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 |
|---|---|---|---|---|---|---|---|---|
[
"425"
] | [
"skywork"
] | d9a340d105b5fbe3167263197a0d261ddc4ecc7d1a5f8af7b1b4a48a61f59ab5 | [
{
"content": "Car $A$ departs from Station $J$ towards Station $Y$, while cars $B$ and $C$ depart from Station $Y$ towards Station $J$ simultaneously, and move in opposite directions towards car $A$. Car $A$ meets car $B$ first, then 20 minutes later it meets car $C$. Given the speeds of cars $A$, $B$, and $C$ ... | Car $A$ departs from Station $J$ towards Station $Y$, while cars $B$ and $C$ depart from Station $Y$ towards Station $J$ simultaneously, and move in opposite directions towards car $A$. Car $A$ meets car $B$ first, then 20 minutes later it meets car $C$. Given the speeds of cars $A$, $B$, and $C$ are $90 \text{ km/h}$,... | "[\"425\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 856, "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:14885"}] | {
"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
} |
[
"36"
] | [
"skywork"
] | f2df54e98f671798b0aa6a8630efbecbc425a331679c0a06d6b9f7f8c87e2eab | [
{
"content": "The graphs $y = 3(x-h)^2 + j$ and $y = 2(x-h)^2 + k$ have y-intercepts of $2013$ and $2014$ , respectively, and each graph has two positive integer x-intercepts. Find $h$ .",
"role": "user"
}
] | The graphs $y = 3(x-h)^2 + j$ and $y = 2(x-h)^2 + k$ have y-intercepts of $2013$ and $2014$ , respectively, and each graph has two positive integer x-intercepts. Find $h$ . | "[\"36\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 859, "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:14886"}, {"dataset": "skywork", "extra_info... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\text{no}"
] | [
"skywork"
] | 022163e77a4ed06f0a98173d75001668a1c17e2db5406801f6f4308f27f95f1e | [
{
"content": "Call a sequence of positive integers $\\{a_n\\}$ good if for any distinct positive integers $m,n$, one has \n$$\\gcd(m,n) \\mid a_m^2 + a_n^2 \\text{ and } \\gcd(a_m,a_n) \\mid m^2 + n^2.$$\nCall a positive integer $a$ to be $k$-good if there exists a good sequence such that $a_k = a$. Does there ... | Call a sequence of positive integers $\{a_n\}$ good if for any distinct positive integers $m,n$, one has
$$\gcd(m,n) \mid a_m^2 + a_n^2 \text{ and } \gcd(a_m,a_n) \mid m^2 + n^2.$$
Call a positive integer $a$ to be $k$-good if there exists a good sequence such that $a_k = a$. Does there exists a $k$ such that there ar... | "[\"\\\\text{no}\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 865, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14887"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"- \\frac { \\sqrt {10}}{10}"
] | [
"skywork"
] | 5d0f61c7903b090efdb8df67418485be54c3d34988770334d606deb04f0adff4 | [
{
"content": "1. Calculate $\\log _{2.5}6.25+ \\lg 0.01+ \\ln \\sqrt {e}-2\\,^{1+\\log _{2}3}$\n2. Given $\\tan \\alpha=-3$, and $\\alpha$ is an angle in the second quadrant, find $\\sin \\alpha$ and $\\cos \\alpha$.",
"role": "user"
}
] | 1. Calculate $\log _{2.5}6.25+ \lg 0.01+ \ln \sqrt {e}-2\,^{1+\log _{2}3}$
2. Given $\tan \alpha=-3$, and $\alpha$ is an angle in the second quadrant, find $\sin \alpha$ and $\cos \alpha$. | "[\"- \\\\frac { \\\\sqrt {10}}{10}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 853, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14888"}] | {
"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 + 5\\sqrt{10}"
] | [
"skywork"
] | c6e42894fce33cedaeaae0ef664fa2d0c24fc73917f80cfbc81bdad18b190495 | [
{
"content": "John is planning to fence a rectangular garden such that the area is at least 150 sq. ft. The length of the garden should be 20 ft longer than its width. Additionally, the total perimeter of the garden must not exceed 70 ft. What should the width, in feet, be?",
"role": "user"
}
] | John is planning to fence a rectangular garden such that the area is at least 150 sq. ft. The length of the garden should be 20 ft longer than its width. Additionally, the total perimeter of the garden must not exceed 70 ft. What should the width, in feet, be? | "[\"-10 + 5\\\\sqrt{10}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 879, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14889"}] | {
"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
} |
[
"19"
] | [
"skywork"
] | a60d76bc4d311e4538729c39182bbe1cb72c9db42dfcfcca37e5101d18d593ec | [
{
"content": "The function $f$ is defined on positive integers as follows:\n\\[f(n) = \\left\\{\n\\begin{array}{cl}\nn + 10 & \\text{if $n < 10$}, \\\\\nf(n - 5) & \\text{if $n \\ge 10$}.\n\\end{array}\n\\right.\\]Find the maximum value of the function.",
"role": "user"
}
] | The function $f$ is defined on positive integers as follows:
\[f(n) = \left\{
\begin{array}{cl}
n + 10 & \text{if $n < 10$}, \\
f(n - 5) & \text{if $n \ge 10$}.
\end{array}
\right.\]Find the maximum value of the function. | "[\"19\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 863, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14890"}] | {
"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"
] | [
"skywork"
] | cd7e18c668e5ad223eaa74311acef4fff00f5a96c2949e04fcbb229c7ab3b372 | [
{
"content": "Let $\\mathcal{P}$ be a convex polygon with $50$ vertices. A set $\\mathcal{F}$ of diagonals of $\\mathcal{P}$ is said to be *$minimally friendly$* if any diagonal $d \\in \\mathcal{F}$ intersects at most one other diagonal in $\\mathcal{F}$ at a point interior to $\\mathcal{P}.$... | Let $\mathcal{P}$ be a convex polygon with $50$ vertices. A set $\mathcal{F}$ of diagonals of $\mathcal{P}$ is said to be *$minimally friendly$* if any diagonal $d \in \mathcal{F}$ intersects at most one other diagonal in $\mathcal{F}$ at a point interior to $\mathcal{P}.$ Find the largest possible ... | "[\"72\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 875, "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:14891"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"n = 15"
] | [
"skywork"
] | 3b4fd25b22222a15be1995cc9394792668b74fdd68f75b8b53a1eec0b993b2c6 | [
{
"content": "There are given $111$ coins and a $n\\times n$ table divided into unit cells. This coins are placed inside the unit cells (one unit cell may contain one coin, many coins, or may be empty), such that the difference between the number of coins from two neighbouring cells (that have a common edge) is... | There are given $111$ coins and a $n\times n$ table divided into unit cells. This coins are placed inside the unit cells (one unit cell may contain one coin, many coins, or may be empty), such that the difference between the number of coins from two neighbouring cells (that have a common edge) is $1$. Find the maximal ... | "[\" n = 15 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 866, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14892"}] | {
"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}{6}"
] | [
"skywork"
] | bc5710e3002b5202b9adfa5bbacc0d1a87e5544ace736f21ca609077d24ca354 | [
{
"content": "The three roots of the equation \\[ax^3 + bx^2 + cx + d = 0\\] are \\(-1,\\) \\(2,\\) and \\(3.\\) Compute \\(\\frac{c}{d}.\\)",
"role": "user"
}
] | The three roots of the equation \[ax^3 + bx^2 + cx + d = 0\] are \(-1,\) \(2,\) and \(3.\) Compute \(\frac{c}{d}.\) | "[\"-\\\\frac{1}{6}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 874, "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:14893"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2/3"
] | [
"skywork"
] | 5feb40ade82258d15cf897e4e23bd2911b55762d22c1a7870dfcc08ce31a19ba | [
{
"content": "A point is randomly thrown on the segment \\([6, 11]\\) and let \\( k \\) be the resulting value. Find the probability that the roots of the equation \\(\\left(k^{2}-2k-24\\right)x^{2}+(3k-8)x+2=0\\) satisfy the condition \\( x_{1} \\leq 2x_{2} \\).",
"role": "user"
}
] | A point is randomly thrown on the segment \([6, 11]\) and let \( k \) be the resulting value. Find the probability that the roots of the equation \(\left(k^{2}-2k-24\right)x^{2}+(3k-8)x+2=0\) satisfy the condition \( x_{1} \leq 2x_{2} \). | "[\"2/3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 858, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14894"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"128"
] | [
"skywork"
] | ae9f5ee9225d681dd405258aa707c67ecaa2efa9c5f4d7db74ab411d577857bf | [
{
"content": "A sequence of positive integers $a_1,a_2,\\ldots $ is such that for each $m$ and $n$ the following holds: if $m$ is a divisor of $n$ and $m<n$, then $a_m$ is a divisor of $a_n$ and $a_m<a_n$. Find the least possible value of $a_{2000}$.",
"role": "user"
}
] | A sequence of positive integers $a_1,a_2,\ldots $ is such that for each $m$ and $n$ the following holds: if $m$ is a divisor of $n$ and $m<n$, then $a_m$ is a divisor of $a_n$ and $a_m<a_n$. Find the least possible value of $a_{2000}$. | "[\"128\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 867, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:14895"}, {"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
} |
[
"3"
] | [
"skywork"
] | aa45ad9bfd82384c46c7229551f0b77a9d9f8e58d4d59ac5929eaabe648bdd18 | [
{
"content": "How many integers between 1000 and 2000 have all three of the numbers 15, 20 and 25 as factors?",
"role": "user"
}
] | How many integers between 1000 and 2000 have all three of the numbers 15, 20 and 25 as factors? | "[\"3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 891, "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:14896"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-\\frac{6}{13},\\frac{9}{26},-\\frac{18}{13}"
] | [
"skywork"
] | fe835bbc33abc31baef4ee6bee2eb9b43a1eaa2223099af7a77b164388914672 | [
{
"content": "11. Solve the system of equations in the set of real numbers $\\left\\{\\begin{array}{l}x^{2}+y^{2}+z^{2}=\\frac{9}{4} \\\\ -8 x+6 y-24 z=39 .\\end{array}\\right.$",
"role": "user"
}
] | 11. Solve the system of equations in the set of real numbers $\left\{\begin{array}{l}x^{2}+y^{2}+z^{2}=\frac{9}{4} \\ -8 x+6 y-24 z=39 .\end{array}\right.$ | "[\"-\\\\frac{6}{13},\\\\frac{9}{26},-\\\\frac{18}{13}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 881, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14897"}] | {
"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"
] | dbf697ad815b7f85ec8e8f5cb58ea9f34dbaad4157af6fa3d98ebfa6242766eb | [
{
"content": "5. Find all values of $a$, for each of which the system\n\n$$\n\\left\\{\\begin{array}{l}\n|y|+|y-x| \\leqslant a-|x-1| \\\\\n(y-4)(y+3) \\geqslant(4-x)(3+x)\n\\end{array}\\right.\n$$\n\nhas exactly two solutions.",
"role": "user"
}
] | 5. Find all values of $a$, for each of which the system
$$
\left\{\begin{array}{l}
|y|+|y-x| \leqslant a-|x-1| \\
(y-4)(y+3) \geqslant(4-x)(3+x)
\end{array}\right.
