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 |
|---|---|---|---|---|---|---|---|---|
[
"\\frac{56}{65}"
] | [
"skywork"
] | e876348777d58a7ce1352a2cf3e515d318794e2f4490fa2363fb010f1307ddd1 | [
{
"content": "Given $\\cos\\alpha = \\frac{5}{13}$ and $\\cos(\\alpha - \\beta) = \\frac{4}{5}$, with $0 < \\beta < \\alpha < \\frac{\\pi}{2}$,\n$(1)$ Find the value of $\\tan 2\\alpha$;\n$(2)$ Find the value of $\\cos\\beta$.",
"role": "user"
}
] | Given $\cos\alpha = \frac{5}{13}$ and $\cos(\alpha - \beta) = \frac{4}{5}$, with $0 < \beta < \alpha < \frac{\pi}{2}$,
$(1)$ Find the value of $\tan 2\alpha$;
$(2)$ Find the value of $\cos\beta$. | "[\"\\\\frac{56}{65}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3533, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:17466"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"32"
] | [
"skywork"
] | 9c5f1a42fca9fd9c099a18d059eb3015e6b2e80bd51cce4db230d09fa3aa1e91 | [
{
"content": "70. At Wang Wang's fruit wholesale store, on a certain day in the morning, $\\frac{3}{8}$ of the inventory of fruits was sold, and in the afternoon, $\\frac{2}{5}$ of the remaining fruits plus 10 tons were sold, leaving 2 tons. Wang Wang's fruit wholesale store had an initial inventory of $\\qquad... | 70. At Wang Wang's fruit wholesale store, on a certain day in the morning, $\frac{3}{8}$ of the inventory of fruits was sold, and in the afternoon, $\frac{2}{5}$ of the remaining fruits plus 10 tons were sold, leaving 2 tons. Wang Wang's fruit wholesale store had an initial inventory of $\qquad$ tons that day. | "[\"32\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3536, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17467"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"16"
] | [
"skywork"
] | c0742f593122520345da7795060d9df6c1f419848a0aaae03793d395f5c0db9a | [
{
"content": "$$\ny=a x^{2}+b x+c(a \\neq 0)\n$$\n\nThe image vertex is $C$, and the two intersections with the $x$-axis are $A$ and $B$. If $\\triangle A B C$ is an acute triangle, and $\\sin \\angle B C A$ $=\\frac{4}{5}$, then $\\Delta=b^{2}-4 a c=$ . $\\qquad$",
"role": "user"
}
] | $$
y=a x^{2}+b x+c(a \neq 0)
$$
The image vertex is $C$, and the two intersections with the $x$-axis are $A$ and $B$. If $\triangle A B C$ is an acute triangle, and $\sin \angle B C A$ $=\frac{4}{5}$, then $\Delta=b^{2}-4 a c=$ . $\qquad$ | "[\"16\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3515, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17468"}] | {
"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<x\\leqslant4"
] | [
"skywork"
] | 2c6e6d89ed43b07ef8d22de75dc828e71b0a9c51712e341b2cac9f965ac81031 | [
{
"content": "Example 9 Let $f(x)$ be defined for $x>0$, $f(2)=1$, $f(xy)=f(x)+f(y)$, and the necessary and sufficient condition for $f(x)>f(y)$ to hold is $x>y>0$. Find: (1) the values of $f(1)$ and $f(4)$; (2) the range of values for $x$ such that $f(x)+f(x-3) \\leqslant 2$.\n\nTranslate the above text into E... | Example 9 Let $f(x)$ be defined for $x>0$, $f(2)=1$, $f(xy)=f(x)+f(y)$, and the necessary and sufficient condition for $f(x)>f(y)$ to hold is $x>y>0$. Find: (1) the values of $f(1)$ and $f(4)$; (2) the range of values for $x$ such that $f(x)+f(x-3) \leqslant 2$.
Translate the above text into English, please retain the... | "[\"3<x\\\\leqslant4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3544, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17469"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | 7f64c4322d9d3c94085ad9b341a577f9a746285d192b6101d303b01de1c534f5 | [
{
"content": "8. If $4^{a}=6^{b}=9^{c}$, then $\\frac{1}{a}-\\frac{2}{b}+\\frac{1}{c}=$ $\\qquad$\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | 8. If $4^{a}=6^{b}=9^{c}$, then $\frac{1}{a}-\frac{2}{b}+\frac{1}{c}=$ $\qquad$
Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly. | "[\"0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3563, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17470"}] | {
"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
} |
[
"402"
] | [
"skywork"
] | 4c2d297ae3d80ed94f9949e8efa6466ac5c2c62d9152a1e6a0d6fea62b482b67 | [
{
"content": "Let $x, y$ and $z$ be consecutive integers such that\n\\[\\frac 1x+\\frac 1y+\\frac 1z >\\frac{1}{45}.\\]\nFind the maximum value of $x + y + z$.",
"role": "user"
}
] | Let $x, y$ and $z$ be consecutive integers such that
\[\frac 1x+\frac 1y+\frac 1z >\frac{1}{45}.\]
Find the maximum value of $x + y + z$. | "[\"402\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3548, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:17471"}, {"dataset": "skywork", "extra_... | {
"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"
] | 6b3dac6f5d5e1d3a61187e69730e607da8ea05c70ba64552bb4b57e952dc5846 | [
{
"content": "10. As shown in the right figure, square $A B C D$ is divided into 8 triangles of equal area. If $D G=5$, then the area of square $A B C D$ is $\\qquad$",
"role": "user"
}
] | 10. As shown in the right figure, square $A B C D$ is divided into 8 triangles of equal area. If $D G=5$, then the area of square $A B C D$ is $\qquad$ | "[\"64\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3546, "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:17472"}, {"dataset": "skywork", "extra_... | {
"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
} |
[
"132"
] | [
"skywork"
] | d9392d9b4003120019663ec7adf6596488a03e244f1af4f7fbd271ff5ba27527 | [
{
"content": "Rewrite $\\sqrt[3]{2^6\\cdot3^3\\cdot11^3}$ as an integer.",
"role": "user"
}
] | Rewrite $\sqrt[3]{2^6\cdot3^3\cdot11^3}$ as an integer. | "[\"132\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3572, "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:17473"}] | {
"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{91(6-\\sqrt{6})}{30}"
] | [
"skywork"
] | c35ae6b04c2e6013c3d904c8adfbf76f0926bc97984cf4b2fda11f7d1dfe6079 | [
{
"content": "[Trigonometric ratios in a right triangle] [Inscribed and circumscribed circles $]$\n\nPoint $O$ lies on segment $A B$, with $A O=13, O B=7$. A circle with center at point $O$ and radius 5 is drawn. Tangents are drawn from $A$ and $B$ to this circle, intersecting at point $M$, and the points of ta... | [Trigonometric ratios in a right triangle] [Inscribed and circumscribed circles $]$
Point $O$ lies on segment $A B$, with $A O=13, O B=7$. A circle with center at point $O$ and radius 5 is drawn. Tangents are drawn from $A$ and $B$ to this circle, intersecting at point $M$, and the points of tangency lie on the same s... | "[\"\\\\frac{91(6-\\\\sqrt{6})}{30}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3551, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:17474"}] | {
"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}{899}"
] | [
"skywork"
] | 4bbdd6f6d6942f61be38c65c4aa1f5a7cec26bbc84f1cde6b07b6968829ba6ee | [
{
"content": "In a class of 32 students, each student is randomly paired with another student for a project. What is the probability that Margo is paired with her best friend Irma, and simultaneously, another student, Joe, is paired with his best friend, Pete? Express your answer as a common fraction.",
"ro... | In a class of 32 students, each student is randomly paired with another student for a project. What is the probability that Margo is paired with her best friend Irma, and simultaneously, another student, Joe, is paired with his best friend, Pete? Express your answer as a common fraction. | "[\"\\\\frac{1}{899}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 3557, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17475"}] | {
"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"
] | e8ee50a8807108f6e2a7140c2156577ee7d0b5e8c9b281845352e8fab6d7640c | [
{
"content": "Brad has a cylindrical barrel with radius 10 inches and height 15 inches. He wants to fill it from a well, using a bucket in the shape of a hemisphere with a radius of 10 inches. How many trips must Brad make to the well in order to fill the barrel?",
"role": "user"
}
] | Brad has a cylindrical barrel with radius 10 inches and height 15 inches. He wants to fill it from a well, using a bucket in the shape of a hemisphere with a radius of 10 inches. How many trips must Brad make to the well in order to fill the barrel? | "[\"3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3559, "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:17476"}] | {
"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
} |
[
"x\\geq4"
] | [
"skywork"
] | bb11ec6c4f674844f94c54aba8b38a5c3bb080f737435597d7ce40f21eb09f48 | [
{
"content": "2. Solve the inequality:\n\n$$\n\\sqrt{x+\\sqrt{x+\\sqrt{x+\\sqrt{x-4}}}} \\geq \\sqrt{4+\\sqrt{6}}\n$$",
"role": "user"
}
] | 2. Solve the inequality:
$$
\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x-4}}}} \geq \sqrt{4+\sqrt{6}}
$$ | "[\"x\\\\geq4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3558, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:17477"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 88359f47cc06102a06ef01fd94aeb9c72d108c8aa9959c7556380832fce0cd4b | [
{
"content": "Given a solid $\\Omega$ which is the larger part obtained by cutting a sphere $O$ with radius $4$ by a plane $\\alpha$, and $\\triangle ABC$ is an inscribed triangle of the circular section $O'$ with $\\angle A=90^{\\circ}$. Point $P$ is a moving point on the solid $\\Omega$, and the projection of... | Given a solid $\Omega$ which is the larger part obtained by cutting a sphere $O$ with radius $4$ by a plane $\alpha$, and $\triangle ABC$ is an inscribed triangle of the circular section $O'$ with $\angle A=90^{\circ}$. Point $P$ is a moving point on the solid $\Omega$, and the projection of $P$ on the circle $O'$ lies... | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3549, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17478"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9.6\\mathrm{~}^{2}"
] | [
"skywork"
] | 0902c30a8808a98633a3684cc7ea3bc82cd523357104295dcb06c985dcf56cd8 | [
{
"content": "1.61. Calculate the area of the common part of two rhombi, the lengths of the diagonals of the first of which are 4 and $6 \\mathrm{~cm}$, and the second is obtained by rotating the first by $90^{\\circ}$ around its center.",
"role": "user"
}
] | 1.61. Calculate the area of the common part of two rhombi, the lengths of the diagonals of the first of which are 4 and $6 \mathrm{~cm}$, and the second is obtained by rotating the first by $90^{\circ}$ around its center. | "[\"9.6\\\\mathrm{~}^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3565, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17479"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | a8ab55159af80964c5ecb94a1c2414596b4ae929c42ecef6dff5964908808bdb | [
{
"content": "7.028. $5^{2\\left(\\log _{5} 2+x\\right)}-2=5^{x+\\log _{5} 2}$.",
"role": "user"
}
] | 7.028. $5^{2\left(\log _{5} 2+x\right)}-2=5^{x+\log _{5} 2}$. | "[\"0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3577, "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:17480"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3}{8}"
] | [
"skywork"
] | 880f12d1a65d3774ff2a9d0c16f232c3b739d8de548153b1515a826bc79a032b | [
{
"content": "Star flips a quarter four times. Find the probability that the quarter lands heads exactly twice.\n\n$\\textbf{(A) }\\dfrac18\\hspace{14em}\\textbf{(B) }\\dfrac3{16}\\hspace{14em}\\textbf{(C) }\\dfrac38$\n\n$\\textbf{(D) }\\dfrac12$",
"role": "user"
}
] | Star flips a quarter four times. Find the probability that the quarter lands heads exactly twice.
