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 |
|---|---|---|---|---|---|---|---|---|
[
"2"
] | [
"skywork"
] | 84b0e2f8d2fc4edd3f04bcda6064124eefbf6c6411ae3eb4e6181640c18fd0e5 | [
{
"content": "4. Let $A B C$ be an acute triangle, $\\mathcal{K}$ a circle with diameter $A B$, $E$ and $F$ the intersections of the circle with sides $A C$ and $B C$, and $P$ the intersection of the tangents to the circle $\\mathcal{K}$ at points $E$ and $F$. Calculate the ratio of the radii of the circumcircl... | 4. Let $A B C$ be an acute triangle, $\mathcal{K}$ a circle with diameter $A B$, $E$ and $F$ the intersections of the circle with sides $A C$ and $B C$, and $P$ the intersection of the tangents to the circle $\mathcal{K}$ at points $E$ and $F$. Calculate the ratio of the radii of the circumcircles of triangles $A B C$ ... | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1284, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15300"}] | {
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} |
[
"1901"
] | [
"skywork"
] | 7c9e4b21127f2d21f597c94a20c83e790fc094390e5556be5ca6476c938ae951 | [
{
"content": "4. On a circle, 1974 children are arranged and are playing a game of elimination as follows: the first child remains in the circle, the second child is eliminated, the third child remains, the fourth child is eliminated, and so on until only one child remains in the circle. Determine which child r... | 4. On a circle, 1974 children are arranged and are playing a game of elimination as follows: the first child remains in the circle, the second child is eliminated, the third child remains, the fourth child is eliminated, and so on until only one child remains in the circle. Determine which child remains. | "[\"1901\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1297, "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:15301"}] | {
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} |
[
"-1"
] | [
"skywork"
] | 6ec5526e5a7aab686112a1c506d8daa0913e82724b4f2bc528a675a1a4f74581 | [
{
"content": "If one minus the reciprocal of $(1-x)$ equals the reciprocal of $(1-x)$, then $x$ equals",
"role": "user"
}
] | If one minus the reciprocal of $(1-x)$ equals the reciprocal of $(1-x)$, then $x$ equals | "[\"-1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1290, "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:15302"}] | {
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[
"986431"
] | [
"skywork"
] | 11cb8cd5daa5a17df95e676ac279ca118303c99459c9b488d08330b9a2ed604f | [
{
"content": "10.4. Find the largest natural number, all digits of which are different, and the product of these digits is a square of a natural number.",
"role": "user"
}
] | 10.4. Find the largest natural number, all digits of which are different, and the product of these digits is a square of a natural number. | "[\"986431\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1304, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15303"}] | {
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} |
[
"39"
] | [
"skywork"
] | 8765bc6bd367f4bacf56050b62d12e6710d31893416bdb6aeddd715373143039 | [
{
"content": "If $x$ and $y$ are positive integers with $x>y$ and $x+x y=391$, what is the value of $x+y$ ?\n(A) 38\n(B) 39\n(C) 40\n(D) 41\n(E) 42",
"role": "user"
}
] | If $x$ and $y$ are positive integers with $x>y$ and $x+x y=391$, what is the value of $x+y$ ?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42 | "[\"39\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1312, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15304"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{2(n-2)}{n-1}"
] | [
"skywork"
] | 7713ffa9e1dde56b70ad2980a9409eaca6085170498acc05f8a29f9124ded9f5 | [
{
"content": "Example 4 Given a positive integer $n(n \\geqslant 2)$. Find the largest real number $\\lambda$, such that the inequality\n$$\na_{n}^{2} \\geqslant \\lambda\\left(a_{1}+a_{2}+\\cdots+a_{n-1}\\right)+2 a_{n},\n$$\n\nholds for any positive integers $a_{1}$, $a_{2}, \\cdots, a_{n}$ satisfying $a_{1}<... | Example 4 Given a positive integer $n(n \geqslant 2)$. Find the largest real number $\lambda$, such that the inequality
$$
a_{n}^{2} \geqslant \lambda\left(a_{1}+a_{2}+\cdots+a_{n-1}\right)+2 a_{n},
$$
holds for any positive integers $a_{1}$, $a_{2}, \cdots, a_{n}$ satisfying $a_{1}<a_{2}<\cdots<a_{n}$.
(2003, Girls' ... | "[\"\\\\frac{2(n-2)}{n-1}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1298, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:15305"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{11}{60}"
] | [
"skywork"
] | 33d8c0f5418edd219371baaf981ce29f7c37e1bd672c8166d3fa6c677fffb66a | [
{
"content": "1. As shown in Figure $4, \\angle B C A$ $=90^{\\circ}, C D$ is the altitude. It is known that the three sides of the right triangle $\\triangle A B C$ are all integers, and $B D=11^{3}$. Find the ratio of the perimeters of the right triangles $\\triangle B C D$ and $\\triangle A C D$.\n(2002, Nat... | 1. As shown in Figure $4, \angle B C A$ $=90^{\circ}, C D$ is the altitude. It is known that the three sides of the right triangle $\triangle A B C$ are all integers, and $B D=11^{3}$. Find the ratio of the perimeters of the right triangles $\triangle B C D$ and $\triangle A C D$.
(2002, National Junior High School Mat... | "[\"\\\\frac{11}{60}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1292, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:15306"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\{6, 9, 7\\}"
] | [
"skywork"
] | a52b9895bb086fbf5a4c35d458d45873ebafc2cc0c446e3db80454a8b176f81b | [
{
"content": "Let $ABCDE$ be a convex pentagon in which $\\angle{A}=\\angle{B}=\\angle{C}=\\angle{D}=120^{\\circ}$ and the side lengths are five [i]consecutive integers[/i] in some order. Find all possible values of $AB+BC+CD$.",
"role": "user"
}
] | Let $ABCDE$ be a convex pentagon in which $\angle{A}=\angle{B}=\angle{C}=\angle{D}=120^{\circ}$ and the side lengths are five [i]consecutive integers[/i] in some order. Find all possible values of $AB+BC+CD$. | "[\" \\\\{6, 9, 7\\\\} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1299, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15308"}] | {
"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
} |
[
"997"
] | [
"skywork"
] | 26c35634a9901493daf8d4a96a6733416082df674ee0985e762d5dee20cdcaff | [
{
"content": "Let $\\overline{CH}$ be an altitude of $\\triangle ABC$. Let $R\\,$ and $S\\,$ be the points where the circles inscribed in the triangles $ACH\\,$ and $BCH$ are tangent to $\\overline{CH}$. If $AB = 1995\\,$, $AC = 1994\\,$, and $BC = 1993\\,$, then $RS\\,$ can be expressed as $m/n\\,$, where $m\\... | Let $\overline{CH}$ be an altitude of $\triangle ABC$. Let $R\,$ and $S\,$ be the points where the circles inscribed in the triangles $ACH\,$ and $BCH$ are tangent to $\overline{CH}$. If $AB = 1995\,$, $AC = 1994\,$, and $BC = 1993\,$, then $RS\,$ can be expressed as $m/n\,$, where $m\,$ and $n\,$ are relatively prime ... | "[\"997\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1293, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15309"}] | {
"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
} |
[
"2400"
] | [
"skywork"
] | ad63561b4bc160fbe35af3447bdcaa3cc74b535d5d38b62e26eda06bfa8bc66e | [
{
"content": "4. The cost of computers is continuously decreasing. If the price of a computer decreases by $\\frac{1}{3}$ every 3 years, and the current price of a computer is 8100 yuan, then the price after 9 years will be ( ).\nA. 2400 yuan\nB. 900 yuan\nC. 300 yuan\nD. 3600 yuan",
"role": "user"
}
] | 4. The cost of computers is continuously decreasing. If the price of a computer decreases by $\frac{1}{3}$ every 3 years, and the current price of a computer is 8100 yuan, then the price after 9 years will be ( ).