$$
has exactly two solutions. | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 883, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14898"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"d_{17} = 28"
] | [
"skywork"
] | a38293f37ba436296068dce5a368cb6561afad6c9f2adb7082d8a230b2a5a72f | [
{
"content": "Let $ d_1,d_2 \\ldots, d_r$ be the positive divisors of $ n$\r\n$ 1\\equal{}d_1<d_2< \\ldots <d_r\\equal{}n$\r\nIf $ (d_7)^2 \\plus{} (d_{15})^2\\equal{} (d_{16})^2$ find all posible values of $ d_{17}$",
"role": "user"
}
] | Let $ d_1,d_2 \ldots, d_r$ be the positive divisors of $ n$
$ 1\equal{}d_1<d_2< \ldots <d_r\equal{}n$
If $ (d_7)^2 \plus{} (d_{15})^2\equal{} (d_{16})^2$ find all posible values of $ d_{17}$ | "[\" d_{17} = 28 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 824, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14899"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"53"
] | [
"skywork"
] | 3cc9887c3fa5d8f42c124ff0a2171c3d4718c2d2578707a9b04d9b7ec1798bf1 | [
{
"content": "When Xiaohong was 3 years old, her mother's age was the same as Xiaohong's age this year. When her mother is 78 years old, Xiaohong's age is the same as her mother’s age this year. How old is Xiaohong’s mother this year?",
"role": "user"
}
] | When Xiaohong was 3 years old, her mother's age was the same as Xiaohong's age this year. When her mother is 78 years old, Xiaohong's age is the same as her mother’s age this year. How old is Xiaohong’s mother this year? | "[\"53\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 895, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14900"}] | {
"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
} |
[
"2012"
] | [
"skywork"
] | aa29babfa996b063ab3dc4578f2096d5f2af7740730fc809fdc4567a38b2a6e6 | [
{
"content": "The function $f$ satisfies the condition $$ f (x + 1) = \\frac{1 + f (x)}{1 - f (x)} $$ for all real $x$ , for which the function is defined. Determine $f(2012)$ , if we known that $f(1000)=2012$ .",
"role": "user"
}
] | The function $f$ satisfies the condition $$ f (x + 1) = \frac{1 + f (x)}{1 - f (x)} $$ for all real $x$ , for which the function is defined. Determine $f(2012)$ , if we known that $f(1000)=2012$ . | "[\"2012\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 873, "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:14901"}, {"dataset": "skywork", "extra_info... | {
"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"
] | [
"skywork"
] | 9c1be552bcf7d94a65f1ce0deb7ccaef0dabb31418b404c0528f13d2e09849f5 | [
{
"content": "Given the real numbers \\( x \\) and \\( y \\) satisfy the equations:\n\\[ 2^x + 4x + 12 = \\log_2{(y-1)^3} + 3y + 12 = 0 \\]\nfind the value of \\( x + y \\).",
"role": "user"
}
] | Given the real numbers \( x \) and \( y \) satisfy the equations:
\[ 2^x + 4x + 12 = \log_2{(y-1)^3} + 3y + 12 = 0 \]
find the value of \( x + y \). | "[\"-2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 850, "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:14902"}] | {
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"reference_components": 1,
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[
"f(x)=\\frac{1}{2}(x+1-\\frac{1}{x}-\\frac{1}{1-x})"
] | [
"skywork"
] | a32b2b9d20a742a4ca168042a6b3cb8a9dac2f24843a2e9017c13f07d6449cd8 | [
{
"content": "Find all functions from $\\mathbb{R}-\\{0,1\\}$ to $\\mathbb{R}$ such that\n\n$$\nf(x)+f\\left(\\frac{1}{1-x}\\right)=x\n$$",
"role": "user"
}
] | Find all functions from $\mathbb{R}-\{0,1\}$ to $\mathbb{R}$ such that
$$
f(x)+f\left(\frac{1}{1-x}\right)=x
$$ | "[\"f(x)=\\\\frac{1}{2}(x+1-\\\\frac{1}{x}-\\\\frac{1}{1-x})\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 872, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:14903"}, {"dataset": "skywork", "extra_inf... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3\\sqrt{6}}{8}"
] | [
"skywork"
] | 4e052c66d4fcd8cd2f05fd0b01fe8893d6fd2f904e12bd20fabeae2f9872ed3e | [
{
"content": "## [ Product of lengths of chord segments and lengths of secant segments ]\n\nThe radii of two concentric circles are in the ratio $1: 2$. A chord of the larger circle is divided into three equal parts by the smaller circle. Find the ratio of this chord to the diameter of the larger circle.",
... | ## [ Product of lengths of chord segments and lengths of secant segments ]
The radii of two concentric circles are in the ratio $1: 2$. A chord of the larger circle is divided into three equal parts by the smaller circle. Find the ratio of this chord to the diameter of the larger circle. | "[\"\\\\frac{3\\\\sqrt{6}}{8}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 885, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14904"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"595"
] | [
"skywork"
] | 4f3f33fdec875fd56c0a1ba213bc57505352f2cf23e4f2726d96c0316df97cc4 | [
{
"content": "10. To pack books when moving a school library, you can buy small boxes that hold 12 books or large ones that hold 25 books. If all the books are packed in small boxes, 7 books will remain, and if all the books are packed in large boxes, there will be room for 5 more books. The library's collectio... | 10. To pack books when moving a school library, you can buy small boxes that hold 12 books or large ones that hold 25 books. If all the books are packed in small boxes, 7 books will remain, and if all the books are packed in large boxes, there will be room for 5 more books. The library's collection contains between 500... | "[\"595\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 889, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14905"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"111\\frac{1}{9}"
] | [
"skywork"
] | 7d770028a7e99548541381cb98967b9debeb1369a5de33f8d191bd9604c16398 | [
{
"content": "[ Percentage and ratio problems ]\n\nHow many pounds of grain need to be milled to have exactly 100 pounds of flour left after paying for the work - 10% of the milling?\n\nThere are no losses during milling.\n\n#",
"role": "user"
}
] | [ Percentage and ratio problems ]
How many pounds of grain need to be milled to have exactly 100 pounds of flour left after paying for the work - 10% of the milling?
There are no losses during milling.