$\textbf{(A) }\dfrac18\hspace{14em}\textbf{(B) }\dfrac3{16}\hspace{14em}\textbf{(C) }\dfrac38$
$\textbf{(D) }\dfrac12$ | "[\"\\\\frac{3}{8}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3581, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17482"}] | {
"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
} |
[
"1594"
] | [
"skywork"
] | df279bb85f18357055ec3928d1699c727a45046fbcf2061204268301b2e5e294 | [
{
"content": "Let $a,b,c$ be positive integers such that $a,b,c,a+b-c,a+c-b,b+c-a,a+b+c$ are $7$ distinct primes. The sum of two of $a,b,c$ is $800$. If $d$ be the difference of the largest prime and the least prime among those $7$ primes, find the maximum value of $d$.",
"role": "user"
}
] | Let $a,b,c$ be positive integers such that $a,b,c,a+b-c,a+c-b,b+c-a,a+b+c$ are $7$ distinct primes. The sum of two of $a,b,c$ is $800$. If $d$ be the difference of the largest prime and the least prime among those $7$ primes, find the maximum value of $d$. | "[\"1594\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3555, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:17483"}, {"dataset": "skywork", "extra_in... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"30"
] | [
"skywork"
] | 1fedb3c084172ee6d10a0ad7bf080747b36e4536d8504d2c79ca361619b3f3a4 | [
{
"content": "5. Given the rectangular prism $A B C D-$ $A^{\\prime} B^{\\prime} C^{\\prime} D^{\\prime}$, among the following twelve lines: $A B^{\\prime}, B A^{\\prime}, C D^{\\prime}, D C^{\\prime}$, $A D^{\\prime}, D A^{\\prime}, B C^{\\prime}, C B^{\\prime}, A C$, $B D, A^{\\prime} C^{\\prime}, B^{\\prime}... | 5. Given the rectangular prism $A B C D-$ $A^{\prime} B^{\prime} C^{\prime} D^{\prime}$, among the following twelve lines: $A B^{\prime}, B A^{\prime}, C D^{\prime}, D C^{\prime}$, $A D^{\prime}, D A^{\prime}, B C^{\prime}, C B^{\prime}, A C$, $B D, A^{\prime} C^{\prime}, B^{\prime} D^{\prime}$, how many pairs of skew ... | "[\"30\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3568, "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:17484"}, {"dataset": "skywork", "extra_... | {
"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
} |
[
"90"
] | [
"skywork"
] | b96876514b3d5b168f19e1ba5cb5d0ba8575cd43aec23a74699b630b8e100f29 | [
{
"content": "How many different $4\\times 4$ arrays whose entries are all 1's and -1's have the property that the sum of the entries in each row is 0 and the sum of the entries in each column is 0?",
"role": "user"
}
] | How many different $4\times 4$ arrays whose entries are all 1's and -1's have the property that the sum of the entries in each row is 0 and the sum of the entries in each column is 0? | "[\"90\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3576, "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:17485"}, {"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
} |
[
"4608"
] | [
"skywork"
] | e29fd0256dd6c4206e39594c866109b99830048cdef5dd7db30fcd771db83eea | [
{
"content": "How many orderings $(a_{1}, \\ldots, a_{8})$ of $(1,2, \\ldots, 8)$ exist such that $a_{1}-a_{2}+a_{3}-a_{4}+a_{5}-a_{6}+a_{7}-a_{8}=0$ ?",
"role": "user"
}
] | How many orderings $(a_{1}, \ldots, a_{8})$ of $(1,2, \ldots, 8)$ exist such that $a_{1}-a_{2}+a_{3}-a_{4}+a_{5}-a_{6}+a_{7}-a_{8}=0$ ? | "[\"4608\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3574, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17486"}, {"dataset": "skywork", "extra_in... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{50}"
] | [
"skywork"
] | 8aa438319bebcc7effce772866c2d70039209f8b3cb58c6c0d5c46c9b5bfefcf | [
{
"content": "The perimeter of a rectangle $A B C D$ measures $20 \\mathrm{~m}$. The smallest length that the diagonal $A C$ can have, in meters, is:\n(a) 0 ;\n(b) $\\sqrt{50}$;\n(c) 10 ;\n(d) $\\sqrt{200}$;\n(e) $20 \\sqrt{5}$.",
"role": "user"
}
] | The perimeter of a rectangle $A B C D$ measures $20 \mathrm{~m}$. The smallest length that the diagonal $A C$ can have, in meters, is:
(a) 0 ;
(b) $\sqrt{50}$;
(c) 10 ;
(d) $\sqrt{200}$;
(e) $20 \sqrt{5}$. | "[\"\\\\sqrt{50}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3560, "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:17487"}] | {
"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-3,B-2,C-4,D-1"
] | [
"skywork"
] | baa4f708ef759671ae8d3de7037b5de31facd51392a5004cfeb61e3c848453a5 | [
{
"content": "Task 1.3. A $4 \\times 4$ table is divided into four $2 \\times 2$ squares.\n\nVika wrote 4 ones, 4 twos, 4 threes, and 4 fours in the cells of the table such that in each column, each row, and each $2 \\times 2$ square, all numbers are different.\n\nThe hooligan Andrey erased some of the numbers.... | Task 1.3. A $4 \times 4$ table is divided into four $2 \times 2$ squares.
Vika wrote 4 ones, 4 twos, 4 threes, and 4 fours in the cells of the table such that in each column, each row, and each $2 \times 2$ square, all numbers are different.
