $ f(m)$ odd? | "[\"242\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2558, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:16516"}, {"dataset": "skywork", "extra_inf... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"190;19"
] | [
"skywork"
] | 6427c43340b5418ed03ddd8b81da01a3ce043d2d528c1f36895503673ead3f50 | [
{
"content": "3. On a very long road, a race was organized. 21 runners started at different times, each running at a constant speed. The race continued until each runner had overtaken all the slower ones. The speeds of the runners who started first and last were the same, and the speeds of the others were diffe... | 3. On a very long road, a race was organized. 21 runners started at different times, each running at a constant speed. The race continued until each runner had overtaken all the slower ones. The speeds of the runners who started first and last were the same, and the speeds of the others were different from theirs and d... | "[\"190;19\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2554, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16517"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"243"
] | [
"skywork"
] | e34c63979b856efa95cea3327c0d49f74050a3e954c7b637ca91713a1b06aefd | [
{
"content": "12. Let the set $M=\\{1,2,3,4,5,6,7,8,9,10\\}, A=\\left\\{(x, y, z) \\mid x, y, z \\in M\\right.$, and $\\left.9 \\mid\\left(x^{3}+y^{3}+z^{3}\\right)\\right\\}$, then the number of elements in set $A$ is",
"role": "user"
}
] | 12. Let the set $M=\{1,2,3,4,5,6,7,8,9,10\}, A=\left\{(x, y, z) \mid x, y, z \in M\right.$, and $\left.9 \mid\left(x^{3}+y^{3}+z^{3}\right)\right\}$, then the number of elements in set $A$ is | "[\"243\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2560, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16518"}, {"dataset": "skywork", "extra_in... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-9;-8;-7;-6;-4;-3;-2;-1"
] | [
"skywork"
] | c11526be10638a80f9c9d1f94001081e4d1bfc0a9066589da106aed82a0ebb72 | [
{
"content": "1. [5 points] $S$ - the sum of the first 7 terms of an increasing arithmetic progression $a_{1}, a_{2}, a_{3}, \\ldots$, consisting of integers. It is known that $a_{7} a_{12}>S+20, a_{9} a_{10}<S+44$. Indicate all possible values of $a_{1}$.",
"role": "user"
}
] | 1. [5 points] $S$ - the sum of the first 7 terms of an increasing arithmetic progression $a_{1}, a_{2}, a_{3}, \ldots$, consisting of integers. It is known that $a_{7} a_{12}>S+20, a_{9} a_{10}<S+44$. Indicate all possible values of $a_{1}$. | "[\"-9;-8;-7;-6;-4;-3;-2;-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2549, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16519"}] | {
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[
"3"
] | [
"skywork"
] | 538e3de5e4b85a568c6fa330add0c0f85cb1de6d745d9716a6b162faf0e13472 | [
{
"content": "If $S=1!+2!+3!+\\cdots +99!$, then the units' digit in the value of S is:",
"role": "user"
}
] | If $S=1!+2!+3!+\cdots +99!$, then the units' digit in the value of S is: | "[\"3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2567, "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:16520"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"160"
] | [
"skywork"
] | 191825b1f4f1bf72bf238611ccb8301e41b1bf2515c3de264dfdd28c66b6f09c | [
{
"content": "I have 8 shirts, 4 pairs of pants, and 6 hats. The pants come in tan, black, blue, and gray. The shirts and hats come in those colors, and also white and yellow. I refuse to wear an outfit in which the shirt and hat are the same color. How many choices for outfits, consisting of one shirt, one hat... | I have 8 shirts, 4 pairs of pants, and 6 hats. The pants come in tan, black, blue, and gray. The shirts and hats come in those colors, and also white and yellow. I refuse to wear an outfit in which the shirt and hat are the same color. How many choices for outfits, consisting of one shirt, one hat, and one pair of pant... | "[\"160\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2574, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16521"}] | {
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} |
[
"2x + 1"
] | [
"skywork"
] | 55cbc64c88a309f135d25cf4b184817044f61c0fed33782574137169e83d2f98 | [
{
"content": "For every real number $x$, what is the value of the expression $(x+1)^{2} - x^{2}$?",
"role": "user"
}
] | For every real number $x$, what is the value of the expression $(x+1)^{2} - x^{2}$? | "[\"2x + 1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2583, "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:16522"}] | {
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} |
[
"\\ln 2 - \\frac{1}{2}"
] | [
"skywork"
] | 119b5e81face66506c6a34724b7d9ecca0fc3f444880788a0dbd1f4b71a67795 | [
{
"content": "Compute the definite integral:\n\n$$\n\\int_{0}^{\\frac{\\pi}{2}} \\frac{\\sin x \\, dx}{(1+\\cos x+\\sin x)^{2}}\n$$",
"role": "user"
}
] | Compute the definite integral:
$$
\int_{0}^{\frac{\pi}{2}} \frac{\sin x \, dx}{(1+\cos x+\sin x)^{2}}
$$ | "[\"\\\\ln 2 - \\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2580, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:16523"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2}"
] | [
"skywork"
] | af9638c589df7552f8611d9a20c1bdc114673600e4d0ea7aae1d671f09495cc4 | [
{