A. 2400 yuan
B. 900 yuan
C. 300 yuan
D. 3600 yuan | "[\"2400\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1306, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15310"}] | {
"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
} |
[
"49"
] | [
"skywork"
] | a4a1af36ef6fb79b08bc8ad7d9321831ee449091f3bd3f098d6dc129439dd231 | [
{
"content": "5. The side-lengths $a, b, c$ of a triangle $A B C$ are positive integers. Let\n\n$$\nT_{n}=(a+b+c)^{2 n}-(a-b+c)^{2 n}-(a+b-c)^{2 n}+(a-b-c)^{2 n}\n$$\n\nfor any positive integer $n$. If $\\frac{T_{2}}{2 T_{1}}=2023$ and $a>b>c$, determine all possible perimeters of the triangle $A B C$.",
"r... | 5. The side-lengths $a, b, c$ of a triangle $A B C$ are positive integers. Let
$$
T_{n}=(a+b+c)^{2 n}-(a-b+c)^{2 n}-(a+b-c)^{2 n}+(a-b-c)^{2 n}
$$
for any positive integer $n$. If $\frac{T_{2}}{2 T_{1}}=2023$ and $a>b>c$, determine all possible perimeters of the triangle $A B C$. | "[\"49\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1303, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15311"}] | {
"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
} |
[
"70"
] | [
"skywork"
] | 7bc8a21b2acb5aaa4444e8d9dfb8fb334a35865d5454740fe4c82072e2e45641 | [
{
"content": "Let \\( A B C D \\) be a quadrilateral and \\( P \\) the intersection of \\( (A C) \\) and \\( (B D) \\). Assume that \\( \\widehat{C A D} = 50^\\circ \\), \\( \\widehat{B A C} = 70^\\circ \\), \\( \\widehat{D C A} = 40^\\circ \\), and \\( \\widehat{A C B} = 20^\\circ \\). Calculate the angle \\( ... | Let \( A B C D \) be a quadrilateral and \( P \) the intersection of \( (A C) \) and \( (B D) \). Assume that \( \widehat{C A D} = 50^\circ \), \( \widehat{B A C} = 70^\circ \), \( \widehat{D C A} = 40^\circ \), and \( \widehat{A C B} = 20^\circ \). Calculate the angle \( \widehat{C P D} \). | "[\"70\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1282, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15312"}] | {
"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"
] | c67a61e99c7aaf2fc1275f1128f690f67c2100ebe46c0e75f2a63ead19677196 | [
{
"content": "The wristwatch is 5 minutes slow per hour; 5.5 hours ago, it was set to the correct time. It is currently 1 PM on a clock that shows the correct time. How many minutes will it take for the wristwatch to show 1 PM?",
"role": "user"
}
] | The wristwatch is 5 minutes slow per hour; 5.5 hours ago, it was set to the correct time. It is currently 1 PM on a clock that shows the correct time. How many minutes will it take for the wristwatch to show 1 PM? | "[\"30\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1305, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15313"}] | {
"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"
] | faafd8db825bd98ac6eede6e699c0003861d8c4dc2e0bbf91440ea72649a6a1a | [
{
"content": "30. Find the largest positive number $x$ such that\n$$\n\\left(2 x^{3}-x^{2}-x+1\\right)^{1+\\frac{1}{2 x+1}}=1\n$$",
"role": "user"
}
] | 30. Find the largest positive number $x$ such that
$$
\left(2 x^{3}-x^{2}-x+1\right)^{1+\frac{1}{2 x+1}}=1
$$ | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1319, "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:15314"}] | {
"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"
] | 135747559fbc2690765cf5f8cb94256976a28d029dd6ff65e04d60a3b1c9d2e2 | [
{
"content": "Suppose $f(x) = 6x - 9$ and $g(x) = \\frac{x}{3} + 2$. Find $f(g(x)) - g(f(x))$.",
"role": "user"
}
] | Suppose $f(x) = 6x - 9$ and $g(x) = \frac{x}{3} + 2$. Find $f(g(x)) - g(f(x))$. | "[\"4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1323, "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:15315"}] | {
"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
} |
[
"\\(\\boxed{4489}\\)"
] | [
"skywork"
] | 6720086e9ed3aee4d621d295a0f89a2717df2cc421d6ee541b545862df0570b2 | [
{
"content": "A permutation of the set of positive integers $[n] = \\{1, 2, \\ldots, n\\}$ is a sequence $(a_1, a_2, \\ldots, a_n)$ such that each element of $[n]$ appears precisely one time as a term of the sequence. For example, $(3, 5, 1, 2, 4)$ is a permutation of $[5]$ . Let $P(n)$ be the number of permuta... | A permutation of the set of positive integers $[n] = \{1, 2, \ldots, n\}$ is a sequence $(a_1, a_2, \ldots, a_n)$ such that each element of $[n]$ appears precisely one time as a term of the sequence. For example, $(3, 5, 1, 2, 4)$ is a permutation of $[5]$ . Let $P(n)$ be the number of permutations of $[n]$ for which $... | "[\"\\\\(\\\\boxed{4489}\\\\)\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1307, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:15316"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-2"
] | [
"skywork"
] | 81666cfbf2ca4ae344dad53dd7da259e8275fbc8aa475bcfe08eed16170384b6 | [
{
"content": "If $f(x) = ax+b$ and $f^{-1}(x) = bx+a$ with $a$ and $b$ real, what is the value of $a+b$? \n$\\mathrm{(A)}\\ -2 \\qquad\\mathrm{(B)}\\ -1 \\qquad\\mathrm{(C)}\\ 0 \\qquad\\mathrm{(D)}\\ 1 \\qquad\\mathrm{(E)}\\ 2$",
"role": "user"
}
] | If $f(x) = ax+b$ and $f^{-1}(x) = bx+a$ with $a$ and $b$ real, what is the value of $a+b$?
$\mathrm{(A)}\ -2 \qquad\mathrm{(B)}\ -1 \qquad\mathrm{(C)}\ 0 \qquad\mathrm{(D)}\ 1 \qquad\mathrm{(E)}\ 2$ | "[\"-2\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 1321, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15317"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | 9e9f4c522e585c7b7dad798e0f824d431689988666b5ae404f9b1402f9188cb1 | [
{
"content": "There are $12$ dentists in a clinic near a school. The students of the $5$th year, who are $29$, attend the clinic. Each dentist serves at least $2$ students. Determine the greater number of students that can attend to a single dentist .",
"role": "user"
}
] | There are $12$ dentists in a clinic near a school. The students of the $5$th year, who are $29$, attend the clinic. Each dentist serves at least $2$ students. Determine the greater number of students that can attend to a single dentist . | "[\"7\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1317, "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:15318"}] | {
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[
"19"
] | [
"skywork"
] | ffcf4050e8c56bafd78ec560b0b159798548e4e7347e97dfaaa6be8bdde31d84 | [
{
"content": "Let $a, b, c, d$ be digits such that $d > c > b > a \\geq 0$. How many numbers of the form $1a1b1c1d1$ are\nmultiples of $33$?",
"role": "user"
}
] | Let $a, b, c, d$ be digits such that $d > c > b > a \geq 0$. How many numbers of the form $1a1b1c1d1$ are
multiples of $33$? | "[\"19\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1302, "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:15319"}] | {
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[
"66"
] | [
"skywork"
] | 1bb1b9e6382a6c1a338fd489351416ef30ea62d521425c142c0085e5780e658c | [
{
"content": "The arithmetic mean of two distinct positive integers $x$ and $y$ is a two-digit integer. The geometric mean of $x$ and $y$ is obtained by reversing the digits of the arithmetic mean. What is $|x - y|$?",
"role": "user"
}
] | The arithmetic mean of two distinct positive integers $x$ and $y$ is a two-digit integer. The geometric mean of $x$ and $y$ is obtained by reversing the digits of the arithmetic mean. What is $|x - y|$? | "[\"66\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1311, "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:15320"}] | {
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[
"132"
] | [
"skywork"
] | eda1c416d9270f358db043efbf1d3661bbd96ba12af65094b4073c0e843c940f | [
{
"content": "12 points are placed around the circumference of a circle. How many ways are there to draw 6 non-intersecting chords joining these points in pairs?",
"role": "user"
}
] | 12 points are placed around the circumference of a circle. How many ways are there to draw 6 non-intersecting chords joining these points in pairs? | "[\"132\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1339, "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:15321"}] | {
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[
"63"
] | [
"skywork"
] | 47c2b19991f32cbafe0e2db071393ab8e48cb592700c5f630b00b25a2d63f87d | [
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"content": "5. On the sides of a rectangle with length $8 \\mathrm{~cm}$ and width $6 \\mathrm{~cm}$, points are placed starting from one vertex, each $2 \\mathrm{~cm}$ apart. How many different lines do these points determine?\n\nNATIONAL MATHEMATICS COMPETITIONPrimošten, April 4-6, 2016.6th grade-elementary... | 5. On the sides of a rectangle with length $8 \mathrm{~cm}$ and width $6 \mathrm{~cm}$, points are placed starting from one vertex, each $2 \mathrm{~cm}$ apart. How many different lines do these points determine?