The hooligan Andrey erased some of the numbers. Help Vika restore which cell... | "[\"A-3,B-2,C-4,D-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3553, "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:17489"}, {"dataset": "skywork", "extra_... | {
"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
} |
[
"15"
] | [
"skywork"
] | 3cf60d73a7f90d2039b2bbe9893e433a23cff37b3878ea6752aed56c821d6538 | [
{
"content": "For any two positive integers m and n, define an operation \"※\" as follows: when m and n are both positive even numbers or positive odd numbers, m※n=m+n; when one of m and n is a positive even number and the other is a positive odd number, m※n=mn. Determine the number of elements in the set M={(a... | For any two positive integers m and n, define an operation "※" as follows: when m and n are both positive even numbers or positive odd numbers, m※n=m+n; when one of m and n is a positive even number and the other is a positive odd number, m※n=mn. Determine the number of elements in the set M={(a,b)|a※b=12, a∈ℕ∗, b∈ℕ∗}. | "[\"15\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3564, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "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:17490"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\pi^2}{4}"
] | [
"skywork"
] | 00876c891438d6155d9935c7458bd45186b9ff49ff40452278ffbecbcad686d9 | [
{
"content": "Find the area bounded by the graph of $y = \\arcsin(\\cos x)$ and the $x$-axis on the interval $0 \\le x \\le 2\\pi.$",
"role": "user"
}
] | Find the area bounded by the graph of $y = \arcsin(\cos x)$ and the $x$-axis on the interval $0 \le x \le 2\pi.$ | "[\"\\\\frac{\\\\pi^2}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3575, "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:17491"}] | {
"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
} |
[
"78"
] | [
"skywork"
] | 12b42cde538d86d570d1608a2098a730334347d694f4b0e5af166326753ba1a4 | [
{
"content": "Given a sequence $\\{a_n\\}$, where $a_{n+1} + (-1)^n a_n = 2n - 1$, calculate the sum of the first 12 terms of $\\{a_n\\}$.",
"role": "user"
}
] | Given a sequence $\{a_n\}$, where $a_{n+1} + (-1)^n a_n = 2n - 1$, calculate the sum of the first 12 terms of $\{a_n\}$. | "[\"78\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3579, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17492"}] | {
"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"
] | ba3d78cb58050e90c742807d94f577b0f9d377ee324accfc8f4dc39af828d8c9 | [
{
"content": "2.204. $\\sqrt{2+\\sqrt{3}} \\cdot \\sqrt{2+\\sqrt{2+\\sqrt{3}}} \\cdot \\sqrt{2+\\sqrt{2+\\sqrt{2+\\sqrt{3}}}} \\cdot \\sqrt{2-\\sqrt{2+\\sqrt{2+\\sqrt{3}}}}$.",
"role": "user"
}
] | 2.204. $\sqrt{2+\sqrt{3}} \cdot \sqrt{2+\sqrt{2+\sqrt{3}}} \cdot \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}} \cdot \sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}$. | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3583, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17493"}] | {
"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{37}{7}"
] | [
"skywork"
] | f4ad0c1b2840429c4abb139bb8b80ea1ec28ba2540095046e1e10c227c3e6e62 | [
{
"content": "Equilateral triangle $ABC$ has circumcircle $\\Omega$. Points $D$ and $E$ are chosen on minor arcs $AB$ and $AC$ of $\\Omega$ respectively such that $BC=DE$. Given that triangle $ABE$ has area 3 and triangle $ACD$ has area 4, find the area of triangle $ABC$.",
"role": "user"
}
] | Equilateral triangle $ABC$ has circumcircle $\Omega$. Points $D$ and $E$ are chosen on minor arcs $AB$ and $AC$ of $\Omega$ respectively such that $BC=DE$. Given that triangle $ABE$ has area 3 and triangle $ACD$ has area 4, find the area of triangle $ABC$. | "[\"\\\\frac{37}{7}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3573, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17494"}] | {
"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
} |
[
"23"
] | [
"skywork"
] | e5b710f191ff864a896e1c3317005f6ae1f104d8c98e6e07eaf5aa419397b80d | [
{
"content": "Find the smallest prime $p$ for which there exist positive integers $a,b$ such that \n\t\\[\n\t\ta^{2} + p^{3} = b^{4}.\n\t\\]",
"role": "user"
}
] | Find the smallest prime $p$ for which there exist positive integers $a,b$ such that
\[
a^{2} + p^{3} = b^{4}.
\] | "[\"23\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3591, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17495"}, {"dataset": "skywork", "extra_in... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"160"
] | [
"skywork"
] | 34c6ef48999347986c12c4870a8d385a5e7e1281fa067ca1fb30912b691384d7 | [
{
"content": "A loonie is a $\\$ 1$ coin and a dime is a $\\$ 0.10$ coin. One loonie has the same mass as 4 dimes. A bag of dimes has the same mass as a bag of loonies. The coins in the bag of loonies are worth $\\$ 400$ in total. How much are the coins in the bag of dimes worth?",
"role": "user"
}
] | A loonie is a $\$ 1$ coin and a dime is a $\$ 0.10$ coin. One loonie has the same mass as 4 dimes. A bag of dimes has the same mass as a bag of loonies. The coins in the bag of loonies are worth $\$ 400$ in total. How much are the coins in the bag of dimes worth? | "[\"160\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3569, "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:17496"}] | {
"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"
] | a0d872e59bb7e89b224e8ece49056e6ef07e5f9f316b4340ecc7849cee71db4e | [
{
"content": "Farmer James has three types of cows on his farm. A cow with zero legs is called a $\\textit{ground beef}$, a cow with one leg is called a $\\textit{steak}$, and a cow with two legs is called a $\\textit{lean beef}$. Farmer James counts a total of $20$ cows and $18$ legs on his farm. How many more... | Farmer James has three types of cows on his farm. A cow with zero legs is called a $\textit{ground beef}$, a cow with one leg is called a $\textit{steak}$, and a cow with two legs is called a $\textit{lean beef}$. Farmer James counts a total of $20$ cows and $18$ legs on his farm. How many more $\textit{ground beef}$s ... | "[\" 2 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3567, "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:17498"}] | {
"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
} |
[
"228"
] | [
"skywork"
] | f59c43c1309717166159dd628d85c0fa161e465642682153bd218eedc0027e5e | [
{
"content": "Calculate the result of the expression \\((19 \\times 19 - 12 \\times 12) \\div \\left(\\frac{19}{12} - \\frac{12}{19}\\right)\\).",
"role": "user"
}
] | Calculate the result of the expression \((19 \times 19 - 12 \times 12) \div \left(\frac{19}{12} - \frac{12}{19}\right)\). | "[\"228\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3599, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:17499"}] | {
"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
} |
[
"361"
] | [
"skywork"
] | fb8b8cbfb2cf4f9ef69a44b43daf32c4cf9480c801981b54e231f3f4a264f049 | [
{
"content": "10.1. What is the sum of the digits of the number $A=100^{40}-100^{30}+100^{20}-100^{10}+1$?",
"role": "user"
}
] | 10.1. What is the sum of the digits of the number $A=100^{40}-100^{30}+100^{20}-100^{10}+1$? | "[\"361\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3580, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17500"}] | {
"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
} |
[
"13"
] | [
"skywork"
] | 93db1b91aa3c34e26f341636d922bcf39f3789418105873bcccf7ce52b12809e | [
{
"content": "Sylvia chose positive integers $a, b$ and $c$.\n\nPeter determined the value of $a+\\frac{b}{c}$ and got an answer of 101 .\n\nPaul determined the value of $\\frac{a}{c}+b$ and got an answer of 68 .\n\nMary determined the value of $\\frac{a+b}{c}$ and got an answer of $k$.\n\nThe value of $k$ is\n... | Sylvia chose positive integers $a, b$ and $c$.
Peter determined the value of $a+\frac{b}{c}$ and got an answer of 101 .
Paul determined the value of $\frac{a}{c}+b$ and got an answer of 68 .
Mary determined the value of $\frac{a+b}{c}$ and got an answer of $k$.
The value of $k$ is
(A) 13
(B) 168
(C) 152
(D) 12
(E) ... | "[\"13\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3556, "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:17501"}] | {
"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
} |
[
"26"
] | [
"skywork"
] | d224ef59c53310a593b46df9586f72b12f398c54cae2931ffc8f5465de511772 | [
{
"content": "A new city is constructed in the form of 12 rectangular blocks of houses, divided by streets; at each corner of the block and at every street intersection, there is a mailbox. The blocks either touch each other along entire sides or share only a single corner.\n\nAssuming that there are 37 segment... | A new city is constructed in the form of 12 rectangular blocks of houses, divided by streets; at each corner of the block and at every street intersection, there is a mailbox. The blocks either touch each other along entire sides or share only a single corner.
Assuming that there are 37 segments of streets enclosing t... | "[\"26\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3570, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17502"}] | {
"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
} |
[
"1/2"
] | [
"skywork"
] | 001cb05b1111a82f9831e8b459afb01e5d1461217be3612a635174a032aafd2a | [
{
"content": "Given the positive numbers \\( a, b, c, x, y, z \\) that satisfy the equations \\( cy + bz = a \\), \\( az + cx = b \\), and \\( bx + ay = c \\), find the minimum value of the function\n\\[ \nf(x, y, z) = \\frac{x^{2}}{1+x} + \\frac{y^{2}}{1+y} + \\frac{z^{2}}{1+z}.\n\\]",
"role": "user"
}
] | Given the positive numbers \( a, b, c, x, y, z \) that satisfy the equations \( cy + bz = a \), \( az + cx = b \), and \( bx + ay = c \), find the minimum value of the function
\[
f(x, y, z) = \frac{x^{2}}{1+x} + \frac{y^{2}}{1+y} + \frac{z^{2}}{1+z}.