# | "[\"111\\\\frac{1}{9}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 864, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14906"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\log_{8192} \\frac{1}{42}"
] | [
"skywork"
] | d195b0356a76dd2d832c139e5553525a983596ec2465c77cfc86fbb80cc706ed | [
{
"content": "For all integers \\(n\\) greater than 1, define \\(a_n = \\frac{1}{\\log_n 8192}\\). Let \\(b = a_3 + a_4\\) and \\(c = a_7 + a_8 + a_9\\). Find \\(b - c.\\)",
"role": "user"
}
] | For all integers \(n\) greater than 1, define \(a_n = \frac{1}{\log_n 8192}\). Let \(b = a_3 + a_4\) and \(c = a_7 + a_8 + a_9\). Find \(b - c.\) | "[\"\\\\log_{8192} \\\\frac{1}{42}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 878, "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:14907"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-16245775"
] | [
"skywork"
] | 66acca7a0607304f779a530d7f2be3d168b22e7e4104af308fdedf97bbec17b5 | [
{
"content": "Evaluate $(a^b)^a - (b^a)^b$ for $a = 3$ and $b = 4$.",
"role": "user"
}
] | Evaluate $(a^b)^a - (b^a)^b$ for $a = 3$ and $b = 4$. | "[\"-16245775\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 902, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14908"}] | {
"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
} |
[
"256"
] | [
"skywork"
] | 963a1c33e2560348430dfd1879bc647fd0a7f081b70ebede01f7f9c44bf30cfb | [
{
"content": "For every positive integer $k$, let $\\mathbf{T}_k = (k(k+1), 0)$, and define $\\mathcal{H}_k$ as the homothety centered at $\\mathbf{T}_k$ with ratio $\\tfrac{1}{2}$ if $k$ is odd and $\\tfrac{2}{3}$ is $k$ is even. Suppose $P = (x,y)$ is a point such that \n$$(\\mathcal{H}_{4} \\circ \\mathcal{H... | For every positive integer $k$, let $\mathbf{T}_k = (k(k+1), 0)$, and define $\mathcal{H}_k$ as the homothety centered at $\mathbf{T}_k$ with ratio $\tfrac{1}{2}$ if $k$ is odd and $\tfrac{2}{3}$ is $k$ is even. Suppose $P = (x,y)$ is a point such that
$$(\mathcal{H}_{4} \circ \mathcal{H}_{3} \circ \mathcal{H}_2 \circ... | "[\"256\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 870, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14909"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"30"
] | [
"skywork"
] | 3e35a4fec2133075fff00a5413f2c3f3a9d5672a810c2aafe8cec58159735924 | [
{
"content": "The car engine operates with a power of \\( P = 60 \\text{ kW} \\). Determine the car's speed \\( v_0 \\) if, after turning off the engine, it stops after traveling a distance of \\( s = 450 \\text{ m} \\). The force resisting the car's motion is proportional to its speed. The mass of the car is \... | The car engine operates with a power of \( P = 60 \text{ kW} \). Determine the car's speed \( v_0 \) if, after turning off the engine, it stops after traveling a distance of \( s = 450 \text{ m} \). The force resisting the car's motion is proportional to its speed. The mass of the car is \( m = 1000 \text{ kg} \). | "[\"30\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 871, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14910"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"110"
] | [
"skywork"
] | e6077987c209580e88a3c35c3a24c625cc905021de80474aed2f0164ce65363f | [
{
"content": "Circle $C_0$ has radius $1$, and the point $A_0$ is a point on the circle. Circle $C_1$ has radius $r<1$ and is internally tangent to $C_0$ at point $A_0$. Point $A_1$ lies on circle $C_1$ so that $A_1$ is located $90^{\\circ}$ counterclockwise from $A_0$ on $C_1$. Circle $C_2$ has radius $r^2$ an... | Circle $C_0$ has radius $1$, and the point $A_0$ is a point on the circle. Circle $C_1$ has radius $r<1$ and is internally tangent to $C_0$ at point $A_0$. Point $A_1$ lies on circle $C_1$ so that $A_1$ is located $90^{\circ}$ counterclockwise from $A_0$ on $C_1$. Circle $C_2$ has radius $r^2$ and is internally tangent... | "[\"110\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 877, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14911"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2}"
] | [
"skywork"
] | c8c5f86cacb64daefafa76fa67481c4149a767d5871708b8a03646d164625438 | [
{
"content": "Find the sum $$\\frac{3^1}{9^1 - 1} + \\frac{3^2}{9^2 - 1} + \\frac{3^3}{9^3 - 1} + \\frac{3^4}{9^4 - 1} + \\cdots.$$",
"role": "user"
}
] | Find the sum $$\frac{3^1}{9^1 - 1} + \frac{3^2}{9^2 - 1} + \frac{3^3}{9^3 - 1} + \frac{3^4}{9^4 - 1} + \cdots.$$ | "[\"\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 903, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14912"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | b4a0018ae33badc0137df272d40589632488f4722bbef75f737c3d0be2ce574d | [
{
"content": "1. Given that $a, b, c$ are non-negative real numbers, and $S=a+2 b+3 c, T=a+b^{2}+c^{3}$.\n(1) Find the minimum value of $T-S$;\n(2) If $S=4$, find the maximum value of $T$.",
"role": "user"
}
] | 1. Given that $a, b, c$ are non-negative real numbers, and $S=a+2 b+3 c, T=a+b^{2}+c^{3}$.
(1) Find the minimum value of $T-S$;
(2) If $S=4$, find the maximum value of $T$. | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 884, "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:14913"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"f(n)=n^{3}"
] | [
"skywork"
] | 686842b4fe676108257d787dbf17e654ad7c9554a1fd6194e17ee4ce1688558a | [
{
"content": "Denote $\\mathbb{Z}_{>0}=\\{1,2,3, \\ldots\\}$ the set of all positive integers. Determine all functions $f: \\mathbb{Z}_{>0} \\rightarrow \\mathbb{Z}_{>0}$ such that, for each positive integer $n$,\ni) $\\sum_{k=1}^{n} f(k)$ is a perfect square, and\nii) $f(n)$ divides $n^{3}$.",
"role": "use... | Denote $\mathbb{Z}_{>0}=\{1,2,3, \ldots\}$ the set of all positive integers. Determine all functions $f: \mathbb{Z}_{>0} \rightarrow \mathbb{Z}_{>0}$ such that, for each positive integer $n$,
i) $\sum_{k=1}^{n} f(k)$ is a perfect square, and
ii) $f(n)$ divides $n^{3}$. | "[\"f(n)=n^{3}\"]" | train-math-numinamath1.5_olympiads_ref | [{"dataset": "skywork", "extra_info": {"index": 880, "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:14914"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2}\\leqx\\leq1"
] | [
"skywork"
] | d9b32feb2116c37bd6eac713d6efd41fccbea5e8a41954867e1fcc80052be615 | [
{
"content": "10.1. Find all solutions of the equation: $\\sqrt{x+\\sqrt{2 x-1}}+\\sqrt{x-\\sqrt{2 x-1}}=\\sqrt{2}$.",
"role": "user"
}
] | 10.1. Find all solutions of the equation: $\sqrt{x+\sqrt{2 x-1}}+\sqrt{x-\sqrt{2 x-1}}=\sqrt{2}$. | "[\"\\\\frac{1}{2}\\\\leqx\\\\leq1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 894, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14915"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"A(0,125),B(5,150),C(-5,150)"
] | [
"skywork"
] | 1b2e4d1a1afa639e16ca7e66a195b103f36555dfc8d932dc2bd84041aed358ea | [
{
"content": "## Zadatak B-2.4.\n\nSva tri vrha trokuta $A B C$ pripadaju paraboli s jednadžbom $y=x^{2}+125$ tako da vrh $A$ leži na njezinoj osi simetrije, a stranica $\\overline{B C}$ je paralelna s osi $x$. Ako površina trokuta $A B C$ iznosi 125 , odredite koordinate njegovih vrhova.",
"role": "user"
... | ## Zadatak B-2.4.
Sva tri vrha trokuta $A B C$ pripadaju paraboli s jednadžbom $y=x^{2}+125$ tako da vrh $A$ leži na njezinoj osi simetrije, a stranica $\overline{B C}$ je paralelna s osi $x$. Ako površina trokuta $A B C$ iznosi 125 , odredite koordinate njegovih vrhova. | "[\"A(0,125),B(5,150),C(-5,150)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 876, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14916"}] | {
"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
} |
[
"200"
] | [
"skywork"
] | b27c21056a93186790dc1cec8b317a57b089a3304b1ec7607144daf3b0b678e4 | [
{
"content": "A line contains 40 characters: 20 crosses and 20 zeros. In one move, you can swap any two adjacent characters. What is the minimum number of moves required to ensure that 20 consecutive characters are crosses?\n\n#",
"role": "user"
}
] | A line contains 40 characters: 20 crosses and 20 zeros. In one move, you can swap any two adjacent characters. What is the minimum number of moves required to ensure that 20 consecutive characters are crosses?
# | "[\"200\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 909, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14917"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"60"
] | [
"skywork"
] | bb46b474d182d6e943d5e51ba7a1b4546b79764ca9c2c5a1e976ba5b410c2fd2 | [
{
"content": "Problem 3. (6 points) What is the maximum number of knights that can be placed on an $8 \\times 8$ chessboard such that each of them threatens at most seven other knights?",
"role": "user"
}
] | Problem 3. (6 points) What is the maximum number of knights that can be placed on an $8 \times 8$ chessboard such that each of them threatens at most seven other knights? | "[\"60\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 901, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14918"}] | {
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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{3}{5}"
] | [
"skywork"
] | d295a91a12209983725f2240ac970da0c911fa62bdf37140e93854ac468a79de | [
{
"content": "Given that 3 people are to be selected from 5 girls and 2 boys, if girl A is selected, determine the probability that at least one boy is selected.",
"role": "user"
}
] | Given that 3 people are to be selected from 5 girls and 2 boys, if girl A is selected, determine the probability that at least one boy is selected. | "[\"\\\\frac{3}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 900, "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:14919"}] | {
"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
} |
[
"16"
] | [
"skywork"
] | 3519ddf182dceab9b570b47f9edf1a232021a0a5059938c5b306f002d6cd02a0 | [
{
"content": "$\\underline{\\text { Folklore }}$\n\nOn a chessboard, $n$ white and $n$ black rooks are placed such that rooks of different colors do not attack each other. Find the maximum possible value of $n$.\n\n#",
"role": "user"
}
] | $\underline{\text { Folklore }}$
On a chessboard, $n$ white and $n$ black rooks are placed such that rooks of different colors do not attack each other. Find the maximum possible value of $n$.