NATIONAL MATHEMATICS COMPETITIONPrimošten, April 4-6, 2016.6th grade-elementary school | "[\"63\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1320, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15322"}] | {
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[
"B"
] | [
"skywork"
] | 64359c325285cc61e6cb757c980e29f09aa0838bdccc6d9e34e274325513a94c | [
{
"content": "1. Let the set $S=\\left\\{A_{0}, A_{1}, A_{2}, A_{3}\\right\\}$, and define the operation “ $\\oplus$ ” on $S$ as: $A_{i} \\oplus A_{j}=A_{k}$, where $k$ is the remainder of $i+j$ divided by 4, $i, j=0,1,2,3$. Then the number of $x(x \\in S)$ that satisfy the relation $(x \\oplus x) \\oplus A_{2}... | 1. Let the set $S=\left\{A_{0}, A_{1}, A_{2}, A_{3}\right\}$, and define the operation “ $\oplus$ ” on $S$ as: $A_{i} \oplus A_{j}=A_{k}$, where $k$ is the remainder of $i+j$ divided by 4, $i, j=0,1,2,3$. Then the number of $x(x \in S)$ that satisfy the relation $(x \oplus x) \oplus A_{2}=A_{0}$ is
A. 1
B. 2
C. 3
D. 4 | "[\"B\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1318, "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:15323"}] | {
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[
"\\frac{4}{5}"
] | [
"skywork"
] | abfbf62eae2fedfee8b5fd959ede24ceb5272b23e320b2aae6595ab8bb04b087 | [
{
"content": "165 Two spheres with a radius of 1 are externally tangent to each other, and both are internally tangent to a cylindrical surface with a radius of 1. Another smaller sphere is externally tangent to both of these spheres and internally tangent to the cylindrical surface. A plane passing through the... | 165 Two spheres with a radius of 1 are externally tangent to each other, and both are internally tangent to a cylindrical surface with a radius of 1. Another smaller sphere is externally tangent to both of these spheres and internally tangent to the cylindrical surface. A plane passing through the center of the smaller... | "[\"\\\\frac{4}{5}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1313, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15324"}] | {
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[
"287"
] | [
"skywork"
] | dbbcd905ce4374882a142d2ed5d0187692191d5f5da37230d5455f50775e5b21 | [
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"content": "13. Two students, Lemuel and Christine, each wrote down an arithmetic sequence on a piece of paper. Lemuel wrote down the sequence $2,9,16,23, \\ldots$, while Christine wrote down the sequence $3,7,11,15, \\ldots$ After they have both written out 2010 terms of their respective sequences, how many ... | 13. Two students, Lemuel and Christine, each wrote down an arithmetic sequence on a piece of paper. Lemuel wrote down the sequence $2,9,16,23, \ldots$, while Christine wrote down the sequence $3,7,11,15, \ldots$ After they have both written out 2010 terms of their respective sequences, how many numbers have they writte... | "[\"287\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1325, "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:15325"}] | {
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[
"192\\mathrm{~}^{2}"
] | [
"skywork"
] | 0b21819b176e7b689e2c8c3d50283872e8bbcc41ae23c41c5d09951b2ed0741d | [
{
"content": "B1. Krogu s ploščino $100 \\pi \\mathrm{cm}^{2}$ včrtamo pravokotnik, katerega dolžini stranic se razlikujeta za $4 \\mathrm{~cm}$. Izračunaj ploščino pravokotnika.",
"role": "user"
}
] | B1. Krogu s ploščino $100 \pi \mathrm{cm}^{2}$ včrtamo pravokotnik, katerega dolžini stranic se razlikujeta za $4 \mathrm{~cm}$. Izračunaj ploščino pravokotnika. | "[\"192\\\\mathrm{~}^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1310, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15326"}] | {
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[
"\\frac{1}{2}\\left(16^{2014}-14^{2014}\\right)"
] | [
"skywork"
] | a2c386f238b951d1ce2f5ecb3e4d01bca4044b5992031bb916787373b0bf67f9 | [
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"content": "A deck of 8056 cards has 2014 ranks numbered 1-2014. Each rank has four suits-hearts, diamonds, clubs, and spades. Each card has a rank and a suit, and no two cards have the same rank and the same suit. How many subsets of the set of cards in this deck have cards from an odd number of distinct ran... | A deck of 8056 cards has 2014 ranks numbered 1-2014. Each rank has four suits-hearts, diamonds, clubs, and spades. Each card has a rank and a suit, and no two cards have the same rank and the same suit. How many subsets of the set of cards in this deck have cards from an odd number of distinct ranks? | "[\"\\\\frac{1}{2}\\\\left(16^{2014}-14^{2014}\\\\right)\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 1331, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:15327"}] | {
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[
"2,8,15"
] | [
"skywork"
] | d5930b53ca524ea192d140b3f75a54859cc414ea37faa141a028ef86b6df805d | [
{
"content": "7. Find all positive integers $n$ such that $n-[n\\{\\sqrt{n}\\}]=2$ holds.\n$(2002$, Bulgarian Spring Mathematical Competition)",
"role": "user"
}
] | 7. Find all positive integers $n$ such that $n-[n\{\sqrt{n}\}]=2$ holds.
$(2002$, Bulgarian Spring Mathematical Competition) | "[\"2,8,15\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1322, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:15328"}] | {
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[
"3705"
] | [
"skywork"
] | 3ba6615b6ee6e79857273b7f294bf64bc6f18076deef1e1b3be57e67143f744f | [
{
"content": "Two joggers each run at their own constant speed and in opposite directions from one another around an oval track. They meet every 36 seconds. The first jogger completes one lap of the track in a time that, when measured in seconds, is a number (not necessarily an integer) between 80 and 100. The ... | Two joggers each run at their own constant speed and in opposite directions from one another around an oval track. They meet every 36 seconds. The first jogger completes one lap of the track in a time that, when measured in seconds, is a number (not necessarily an integer) between 80 and 100. The second jogger complete... | "[\"3705\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1301, "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:15329"}] | {
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[
"100"
] | [
"skywork"
] | 31f1be3364cbbfea6a57ac34e018ca53f7bec1e29c3fc9a91e5d681df0579d74 | [
{
"content": "7.228. $5^{\\lg x}=50-x^{\\lg 5}$.",
"role": "user"
}
] | 7.228. $5^{\lg x}=50-x^{\lg 5}$. | "[\"100\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1340, "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:15330"}] | {
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} |
[
"431"
] | [
"skywork"
] | cfa7fe72d5e8d85d47cf972ef910dcff7f540c5d18225974b364fe5b7a501fa2 | [
{
"content": "Consider all 1000-element subsets of the set $\\{1, 2, 3, ... , 2015\\}$. From each such subset choose the least element. The arithmetic mean of all of these least elements is $\\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p + q$.",
"role": "user"
}
] | Consider all 1000-element subsets of the set $\{1, 2, 3, ... , 2015\}$. From each such subset choose the least element. The arithmetic mean of all of these least elements is $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p + q$. | "[\"431\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 1335, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:15331"}, {"dataset": "skywork", "extra_inf... | {
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[
"1"
] | [
"skywork"
] | 7576a7799ec4e0e86bb9d705ae929fc1e612c63436e2b3b094c7fd992efff123 | [
{
"content": "1. The function $y=f(x)$ is defined on the set $(0,+\\infty)$ and takes positive values on it. It is known that for any points $A$ and $B$ on the graph of the function, the areas of the triangle $A O B$ and the trapezoid $A B H_{B} H_{A}$ are equal to each other $\\left(H_{A}, H_{B}\\right.$ - the... | 1. The function $y=f(x)$ is defined on the set $(0,+\infty)$ and takes positive values on it. It is known that for any points $A$ and $B$ on the graph of the function, the areas of the triangle $A O B$ and the trapezoid $A B H_{B} H_{A}$ are equal to each other $\left(H_{A}, H_{B}\right.$ - the bases of the perpendicul... | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1308, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15333"}] | {
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[
"\\sqrt{5} + 1"
] | [
"skywork"
] | c7adb25b0b8dfdbef9d01dfcc0a8f22c206277fd5ef21d6411241afcd3ba3079 | [
{
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, with $c=2$ and $A \\neq B$.\n\n1. Find the value of $\\frac{a \\sin A - b \\sin B}{\\sin (A-B)}$.\n2. If the area of $\\triangle ABC$ is $1$ and $\\tan C = 2$, find the value of $a+b$.",
"ro... | In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, with $c=2$ and $A \neq B$.