\] | "[\"1/2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3561, "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:17503"}] | {
"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
} |
[
"168"
] | [
"skywork"
] | e669dda6340081b5d72f59dc8bc9b2185d0584d460f1f1a6ddb9f602b6f44b9b | [
{
"content": "In $\\triangle PQR$, $\\angle RPQ = 90^{\\circ}$ and $S$ is on $PQ$. If $SQ = 14$, $SP = 18$, and $SR = 30$, then the area of $\\triangle QRS$ is",
"role": "user"
}
] | In $\triangle PQR$, $\angle RPQ = 90^{\circ}$ and $S$ is on $PQ$. If $SQ = 14$, $SP = 18$, and $SR = 30$, then the area of $\triangle QRS$ is | "[\"168\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 3586, "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:17504"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"skywork"
] | eba93221249fed1ac48a819406126f6cdd1f9096212e9e6b2a1126f6c3de2067 | [
{
"content": "Samuel's birthday cake is in the form of a $4 \\times 4 \\times 4$ inch cube. The cake has icing on the top and the four side faces, and no icing on the bottom. Suppose the cake is cut into $64$ smaller cubes, each measuring $1 \\times 1 \\times 1$ inch, as shown below. How many of the small piece... | Samuel's birthday cake is in the form of a $4 \times 4 \times 4$ inch cube. The cake has icing on the top and the four side faces, and no icing on the bottom. Suppose the cake is cut into $64$ smaller cubes, each measuring $1 \times 1 \times 1$ inch, as shown below. How many of the small pieces will have icing on exact... | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3587, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17505"}] | {
"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
} |
[
"2880"
] | [
"skywork"
] | 66d1a2607476d390fec28635136144923f11c858e5fa375f6eeaefb8252d46f7 | [
{
"content": "What is the smallest four-digit positive integer that is divisible by both 5 and 9 and has only even digits?",
"role": "user"
}
] | What is the smallest four-digit positive integer that is divisible by both 5 and 9 and has only even digits? | "[\"2880\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 3595, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17506"}] | {
"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
} |
[
"(x^2 + y^2z^2)(y^2 + x^2z^2)(z^2 + x^2y^2) \\geq 8xy^2z^3"
] | [
"skywork"
] | a8d374db206678e691dcce2e5739fd22c640e4810ce133a3abab7a792d6be817 | [
{
"content": "Show that the inequality $(x^2 + y^2z^2) (y^2 + x^2z^2) (z^2 + x^2y^2) \\ge 8xy^2z^3$ is valid for all integers $x, y$ and $z$.When does equality apply?",
"role": "user"
}
] | Show that the inequality $(x^2 + y^2z^2) (y^2 + x^2z^2) (z^2 + x^2y^2) \ge 8xy^2z^3$ is valid for all integers $x, y$ and $z$.When does equality apply? | "[\" (x^2 + y^2z^2)(y^2 + x^2z^2)(z^2 + x^2y^2) \\\\geq 8xy^2z^3 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3588, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:17507"}] | {
"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"
] | 92dbd38d73e01c13aba9f3d1a3e96570396a1f11cc6ff8de3fce6cc966ea17c8 | [
{
"content": "The value of the quadratic polynomial $a(x^3 - x^2 + 3x) + b(2x^2 + x) + x^3 - 5$ when $x = 2$ is $-17$. What is the value of this polynomial when $x = -2$?",
"role": "user"
}
] | The value of the quadratic polynomial $a(x^3 - x^2 + 3x) + b(2x^2 + x) + x^3 - 5$ when $x = 2$ is $-17$. What is the value of this polynomial when $x = -2$? | "[\"-1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3585, "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:17508"}] | {
"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{79}{65}"
] | [
"skywork"
] | b2baa8801237189e2ad9c8fc662802d379dfb193ddfee4c7ec61e7eb889e89bb | [
{
"content": "4. Let the set $A=\\left\\{\\frac{1}{2}, \\frac{1}{7}, \\frac{1}{11}, \\frac{1}{13}, \\frac{1}{15}, \\frac{1}{32}\\right\\}$ have non-empty subsets $A_{1}, A_{2}, \\cdots, A_{63}$. Denote the product of all elements in the set $A_{i}$ as $p_{i}$ (the product of elements in a singleton set is the e... | 4. Let the set $A=\left\{\frac{1}{2}, \frac{1}{7}, \frac{1}{11}, \frac{1}{13}, \frac{1}{15}, \frac{1}{32}\right\}$ have non-empty subsets $A_{1}, A_{2}, \cdots, A_{63}$. Denote the product of all elements in the set $A_{i}$ as $p_{i}$ (the product of elements in a singleton set is the element itself), $i=1,2, \cdots, 6... | "[\"\\\\frac{79}{65}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3590, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17509"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | f85f4ad499c98701c4889ee5a4396d102ab85464c74f8dc3c8425ab0341cb32d | [
{
"content": "438*. What remainder does $46^{925}$ give when divided by $21?$",
"role": "user"
}
] | 438*. What remainder does $46^{925}$ give when divided by $21?$ | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3611, "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:17510"}] | {
"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
} |
[
"5985"
] | [
"skywork"
] | a9f4750d0be62ad4ad38af7755d632428227ddff674722e0683099b8e6be598f | [
{
"content": "A four-digit integer \\( p \\) and the four-digit integer obtained by reversing the order of the digits of \\( p \\) are both divisible by \\( 63 \\) (product of primes \\( 7 \\) and \\( 9 \\)). Additionally, \\( p \\) must be divisible by \\( 19 \\). Determine the greatest possible value of \\( p... | A four-digit integer \( p \) and the four-digit integer obtained by reversing the order of the digits of \( p \) are both divisible by \( 63 \) (product of primes \( 7 \) and \( 9 \)). Additionally, \( p \) must be divisible by \( 19 \). Determine the greatest possible value of \( p \). | "[\"5985\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3578, "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:17511"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{3} \\ln ^{3}(2)"
] | [
"skywork"
] | ad5863a6c129853d87ab51aead2dc70157e3305c5c6538489c62d68f8d55fabc | [
{
"content": "Determine the value of \\(\\sum_{n=1}^{\\infty} \\ln \\left(1+\\frac{1}{n}\\right) \\cdot \\ln \\left(1+\\frac{1}{2 n}\\right) \\cdot \\ln \\left(1+\\frac{1}{2 n+1}\\right)\\).",
"role": "user"
}
] | Determine the value of \(\sum_{n=1}^{\infty} \ln \left(1+\frac{1}{n}\right) \cdot \ln \left(1+\frac{1}{2 n}\right) \cdot \ln \left(1+\frac{1}{2 n+1}\right)\). | "[\"\\\\frac{1}{3} \\\\ln ^{3}(2)\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3584, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17512"}] | {
"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
} |
[
"1376"
] | [
"skywork"
] | 3f24a13a3b0d79233bd6b1a1296df00e19d46bab38c9c2075b2f971e822c68c7 | [
{
"content": "**p1.** Is it possible to place six points in the plane and connect them by nonintersecting segments so that each point will be connected with exactly\na) Three other points?\nb) Four other points?**p2.** Martian bank notes can have denomination of $1, 3, 5, 25$ marts. Is it possible to change a... | **p1.** Is it possible to place six points in the plane and connect them by nonintersecting segments so that each point will be connected with exactly
a) Three other points?
b) Four other points?**p2.** Martian bank notes can have denomination of $1, 3, 5, 25$ marts. Is it possible to change a note of $25$ marts to... | "[\"1376\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3528, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:17513"}] | {
"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"
] | a9acb5c99cf444acc92dea722dae0c36fc31317844f3690537dfff1e149bfb6b | [
{
"content": "For the real pairs $(x,y)$ satisfying the equation $x^2 + y^2 + 2x - 6y = 6$, which of the following cannot be equal to $(x-1)^2 + (y-2)^2$?\n\n$ \n\\textbf{(A)}\\ 2\n\\qquad\\textbf{(B)}\\ 9\n\\qquad\\textbf{(C)}\\ 16\n\\qquad\\textbf{(D)}\\ 23\n\\qquad\\textbf{(E)}\\ 30\n$",
"role": "user"
... | For the real pairs $(x,y)$ satisfying the equation $x^2 + y^2 + 2x - 6y = 6$, which of the following cannot be equal to $(x-1)^2 + (y-2)^2$?
$
\textbf{(A)}\ 2
\qquad\textbf{(B)}\ 9
\qquad\textbf{(C)}\ 16
\qquad\textbf{(D)}\ 23
\qquad\textbf{(E)}\ 30
$ | "[\"2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3609, "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:17514"}] | {
"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
} |
[
"1140"
] | [
"skywork"
] | f7074b90d763d0ff364c9a93033e8b16da8f320462ea9ee811fb4c5366ccb896 | [
{
"content": "9.10 In how many ways can three duty officers be selected from a group of 20 people?",
"role": "user"
}
] | 9.10 In how many ways can three duty officers be selected from a group of 20 people? | "[\"1140\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3625, "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:17515"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.04"
] | [
"skywork"
] | 71e4a1ee9e8eadcbbdbc3412318efcabf80269a84a3170fba93592600f337d9c | [
{
"content": "3. From a vessel containing 5 liters of a $6 \\%$ acid solution, 1 liter was poured out, after which 2 liters of water were added. Find the concentration of the resulting solution.",
"role": "user"
}
] | 3. From a vessel containing 5 liters of a $6 \%$ acid solution, 1 liter was poured out, after which 2 liters of water were added. Find the concentration of the resulting solution. | "[\"0.04\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3606, "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:17516"}] | {
"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{14}{5}"
] | [
"skywork"
] | db616af2b719b72ca86163697e29cba8ec0606abe3eee42f4de53cbeb404af17 | [
{
"content": "In the notebooks of Peter and Nick, two numbers are written. Initially, these two numbers are 1 and 2 for Peter and 3 and 4 for Nick. Once a minute, Peter writes a quadratic trinomial $f(x)$, the roots of which are the two numbers in his notebook, while Nick writes a quadratic trinomial $g(x)$ the... | In the notebooks of Peter and Nick, two numbers are written. Initially, these two numbers are 1 and 2 for Peter and 3 and 4 for Nick. Once a minute, Peter writes a quadratic trinomial $f(x)$, the roots of which are the two numbers in his notebook, while Nick writes a quadratic trinomial $g(x)$ the roots of which are th... | "[\"\\\\frac{14}{5}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3552, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17517"}] | {
"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"
] | 65a762ddac2a682f46943c4d49509a975a7ce4fdf1d71811c88c349a50e0ba02 | [
{
"content": "4 、There is a number, when divided by 3 the remainder is 1, when divided by 5 the remainder is 2, so what is the remainder when this number is divided by 15?",
"role": "user"
}
] | 4 、There is a number, when divided by 3 the remainder is 1, when divided by 5 the remainder is 2, so what is the remainder when this number is divided by 15? | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3613, "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:17518"}] | {
"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
} |
[
"372"
] | [
"skywork"
] | 6b0184d7b3016468cdfa1af951c7eb1800cf5301531b014f4dca17dd7d533965 | [
{
"content": "4. A natural number that reads the same from left to right as it does from right to left is called a \"palindromic number\". $a, b, c$ are all three-digit \"palindromic numbers\", and $b=2a+1, c=2b+1$. Then the sum of all possible values of $a$ is $\\qquad$",
"role": "user"
}
] | 4. A natural number that reads the same from left to right as it does from right to left is called a "palindromic number". $a, b, c$ are all three-digit "palindromic numbers", and $b=2a+1, c=2b+1$. Then the sum of all possible values of $a$ is $\qquad$ | "[\"372\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3603, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17519"}] | {
"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
} |
[
"63"
] | [
"skywork"
] | 17bfd3dff76c2752ad513d541d670d7852806b3ee4549944691f51d7ff5b08d7 | [
{
"content": "10. (20 points) Given the sequence $\\left\\{a_{n}\\right\\}:$\n$$\n\\begin{array}{l}\na_{1}=1, a_{2}=2, \\\\\n\\frac{a_{n+2}}{a_{n}}=\\frac{a_{n+1}^{2}+1}{a_{n}^{2}+1}(n=1,2, \\cdots) .\n\\end{array}\n$$\n\nFind $\\left[a_{2021}\\right]$.",
"role": "user"
}
] | 10. (20 points) Given the sequence $\left\{a_{n}\right\}:$
$$
\begin{array}{l}
a_{1}=1, a_{2}=2, \\
\frac{a_{n+2}}{a_{n}}=\frac{a_{n+1}^{2}+1}{a_{n}^{2}+1}(n=1,2, \cdots) .