# | "[\"16\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 890, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14920"}] | {
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[
"1"
] | [
"skywork"
] | f03e337ec133816b62e52809741e22c4206d50c032eef0c5736a8d76e40da3a0 | [
{
"content": "G3.2 It is given that $f(x)=\\frac{1}{3} x^{3}-2 x^{2}+\\frac{2}{3} x^{3}+3 x^{2}+5 x+7-4 x$. If $f(-2)=b$, find $b$.",
"role": "user"
}
] | G3.2 It is given that $f(x)=\frac{1}{3} x^{3}-2 x^{2}+\frac{2}{3} x^{3}+3 x^{2}+5 x+7-4 x$. If $f(-2)=b$, find $b$. | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 893, "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:14921"}] | {
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} |
[
"14"
] | [
"skywork"
] | ca1dc467ca16219ee1514e9d6ce324869fca7322ce09f98bcbbdd72280c71f1f | [
{
"content": "In the diagram, triangles $ABC$ and $CBD$ are isosceles with $\\angle ABC = \\angle BAC$ and $\\angle CBD = \\angle CDB$. The perimeter of $\\triangle CBD$ is $18,$ the perimeter of $\\triangle ABC$ is $24,$ and the length of $BD$ is $8.$ If $\\angle ABC = \\angle CBD$, find the length of $AB.$",
... | In the diagram, triangles $ABC$ and $CBD$ are isosceles with $\angle ABC = \angle BAC$ and $\angle CBD = \angle CDB$. The perimeter of $\triangle CBD$ is $18,$ the perimeter of $\triangle ABC$ is $24,$ and the length of $BD$ is $8.$ If $\angle ABC = \angle CBD$, find the length of $AB.$ | "[\"14\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 888, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14922"}] | {
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"plain_numeric_reference": true,
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} |
[
"29"
] | [
"skywork"
] | ec6d997d4ce8530cccc0dc116802b7070f66007bd40886b1a3eb0d24cb708e0c | [
{
"content": "A regular hexagon with center at the origin in the complex plane has opposite pairs of sides one unit apart. One pair of sides is parallel to the imaginary axis. Let $R$ be the region outside the hexagon, and let $S = \\left\\lbrace\\frac{1}{z}|z \\in R\\right\\rbrace$. Then the area of $S$ has th... | A regular hexagon with center at the origin in the complex plane has opposite pairs of sides one unit apart. One pair of sides is parallel to the imaginary axis. Let $R$ be the region outside the hexagon, and let $S = \left\lbrace\frac{1}{z}|z \in R\right\rbrace$. Then the area of $S$ has the form $a\pi + \sqrt{b}$, wh... | "[\"29\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 905, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14923"}, {"dataset": "skywork", "extra_in... | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"80^\\circ"
] | [
"skywork"
] | 79009a66ba4d26e2ab0f2112d5b48ec3f47b0dece41b78f11affff1c5d035d5a | [
{
"content": "Let $P$ and $Q$ be the midpoints of sides $AB$ and $BC,$ respectively, of $\\triangle ABC.$ Suppose $\\angle A = 30^{\\circ}$ and $\\angle PQC = 110^{\\circ}.$ Find $\\angle B$ in degrees.",
"role": "user"
}
] | Let $P$ and $Q$ be the midpoints of sides $AB$ and $BC,$ respectively, of $\triangle ABC.$ Suppose $\angle A = 30^{\circ}$ and $\angle PQC = 110^{\circ}.$ Find $\angle B$ in degrees. | "[\"80^\\\\circ\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 919, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14924"}, {"dataset": "skywork", "extra_inf... | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | 3f4bc3c6825508c1627c2aca287cc8390fcb682de5fc4c99396dee915307a1a6 | [
{
"content": "$f$ is a differentiable function such that $f(f(x))=x$ where $x \\in [0,1]$.Also $f(0)=1$.Find the value of \n\n$$\\int_0^1(x-f(x))^{2016}dx$$",
"role": "user"
}
] | $f$ is a differentiable function such that $f(f(x))=x$ where $x \in [0,1]$.Also $f(0)=1$.Find the value of
$$\int_0^1(x-f(x))^{2016}dx$$ | "[\"0\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 892, "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:14925"}] | {
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"65"
] | [
"skywork"
] | 9bf0dcad7610ced86160bd8f7fd73d18b85c642666bf2326b49c6631d0bebbfc | [
{
"content": "On Day $1$, Alice starts with the number $a_1=5$. For all positive integers $n>1$, on Day $n$, Alice randomly selects a positive integer $a_n$ between $a_{n-1}$ and $2a_{n-1}$, inclusive. Given that the probability that all of $a_2,a_3,\\ldots,a_7$ are odd can be written as $\\frac{m}{n}$, where $... | On Day $1$, Alice starts with the number $a_1=5$. For all positive integers $n>1$, on Day $n$, Alice randomly selects a positive integer $a_n$ between $a_{n-1}$ and $2a_{n-1}$, inclusive. Given that the probability that all of $a_2,a_3,\ldots,a_7$ are odd can be written as $\frac{m}{n}$, where $m$ and $n$ are relativel... | "[\"65\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 882, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14926"}] | {
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} |
[
"\\frac{12005}{625000}"
] | [
"skywork"
] | e973d8a3a7c2faae6c7ce307f94d8f29216278028354a2feccd861715814b04d | [
{
"content": "A pirate is searching for buried treasure on 7 islands. Each island has a $\\frac{1}{5}$ chance of containing buried treasure and no traps, a $\\frac{1}{10}$ chance of having traps but no treasure, and a $\\frac{7}{10}$ chance of having neither traps nor treasure. What is the probability that, aft... | A pirate is searching for buried treasure on 7 islands. Each island has a $\frac{1}{5}$ chance of containing buried treasure and no traps, a $\frac{1}{10}$ chance of having traps but no treasure, and a $\frac{7}{10}$ chance of having neither traps nor treasure. What is the probability that, after exploring all 7 island... | "[\"\\\\frac{12005}{625000}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 912, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14927"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"AP:PC=4,BD=\\frac{35}{\\sqrt{19}}"
] | [
"skywork"
] | 01a5af90cecfb842b0eebb3304e6fb6d3de1c20ba813197b7357b3e971520f2a | [
{
"content": "5. The diagonals $A C$ and $B D$ of the quadrilateral $A B C D$, inscribed in a circle, intersect at point $P$. It is known that the distances from point $P$ to the sides $A B, B C, C D, D A$ are $4, \\sqrt{3}, \\frac{8}{\\sqrt{19}}$ and $8 \\sqrt{\\frac{3}{19}}$ respectively (the bases of the per... | 5. The diagonals $A C$ and $B D$ of the quadrilateral $A B C D$, inscribed in a circle, intersect at point $P$. It is known that the distances from point $P$ to the sides $A B, B C, C D, D A$ are $4, \sqrt{3}, \frac{8}{\sqrt{19}}$ and $8 \sqrt{\frac{3}{19}}$ respectively (the bases of the perpendiculars dropped from po... | "[\"AP:PC=4,BD=\\\\frac{35}{\\\\sqrt{19}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 886, "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:14928"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac {\\pi}{3}"
] | [
"skywork"
] | c10f18935c958f1ea0bd0670da8a250854b1271962abc5f356f13179b07c894e | [
{
"content": "Given the function $$f(x)=2\\sin x( \\sqrt {3}\\cos x-\\sin x)+1$$, if $f(x-\\varphi)$ is an even function, determine the value of $\\varphi$.",
"role": "user"
}
] | Given the function $$f(x)=2\sin x( \sqrt {3}\cos x-\sin x)+1$$, if $f(x-\varphi)$ is an even function, determine the value of $\varphi$. | "[\"\\\\frac {\\\\pi}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 899, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14929"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-\\frac{7\\sqrt{2}}{26}"
] | [
"skywork"
] | 88dadadc2aa7693355af8c6e36c25398030db0a04f68184e9906a84e67284c89 | [
{
"content": "7. If $\\cos \\theta=-\\frac{12}{13}, \\theta \\in\\left(\\pi, \\frac{3}{2} \\pi\\right)$, then $\\cos \\left(\\theta+\\frac{\\pi}{4}\\right)=$",
"role": "user"
}
] | 7. If $\cos \theta=-\frac{12}{13}, \theta \in\left(\pi, \frac{3}{2} \pi\right)$, then $\cos \left(\theta+\frac{\pi}{4}\right)=$ | "[\"-\\\\frac{7\\\\sqrt{2}}{26}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 917, "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:14930"}, {"dataset": "skywork", "extra_info... | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-8"
] | [
"skywork"
] | 4175e00258266f315ee04a22a3aabe1a18b14610fcba35c172c4b861bfa806ab | [
{
"content": "Solve\n\\[\\frac{1}{x + 9} + \\frac{1}{x + 7} = \\frac{1}{x + 10} + \\frac{1}{x + 6}.\\]",
"role": "user"
}
] | Solve
\[\frac{1}{x + 9} + \frac{1}{x + 7} = \frac{1}{x + 10} + \frac{1}{x + 6}.\] | "[\"-8\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 916, "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:14931"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"500"
] | [
"skywork"
] | 5900644e5e9a64995e526585c6c4bb59f73b2910725cec86a4b5edbb43e25ba2 | [
{
"content": "9.2. A merchant bought several bags of salt in Tver and sold them in Moscow with a profit of 100 rubles. With all the money earned, he again bought salt in Tver (at the Tver price) and sold it in Moscow (at the Moscow price). This time the profit was 120 rubles. How much money did he spend on the ... | 9.2. A merchant bought several bags of salt in Tver and sold them in Moscow with a profit of 100 rubles. With all the money earned, he again bought salt in Tver (at the Tver price) and sold it in Moscow (at the Moscow price). This time the profit was 120 rubles. How much money did he spend on the first purchase? | "[\"500\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 907, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14932"}] | {
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"plain_numeric_reference": true,
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"reference_present": true
} |
[
"x"
] | [
"skywork"
] | 4c333ff798e522802261c14f614ecdbf7e7df91187645700ad8ecfe07765a6a6 | [
{
"content": "Simplify the following expression as much as possible.\n\n$$\n\\left[x(1-x)^{-\\frac{2}{3}}+\\frac{x^{2}}{(1-x)^{\\frac{5}{3}}}\\right]:\\left[(1-x)^{\\frac{1}{3}}\\left(1-2 x+x^{2}\\right)^{-1}\\right] .\n$$",
"role": "user"
}
] | Simplify the following expression as much as possible.