1. Find the value of $\frac{a \sin A - b \sin B}{\sin (A-B)}$.
2. If the area of $\triangle ABC$ is $1$ and $\tan C = 2$, find the value of $a+b$. | "[\"\\\\sqrt{5} + 1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1309, "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:15334"}] | {
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[
"0"
] | [
"skywork"
] | fd166b2b6760cff5cc62721201e15764db337f7124437c51b94b9cbde0348de3 | [
{
"content": "The Devil and the Man play a game. Initially, the Man pays some cash $s$ to the Devil. Then he lists some $97$ triples $\\{i,j,k\\}$ consisting of positive integers not exceeding $100$. After that, the Devil draws some convex polygon $A_1A_2...A_{100}$ with area $100$ and pays to the Man, the sum ... | The Devil and the Man play a game. Initially, the Man pays some cash $s$ to the Devil. Then he lists some $97$ triples $\{i,j,k\}$ consisting of positive integers not exceeding $100$. After that, the Devil draws some convex polygon $A_1A_2...A_{100}$ with area $100$ and pays to the Man, the sum of areas of all triangle... | "[\" 0 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1324, "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:15335"}] | {
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[
"56"
] | [
"skywork"
] | d47cb82159f4c65c9d83388efe7ef77bc9309fc63c1216cdcdc5263d209f982b | [
{
"content": "Regular polygons with $4, 5, 6,$ and $7$ sides are inscribed in the same circle. No two of the polygons share a vertex, and no three of their sides intersect at a common point. Determine the number of points inside the circle where two of their sides intersect.",
"role": "user"
}
] | Regular polygons with $4, 5, 6,$ and $7$ sides are inscribed in the same circle. No two of the polygons share a vertex, and no three of their sides intersect at a common point. Determine the number of points inside the circle where two of their sides intersect. | "[\"56\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1326, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15336"}] | {
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[
"27"
] | [
"skywork"
] | 7871573e7917b71dce4bcd357f1e4ad9f1288dd90a234123d6aa737ec46252b8 | [
{
"content": "34. Given that one of the interior angles of a triangle is $63^{\\circ}$, and there is an exterior angle that is equal to one of the interior angles of the triangle, then the smallest interior angle of the triangle is $\\qquad$.",
"role": "user"
}
] | 34. Given that one of the interior angles of a triangle is $63^{\circ}$, and there is an exterior angle that is equal to one of the interior angles of the triangle, then the smallest interior angle of the triangle is $\qquad$. | "[\"27\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1329, "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:15337"}] | {
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[
"\\frac{1}{3}"
] | [
"skywork"
] | b9e3c735eeccace23c38b83b37771f45e86aed610b506c465f6a3061c8e9ff17 | [
{
"content": "It is known that $\\sin \\alpha+\\sin \\beta=2 \\sin (\\alpha+\\beta)$ and $\\alpha+\\beta \\neq 2 \\pi n (n \\in \\mathbb{Z})$. Find $\\operatorname{tg} \\frac{\\alpha}{2} \\operatorname{tg} \\frac{\\beta}{2}$.",
"role": "user"
}
] | It is known that $\sin \alpha+\sin \beta=2 \sin (\alpha+\beta)$ and $\alpha+\beta \neq 2 \pi n (n \in \mathbb{Z})$. Find $\operatorname{tg} \frac{\alpha}{2} \operatorname{tg} \frac{\beta}{2}$. | "[\"\\\\frac{1}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1332, "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:15338"}] | {
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[
"101"
] | [
"skywork"
] | ec76043f495f769c473eadeba4927e66dc6fb47a70f65a534734ef2a1002f816 | [
{
"content": "Let $d_1 = a^2 + 2^a + a \\cdot 2^{(a+1)/2}$ and $d_2 = a^2 + 2^a - a \\cdot 2^{(a+1)/2}$. If $1 \\le a \\le 251$, how many integral values of $a$ are there such that $d_1 \\cdot d_2$ is a multiple of $5$?",
"role": "user"
}
] | Let $d_1 = a^2 + 2^a + a \cdot 2^{(a+1)/2}$ and $d_2 = a^2 + 2^a - a \cdot 2^{(a+1)/2}$. If $1 \le a \le 251$, how many integral values of $a$ are there such that $d_1 \cdot d_2$ is a multiple of $5$? | "[\"101\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1346, "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:15339"}] | {
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} |
[
"162"
] | [
"skywork"
] | 66f3b3992f8449f9e5bdebf540e9066b05dc6f204f9c0ea233195377af9c382d | [
{
"content": "For a permutation $p = (a_1,a_2,\\ldots,a_9)$ of the digits $1,2,\\ldots,9$ , let $s(p)$ denote the sum of the three $3$ -digit numbers $a_1a_2a_3$ , $a_4a_5a_6$ , and $a_7a_8a_9$ . Let $m$ be the minimum value of $s(p)$ subject to the condition that the units digit of $s(p)$ is $0$ . Let $n$ deno... | For a permutation $p = (a_1,a_2,\ldots,a_9)$ of the digits $1,2,\ldots,9$ , let $s(p)$ denote the sum of the three $3$ -digit numbers $a_1a_2a_3$ , $a_4a_5a_6$ , and $a_7a_8a_9$ . Let $m$ be the minimum value of $s(p)$ subject to the condition that the units digit of $s(p)$ is $0$ . Let $n$ denote the number of permuta... | "[\"162\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 1328, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15340"}, {"dataset": "skywork", "extra_in... | {
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[
"(5,7)"
] | [
"skywork"
] | 0a7659f97e26bd5e48f13db2ef7c5a7ae5461e0b0553b97db2d1e5319f507083 | [
{
"content": "Circle $O$ is located on the coordinate plane with center at $(2,3)$. One endpoint of a diameter is at $(-1,-1)$. What are the coordinates of the other endpoint of this diameter? Express your answer as an ordered pair.",
"role": "user"
}
] | Circle $O$ is located on the coordinate plane with center at $(2,3)$. One endpoint of a diameter is at $(-1,-1)$. What are the coordinates of the other endpoint of this diameter? Express your answer as an ordered pair. | "[\"(5,7)\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1347, "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:15341"}] | {
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[
"2^{-\\frac{n(n-1)}{2}}"
] | [
"skywork"
] | 48e58aab693cbb877a94e3a121bb74d1093d8f0bfc3b4ce5465a690ed11b81a3 | [
{
"content": "3. 23 Given the numbers $1,2,2^{2}, \\cdots, 2^{n-1}$, for any permutation $\\sigma=\\left(x_{1}\\right.$, $\\left.x_{2}, \\cdots, x_{n}\\right)$ of them, define $S_{1}(\\sigma)=x_{1}, S_{2}(\\sigma)=x_{1}+x_{2}, S_{3}(\\sigma)=x_{1}+x_{2}+$ $x_{3}, \\cdots, S_{n}(\\sigma)=x_{1}+x_{2}+\\cdots+x_{n... | 3. 23 Given the numbers $1,2,2^{2}, \cdots, 2^{n-1}$, for any permutation $\sigma=\left(x_{1}\right.$, $\left.x_{2}, \cdots, x_{n}\right)$ of them, define $S_{1}(\sigma)=x_{1}, S_{2}(\sigma)=x_{1}+x_{2}, S_{3}(\sigma)=x_{1}+x_{2}+$ $x_{3}, \cdots, S_{n}(\sigma)=x_{1}+x_{2}+\cdots+x_{n}$, and let $Q(\sigma)=S_{1}(\sigma... | "[\"2^{-\\\\frac{n(n-1)}{2}}\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 1330, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15342"}] | {
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} |
[
"\\frac{4}{\\sqrt{17}}"
] | [
"skywork"
] | 0d897cc9533336f7d81890d86bfb25f5a6a42c0f777b637ab52a59c52680e636 | [
{
"content": "[ Median to the hypotenuse ] [ Area of a triangle (using height and base).]\n\nOutside the right triangle $A B C$ on its legs $A C$ and $B C$, squares $A C D E$ and $B C F G$ are constructed.\n\nThe extension of the median $C M$ of triangle $A B C$ intersects the line $D F$ at point $N$. Find the ... | [ Median to the hypotenuse ] [ Area of a triangle (using height and base).]
Outside the right triangle $A B C$ on its legs $A C$ and $B C$, squares $A C D E$ and $B C F G$ are constructed.