\end{array}
$$
Find $\left[a_{2021}\right]$. | "[\"63\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3597, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17520"}] | {
"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
} |
[
"6:1"
] | [
"skywork"
] | f790e04eee7d15a499300988b70779431882f4fc9a2788e86b262e2d12bf7b62 | [
{
"content": "Daniel, Clarence, and Matthew split a \\$20.20 dinner bill so that Daniel pays half of what Clarence pays. If Daniel pays \\$6.06, what is the ratio of Clarence's pay to Matthew's pay?\n\n[i]Proposed by Henry Ren[/i]",
"role": "user"
}
] | Daniel, Clarence, and Matthew split a \$20.20 dinner bill so that Daniel pays half of what Clarence pays. If Daniel pays \$6.06, what is the ratio of Clarence's pay to Matthew's pay?
[i]Proposed by Henry Ren[/i] | "[\"6:1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3615, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:17521"}] | {
"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\\mathrm{~}^{2}"
] | [
"skywork"
] | 74d1d651fab892d898231a97796a498fba966fecfa5adbf16757fd6338328fb1 | [
{
"content": "19. In the diagram, $P Q R S$ and $W X Y Z$ are congruent squares. The sides $P S$ and $W Z$ are parallel. The shaded area is equal to $1 \\mathrm{~cm}^{2}$.\nWhat is the area of square $P Q R S$ ?\nA $1 \\mathrm{~cm}^{2}$\nB $2 \\mathrm{~cm}^{2}$\nC $\\frac{1}{2} \\mathrm{~cm}^{2}$\nD $1 \\frac{1... | 19. In the diagram, $P Q R S$ and $W X Y Z$ are congruent squares. The sides $P S$ and $W Z$ are parallel. The shaded area is equal to $1 \mathrm{~cm}^{2}$.
What is the area of square $P Q R S$ ?
A $1 \mathrm{~cm}^{2}$
B $2 \mathrm{~cm}^{2}$
C $\frac{1}{2} \mathrm{~cm}^{2}$
D $1 \frac{1}{2} \mathrm{~cm}^{2}$
E $\frac{3... | "[\"1\\\\mathrm{~}^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3592, "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:17522"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{\\log_4 3} + \\sqrt{\\log_3 4}"
] | [
"skywork"
] | f3997f492c4d396d01ef3d679ea02365cd9b91128ca4a48479c1ed9b6f24db0f | [
{
"content": "Calculate the value of $\\sqrt{\\log_3{12} + \\log_4{12}}$.\nA) $\\sqrt{\\log_4 3 + \\log_3 4}$\nB) $\\sqrt{\\log_4 3} + \\sqrt{\\log_3 4}$\nC) $1$\nD) $2$\nE) $\\log_{12}(3) + \\log_{12}(4)$",
"role": "user"
}
] | Calculate the value of $\sqrt{\log_3{12} + \log_4{12}}$.
A) $\sqrt{\log_4 3 + \log_3 4}$
B) $\sqrt{\log_4 3} + \sqrt{\log_3 4}$
C) $1$
D) $2$
E) $\log_{12}(3) + \log_{12}(4)$ | "[\"\\\\sqrt{\\\\log_4 3} + \\\\sqrt{\\\\log_3 4}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 3617, "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:17523"}] | {
"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
} |
[
"190"
] | [
"skywork"
] | 480315796b74157030ca19feea9e146b4e00e087f4d196392cd5894f760e0235 | [
{
"content": "Among the triangles with natural number side lengths, a perimeter not exceeding 100, and the difference between the longest and shortest sides not greater than 2, there are a total of different triangles that are not congruent to each other.",
"role": "user"
}
] | Among the triangles with natural number side lengths, a perimeter not exceeding 100, and the difference between the longest and shortest sides not greater than 2, there are a total of different triangles that are not congruent to each other. | "[\"190\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3596, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17524"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3}{4}"
] | [
"skywork"
] | f5478adc4ac2bbc7da60f0f6d2f90562cfff99b15c8a05a6976a2f6a61313d0b | [
{
"content": "Given the presence of hereditary traits determined by paired genes $A$ and $a$ in peas, where $A$ is dominant and $a$ is recessive, and the offspring $Aa$ is yellow, determine the probability that the offspring will produce yellow peas after self-crossing.",
"role": "user"
}
] | Given the presence of hereditary traits determined by paired genes $A$ and $a$ in peas, where $A$ is dominant and $a$ is recessive, and the offspring $Aa$ is yellow, determine the probability that the offspring will produce yellow peas after self-crossing. | "[\"\\\\frac{3}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3589, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17525"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"28"
] | [
"skywork"
] | 1d51818b58fe53d8b3a2f751bace0dc99ea9c0fa810eae5ea112085f62776a08 | [
{
"content": "A game board consists of $64$ squares that alternate in color between black and white. The figure below shows square $P$ in the bottom row and square $Q$ in the top row. A marker is placed at $P.$ A step consists of moving the marker onto one of the adjoining white squares in the row above. How ma... | A game board consists of $64$ squares that alternate in color between black and white. The figure below shows square $P$ in the bottom row and square $Q$ in the top row. A marker is placed at $P.$ A step consists of moving the marker onto one of the adjoining white squares in the row above. How many $7$-step paths are ... | "[\"28\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3601, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17526"}] | {
"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
} |
[
"81"
] | [
"skywork"
] | a48360718f15ddb55f0ec37bcf350faf478b532530041fc26dfefdc474af1e89 | [
{
"content": "10 (15 points) Find the number of positive integer solutions to the indeterminate equation $x_{1}+x_{2}+x_{3}+3 x_{4}+3 x_{5}+5 x_{6}=21$.",
"role": "user"
}
] | 10 (15 points) Find the number of positive integer solutions to the indeterminate equation $x_{1}+x_{2}+x_{3}+3 x_{4}+3 x_{5}+5 x_{6}=21$. | "[\"81\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3604, "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:17527"}] | {
"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
} |
[
"26"
] | [
"skywork"
] | 642c8928173c5c6e47354183759f8a9881744e93a6d07f237fcde6676c9d5ae0 | [
{
"content": "Find the smallest positive integer $ K$ such that every $ K$-element subset of $ \\{1,2,...,50 \\}$ contains two distinct elements $ a,b$ such that $ a\\plus{}b$ divides $ ab$.",
"role": "user"
}
] | Find the smallest positive integer $ K$ such that every $ K$-element subset of $ \{1,2,...,50 \}$ contains two distinct elements $ a,b$ such that $ a\plus{}b$ divides $ ab$. | "[\"26\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3607, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17528"}] | {
"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,\\frac{1}{3},\\frac{1}{4}"
] | [
"skywork"
] | c1cbd714c7bac8daec5ba213b8358c5a6b5d46e5442346d405b5c509fcef9081 | [
{
"content": "7. Find all positive real numbers $a$ such that the equation\n$$\na^{2} x^{2}+a x+1-13 a^{2}=0\n$$\n\nhas two integer roots. $\\qquad$",
"role": "user"
}
] | 7. Find all positive real numbers $a$ such that the equation
$$
a^{2} x^{2}+a x+1-13 a^{2}=0
$$
has two integer roots. $\qquad$ | "[\"1,\\\\frac{1}{3},\\\\frac{1}{4}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3610, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17529"}, {"dataset": "skywork", "extra_inf... | {