$$
\left[x(1-x)^{-\frac{2}{3}}+\frac{x^{2}}{(1-x)^{\frac{5}{3}}}\right]:\left[(1-x)^{\frac{1}{3}}\left(1-2 x+x^{2}\right)^{-1}\right] .
$$ | "[\"x\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 914, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14933"}] | {
"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{22}{35}"
] | [
"skywork"
] | 5557fef9c8eb4a7a96f13584f22b397a3246909c5e300be8bde261f205107abc | [
{
"content": "5. Triangle $A B C$ has side lengths $A B=2 \\sqrt{5}, B C=1$, and $C A=5$. Point $D$ is on side $A C$ such that $C D=1$, and $F$ is a point such that $B F=2$ and $C F=3$. Let $E$ be the intersection of lines $A B$ and $D F$. Find the area of $C D E B$.",
"role": "user"
}
] | 5. Triangle $A B C$ has side lengths $A B=2 \sqrt{5}, B C=1$, and $C A=5$. Point $D$ is on side $A C$ such that $C D=1$, and $F$ is a point such that $B F=2$ and $C F=3$. Let $E$ be the intersection of lines $A B$ and $D F$. Find the area of $C D E B$. | "[\"\\\\frac{22}{35}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 898, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14934"}] | {
"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
} |
[
"312"
] | [
"skywork"
] | 61b420afc5fbaf4d6627735a3f26f1299a788cf054a8e5bf8f4b3c5a86414978 | [
{
"content": "Example 9 (1994, 12th American Invitational Mathematics Examination) For a real number $x$, $[x]$ denotes the greatest integer not exceeding $x$. Find the positive integer $n$ such that $\\left[\\log _{2} 1\\right]+\\left[\\log _{2} 2\\right]+\\left[\\log _{2} 3\\right]+\\cdots+\\left[\\log _{2} n... | Example 9 (1994, 12th American Invitational Mathematics Examination) For a real number $x$, $[x]$ denotes the greatest integer not exceeding $x$. Find the positive integer $n$ such that $\left[\log _{2} 1\right]+\left[\log _{2} 2\right]+\left[\log _{2} 3\right]+\cdots+\left[\log _{2} n\right]=1994$. | "[\"312\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 910, "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:14935"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"f(x)=x-1"
] | [
"skywork"
] | 75a05bf87ed78cb4afe132bc42f154e1818bae3948c8055c860b7ef6a8532f87 | [
{
"content": "**Problem 3** Find all functions $f: \\mathbf{R} \\rightarrow \\mathbf{R}$, such that for all $x, y \\in \\mathbf{R}$, we have\n$$\nf(1+x y)-f(x+y)=f(x) f(y),\n$$\n\nand $f(-1) \\neq 0$.",
"role": "user"
}
] | **Problem 3** Find all functions $f: \mathbf{R} \rightarrow \mathbf{R}$, such that for all $x, y \in \mathbf{R}$, we have
$$
f(1+x y)-f(x+y)=f(x) f(y),
$$
and $f(-1) \neq 0$. | "[\"f(x)=x-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 915, "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:14936"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"x_{1}=2,x_{2}=4"
] | [
"skywork"
] | e478e1ee2791506ecfe3adc05d2c2efd7bc0119b172840c805719cc1dc811f33 | [
{
"content": "## Task B-3.1.\n\nSolve the equation $x^{2}-6 x+\\frac{17}{2}=\\left|\\sin \\frac{(2021+18 k) \\pi}{6}\\right|$, for each $k \\in \\mathbb{Z}$.",
"role": "user"
}
] | ## Task B-3.1.
Solve the equation $x^{2}-6 x+\frac{17}{2}=\left|\sin \frac{(2021+18 k) \pi}{6}\right|$, for each $k \in \mathbb{Z}$. | "[\"x_{1}=2,x_{2}=4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 911, "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:14937"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1494"
] | [
"skywork"
] | be20b9c7a246dd0ae5f4fd71f5e1d5cec60dca2697e2bf6d48e934c7c0df61f6 | [
{
"content": "6.4. Find all such four-digit numbers: they are all 83 times the sum of their digits.",
"role": "user"
}
] | 6.4. Find all such four-digit numbers: they are all 83 times the sum of their digits. | "[\"1494\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 922, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14938"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{(n^2 + n)^2}{4}"
] | [
"skywork"
] | 7f04512f81579c0f822f2803e34d94406c1e267a0de2ada6439a698a3ab234b6 | [
{
"content": "Let $n$ be a positive integer. A regular hexagon with side length $n$ is divided into equilateral triangles with side length $1$ by lines parallel to its sides. \nFind the number of regular hexagons all of whose vertices are among the vertices of those equilateral triangles.\n\n[i]UK - Sahl Khan[/... | Let $n$ be a positive integer. A regular hexagon with side length $n$ is divided into equilateral triangles with side length $1$ by lines parallel to its sides.
Find the number of regular hexagons all of whose vertices are among the vertices of those equilateral triangles.
[i]UK - Sahl Khan[/i] | "[\"\\\\frac{(n^2 + n)^2}{4}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 913, "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:14939"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{8}{9}"
] | [
"skywork"
] | d72e32d2a190d0cd6ba63691525c908dd73c615d8572020c79867e3ca85e387b | [
{
"content": "We call a dice roll successful if the rolled number is at least three. What is more likely: that at least one out of two rolls is successful, or that at least two out of four rolls are successful?",
"role": "user"
}
] | We call a dice roll successful if the rolled number is at least three. What is more likely: that at least one out of two rolls is successful, or that at least two out of four rolls are successful? | "[\"\\\\frac{8}{9}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 942, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14940"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{3}"
] | [
"skywork"
] | f68c6846589bc00e131f181a1d357c8633a25f77546e4dc79be2b2de3d51cbd4 | [
{
"content": "6. In quadrilateral $A B C D$, we have $A B=5, B C=6, C D=5, D A=4$, and $\\angle A B C=90^{\\circ}$. Let $A C$ and $B D$ meet at $E$. Compute $\\frac{B E}{E D}$.",
"role": "user"
}
] | 6. In quadrilateral $A B C D$, we have $A B=5, B C=6, C D=5, D A=4$, and $\angle A B C=90^{\circ}$. Let $A C$ and $B D$ meet at $E$. Compute $\frac{B E}{E D}$. | "[\"\\\\sqrt{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 924, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14941"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"624"
] | [
"skywork"
] | 83a557d507f2f0d3ea54176a76a0a7499330dac64e6e308741a4278ba0ef4c62 | [
{
"content": "Six. (16 points) As shown in Figure 3, there is a fixed point $P$ inside $\\angle M A N$. It is known that $\\tan \\angle M A N=3, P$ is at a distance $P D=12$ from the line $A N$, and $A D=30$. A line through $P$ intersects $A N$ and $A M$ at points $B$ and $C$ respectively. Find the minimum area... | Six. (16 points) As shown in Figure 3, there is a fixed point $P$ inside $\angle M A N$. It is known that $\tan \angle M A N=3, P$ is at a distance $P D=12$ from the line $A N$, and $A D=30$. A line through $P$ intersects $A N$ and $A M$ at points $B$ and $C$ respectively. Find the minimum area of $\triangle A B C$.
-... | "[\"624\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 906, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14942"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"99"
] | [
"skywork"
] | 172bcb6d904fa8a1ac3d521c918c40c272c4a9849bd1b5c149b3f4fc978547fb | [
{
"content": "How many times do you have to subtract 8 from 792 to get 0?",
"role": "user"
}
] | How many times do you have to subtract 8 from 792 to get 0? | "[\"99\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 946, "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:14943"}] | {
"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
} |
[
"103"
] | [
"skywork"
] | b28d65e3561f8cd982cf0336e99973e640aa1725f56206233565ba21308fd601 | [
{
"content": "Each positive integer number $n \\ ge 1$ is assigned the number $p_n$ which is the product of all its non-zero digits. For example, $p_6 = 6$ , $p_ {32} = 6$ , $p_ {203} = 6$ . Let $S = p_1 + p_2 + p_3 + \\dots + p_ {999}$ . Find the largest prime that divides $S $ .",
"role": "user"
... | Each positive integer number $n \ ge 1$ is assigned the number $p_n$ which is the product of all its non-zero digits. For example, $p_6 = 6$ , $p_ {32} = 6$ , $p_ {203} = 6$ . Let $S = p_1 + p_2 + p_3 + \dots + p_ {999}$ . Find the largest prime that divides $S $ . | "[\"103\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 921, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14944"}, {"dataset": "skywork", "extra_inf... | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"38.5"
] | [
"skywork"
] | 6a81ff8e56a027da1fef1141712a4a97680bc1cae19588926423e61493360a4f | [
{
"content": "A store sold an air conditioner for 2000 yuan and a color TV for 2000 yuan. The air conditioner made a 30% profit, while the color TV incurred a 20% loss. Could you help the store owner calculate whether the store made a profit or a loss on this transaction, and by how much?",
"role": "user"
... | A store sold an air conditioner for 2000 yuan and a color TV for 2000 yuan. The air conditioner made a 30% profit, while the color TV incurred a 20% loss. Could you help the store owner calculate whether the store made a profit or a loss on this transaction, and by how much? | "[\"38.5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 925, "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:14945"}] | {
"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
} |
[
"208"
] | [
"skywork"
] | 5b495103d0b87b0e539c21050df746698050cf179a64e65d76b80b6365b274fd | [
{
"content": "Auto: : Agakhanov N. $\\mathbf{H}$.\n\nFind the free term of the polynomial $P(x)$ with integer coefficients, if it is known that it is less than a thousand in absolute value, and $P(19)=P(94)=1994$.",
"role": "user"
}
] | Auto: : Agakhanov N. $\mathbf{H}$.