The extension of the median $C M$ of triangle $A B C$ intersects the line $D F$ at point $N$. Find the segment $C N$, if $A C=$ $... | "[\"\\\\frac{4}{\\\\sqrt{17}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1333, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15343"}] | {
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} |
[
"9"
] | [
"skywork"
] | 765c56932d3b8bce5d0b6c0be4b149dc6bdfaa5c4f238a3f69eac6a74ac20fc1 | [
{
"content": "3. Determinare il numero di coppie $(m, n)$ di numeri interi di modulo minore di 10000 che risolvono l'equazione $n^{2}+2024 n+2024 m=2024$.\n(A) 4\n(B) 9\n(C) 10\n(D) 18\n(E) 19",
"role": "user"
}
] | 3. Determinare il numero di coppie $(m, n)$ di numeri interi di modulo minore di 10000 che risolvono l'equazione $n^{2}+2024 n+2024 m=2024$.
(A) 4
(B) 9
(C) 10
(D) 18
(E) 19 | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1338, "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:15344"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{(n+1)^{2}}{4n}"
] | [
"skywork"
] | e80b16654d4dd18ce8983dc0db0ee9db66ce8cf0401e874640226a0b89a2d2b4 | [
{
"content": "Three. (50 points) Given $n$ as a positive integer no less than 2. For all non-negative arrays $a_{i}(i=1,2, \\cdots, n)$, find the maximum value of $\\frac{\\left(\\sum_{i=1}^{n} i a_{i}\\right)\\left(\\sum_{i=1}^{n} \\frac{a_{i}}{i}\\right)}{\\left(\\sum_{i=1}^{n} a_{i}\\right)^{2}}$.",
"rol... | Three. (50 points) Given $n$ as a positive integer no less than 2. For all non-negative arrays $a_{i}(i=1,2, \cdots, n)$, find the maximum value of $\frac{\left(\sum_{i=1}^{n} i a_{i}\right)\left(\sum_{i=1}^{n} \frac{a_{i}}{i}\right)}{\left(\sum_{i=1}^{n} a_{i}\right)^{2}}$. | "[\"\\\\frac{(n+1)^{2}}{4n}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1334, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15345"}] | {
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} |
[
"F_{n+2} - 2"
] | [
"skywork"
] | 7915d46b5279b983d0789d8b397aaa67ace020cf0160e9ef553a235469c05ed5 | [
{
"content": "Let $n$ be a positive integer. We call a $n$-tuple $(a_1, . . . , a_n)$ of positive integers [i]nice [/i] if\n$\\bullet$ $gcd (a_1, . . . , a_n) = 1$, and\n$\\bullet$ $a_i|a_{i-1} + a_{i+1}$, for all $i = 1, . . . , n$ (we define $a_0 = a_n$ and $a_{n+1} = a1$ here).\nFind the maximal possible val... | Let $n$ be a positive integer. We call a $n$-tuple $(a_1, . . . , a_n)$ of positive integers [i]nice [/i] if
$\bullet$ $gcd (a_1, . . . , a_n) = 1$, and
$\bullet$ $a_i|a_{i-1} + a_{i+1}$, for all $i = 1, . . . , n$ (we define $a_0 = a_n$ and $a_{n+1} = a1$ here).
Find the maximal possible value of the sum $a_1 +...+ a_... | "[\"F_{n+2} - 2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1337, "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:15346"}] | {
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"reference_components": 1,
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} |
[
"4"
] | [
"skywork"
] | 6bc73c22e8aca4349b14932a9ee2d995b98b991de24a056d19b14be7572484f7 | [
{
"content": "82. There is a water tap and two containers: a three-liter and a five-liter. How can you get 4 liters of water in the larger one?",
"role": "user"
}
] | 82. There is a water tap and two containers: a three-liter and a five-liter. How can you get 4 liters of water in the larger one? | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1348, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:15347"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"133"
] | [
"skywork"
] | f30779ea02bae52007264e95827198ee499efb87d67b4e7667d219133e546d25 | [
{
"content": "13. (3 points) There is a rectangle, the lengths of whose sides are natural numbers less than 10. If the width is used as the numerator and the length as the denominator, then the value of the resulting fraction is greater than $\\frac{3}{10}$ and less than $\\frac{1}{2}$. The sum of the areas of ... | 13. (3 points) There is a rectangle, the lengths of whose sides are natural numbers less than 10. If the width is used as the numerator and the length as the denominator, then the value of the resulting fraction is greater than $\frac{3}{10}$ and less than $\frac{1}{2}$. The sum of the areas of all such rectangles is .... | "[\"133\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1336, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "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:15348"}] | {
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} |
[
"1710"
] | [
"skywork"
] | b45fee1b5172d49ee4fee9a5f6b9ac9229b1fda3ce8f7460fd3591cdc3b48c67 | [
{
"content": "4. Dima drew a parallelogram $A B C D$ and points $M$ and $N$ on sides $B C$ and $C D$ respectively such that $B M: M C=D N: N C=2: 3$. After that, he erased everything except points $A, M$ and $N$ using a cloth. Vova restored the drawing using a ruler and a compass. How did he do it?",
"role"... | 4. Dima drew a parallelogram $A B C D$ and points $M$ and $N$ on sides $B C$ and $C D$ respectively such that $B M: M C=D N: N C=2: 3$. After that, he erased everything except points $A, M$ and $N$ using a cloth. Vova restored the drawing using a ruler and a compass. How did he do it? | "[\"1710\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1316, "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:15349"}] | {
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} |
[
"600"
] | [
"skywork"
] | df9739dc07aea7d2db5025fee87109b5e5ea0cad2ea8705e85eba440cec452c7 | [
{
"content": "Find the number of square units in the area of the shaded region. Consider a rectangular plot with vertices at points (0,0), (40,0), (40,20), and (0,20). Within this rectangle, a shaded polygon is formed with vertices at (0,0), (20,0), (40,10), (40,20), and (10,20). Determine the area of this shad... | Find the number of square units in the area of the shaded region. Consider a rectangular plot with vertices at points (0,0), (40,0), (40,20), and (0,20). Within this rectangle, a shaded polygon is formed with vertices at (0,0), (20,0), (40,10), (40,20), and (10,20). Determine the area of this shaded region. | "[\"600\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1350, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15350"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"505"
] | [
"skywork"
] | 11ff11043684e685febefc01c514f7e2c3d913bac37f7b4ee79aa7597e7ffa42 | [
{
"content": "Let $A$ be a subset of $\\{1,2,\\ldots,2020\\}$ such that the difference of any two distinct elements in $A$ is not prime. Determine the maximum number of elements in set $A$.",
"role": "user"
}
] | Let $A$ be a subset of $\{1,2,\ldots,2020\}$ such that the difference of any two distinct elements in $A$ is not prime. Determine the maximum number of elements in set $A$. | "[\"505\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1352, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15351"}, {"dataset": "skywork", "extra_in... | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\sqrt{30}}{30 + 12\\sqrt{6}}"
] | [
"skywork"
] | 6bd3f5fd59b28a45dca398d297158a07f4a5218122e5d59693b78d3a22b33776 | [
{
"content": "Find the largest real $ T$ such that for each non-negative real numbers $ a,b,c,d,e$ such that $ a\\plus{}b\\equal{}c\\plus{}d\\plus{}e$ : \\[ \\sqrt{a^{2}\\plus{}b^{2}\\plus{}c^{2}\\plus{}d^{2}\\plus{}e^{2}}\\geq T(\\sqrt a\\plus{}\\sqrt b\\plus{}\\sqrt c\\plus{}\\sqrt d\\plus{}\\sqrt e)^{2}... | Find the largest real $ T$ such that for each non-negative real numbers $ a,b,c,d,e$ such that $ a\plus{}b\equal{}c\plus{}d\plus{}e$ : \[ \sqrt{a^{2}\plus{}b^{2}\plus{}c^{2}\plus{}d^{2}\plus{}e^{2}}\geq T(\sqrt a\plus{}\sqrt b\plus{}\sqrt c\plus{}\sqrt d\plus{}\sqrt e)^{2}\] | "[\"\\\\frac{\\\\sqrt{30}}{30 + 12\\\\sqrt{6}}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1343, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:15352"}, {"dataset": "skywork", "extra_in... | {
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"plain_numeric_reference": false,
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} |
[
"\\sqrt{173}"
] | [
"skywork"
] | b04992f2e557dc3b9046ddb9891677c9cfb90a23d7ae3cdb3025e2aa29f43aea | [
{
"content": "Let \\(x,\\) \\(y,\\) \\(z\\) be real numbers such that \\(9x^2 + 4y^2 + 25z^2 = 1.\\) Find the maximum value of\n\\[8x + 3y + 10z.\\]",
"role": "user"
}
] | Let \(x,\) \(y,\) \(z\) be real numbers such that \(9x^2 + 4y^2 + 25z^2 = 1.\) Find the maximum value of
\[8x + 3y + 10z.\] | "[\"\\\\sqrt{173}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1365, "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:15353"}] | {
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} |
[
"B"
] | [
"skywork"
] | db0304c50beeb05390019b381f0fe4862b105493af06e2d6dc442a3bb2155827 | [
{
"content": "1. Set $A=\\{a \\mid a=12 m+8 n+4 l, m, n, l \\in \\mathbf{Z}\\}, B=\\{b \\mid b=20 p+$ $16 q+12 r, p, q, r \\in \\mathbf{Z}\\}, A, B$ the relationship between is ( ).\nA. $A=B$\nB. $A \\nsubseteq B, B \\nsubseteq A$\nC. $A \\supset B$\nD. $A \\subset B$",
"role": "user"
}
] | 1. Set $A=\{a \mid a=12 m+8 n+4 l, m, n, l \in \mathbf{Z}\}, B=\{b \mid b=20 p+$ $16 q+12 r, p, q, r \in \mathbf{Z}\}, A, B$ the relationship between is ( ).