"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
} |
[
"64,\\!328"
] | [
"skywork"
] | 6b170364178592acb4d511c9f1c752f4f4dfa84c11a8e5adcff94fca5761ef8d | [
{
"content": "The sum of three numbers $x$ ,$y$, $z$ is 165. When the smallest number $x$ is multiplied by 7, the result is $n$. The value $n$ is obtained by subtracting 9 from the largest number $y$. This number $n$ also results by adding 9 to the third number $z$. What is the product of the three numbers?",
... | The sum of three numbers $x$ ,$y$, $z$ is 165. When the smallest number $x$ is multiplied by 7, the result is $n$. The value $n$ is obtained by subtracting 9 from the largest number $y$. This number $n$ also results by adding 9 to the third number $z$. What is the product of the three numbers? | "[\"64,\\\\!328\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3594, "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:17530"}] | {
"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
} |
[
"784"
] | [
"skywork"
] | c9fa119b055ffaa3314072fa05c448f79996e06b368b7e35c1513eec8dc97c84 | [
{
"content": "Parallelogram $ABCD$ has area $1,\\!000,\\!000$. Vertex $A$ is at $(0,0)$ and all other vertices are in the first quadrant. Vertices $B$ and $D$ are lattice points on the lines $y = x$ and $y = kx$ for some integer $k > 1$, respectively. How many such parallelograms are there? (A lattice point is ... | Parallelogram $ABCD$ has area $1,\!000,\!000$. Vertex $A$ is at $(0,0)$ and all other vertices are in the first quadrant. Vertices $B$ and $D$ are lattice points on the lines $y = x$ and $y = kx$ for some integer $k > 1$, respectively. How many such parallelograms are there? (A lattice point is any point whose coordina... | "[\"784\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3605, "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:17531"}] | {
"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
} |
[
"5"
] | [
"skywork"
] | e579198cda6c72193d2c7e784e94879315852bb4fad2f087768f16e93e396a4f | [
{
"content": "12. $S-A B C D$ is a regular quadrilateral pyramid, $P, Q$ are the midpoints of $S B, S D$ respectively, the plane through points $A, P, Q$ divides $S$ $A B C D$ into two parts with volumes $V_{1} \\cdot V_{2}\\left(V_{1}<V_{2}\\right)$, then the ratio $\\frac{V_{2}}{V_{1}}$ equals $\\qquad$ .",
... | 12. $S-A B C D$ is a regular quadrilateral pyramid, $P, Q$ are the midpoints of $S B, S D$ respectively, the plane through points $A, P, Q$ divides $S$ $A B C D$ into two parts with volumes $V_{1} \cdot V_{2}\left(V_{1}<V_{2}\right)$, then the ratio $\frac{V_{2}}{V_{1}}$ equals $\qquad$ . | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3608, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:17532"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3+\\sqrt{7}"
] | [
"skywork"
] | 558996befcce48e280d5bd974e0cf6d3b55669cb19b980eb05d6d98b158c3ba3 | [
{
"content": "1. Let $x$ and $y$ be real numbers with $x>y$ such that $x^{2} y^{2}+x^{2}+y^{2}+2 x y=40$ and $x y+x+y=8$. Find the value of $x$.",
"role": "user"
}
] | 1. Let $x$ and $y$ be real numbers with $x>y$ such that $x^{2} y^{2}+x^{2}+y^{2}+2 x y=40$ and $x y+x+y=8$. Find the value of $x$. | "[\"3+\\\\sqrt{7}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3627, "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:17533"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"n + 1"
] | [
"skywork"
] | 19c01e970b937cb55dc2b69f5b97f7adf882640b60f4bd8c63692653f4bbb915 | [
{
"content": "A set $S$ consists of $k$ sequences of $0,1,2$ of length $n$. For any two sequences $(a_i),(b_i)\\in S$ we can construct a new sequence $(c_i)$ such that $c_i=\\left\\lfloor\\frac{a_i+b_i+1}2\\right\\rfloor$ and include it in $S$. Assume that after performing finitely many such operations we obtai... | A set $S$ consists of $k$ sequences of $0,1,2$ of length $n$. For any two sequences $(a_i),(b_i)\in S$ we can construct a new sequence $(c_i)$ such that $c_i=\left\lfloor\frac{a_i+b_i+1}2\right\rfloor$ and include it in $S$. Assume that after performing finitely many such operations we obtain all the $3n$ sequences of ... | "[\"n + 1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3619, "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:17534"}] | {
"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
} |
[
"43215,41235,42135,51234,53214,53124,54321,12345"
] | [
"skywork"
] | a4c7941d949903087e1033e7a88badd567a757b3d1e1a69bc4becc7134847dc2 | [
{
"content": "【Question 11】 \nArrange the numbers $1 \\sim 5$ in a row to form a five-digit number, such that each digit is not greater than the average of the two adjacent digits (excluding the ten-thousands and units place). The five-digit numbers that meet the requirement are $\\qquad$.",
"role": "user"... | 【Question 11】
Arrange the numbers $1 \sim 5$ in a row to form a five-digit number, such that each digit is not greater than the average of the two adjacent digits (excluding the ten-thousands and units place). The five-digit numbers that meet the requirement are $\qquad$. | "[\"43215,41235,42135,51234,53214,53124,54321,12345\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3600, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17535"}] | {
"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, y) \\in \\left\\{\\left(\\frac{\\pi}{4}, \\frac{3\\pi}{4}\\right), \\left(\\frac{\\pi}{4}, -\\frac{3\\pi}{4}\\right)\\right\\}"
] | [
"skywork"
] | 288b507bfe0203f52616403774afa2448003a0622c4b51ebabb866a2d7ce1891 | [
{
"content": "9・13 Solve the inequality\n$$\\sqrt{\\frac{\\pi}{4}-\\operatorname{arctg} \\frac{|x|+|y|}{\\pi}}+\\operatorname{tg}^{2} x+1 \\leqslant \\sqrt{2}|\\operatorname{tg} x|(\\sin x+\\cos x)$$",
"role": "user"
}
] | 9・13 Solve the inequality
$$\sqrt{\frac{\pi}{4}-\operatorname{arctg} \frac{|x|+|y|}{\pi}}+\operatorname{tg}^{2} x+1 \leqslant \sqrt{2}|\operatorname{tg} x|(\sin x+\cos x)$$ | "[\"(x, y) \\\\in \\\\left\\\\{\\\\left(\\\\frac{\\\\pi}{4}, \\\\frac{3\\\\pi}{4}\\\\right), \\\\left(\\\\frac{\\\\pi}{4}, -\\\\frac{3\\\\pi}{4}\\\\right)\\\\right\\\\}\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 3621, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17536"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"63"
] | [
"skywork"
] | 93e17902f9a1d70b15f7a770dd8c6e35824b2c452bd78e30ff0f57a2bb32629e | [
{
"content": "5. As shown in Figure 2, with the sides $AB$ and $AD$ of the square $ABCD$ as diameters, semicircles are drawn outside the square. A line is drawn through $A$ intersecting the two semicircles at $E$ and $F$. If the area of the square $ABCD$ is $1997$, and $AE$ and $AF$ are integers, then the lengt... | 5. As shown in Figure 2, with the sides $AB$ and $AD$ of the square $ABCD$ as diameters, semicircles are drawn outside the square. A line is drawn through $A$ intersecting the two semicircles at $E$ and $F$. If the area of the square $ABCD$ is $1997$, and $AE$ and $AF$ are integers, then the length of $EF$ is ( ).