Find the free term of the polynomial $P(x)$ with integer coefficients, if it is known that it is less than a thousand in absolute value, and $P(19)=P(94)=1994$. | "[\"208\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 936, "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:14946"}] | {
"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
} |
[
"64"
] | [
"skywork"
] | 5eeed20a307c525f3e67f48fdc8e63c5a25b72be8f8a8bf5baa1e9c552e2f9d5 | [
{
"content": "Find $x$ such that $\\log_x 4=\\log_{27} 3$.",
"role": "user"
}
] | Find $x$ such that $\log_x 4=\log_{27} 3$. | "[\"64\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 939, "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:14947"}] | {
"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
} |
[
"\\ln 2"
] | [
"skywork"
] | d79491fb8e0d08b90dc86b95a6fa50e1d28f74322012d0701a35ae855ea376be | [
{
"content": "Given that the function $f(x) = e^x + \\frac{a}{e^x}$ has a derivative $y = f'(x)$ that is an odd function and the slope of a tangent line to the curve $y = f(x)$ is $\\frac{3}{2}$, determine the abscissa of the tangent point.",
"role": "user"
}
] | Given that the function $f(x) = e^x + \frac{a}{e^x}$ has a derivative $y = f'(x)$ that is an odd function and the slope of a tangent line to the curve $y = f(x)$ is $\frac{3}{2}$, determine the abscissa of the tangent point. | "[\"\\\\ln 2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 918, "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:14948"}] | {
"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"
] | 57782bcc752309303c0e6163a64f2d10e045de63ac91e9e5a98a3f1152926d04 | [
{
"content": "Farmer Boso has a busy farm with lots of animals. He tends to $5b$ cows, $5a +7$ chickens, and $b^{a-5}$ insects. Note that each insect has $6$ legs. The number of cows is equal to the number of insects. The total number of legs present amongst his animals can be expressed as $\\overline{LLL }+1$,... | Farmer Boso has a busy farm with lots of animals. He tends to $5b$ cows, $5a +7$ chickens, and $b^{a-5}$ insects. Note that each insect has $6$ legs. The number of cows is equal to the number of insects. The total number of legs present amongst his animals can be expressed as $\overline{LLL }+1$, where $L$ stands for a... | "[\"3\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 896, "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:14950"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-\\frac{52 \\pi}{3}"
] | [
"skywork"
] | 135a2cfad0662ecee10c98315722923115e858e6653b4a97458fa0ad68342eff | [
{
"content": "Find the circulation of the vector field\n\n$$\n\\vec{a}=\\frac{y}{3} \\vec{i} 3-3 x \\vec{j}+x \\vec{k}\n$$\n\nalong the closed contour $\\Gamma$\n\n$$\n\\left\\{\\begin{array}{l}\nx=2 \\cos t \\\\\ny=2 \\sin t \\\\\nz=1-2 \\cos t - 2 \\sin t\n\\end{array} \\quad t \\in [0,2\\pi]\n\\right.\n$$",
... | Find the circulation of the vector field
$$
\vec{a}=\frac{y}{3} \vec{i} 3-3 x \vec{j}+x \vec{k}
$$
along the closed contour $\Gamma$
$$
\left\{\begin{array}{l}
x=2 \cos t \\
y=2 \sin t \\
z=1-2 \cos t - 2 \sin t
\end{array} \quad t \in [0,2\pi]
\right.
$$ | "[\"-\\\\frac{52 \\\\pi}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 931, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "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:14951"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 33774bdced620890da812a0dd55b0be99a8472de2fb5182d5d38afb92418bcba | [
{
"content": "Determine the maximum possible real value of the number $ k$, such that\n\\[ (a \\plus{} b \\plus{} c)\\left (\\frac {1}{a \\plus{} b} \\plus{} \\frac {1}{c \\plus{} b} \\plus{} \\frac {1}{a \\plus{} c} \\minus{} k \\right )\\ge k\\]\nfor all real numbers $ a,b,c\\ge 0$ with $ a \\plus{} b \\plus{... | Determine the maximum possible real value of the number $ k$, such that
\[ (a \plus{} b \plus{} c)\left (\frac {1}{a \plus{} b} \plus{} \frac {1}{c \plus{} b} \plus{} \frac {1}{a \plus{} c} \minus{} k \right )\ge k\]
for all real numbers $ a,b,c\ge 0$ with $ a \plus{} b \plus{} c \equal{} ab \plus{} bc \plus{} ca$. | "[\"1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 920, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14952"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"\\frac{3}{8}"
] | [
"skywork"
] | 30e464714cbc27c9f210eccfd0dc548cfddcdbd24eb5e038d536545f7b0547d5 | [
{
"content": "Real numbers $x, y$, and $z$ are chosen from the interval $[-1,1]$ independently and uniformly at random. What is the probability that $|x|+|y|+|z|+|x+y+z|=|x+y|+|y+z|+|z+x|$?",
"role": "user"
}
] | Real numbers $x, y$, and $z$ are chosen from the interval $[-1,1]$ independently and uniformly at random. What is the probability that $|x|+|y|+|z|+|x+y+z|=|x+y|+|y+z|+|z+x|$? | "[\"\\\\frac{3}{8}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 929, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14953"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2}"
] | [
"skywork"
] | aae16c5c737e343a2e92953566ffc9f607666bb6188f133d46b4b4af35a8eb82 | [
{
"content": "Let $M$ be the midpoint of side $AC$ of the triangle $ABC$. Let $P$ be a point on the side $BC$. If $O$ is the point of intersection of $AP$ and $BM$ and $BO = BP$, determine the ratio $\\frac{OM}{PC}$ .",
"role": "user"
}
] | Let $M$ be the midpoint of side $AC$ of the triangle $ABC$. Let $P$ be a point on the side $BC$. If $O$ is the point of intersection of $AP$ and $BM$ and $BO = BP$, determine the ratio $\frac{OM}{PC}$ . | "[\"\\\\frac{1}{2}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 927, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14954"}, {"dataset": "skywork", "extra_info... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"8899"
] | [
"skywork"
] | 14c1eeff5cac135604a1eaafc8ea9c6767923bf68363fb37947f2728448f22d8 | [
{
"content": "Find the smallest natural number \\( n \\) such that the sum of the digits of each of the numbers \\( n \\) and \\( n+1 \\) is divisible by 17.",
"role": "user"
}
] | Find the smallest natural number \( n \) such that the sum of the digits of each of the numbers \( n \) and \( n+1 \) is divisible by 17. | "[\"8899\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 930, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14955"}] | {
"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
} |
[
"598"
] | [
"skywork"
] | c6fb79552787a8b5d263da5a24cef741542f3739bb31c70c074f40d21ec8353c | [
{
"content": "Let $a$ and $b$ be such that $a+b=13$ and $a b=41$. Calculate $a^{3}+b^{3}$.",
"role": "user"
}
] | Let $a$ and $b$ be such that $a+b=13$ and $a b=41$. Calculate $a^{3}+b^{3}$. | "[\"598\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 941, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:14956"}] | {
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"reference_components": 1,
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} |
[
"\\frac{1}{2}"
] | [
"skywork"
] | 09b2d98fa61ca82c5cbaf52e435a7d4cc3203cb8dcc6a1040053de91f2e6c8e3 | [
{
"content": "[Example 3.4.4] Given non-negative real numbers $x_{1}, x_{2}, \\cdots, x_{n}$ satisfy the inequality\n$$\nx_{1}+x_{2}+\\cdots+x_{n} \\leqslant \\frac{1}{2} \\text {. }\n$$\n\nFind the minimum value of $\\left(1-x_{1}\\right)\\left(1-x_{2}\\right) \\cdots\\left(1-x_{n}\\right)$.",
"role": "use... | [Example 3.4.4] Given non-negative real numbers $x_{1}, x_{2}, \cdots, x_{n}$ satisfy the inequality
$$
x_{1}+x_{2}+\cdots+x_{n} \leqslant \frac{1}{2} \text {. }
$$
Find the minimum value of $\left(1-x_{1}\right)\left(1-x_{2}\right) \cdots\left(1-x_{n}\right)$. | "[\"\\\\frac{1}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 947, "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:14957"}] | {
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} |
[
"\\sqrt{1105}"
] | [
"skywork"
] | db144f969b05680d37bf44c2f3bf2f47f3ad82b1f29d1ea45eebb6d91d4f74bc | [
{
"content": "8. On the Cartesian plane, consider a circle of radius $R$ centered at the origin. Specify at least one value of $R$ for which exactly 32 integer points lie on such a circle (a point is called integer if its abscissa and ordinate are integers).\n\nHint. A natural number $x$ can be represented as t... | 8. On the Cartesian plane, consider a circle of radius $R$ centered at the origin. Specify at least one value of $R$ for which exactly 32 integer points lie on such a circle (a point is called integer if its abscissa and ordinate are integers).