A. $A=B$
B. $A \nsubseteq B, B \nsubseteq A$
C. $A \supset B$
D. $A \subset B$ | "[\"B\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1341, "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:15354"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"53.85\\%"
] | [
"skywork"
] | b315d6a55c72a3e989a76acbf7b286e7a3961aad9a26cece27130a4854550c18 | [
{
"content": "Jennifer plans a profit of 20% on the selling price of an item, and her expenses are 10% of the selling price. There is also a sales tax of 5% on the selling price of the item. The item sells for $10.00. Calculate the rate of markup on cost of this item.",
"role": "user"
}
] | Jennifer plans a profit of 20% on the selling price of an item, and her expenses are 10% of the selling price. There is also a sales tax of 5% on the selling price of the item. The item sells for $10.00. Calculate the rate of markup on cost of this item. | "[\"53.85\\\\%\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1353, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:15355"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"a_i = 1"
] | [
"skywork"
] | 3a9d94b6715929afd822b303c9a6bb0724ee1c0777513cffa9083e9c2dd95671 | [
{
"content": "Let $n>k>1$ be positive integers. Determine all positive real numbers $a_1, a_2, \\ldots, a_n$ which satisfy\n$$\n\\sum_{i=1}^n \\sqrt{\\frac{k a_i^k}{(k-1) a_i^k+1}}=\\sum_{i=1}^n a_i=n .\n$$",
"role": "user"
}
] | Let $n>k>1$ be positive integers. Determine all positive real numbers $a_1, a_2, \ldots, a_n$ which satisfy
$$
\sum_{i=1}^n \sqrt{\frac{k a_i^k}{(k-1) a_i^k+1}}=\sum_{i=1}^n a_i=n .
$$ | "[\" a_i = 1 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1351, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15357"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"43"
] | [
"skywork"
] | f8efc1a154e7ff8fe181d73a8be074ab9ac55150702f8f61a16ba94d0dab9122 | [
{
"content": "The lattice shown is continued for $9$ rows. What will be the third number in the $9$th row? \\begin{tabular}{rccccc}\nRow 1: & 1 & 2 & 3 & 4 & 5 \\\\\nRow 2: & 6 & 7 & 8 & 9 & 10 \\\\\nRow 3: & 11 & 12 & 13 & 14 & 15 \\\\\nRow 4: & 16 & 17 & 18 & 19 & 20\n\\end{tabular}",
"role": "user"
}
] | The lattice shown is continued for $9$ rows. What will be the third number in the $9$th row? \begin{tabular}{rccccc}
Row 1: & 1 & 2 & 3 & 4 & 5 \\
Row 2: & 6 & 7 & 8 & 9 & 10 \\
Row 3: & 11 & 12 & 13 & 14 & 15 \\
Row 4: & 16 & 17 & 18 & 19 & 20
\end{tabular} | "[\"43\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1358, "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:15358"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"n \\neq 3"
] | [
"skywork"
] | 50fc3bb5a95078c28ff49ba0293422fb5ea8831ce5396865681b6952dae10a14 | [
{
"content": "Let $n$ be a positive integer. The numbers $\\{1, 2, ..., n^2\\}$ are placed in an $n \\times n$ grid, each exactly once. The grid is said to be [i]Muirhead-able[/i] if the sum of the entries in each column is the same, but for every $1 \\le i,k \\le n-1$, the sum of the first $k$ entries in col... | Let $n$ be a positive integer. The numbers $\{1, 2, ..., n^2\}$ are placed in an $n \times n$ grid, each exactly once. The grid is said to be [i]Muirhead-able[/i] if the sum of the entries in each column is the same, but for every $1 \le i,k \le n-1$, the sum of the first $k$ entries in column $i$ is at least the sum... | "[\" n \\\\neq 3 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1344, "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:15359"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"1"
] | [
"skywork"
] | 5e9125bfa6b7af6e8ffc818f7eaf26e2c541581a5f380979faaf6537694a927c | [
{
"content": "58. Compute the integral\n\n$$\n\\int_{-1}^{1} \\frac{d x}{1+x^{3}+\\sqrt{1+x^{6}}}\n$$",
"role": "user"
}
] | 58. Compute the integral
$$
\int_{-1}^{1} \frac{d x}{1+x^{3}+\sqrt{1+x^{6}}}
$$ | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1372, "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:15360"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | f8c3feb34f93e6303a62156e6f606ba87f0cb450ca7f705a71961079dc412e91 | [
{
"content": "11. Let $a, b, c$ be distinct positive integers. Then the minimum value of $\\frac{a b c}{a+b+c}$ is . $\\qquad$",
"role": "user"
}
] | 11. Let $a, b, c$ be distinct positive integers. Then the minimum value of $\frac{a b c}{a+b+c}$ is . $\qquad$ | "[\"1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1355, "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:15361"}] | {
"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
} |
[
"10"
] | [
"skywork"
] | b3f6aa175ff649e9668a9b66b44fb31039378c68e4f4f530639eb75d026d72f4 | [
{
"content": "A batch of disaster relief supplies is loaded into 26 trucks. The trucks travel at a constant speed of \\( v \\) kilometers per hour directly to the disaster area. If the distance between the two locations is 400 kilometers and the distance between every two trucks must be at least \\( \\left(\\fr... | A batch of disaster relief supplies is loaded into 26 trucks. The trucks travel at a constant speed of \( v \) kilometers per hour directly to the disaster area. If the distance between the two locations is 400 kilometers and the distance between every two trucks must be at least \( \left(\frac{v}{20}\right)^{2} \) kil... | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1327, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15362"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"38"
] | [
"skywork"
] | 37c3a8eb3adef8034ec6fc6c6e949dbdc85632c0a2b7a0901417cf13ffaeb2fe | [
{
"content": "Find the sum of all positive integers $n$ for which $n^2-19n+99$ is a perfect square.",
"role": "user"
}
] | Find the sum of all positive integers $n$ for which $n^2-19n+99$ is a perfect square. | "[\"38\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1371, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15363"}] | {
"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
} |
[
"2004"
] | [
"skywork"
] | 0e1c91a1f65c45ea3f9cee8e794faf31d0bb9bb744107a2c7af92288f2da9a50 | [
{
"content": "A total of $2010$ coins are distributed in $5$ boxes. At the beginning the quantities of coins in the boxes are consecutive natural numbers. Martha should choose and take one of the boxes, but before that she can do the following transformation finitely many times: from a box with at least 4 coins... | A total of $2010$ coins are distributed in $5$ boxes. At the beginning the quantities of coins in the boxes are consecutive natural numbers. Martha should choose and take one of the boxes, but before that she can do the following transformation finitely many times: from a box with at least 4 coins she can transfer one ... | "[\"2004\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1357, "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:15364"}] | {
"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
} |
[
"27.5"
] | [
"skywork"
] | 0b0bd74a887f58ab2c82cef4bd3af50ca46df70989f7ed7ba336fd05001ef084 | [
{
"content": "Given 5 distinct real numbers, any two of which are summed to yield 10 sums. Among these sums, the smallest three are 32, 36, and 37, and the largest two are 48 and 51. What is the largest of these 5 numbers?",
"role": "user"
}
] | Given 5 distinct real numbers, any two of which are summed to yield 10 sums. Among these sums, the smallest three are 32, 36, and 37, and the largest two are 48 and 51. What is the largest of these 5 numbers? | "[\"27.5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1359, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15365"}] | {
"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{31}{3}"
] | [
"skywork"
] | 4740fae51b2938d03bbdaa1c0f0e4b4954e2a535bb3eec2203380fd2143e2252 | [
{
"content": "1. Given the sequence $\\left\\{a_{n}\\right\\}$ satisfies $a_{1}=32, a_{n+1}-a_{n}=2 n\\left(n \\in \\mathbf{Z}_{+}\\right)$. Then the minimum value of $\\frac{a_{n}}{n}$ is $\\qquad$.",
"role": "user"
}
] | 1. Given the sequence $\left\{a_{n}\right\}$ satisfies $a_{1}=32, a_{n+1}-a_{n}=2 n\left(n \in \mathbf{Z}_{+}\right)$. Then the minimum value of $\frac{a_{n}}{n}$ is $\qquad$. | "[\"\\\\frac{31}{3}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1356, "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:15366"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3\\sqrt{3}}{8}"
] | [
"skywork"
] | 30c3adc680de4d93259eac96b3877ff9d2589b139321c9b33b8120ea09d5466b | [
{
"content": "1. In $\\triangle A B C$, $a^{2}+b^{2}+c^{2}=2 \\sqrt{3} a b \\sin C$, then $\\cos \\frac{A}{2} \\cos \\frac{B}{2} \\cos \\frac{C}{2}=$ $\\qquad$",
"role": "user"
}
] | 1. In $\triangle A B C$, $a^{2}+b^{2}+c^{2}=2 \sqrt{3} a b \sin C$, then $\cos \frac{A}{2} \cos \frac{B}{2} \cos \frac{C}{2}=$ $\qquad$ | "[\"\\\\frac{3\\\\sqrt{3}}{8}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1360, "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:15367"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"21"
] | [
"skywork"
] | 833b76e4fa48337cb7ee5ef6454bdf9b417558ab3ca140f8dfedb0699b51693e | [
{
"content": "\\section*{Problem 3 - 021133}\n\nIn how many different ways can the number 99 be expressed as the sum of three distinct prime numbers?\n\n(Two cases are considered the same if the same addends appear, merely in a different order.)",
"role": "user"
}
] | \section*{Problem 3 - 021133}
In how many different ways can the number 99 be expressed as the sum of three distinct prime numbers?