"content": "4.4.9 ** Let $x_{1}, x_{2}, \\cdots, x_{n}$ and $a_{1}, a_{2}, \\cdots, a_{n}(n>2)$ be two sets of arbitrary real numbers satisfying the conditions:\n(1) $x_{1}+x_{2}+\\cdots+x_{n}=0$;\n(2) $\\left|x_{1}\\right|+\\left|x_{2}\\right|+\\cdots+\\left|x_{n}\\right|=1$;\n(3) $a_{1} \\geqslant a_{2} \\g... | 4.4.9 ** Let $x_{1}, x_{2}, \cdots, x_{n}$ and $a_{1}, a_{2}, \cdots, a_{n}(n>2)$ be two sets of arbitrary real numbers satisfying the conditions:
(1) $x_{1}+x_{2}+\cdots+x_{n}=0$;
(2) $\left|x_{1}\right|+\left|x_{2}\right|+\cdots+\left|x_{n}\right|=1$;
(3) $a_{1} \geqslant a_{2} \geqslant \cdots \geqslant a_{n}$. To m... | "[\"\\\\frac{1}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2565, "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:16524"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"C_{1}e^{-3x}+C_{2}e^{-x}+(x^{2}+9x-7)e^{x}"
] | [
"skywork"
] | 4e0b987fe5dc6ed53f257b74c9358a9733eb23c6c62a166c0768e7397f9a7cce | [
{
"content": "Example 4.21. Find the general solution of the equation\n\n$$\ny^{\\prime \\prime}+4 y^{\\prime}+3 y=\\left(8 x^{2}+84 x\\right) e^{x}\n$$",
"role": "user"
}
] | Example 4.21. Find the general solution of the equation
$$
y^{\prime \prime}+4 y^{\prime}+3 y=\left(8 x^{2}+84 x\right) e^{x}
$$ | "[\"C_{1}e^{-3x}+C_{2}e^{-x}+(x^{2}+9x-7)e^{x}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2584, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16525"}] | {
"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
} |
[
"769"
] | [
"skywork"
] | 5a28ba0be78536b79ac129f1299b4fb83fb4310aa8fbff788cb8d30a7957f530 | [
{
"content": "A quadrilateral $ABCD$ has a right angle at $\\angle ABC$ and satisfies $AB = 12$ , $BC = 9$ , $CD = 20$ , and $DA = 25$ . Determine $BD^2$ .\n.",
"role": "user"
}
] | A quadrilateral $ABCD$ has a right angle at $\angle ABC$ and satisfies $AB = 12$ , $BC = 9$ , $CD = 20$ , and $DA = 25$ . Determine $BD^2$ .
. | "[\"769\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2582, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:16526"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"450"
] | [
"skywork"
] | 05288606a0bcb88d0379f8201016ad11bec1ec4ee8db830c3f7d3c6a81be7401 | [
{
"content": "The main structure of the Chinese space station includes the Tianhe core module, the Wentian experiment module, and the Mengtian experiment module. Assuming that the space station needs to arrange 6 astronauts, including astronauts A and B, to conduct experiments, with each module having at least ... | The main structure of the Chinese space station includes the Tianhe core module, the Wentian experiment module, and the Mengtian experiment module. Assuming that the space station needs to arrange 6 astronauts, including astronauts A and B, to conduct experiments, with each module having at least one person and at most... | "[\"450\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2563, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16527"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"24"
] | [
"skywork"
] | 6314aa719226b0f97baf46ccf575854b9e90bbc6ff570f29db83db807b7e30be | [
{
"content": "## Task 1\n\nIn 5 windows of a residential building, there are a total of 40 glass panes.\n\nHow many panes are in 3 windows?",
"role": "user"
}
] | ## Task 1
In 5 windows of a residential building, there are a total of 40 glass panes.
How many panes are in 3 windows? | "[\"24\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2586, "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:16528"}] | {
"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"
] | 80d947a7fbe69109db5ba873cb09523d9860f31117045c3b16ebb5e6de115288 | [
{
"content": "Consider the function \\( y = g(x) = \\frac{x^2}{Ax^2 + Bx + C} \\), where \\( A, B, \\) and \\( C \\) are integers. The function has vertical asymptotes at \\( x = -1 \\) and \\( x = 2 \\), and for all \\( x > 4 \\), it is true that \\( g(x) > 0.5 \\). Determine the value of \\( A + B + C \\).",
... | Consider the function \( y = g(x) = \frac{x^2}{Ax^2 + Bx + C} \), where \( A, B, \) and \( C \) are integers. The function has vertical asymptotes at \( x = -1 \) and \( x = 2 \), and for all \( x > 4 \), it is true that \( g(x) > 0.5 \). Determine the value of \( A + B + C \). | "[\"-4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2513, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16529"}] | {
"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
} |
[
"1881"
] | [
"skywork"
] | 10857ccd78b274dc0ac3ece4108a6c3f4272160e7155dbac853aa88764a3e2a5 | [
{
"content": "With about six hours left on the van ride home from vacation, Wendy looks for something to do. She starts working on a project for the math team.\n\nThere are sixteen students, including Wendy, who are about to be sophomores on the math team. Elected as a math team officer, one of Wendy's jobs i... | With about six hours left on the van ride home from vacation, Wendy looks for something to do. She starts working on a project for the math team.
There are sixteen students, including Wendy, who are about to be sophomores on the math team. Elected as a math team officer, one of Wendy's jobs is to schedule groups of ... | "[\"1881\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2550, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:16530"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
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