Hint. A natural number $x$ can be represented as the sum of the squares of... | "[\"\\\\sqrt{1105}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 904, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14958"}, {"dataset": "skywork", "extra_inf... | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"308"
] | [
"skywork"
] | ffee5b34b22b9978dbb2082ec7ad0375623af220b3c5a09d0c553b65a8e43450 | [
{
"content": "The number \\( C \\) is defined as the sum of all the positive integers \\( n \\) such that \\( n-6 \\) is the second largest factor of \\( n \\). What is the value of \\( 11C \\)?",
"role": "user"
}
] | The number \( C \) is defined as the sum of all the positive integers \( n \) such that \( n-6 \) is the second largest factor of \( n \). What is the value of \( 11C \)? | "[\"308\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 932, "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:14959"}] | {
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"reference_components": 1,
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} |
[
"28"
] | [
"skywork"
] | 06f0bceafd99b07b41db34197e49f0bf255a063eb4e33f2b8592f8f5b56d97b3 | [
{
"content": "3. (5 points) 190 is expressed as the sum of 10 consecutive even numbers, the largest of which is\n\nExpress the above text in English, keeping the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | 3. (5 points) 190 is expressed as the sum of 10 consecutive even numbers, the largest of which is
Express the above text in English, keeping the original text's line breaks and format, and output the translation result directly. | "[\"28\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 933, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14960"}] | {
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} |
[
"\\sqrt{7}"
] | [
"skywork"
] | 28afca0f35fa6ee514b6cddd147430a6410a79a57cae8b1ecf59b71a54608446 | [
{
"content": "Task 1. 15 points\n\nFind the minimum value of the expression\n\n$$\n\\sqrt{x^{2}-\\sqrt{3} \\cdot|x|+1}+\\sqrt{x^{2}+\\sqrt{3} \\cdot|x|+3}\n$$\n\nas well as the values of $x$ at which it is achieved.",
"role": "user"
}
] | Task 1. 15 points
Find the minimum value of the expression
$$
\sqrt{x^{2}-\sqrt{3} \cdot|x|+1}+\sqrt{x^{2}+\sqrt{3} \cdot|x|+3}
$$
as well as the values of $x$ at which it is achieved. | "[\"\\\\sqrt{7}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 934, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14961"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"skywork"
] | 312815b557f09e07fc8a9264e049a4111f80e665506fff7e18170705226170ef | [
{
"content": "Zhendarov R.G.\n\nCells of a $9 \\times 9$ board are painted in a checkerboard pattern with black and white colors (corner cells are white). What is the minimum number of rooks needed to be placed on this board so that all white cells are under attack by these rooks? (A rook attacks all cells in t... | Zhendarov R.G.
Cells of a $9 \times 9$ board are painted in a checkerboard pattern with black and white colors (corner cells are white). What is the minimum number of rooks needed to be placed on this board so that all white cells are under attack by these rooks? (A rook attacks all cells in the row and column where i... | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 951, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14962"}] | {
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"reference_components": 1,
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} |
[
"\\frac{4}{3}"
] | [
"skywork"
] | 27e5d6ec19ff8ba8d615345d511a9545ebd9b13e2b9110762e8009acefc3acaa | [
{
"content": "Let ABC be a right triangle with $\\angle B = 90^{\\circ}$.Let E and F be respectively the midpoints of AB and AC.Suppose the incentre I of ABC lies on the circumcircle of triangle AEF,find the ratio BC/AB.",
"role": "user"
}
] | Let ABC be a right triangle with $\angle B = 90^{\circ}$.Let E and F be respectively the midpoints of AB and AC.Suppose the incentre I of ABC lies on the circumcircle of triangle AEF,find the ratio BC/AB. | "[\"\\\\frac{4}{3}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 944, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14963"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | d470c4ef9eb0302c00f4d767df64681cc9867b8c5eef90d9e3cf18ff670b0b1f | [
{
"content": "7. Convert the product $0.243 \\times 0.325233$ to a decimal, the digit at the 2013th position after the decimal point is",
"role": "user"
}
] | 7. Convert the product $0.243 \times 0.325233$ to a decimal, the digit at the 2013th position after the decimal point is | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 926, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14964"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 0d5479e9cc5ef68a40e632efcb7e6175138060131e2c798f904009b619175b60 | [
{
"content": "What is the minimum number of points in which 5 different non-parallel lines, not passing through a single point, can intersect?",
"role": "user"
}
] | What is the minimum number of points in which 5 different non-parallel lines, not passing through a single point, can intersect? | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 957, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14965"}] | {
"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
} |
[
"320"
] | [
"skywork"
] | 2554d83aaf712fbe07ce9f97c08760cb69309a7fb6d88b01e96802810d10e878 | [
{
"content": "How many odd numbers between $100$ and $999$ have distinct digits?",
"role": "user"
}
] | How many odd numbers between $100$ and $999$ have distinct digits? | "[\"320\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 956, "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:14966"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3750"
] | [
"skywork"
] | 13d771e94cbc43be0d301a74ad1659f78c857cf7d68bc055caa9b469c5638389 | [
{
"content": "12. (12 points) Person A and Person B start from points $A$ and $B$ respectively at the same time, walking back and forth between $A$ and $B$; at the same time Person A starts, Person C also departs from $A$ to $B$. When Person A and Person B meet for the first time at point $C$, Person C is still... | 12. (12 points) Person A and Person B start from points $A$ and $B$ respectively at the same time, walking back and forth between $A$ and $B$; at the same time Person A starts, Person C also departs from $A$ to $B$. When Person A and Person B meet for the first time at point $C$, Person C is still 100 meters away from ... | "[\"3750\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 940, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14967"}] | {
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} |
[
"2161"
] | [
"skywork"
] | cc61b8e99bba5de20cbfd263ed9aa48067507ed27e8f1d82b300828dce9732c7 | [
{
"content": "Let $T = TNFTPP$. When properly sorted, $T - 35$ math books on a shelf are arranged in alphabetical order from left to right. An eager student checked out and read all of them. Unfortunately, the student did not realize how the books were sorted, and so ... | Let $T = TNFTPP$. When properly sorted, $T - 35$ math books on a shelf are arranged in alphabetical order from left to right. An eager student checked out and read all of them. Unfortunately, the student did not realize how the books were sorted, and so after finishing the ... | "[\"2161\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 928, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14968"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"-3"
] | [
"skywork"
] | f66989b2cf242f714f4ce1339976110c7e7b1a1c770ed8855bf7d07af12db8c0 | [
{
"content": "If three angles \\(x, y, z\\) form an arithmetic sequence with a common difference of \\(\\frac{\\pi}{2}\\), then \\(\\tan x \\tan y + \\tan y \\tan z + \\tan z \\tan x = \\) ______.",
"role": "user"
}
] | If three angles \(x, y, z\) form an arithmetic sequence with a common difference of \(\frac{\pi}{2}\), then \(\tan x \tan y + \tan y \tan z + \tan z \tan x = \) ______. | "[\"-3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 948, "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:14969"}] | {
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[
"\\sqrt{\\frac{51}{2}}"
] | [
"skywork"
] | 3028aa24f4812f92a39200f2fbcab3559df20964c824db9945da535a4d59ea9a | [
{
"content": "The side of the base of a regular triangular prism $A B C A_1 B_1 C_1$ is 4, and the lateral edge is 3. On the edge $B B_1$, a point $F$ is taken, and on the edge $C C_1$, a point $G$ is taken such that $B_1 F=1, C G=\\frac{2}{3}$. Points $E$ and $D$ are the midpoints of edges $A C$ and $B_1 C_1$ ... | The side of the base of a regular triangular prism $A B C A_1 B_1 C_1$ is 4, and the lateral edge is 3. On the edge $B B_1$, a point $F$ is taken, and on the edge $C C_1$, a point $G$ is taken such that $B_1 F=1, C G=\frac{2}{3}$. Points $E$ and $D$ are the midpoints of edges $A C$ and $B_1 C_1$ respectively. Find the ... | "[\"\\\\sqrt{\\\\frac{51}{2}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 938, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14970"}] | {
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} |
[
"1"
] | [
"skywork"
] | 9bf6d38485d9e7e37ca610b5036f7ca5ab4784987bd5867ead8f2e792f182cc3 | [
{
"content": "1. (2 points) Boy Vasya tried to recall the distributive law of multiplication and wrote the formula: $a+(b \\times c)=(a+b) \\times(a+c)$. Then he substituted three non-zero numbers into this formula and found that it resulted in a true equality. Find the sum of these numbers.",
"role": "user... | 1. (2 points) Boy Vasya tried to recall the distributive law of multiplication and wrote the formula: $a+(b \times c)=(a+b) \times(a+c)$. Then he substituted three non-zero numbers into this formula and found that it resulted in a true equality. Find the sum of these numbers. | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 935, "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:14971"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\binom{n-k-1}{k-1} + \\binom{n-k}{k}"
] | [
"skywork"
] | c583c171527b4054f27611ea440ea9e7653ee3afbedb548134fabf211cdf0e35 | [
{
"content": "In how many ways can we color exactly $k$ vertices of an $n$-gon in red such that any $2$ consecutive vertices are not both red. (Vertices are considered to be labeled)",