(Two cases are considered the same if the same addends appear, merely in a different order.) | "[\"21\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1380, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:15368"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2},-\\frac{3}{4},\\frac{3}{2}"
] | [
"skywork"
] | 8251b661ee9b2d1525a791dc32c3bc231e9400f782d88ebed8a1c8f3f5187e52 | [
{
"content": "1. In the set of real numbers, solve the equation\n\n$$\n\\left(x^{2}-x+1\\right)\\left(4 y^{2}+6 y+4\\right)\\left(4 z^{2}-12 z+25\\right)=21\n$$",
"role": "user"
}
] | 1. In the set of real numbers, solve the equation
$$
\left(x^{2}-x+1\right)\left(4 y^{2}+6 y+4\right)\left(4 z^{2}-12 z+25\right)=21
$$ | "[\"\\\\frac{1}{2},-\\\\frac{3}{4},\\\\frac{3}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1368, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15369"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{5}{2}"
] | [
"skywork"
] | 116584af9d731021fd3832f0e44133a331c5cf293cc70fdf9cf00702a8458362 | [
{
"content": "Given $f(x)=\\sin \\left( 2x+ \\frac{π}{6} \\right)+ \\frac{3}{2}$, $x\\in R$.\n\n(1) Find the minimum positive period of the function $f(x)$;\n\n(2) Find the interval(s) where the function $f(x)$ is monotonically decreasing;\n\n(3) Find the maximum value of the function and the corresponding $x$ ... | Given $f(x)=\sin \left( 2x+ \frac{π}{6} \right)+ \frac{3}{2}$, $x\in R$.
(1) Find the minimum positive period of the function $f(x)$;
(2) Find the interval(s) where the function $f(x)$ is monotonically decreasing;
(3) Find the maximum value of the function and the corresponding $x$ value(s). | "[\"\\\\frac{5}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1349, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15370"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | bf4889ad5f89af49a44a60e90c76a48c1d22bed1d78721b4db182c5412334214 | [
{
"content": "A rectangular box measures $a \\times b \\times c$, where $a$, $b$, and $c$ are integers and $1\\leq a \\leq b \\leq c$. The volume and the surface area of the box are numerically equal, find the number of ordered triples $(a,b,c)$.",
"role": "user"
}
] | A rectangular box measures $a \times b \times c$, where $a$, $b$, and $c$ are integers and $1\leq a \leq b \leq c$. The volume and the surface area of the box are numerically equal, find the number of ordered triples $(a,b,c)$. | "[\"10\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1369, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15371"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9981"
] | [
"skywork"
] | dff08396ff736dbcf54a927ac8db4d7c0ba6d05a1193c375b985ed9bf3eb2828 | [
{
"content": "What is the largest $4$ digit integer congruent to $15 \\pmod{22}?$",
"role": "user"
}
] | What is the largest $4$ digit integer congruent to $15 \pmod{22}?$ | "[\"9981\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1392, "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:15372"}] | {
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} |
[
"\\frac{\\ln 5}{2 \\ln 2 - 3 \\ln 5}"
] | [
"skywork"
] | 1ccbdd269aae77c91ffad6a87bc2382ac03c43baa3d8874208aa16631fb4b069 | [
{
"content": "Given that \\(x\\) satisfies \\(\\log _{5x} (2x) = \\log _{625x} (8x)\\), find the value of \\(\\log _{2} x\\).",
"role": "user"
}
] | Given that \(x\) satisfies \(\log _{5x} (2x) = \log _{625x} (8x)\), find the value of \(\log _{2} x\). | "[\"\\\\frac{\\\\ln 5}{2 \\\\ln 2 - 3 \\\\ln 5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1370, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15373"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4\\sqrt{3}\\sin7"
] | [
"skywork"
] | a3efaa3fee930abe6473a83203eaad49df7f134fce1bb6defe6a05116b09eaad | [
{
"content": "[ Law of Sines [ Inscribed angle is half of the central angle ]\n\n## Diameter $A B$ of the circle is extended beyond point $B$ and a point $C$ is marked on the extension. From point $C$,\n\n a secant is drawn at an angle of $7^{\\circ}$ to $A C$, intersecting the circle at points $D$ and $E$, cou... | [ Law of Sines [ Inscribed angle is half of the central angle ]
## Diameter $A B$ of the circle is extended beyond point $B$ and a point $C$ is marked on the extension. From point $C$,
a secant is drawn at an angle of $7^{\circ}$ to $A C$, intersecting the circle at points $D$ and $E$, counting from point $C$. It is... | "[\"4\\\\sqrt{3}\\\\sin7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1364, "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:15374"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"13"
] | [
"skywork"
] | 7a3e042972497b0b0059915eaf63996526a85981a25680288c318105b5fd7921 | [
{
"content": "My friend Ana likes numbers that are divisible by 8. How many different pairs of last two digits are possible in numbers that Ana likes?",
"role": "user"
}
] | My friend Ana likes numbers that are divisible by 8. How many different pairs of last two digits are possible in numbers that Ana likes? | "[\"13\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1379, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15375"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"B"
] | [
"skywork"
] | 4a93779b8c02967cfb23a061c58bab5a9c695c7b078aa3c9f551f38001c6eb31 | [
{
"content": "Consider the statements: I: $ (\\sqrt { \\minus{} 4})(\\sqrt { \\minus{} 16}) \\equal{} \\sqrt {( \\minus{} 4)( \\minus{} 16)}$, II: $ \\sqrt {( \\minus{} 4)( \\minus{} 16)} \\equal{} \\sqrt {64}$, and $ \\sqrt {64} \\equal{} 8$. Of these the following are [u]incorrect[/u].\r\n\r\n$ \\textbf{(A)}... | Consider the statements: I: $ (\sqrt { \minus{} 4})(\sqrt { \minus{} 16}) \equal{} \sqrt {( \minus{} 4)( \minus{} 16)}$, II: $ \sqrt {( \minus{} 4)( \minus{} 16)} \equal{} \sqrt {64}$, and $ \sqrt {64} \equal{} 8$. Of these the following are [u]incorrect[/u].