(A) ... | "[\"63\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3602, "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:17537"}] | {
"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"
] | 74350a38b09345781b18d65a14ba2e0f4a949fa7515b0341d4d93e21da9ab60f | [
{
"content": "G2.2 If there are $K$ integers that satisfy the equation $\\left(x^{2}-3 x+2\\right)^{2}-3\\left(x^{2}-3 x\\right)-4=0$, find the value of $K$",
"role": "user"
}
] | G2.2 If there are $K$ integers that satisfy the equation $\left(x^{2}-3 x+2\right)^{2}-3\left(x^{2}-3 x\right)-4=0$, find the value of $K$ | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3632, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17538"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt[3]{729},\\sqrt{121},\\sqrt[4]{38416}"
] | [
"skywork"
] | c60fcfbf32e5ccd9957b2fc176c6502a7a5444f9f001e06f9f41851f18681822 | [
{
"content": "Write in ascending order the numbers: $\\sqrt{121}$, $\\sqrt[3]{729}$, and $\\sqrt[4]{38416}$.",
"role": "user"
}
] | Write in ascending order the numbers: $\sqrt{121}$, $\sqrt[3]{729}$, and $\sqrt[4]{38416}$. | "[\"\\\\sqrt[3]{729},\\\\sqrt{121},\\\\sqrt[4]{38416}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3643, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17540"}] | {
"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}{2}"
] | [
"skywork"
] | 6ffad122875ef8e00e142a814ccb4ce12622b20e26eeb41077b9404597683923 | [
{
"content": "Find the distance between the planes $x + 2y - 2z + 1 = 0$ and $2x + 4y - 4z + 5 = 0.$",
"role": "user"
}
] | Find the distance between the planes $x + 2y - 2z + 1 = 0$ and $2x + 4y - 4z + 5 = 0.$ | "[\"\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3639, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17541"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"27"
] | [
"skywork"
] | e271532277c8beeb214fd30d9626949ceb092425e655c59ccd9918d923ce62f3 | [
{
"content": "Three. (50 points) Given a set of 9 points in space\n$$\nM=\\left\\{A_{1}, A_{2}, \\cdots, A_{9}\\right\\} \\text {, }\n$$\n\nwhere no four points are coplanar. Connect some line segments between these 9 points to form a graph $G$, such that the graph contains no tetrahedra. How many triangles can... | Three. (50 points) Given a set of 9 points in space
$$
M=\left\{A_{1}, A_{2}, \cdots, A_{9}\right\} \text {, }
$$
where no four points are coplanar. Connect some line segments between these 9 points to form a graph $G$, such that the graph contains no tetrahedra. How many triangles can graph $G$ have at most? | "[\"27\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3612, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17542"}] | {
"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
} |
[
"90"
] | [
"skywork"
] | 77ce30709ebddbd72a0b2d0b1a1429d98b4e79ac7d8b6be061386c3676699677 | [
{
"content": "8. Find the angle between the tangents to the graph of the function $y=x^{2} \\sqrt{3} / 6$, passing through the point $M(1 ;-\\sqrt{3} / 2)$.",
"role": "user"
}
] | 8. Find the angle between the tangents to the graph of the function $y=x^{2} \sqrt{3} / 6$, passing through the point $M(1 ;-\sqrt{3} / 2)$. | "[\"90\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3629, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:17543"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2}"
] | [
"skywork"
] | 8793af0eef4aaa40beaf78b3bb846ee08a7b1a4e25ac047db5a7477d795d321f | [
{
"content": "Find\n\\[\\sum_{n = 1}^\\infty \\frac{n^2 + n - 1}{(n + 2)!}.\\]",
"role": "user"
}
] | Find
\[\sum_{n = 1}^\infty \frac{n^2 + n - 1}{(n + 2)!}.\] | "[\"\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3636, "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:17544"}] | {
"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
} |
[
"153"
] | [
"skywork"
] | f130d1ba2f1462dd24b2fb030f20842ed8e514ceaf8b377c03b31efe26c53911 | [
{
"content": "8. It is known that two engineering teams, Team A and Team B, have several people each. If 90 people are transferred from Team A to Team B, then the total number of people in Team B will be twice that of Team A; if some people are transferred from Team B to Team A, then the total number of people ... | 8. It is known that two engineering teams, Team A and Team B, have several people each. If 90 people are transferred from Team A to Team B, then the total number of people in Team B will be twice that of Team A; if some people are transferred from Team B to Team A, then the total number of people in Team A will be 6 ti... | "[\"153\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3618, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17545"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{9}"
] | [
"skywork"
] | e925f6a261058ab58aae27a7647a0c4dc3d2223c8b15ea9d1ded1c16e7f80c4c | [
{
"content": "Points $ A$ and $ B$ lie on a circle centered at $ O$ , and $ \\angle AOB=60^\\circ$ . A second circle is internally tangent to the first and tangent to both $ \\overline{OA}$ and $ \\overline{OB}$ . What is the ratio of the area of the smaller circle to that of the larger circle?",
"... | Points $ A$ and $ B$ lie on a circle centered at $ O$ , and $ \angle AOB=60^\circ$ . A second circle is internally tangent to the first and tangent to both $ \overline{OA}$ and $ \overline{OB}$ . What is the ratio of the area of the smaller circle to that of the larger circle? | "[\"\\\\frac{1}{9}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3626, "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:17546"}] | {
"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
} |
[
"299"
] | [
"skywork"
] | 00ed3c0581754379253d7049de32a4971c7fa06f750150835629b6b88fd01594 | [
{
"content": "Call a pair of integers $(a,b)$ [i]primitive[/i] if there exists a positive integer $\\ell$ such that $(a+bi)^\\ell$ is real. Find the smallest positive integer $n$ such that less than $1\\%$ of the pairs $(a, b)$ with $0 \\le a, b \\le n$ are primitive.\n\n[i]Proposed by Mehtaab Sawhney[/i]",
... | Call a pair of integers $(a,b)$ [i]primitive[/i] if there exists a positive integer $\ell$ such that $(a+bi)^\ell$ is real. Find the smallest positive integer $n$ such that less than $1\%$ of the pairs $(a, b)$ with $0 \le a, b \le n$ are primitive.
[i]Proposed by Mehtaab Sawhney[/i] | "[\"299\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3624, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:17547"}] | {
"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
} |
[
"1,3,4,9,12,36"
] | [
"skywork"
] | 864ec96bb07bdfad528bdca942a95c7550f02a412a0cc38141a2fbec39880ec5 | [
{
"content": "Problem 6.5. An equilateral triangle is divided into 36 identical equilateral triangles. For which $k$ can it be cut along the grid lines into $k$ identical polygons?",
"role": "user"
}
] | Problem 6.5. An equilateral triangle is divided into 36 identical equilateral triangles. For which $k$ can it be cut along the grid lines into $k$ identical polygons? | "[\"1,3,4,9,12,36\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3614, "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:17548"}] | {
"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"
] | 757731d2255d90dae4777c76d995cab93b84835e3d03e2bddd69b0ec41c77e1b | [
{
"content": "If \\( (2^{a})(2^{b})=64 \\), what is the mean (average) of \\( a \\) and \\( b \\)?",
"role": "user"
}
] | If \( (2^{a})(2^{b})=64 \), what is the mean (average) of \( a \) and \( b \)? | "[\"3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3637, "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:17549"}] | {
"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
} |
[
"2L"
] | [
"skywork"
] | bdfc542d7b715b5a58bfe31408889f07bacb0298474eeb33f6877bcbf32625be | [
{
"content": "A regular tetrahedron has side $L$. What is the smallest $x$ such that the tetrahedron can be passed through a loop of twine of length $x$?",
"role": "user"
}
] | A regular tetrahedron has side $L$. What is the smallest $x$ such that the tetrahedron can be passed through a loop of twine of length $x$? | "[\"2L\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3616, "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:17550"}] | {
"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{n+1}{n}, \\text {for any nonzero integer } n"
] | [
"skywork"
] | ab43d198dcf52d0cad017b13f3d576de7cc4a9eb7542d6da6ae6bcbfa84b5f07 | [
{
"content": "Let $\\mathbb R$ be the set of real numbers. We denote by $\\mathcal F$ the set of all functions $f\\colon\\mathbb R\\to\\mathbb R$ such that\n$$f(x + f(y)) = f(x) + f(y)$$\nfor every $x,y\\in\\mathbb R$ Find all rational numbers $q$ such that for every function $f\\in\\mathcal F$, there exists so... | Let $\mathbb R$ be the set of real numbers. We denote by $\mathcal F$ the set of all functions $f\colon\mathbb R\to\mathbb R$ such that
$$f(x + f(y)) = f(x) + f(y)$$
for every $x,y\in\mathbb R$ Find all rational numbers $q$ such that for every function $f\in\mathcal F$, there exists some $z\in\mathbb R$ satisfying $f(z... | "[\"\\\\frac{n+1}{n}, \\\\text {for any nonzero integer } n\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 3631, "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:17551"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"P(x) = \\binom{\\frac{x}{c}}{a}"
] | [
"skywork"
] | 42a25b5764efa19ba165b53cd0b8ba314e977af56311b89a696a82b5069c9095 | [
{
"content": "Find all polynomials $P(x)$ with real coefficients such that $P(2014) = 1$ and, for some integer $c$:\n\n$xP(x-c) = (x - 2014)P(x)$",
"role": "user"
}
] | Find all polynomials $P(x)$ with real coefficients such that $P(2014) = 1$ and, for some integer $c$:
$xP(x-c) = (x - 2014)P(x)$ | "[\" P(x) = \\\\binom{\\\\frac{x}{c}}{a} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3622, "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:17552"}] | {
"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{15}{2};-\\frac{1}{2})"
] | [
"skywork"
] | ac0359870c62c26b35c38d277d2b929ba1282d9012c94a0b8fb9cdfb832238cf | [
{
"content": "5. Solve the inequality $\\frac{3-x}{2 x+1}<-\\frac{3}{4}$.\n\n#",
"role": "user"
}
] | 5. Solve the inequality $\frac{3-x}{2 x+1}<-\frac{3}{4}$.