"role": "user"
}
] | In how many ways can we color exactly $k$ vertices of an $n$-gon in red such that any $2$ consecutive vertices are not both red. (Vertices are considered to be labeled) | "[\" \\\\binom{n-k-1}{k-1} + \\\\binom{n-k}{k} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 950, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14972"}] | {
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} |
[
"123+6\\sqrt{119}"
] | [
"skywork"
] | fe97df8007618782bd2e7a9eff9f4bcc477e372dda43c1d93e9f2de5ce8d2fc0 | [
{
"content": "Point $P$ is inside a square $A B C D$ such that $\\angle A P B=135^{\\circ}, P C=12$, and $P D=15$. Compute the area of this square.",
"role": "user"
}
] | Point $P$ is inside a square $A B C D$ such that $\angle A P B=135^{\circ}, P C=12$, and $P D=15$. Compute the area of this square. | "[\"123+6\\\\sqrt{119}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 954, "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:14973"}] | {
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} |
[
"4"
] | [
"skywork"
] | 0a7f2537c920d2a152f6724b54dcff6b7e26826113feb29b6a0dc75344c5c85e | [
{
"content": "Consider the graphs $y=Ax^2$ and $y^2+3=x^2+4y$, where $A$ is a positive constant and $x$ and $y$ are real variables. In how many points do the two graphs intersect?",
"role": "user"
}
] | Consider the graphs $y=Ax^2$ and $y^2+3=x^2+4y$, where $A$ is a positive constant and $x$ and $y$ are real variables. In how many points do the two graphs intersect? | "[\"4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 923, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14974"}] | {
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} |
[
"2.5"
] | [
"skywork"
] | a5212906df33ba3f70a4b8bcb295ebcfcc0a193dc76e26dd84c8c4d670601b2a | [
{
"content": "Problem 1. Two runners started simultaneously in the same direction from one point of a circular distance, and the first runner, having moved ahead, caught up with the second again at the moment when the second had only run half a circle. From this moment, the second runner doubled his speed. Will... | Problem 1. Two runners started simultaneously in the same direction from one point of a circular distance, and the first runner, having moved ahead, caught up with the second again at the moment when the second had only run half a circle. From this moment, the second runner doubled his speed. Will the first runner catc... | "[\"2.5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 943, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14975"}] | {
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} |
[
"45"
] | [
"skywork"
] | 68a8af75fa7bec8cbe705a2ba9da59c75cd53b709a347564ccb82f2d8125105d | [
{
"content": "3. (10 points) A water pool has two drainage taps, $A$ and $B$. When both taps are opened simultaneously, it takes 30 minutes to drain the full pool; if both taps are opened for 10 minutes, then tap $A$ is closed and tap $B$ continues to drain, it also takes 30 more minutes to drain the full pool.... | 3. (10 points) A water pool has two drainage taps, $A$ and $B$. When both taps are opened simultaneously, it takes 30 minutes to drain the full pool; if both taps are opened for 10 minutes, then tap $A$ is closed and tap $B$ continues to drain, it also takes 30 more minutes to drain the full pool. How many minutes does... | "[\"45\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 949, "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:14976"}] | {
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} |
[
"C"
] | [
"skywork"
] | 3dab75dc9811c3de5f3fbbf2db1dc996dc4f849c8fa69b2114f5df5fc5ae49ea | [
{
"content": "22) On an island, there live three categories of people: the knights, who always tell the truth, the knaves, who always lie, and the pages, who after telling a truth always tell a lie and vice versa. On the island, I meet an old man, a boy, and a girl.\n\nThe old man states: \"I am a page\"; \"The... | 22) On an island, there live three categories of people: the knights, who always tell the truth, the knaves, who always lie, and the pages, who after telling a truth always tell a lie and vice versa. On the island, I meet an old man, a boy, and a girl.
The old man states: "I am a page"; "The boy is a knight".
The boy... | "[\"C\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 959, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:14977"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | 7f97c6ac7c75efd035caf347a77542e7bc87aee969e50154eaf314c6c190b71b | [
{
"content": "Example 1 If $\\frac{2}{x}+\\frac{3}{y}=2(x>0, y>0)$, find the minimum value of $x y$.",
"role": "user"
}
] | Example 1 If $\frac{2}{x}+\frac{3}{y}=2(x>0, y>0)$, find the minimum value of $x y$. | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 967, "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:14978"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"11^{1/6} \\cdot 2 \\sqrt{2}"
] | [
"skywork"
] | c6bbd3ab6cc17ecca8079ce6f9766015063cfef80893aa7b4a6b2287ec74fa68 | [
{
"content": "If $8^{2x} = 11$, evaluate $2^{x + 1.5}$.",
"role": "user"
}
] | If $8^{2x} = 11$, evaluate $2^{x + 1.5}$. | "[\"11^{1/6} \\\\cdot 2 \\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 953, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14979"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2.4+1.8i"
] | [
"skywork"
] | fd659167760bd9a1ab12508d82ac651a51d33e0db38e6c3eac6443737026e21a | [
{
"content": "10.50 Among the complex numbers satisfying the condition $|z-5 i| \\leq 4$, find the one whose argument has the smallest positive value.",
"role": "user"
}
] | 10.50 Among the complex numbers satisfying the condition $|z-5 i| \leq 4$, find the one whose argument has the smallest positive value. | "[\"2.4+1.8i\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 964, "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:14980"}] | {
"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
} |
[
"\\text{No}"
] | [
"skywork"
] | a4d40242bd43d6336e0befec3796a91e678de253b8df6ba812ad6fd109da57fc | [
{
"content": "Are there positive integers $a, b, c$, such that the numbers $a^2bc+2, b^2ca+2, c^2ab+2$ be perfect squares?",
"role": "user"
}
] | Are there positive integers $a, b, c$, such that the numbers $a^2bc+2, b^2ca+2, c^2ab+2$ be perfect squares? | "[\"\\\\text{No}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 966, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14981"}] | {
"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
} |
[
"324"
] | [
"skywork"
] | e2d05238c3be77ab08af53a2b0e1b7adab37030f8f70cab24c9691f455ea96ea | [
{
"content": "Jesse has ten squares, which are labeled $1, 2, \\dots, 10$. In how many ways can he color each square either red, green, yellow, or blue such that for all $1 \\le i < j \\le 10$, if $i$ divides $j$, then the $i$-th and $j$-th squares have different colors?",
"role": "user"
}
] | Jesse has ten squares, which are labeled $1, 2, \dots, 10$. In how many ways can he color each square either red, green, yellow, or blue such that for all $1 \le i < j \le 10$, if $i$ divides $j$, then the $i$-th and $j$-th squares have different colors? | "[\"324\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 952, "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:14982"}] | {
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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"
] | 8022d430f62e212361dfff02b4c4d73a351ff683a7045f5e1a932c0a35ba317f | [
{
"content": "3. (7 points) Guangming Primary School planted a total of 120 poplar and willow trees this spring, among which the number of poplar trees is 10 less than that of willow trees. The number of poplar trees planted is $\\qquad$.",
"role": "user"
}
] | 3. (7 points) Guangming Primary School planted a total of 120 poplar and willow trees this spring, among which the number of poplar trees is 10 less than that of willow trees. The number of poplar trees planted is $\qquad$. | "[\"55\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 965, "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:14983"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | de1612a9301f72dfc6e631c5342e1543dbc6a6a7048cccbcc0e501b53a1e69fd | [
{
"content": "Reduce the number $\\sqrt[3]{2+\\sqrt{5}}+\\sqrt[3]{2-\\sqrt{5}}$",
"role": "user"
}
] | Reduce the number $\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}$ | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 976, "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:14984"}, {"dataset": "skywork", "extra_info... | {
"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
} |
[
"\\[\na_{u+vn} = \n\\begin{cases} \n0, & u+v \\le n, \\\\ \n1, & u+v \\ge n+1 \n\\end{cases} \n\\quad \\text{for all } 1 \\le u \\le n \\text{ and } 0 \\le v \\le n.\n\\]\n\\[\n\\text{The terms can be arranged into blocks of length } n \\text{ as}\n\\]\n\\[\n\\underbrace{(0 \\cdots 0)}_{n} \\underbrace{(0 \\cdots 0... | [
"skywork"
] | 0620abc82e536bc6edf71c2e5c8ef32667c34b50adc97e31a6b7f2e117e20dd5 | [
{
"content": "Let $ n > 1$ be an integer. Find all sequences $ a_1, a_2, \\ldots a_{n^2 \\plus{} n}$ satisfying the following conditions:\n\\[ \\text{ (a) } a_i \\in \\left\\{0,1\\right\\} \\text{ for all } 1 \\leq i \\leq n^2 \\plus{} n;\n\\]\n\n\\[ \\text{ (b) } a_{i \\plus{} 1} \\plus{} a_{i \\plus{} 2} \\pl... | Let $ n > 1$ be an integer. Find all sequences $ a_1, a_2, \ldots a_{n^2 \plus{} n}$ satisfying the following conditions:
\[ \text{ (a) } a_i \in \left\{0,1\right\} \text{ for all } 1 \leq i \leq n^2 \plus{} n;
\]
\[ \text{ (b) } a_{i \plus{} 1} \plus{} a_{i \plus{} 2} \plus{} \ldots \plus{} a_{i \plus{} n} < a_{i \pl... | "[\"\\\\[\\na_{u+vn} = \\n\\\\begin{cases} \\n0, & u+v \\\\le n, \\\\\\\\ \\n1, & u+v \\\\ge n+1 \\n\\\\end{cases} \\n\\\\quad \\\\text{for all } 1 \\\\le u \\\\le n \\\\text{ and } 0 \\\\le v \\\\le n.\\n\\\\]\\n\\\\[\\n\\\\text{The terms can be arranged into blocks of length } n \\\\text{ as}\\n\\\\]\\n\\\\[\\n\\\\un... | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 961, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14985"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
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