# | "[\"(-\\\\frac{15}{2};-\\\\frac{1}{2})\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3648, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17553"}] | {
"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
} |
[
"325/648"
] | [
"skywork"
] | 2a2277f54db2784ba381ecfc671d8c511ba3cf8949d4657513a7de824ef0cf7f | [
{
"content": "Throw 6 dice at a time, find the probability, in the lowest form, such that there will be exactly four kinds of the outcome.",
"role": "user"
}
] | Throw 6 dice at a time, find the probability, in the lowest form, such that there will be exactly four kinds of the outcome. | "[\"325/648\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3633, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17554"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"skywork"
] | 8d07165607f816861f120f408ad3bc50c3f3f1830994656d1268617415187aa8 | [
{
"content": "$A, B, C$ and $D$ are distinct positive integers such that the product $AB = 60$, the product $CD = 60$ and $A - B = C + D$ . What is the value of $A$?",
"role": "user"
}
] | $A, B, C$ and $D$ are distinct positive integers such that the product $AB = 60$, the product $CD = 60$ and $A - B = C + D$ . What is the value of $A$? | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3647, "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:17555"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | f1dee27042197aec437e9e1548d811bb435f5b7d8a9c8d48beb54d0325357fc0 | [
{
"content": "In a forest each of $n$ animals ($n\\ge 3$) lives in its own cave, and there is exactly one separate path between any two of these caves. Before the election for King of the Forest some of the animals make an election campaign. Each campaign-making animal visits each of the other caves exactly onc... | In a forest each of $n$ animals ($n\ge 3$) lives in its own cave, and there is exactly one separate path between any two of these caves. Before the election for King of the Forest some of the animals make an election campaign. Each campaign-making animal visits each of the other caves exactly once, uses only the paths ... | "[\"4\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3598, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17556"}] | {
"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{21\\sqrt{55}}{4}"
] | [
"skywork"
] | 79878f9519bdec858ff3ba95f85e31227353725918ae5283394b205d2adf952b | [
{
"content": "5.2.2. $B L$ is the bisector of triangle $A B C$. Find its area, given that $|A L|=3$, $|B L|=6 \\sqrt{5},|C L|=4$.",
"role": "user"
}
] | 5.2.2. $B L$ is the bisector of triangle $A B C$. Find its area, given that $|A L|=3$, $|B L|=6 \sqrt{5},|C L|=4$. | "[\"\\\\frac{21\\\\sqrt{55}}{4}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3635, "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:17558"}] | {
"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
} |
[
"15"
] | [
"skywork"
] | df34a1e3e8ece848c7568db2460c219bdadc88da43493b419c0a2ce72bdb544a | [
{
"content": "There is a magical tree with 63 fruits. On the first day, 1 fruit will fall from the tree. Starting from the second day, the number of fruits falling each day increases by 1 compared to the previous day. However, if the number of fruits on the tree is less than the number that should fall on that ... | There is a magical tree with 63 fruits. On the first day, 1 fruit will fall from the tree. Starting from the second day, the number of fruits falling each day increases by 1 compared to the previous day. However, if the number of fruits on the tree is less than the number that should fall on that day, then the sequence... | "[\"15\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3623, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17559"}] | {
"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
} |
[
"120"
] | [
"skywork"
] | f345771e047e2ba1525d79cb34c2ee1eb09f8746525ef58d4ff1bae9eaac50be | [
{
"content": "3. A little squirrel picked many pine nuts. On the first day, it ate 10, and every day after that, it ate 4 more than the previous day. By the 6th day, it had just finished eating all the pine nuts. The little squirrel ate $\\qquad$ pine nuts in total.",
"role": "user"
}
] | 3. A little squirrel picked many pine nuts. On the first day, it ate 10, and every day after that, it ate 4 more than the previous day. By the 6th day, it had just finished eating all the pine nuts. The little squirrel ate $\qquad$ pine nuts in total. | "[\"120\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3642, "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:17560"}] | {
"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
} |
[
"6"
] | [
"skywork"
] | 38af27207cb0c4cc6fb41f912a5575571406243e7898e2ed7bba70b52d5ae72f | [
{
"content": "Four. (Total 20 points) On the 6 lines of the three edges of the tetrahedron $V-A B C$, what is the maximum number of pairs of lines that are perpendicular to each other? (Each pair consists of two lines)\n\n保留源文本的换行和格式，翻译结果如下：\n\nFour. (Total 20 points) On the 6 lines of the three edges of the te... | Four. (Total 20 points) On the 6 lines of the three edges of the tetrahedron $V-A B C$, what is the maximum number of pairs of lines that are perpendicular to each other? (Each pair consists of two lines)
保留源文本的换行和格式，翻译结果如下：
Four. (Total 20 points) On the 6 lines of the three edges of the tetrahedron $V-A B C$, what ... | "[\"6\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 3641, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17561"}] | {
"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"
] | b214933a72901aacca6d9014f0df8eca66ab797f09fd744a87552fbdf263f074 | [
{
"content": "Given that $n$ is a positive integer, and given that $\\mathop{\\text{lcm}}[24,n]=72$ and $\\mathop{\\text{lcm}}[n,27]=108$, what is $n$?",
"role": "user"
}
] | Given that $n$ is a positive integer, and given that $\mathop{\text{lcm}}[24,n]=72$ and $\mathop{\text{lcm}}[n,27]=108$, what is $n$? | "[\"36\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3652, "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:17562"}] | {
"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
} |
[
"56"
] | [
"skywork"
] | 15f49b764e081c888f350dc4c7aa292cd0baea44f167b8dcf041e50d111028e1 | [
{
"content": "Jeff has a deck of $12$ cards: $4$ $L$s, $4$ $M$s, and $4$ $T$s. Armaan randomly draws three cards without replacement. The probability that he takes $3$ $L$s can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m +n$.",
"role": "user"
}
] | Jeff has a deck of $12$ cards: $4$ $L$s, $4$ $M$s, and $4$ $T$s. Armaan randomly draws three cards without replacement. The probability that he takes $3$ $L$s can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m +n$. | "[\"56\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3630, "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:17563"}] | {
"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
} |
[
"26"
] | [
"skywork"
] | 4cadc06d94c16fb953bf387bc8550d7f87aa7b13a1d4d9f61ac008d51d9dfe33 | [
{
"content": "What is the minimum number of digits to the right of the decimal point needed to express the fraction $\\frac{123456789}{2^{26}\\cdot 5^4}$ as a decimal?",
"role": "user"
}
] | What is the minimum number of digits to the right of the decimal point needed to express the fraction $\frac{123456789}{2^{26}\cdot 5^4}$ as a decimal? | "[\"26\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3655, "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:17564"}] | {
"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
} |
[
"2024"
] | [
"skywork"
] | 6b44708520245c3526f8c54b65100a6cdfdbdaeb7fec856cc1afd3ed5afed7b3 | [
{
"content": "Find the smallest positive integer $n$ that has at least $7$ positive divisors $1 = d_1 < d_2 < \\ldots < d_k = n$, $k \\geq 7$, and for which the following equalities hold:\n\n$$d_7 = 2d_5 + 1\\text{ and }d_7 = 3d_4 - 1$$\n\n[i]Proposed by Mykyta Kharin[/i]",
"role": "user"
}
] | Find the smallest positive integer $n$ that has at least $7$ positive divisors $1 = d_1 < d_2 < \ldots < d_k = n$, $k \geq 7$, and for which the following equalities hold:
$$d_7 = 2d_5 + 1\text{ and }d_7 = 3d_4 - 1$$
[i]Proposed by Mykyta Kharin[/i] | "[\"2024\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 3646, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17565"}] | {
"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
} |
[
"612360"
] | [
"skywork"
] | bc2b5f3124ab87993577373c5d9bdf12cc5aac65cb9bf97c2daace8bc73de171 | [
{
"content": "u上as $8$ 个乘客随意登上 6 节车相, 使恰有两节车厢空着的上车方法总数是多少?\n\nThere are $8$ passengers boarding 6 carriages randomly. How many ways are there for the passengers to board the carriages such that exactly two carriages are empty?",
"role": "user"
}
] | u上as $8$ 个乘客随意登上 6 节车相, 使恰有两节车厢空着的上车方法总数是多少?
There are $8$ passengers boarding 6 carriages randomly. How many ways are there for the passengers to board the carriages such that exactly two carriages are empty? | "[\"612360\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3645, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17566"}] | {
"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
} |
[
"82"
] | [
"skywork"
] | 1dd6ad914ed2b6b96a885ff177ea648cd79c9d47681cd27704cfe300fb5a2c93 | [
{
"content": "39. Two ants, a red one and a black one, crawl back and forth between points $A$ and $B$ on a ruler. The red ant starts from point $A$, and the black ant starts from point $B$ at the same time. The black ant's speed is 1.25 times that of the red ant. They meet for the second time at the $124 \\mat... | 39. Two ants, a red one and a black one, crawl back and forth between points $A$ and $B$ on a ruler. The red ant starts from point $A$, and the black ant starts from point $B$ at the same time. The black ant's speed is 1.25 times that of the red ant. They meet for the second time at the $124 \mathrm{~cm}$ mark on the r... | "[\"82\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3653, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17567"}] | {
"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
} |
[
"40"
] | [
"skywork"
] | 4e7e5e08a3d26adea88b326f28923f302bbba551cec2ca6cdb61d0e21c16e7a7 | [
{
"content": "From the set of three-digit numbers that do not contain the digits $0,1,2,3,4,5$, several numbers were written down in such a way that no two numbers could be obtained from each other by swapping two adjacent digits. What is the maximum number of such numbers that could have been written?",
"r... | From the set of three-digit numbers that do not contain the digits $0,1,2,3,4,5$, several numbers were written down in such a way that no two numbers could be obtained from each other by swapping two adjacent digits. What is the maximum number of such numbers that could have been written? | "[\"40\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 3644, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:17568"}] | {
"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
} |
[
"1000000^2"
] | [
"skywork"
] | fc5e66ae48bc3bfc319f1be39bf35e02ee5057ad75098f7875593c81247ac585 | [
{
"content": "6,7\n\nThe population of China is one billion people. It would seem that on a map of China with a scale of $1: 1000000$ (1 cm $: 10$ km), one million times fewer people could fit, compared to the entire territory of the country. However, in reality, not only 1000, but even 100 people would not be ... | 6,7
The population of China is one billion people. It would seem that on a map of China with a scale of $1: 1000000$ (1 cm $: 10$ km), one million times fewer people could fit, compared to the entire territory of the country. However, in reality, not only 1000, but even 100 people would not be able to fit on this map.... | "[\"1000000^2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3634, "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:17569"}] | {
"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
} |
[
"-125"
] | [
"skywork"
] | ca40d3e0a567e8af1a8778d8582406324d64aaa09d2754bf2a2541bf04acd29d | [
{
"content": "Let $x_{1}, x_{2}, \\ldots, x_{n}$ be a sequence where each term is 0, 1, or -2. If\n\n$$\n\\left\\{\\begin{array}{l}\nx_{1}+x_{2}+\\cdots+x_{n}=-5 \\\\\nx_{1}^{2}+x_{2}^{2}+\\cdots+x_{n}^{2}=19\n\\end{array}\\right.\n$$\n\ndetermine $x_{1}^{5}+x_{2}^{5}+\\cdots+x_{n}^{5}$.",
"role": "user"
... | Let $x_{1}, x_{2}, \ldots, x_{n}$ be a sequence where each term is 0, 1, or -2. If
$$
\left\{\begin{array}{l}
x_{1}+x_{2}+\cdots+x_{n}=-5 \\
x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}=19
\end{array}\right.
$$
determine $x_{1}^{5}+x_{2}^{5}+\cdots+x_{n}^{5}$. | "[\"-125\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 3654, "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:17570"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.