$ \textbf{(A)}\ \text{none} \qquad \textbf{(B)}\ \text{I... | "[\"B\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1363, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15376"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3\\sqrt{3}}{13}"
] | [
"skywork"
] | 0bdf05218f91a356ceecd043fd47e820f46a1d96740efabbea06412380f37b09 | [
{
"content": "[ Linear dependence of vectors $]$ [ Angles between lines and planes $]$\n\nThe lateral edge of a regular triangular pyramid forms an angle of $60^{\\circ}$ with the base plane. Find the angle between the apothem and the plane of the adjacent lateral face.",
"role": "user"
}
] | [ Linear dependence of vectors $]$ [ Angles between lines and planes $]$
The lateral edge of a regular triangular pyramid forms an angle of $60^{\circ}$ with the base plane. Find the angle between the apothem and the plane of the adjacent lateral face. | "[\"\\\\frac{3\\\\sqrt{3}}{13}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1375, "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:15377"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\textbf{(A)}"
] | [
"skywork"
] | 61de7058474a94cc1c1a49e7cdd273b3a064dc8ae10c242fe8aefbb9e62abb1b | [
{
"content": "Let S be the set of values assumed by the fraction $\\frac{2x+3}{x+2}$.\nWhen $x$ is any member of the interval $x \\ge 0$. If there exists a number $M$ such that no number of the set $S$ is greater than $M$, \nthen $M$ is an upper bound of $S$. If there exists a number $m$ such that such that no ... | Let S be the set of values assumed by the fraction $\frac{2x+3}{x+2}$.
When $x$ is any member of the interval $x \ge 0$. If there exists a number $M$ such that no number of the set $S$ is greater than $M$,
then $M$ is an upper bound of $S$. If there exists a number $m$ such that such that no number of the set $S$ is l... | "[\"\\\\textbf{(A)}\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 1373, "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:15378"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4n"
] | [
"skywork"
] | da9a26589147578f2604e3a7740f13c19402ea53c6bd6bd5326c8ee58e5735c3 | [
{
"content": "8.60 What is the maximum number of \"rooks\" that can be placed on a $3 n \\times 3 n$ chessboard such that each rook is attacked by at most one other rook?",
"role": "user"
}
] | 8.60 What is the maximum number of "rooks" that can be placed on a $3 n \times 3 n$ chessboard such that each rook is attacked by at most one other rook? | "[\"4n\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1376, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15379"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"17"
] | [
"skywork"
] | c59f9a734b54b976c102f2d6a8b85185dfdc0ecfa736a9cc7a80c0ba619db78c | [
{
"content": "9. Four cousins Alan, Bob, Carl and Dan are $3,8,12$ and 14 years old, although not necessarily in that order. Alan is younger than Carl. The sum of the ages of Alan and Dan is divisible by 5. The sum of the ages of Carl and Dan is divisible by 5. What is the sum of the ages of Alan and Bob?\nA 26... | 9. Four cousins Alan, Bob, Carl and Dan are $3,8,12$ and 14 years old, although not necessarily in that order. Alan is younger than Carl. The sum of the ages of Alan and Dan is divisible by 5. The sum of the ages of Carl and Dan is divisible by 5. What is the sum of the ages of Alan and Bob?
A 26
B 22
C 17
D 15
E 11 | "[\"17\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1367, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15380"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"18"
] | [
"skywork"
] | ff3eb360e3a1975d3c1554b0d4f3974ef1b99c249215459450d7c8ac3d72a976 | [
{
"content": "and 3, 6, 12. In each of them, each number is obtained from the previous one according to the same rule.\n\na) Find this rule.\n\nb) Find all natural numbers that transform into themselves (according to this rule).\n\nc) Prove that the number $2^{1991}$ will become a single-digit number after seve... | and 3, 6, 12. In each of them, each number is obtained from the previous one according to the same rule.
a) Find this rule.
b) Find all natural numbers that transform into themselves (according to this rule).
c) Prove that the number $2^{1991}$ will become a single-digit number after several transformations. | "[\"18\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1342, "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:15381"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"C"
] | [
"skywork"
] | 460fa2a636d666ee6c4a0682682035ebee5ce3078e2340f0b1facf9e31765494 | [
{
"content": "1. Let $p, q$ be natural numbers, condition A: $p^{3}-q^{3}$ is even; condition B: $p+q$ is even, then\nA. A is a sufficient but not necessary condition for B\nB. A is a necessary but not sufficient condition for B\nC. A is a necessary and sufficient condition for B\nD. A is neither a sufficient c... | 1. Let $p, q$ be natural numbers, condition A: $p^{3}-q^{3}$ is even; condition B: $p+q$ is even, then
A. A is a sufficient but not necessary condition for B
B. A is a necessary but not sufficient condition for B
C. A is a necessary and sufficient condition for B
D. A is neither a sufficient condition nor a necessary c... | "[\"C\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1374, "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:15382"}] | {
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"label_correctness_independently_verified": false,
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"reference_components": 1,
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} |
[
"512820"
] | [
"skywork"
] | fffbc0317c5453a4585ae6aea497ac70e64f69f57ad52de0f27e0fc9363687ca | [
{
"content": "Find the smallest natural number that begins with the digit five, which is reduced by four times if this five is removed from the beginning of its decimal representation and appended to its end.",
"role": "user"
}
] | Find the smallest natural number that begins with the digit five, which is reduced by four times if this five is removed from the beginning of its decimal representation and appended to its end. | "[\"512820\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1394, "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:15383"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"76"
] | [
"skywork"
] | cf4a23b0fe9b1d70e633b44057abbc9f9d67d412b4abee863a76699c69de1fb2 | [
{
"content": "A box contains 28 red balls, 20 green balls, 19 yellow balls, 13 blue balls, 11 white balls, and 9 black balls. Calculate the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 15 balls of a single color will be drawn.",
"role": "user"
}
] | A box contains 28 red balls, 20 green balls, 19 yellow balls, 13 blue balls, 11 white balls, and 9 black balls. Calculate the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 15 balls of a single color will be drawn. | "[\"76\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1384, "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:15384"}] | {
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"reference_components": 1,
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} |
[
"0.49"
] | [
"skywork"
] | dc5bc4a2644e7249b5bc3a7313cebc922e7322161a7a7d7f9ec4a8864f643725 | [
{
"content": "Example 1 Remove the big and small jokers from a deck of cards, and randomly draw five cards from the remaining 52 cards. The probability that at least two of the cards have the same number (or letter $K, Q, J, A$) is $\\qquad$ (require calculating the numerical value of this probability, accurate... | Example 1 Remove the big and small jokers from a deck of cards, and randomly draw five cards from the remaining 52 cards. The probability that at least two of the cards have the same number (or letter $K, Q, J, A$) is $\qquad$ (require calculating the numerical value of this probability, accurate to 0.01).
(2014, Natio... | "[\"0.49\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1381, "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:15385"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"14"
] | [
"skywork"
] | d387387aec8b1eb62736418852ab345764119d7f7a402410da014720468231a7 | [
{
"content": "1. How many natural numbers from 1 to 2017 have exactly three distinct natural divisors?",
"role": "user"
}
] | 1. How many natural numbers from 1 to 2017 have exactly three distinct natural divisors? | "[\"14\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1404, "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:15386"}, {"dataset": "skywork", "extra_inf... | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"565"
] | [
"skywork"
] | 0c1a43033e03328b689d561ef22db7aaaa7f4b3ae73ac4ae44cb98c440ecffa4 | [
{
"content": "1. Let \\( x_i \\in \\{0,1\\} \\) (for \\( i=1,2,\\cdots,n \\)). If the value of the function \\( f=f(x_1, x_2, \\cdots, x_n) \\) only takes 0 or 1, then \\( f \\) is called an n-ary Boolean function. We denote\n \\[\n D_{n}(f)=\\left\\{(x_1, x_2, \\cdots, x_n) \\mid f(x_1, x_2, \\cdots, x_n)=... | 1. Let \( x_i \in \{0,1\} \) (for \( i=1,2,\cdots,n \)). If the value of the function \( f=f(x_1, x_2, \cdots, x_n) \) only takes 0 or 1, then \( f \) is called an n-ary Boolean function. We denote
\[
D_{n}(f)=\left\{(x_1, x_2, \cdots, x_n) \mid f(x_1, x_2, \cdots, x_n)=0\right\}.
\]
(1) Find the number of ... | "[\"565\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1366, "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:15387"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"f(n) = (n + 2\\ell)^2 - 2\\ell^2"
] | [
"skywork"
] | 52cc76b98aadf30c2a24262a0239e9bb876978ced4d206ada25fa18a6df1cfbb | [
{
"content": "Find all functions $f:\\mathbb{N}\\to \\mathbb{N}$ so that for every natural numbers $m,n$ :$f(n)+2mn+f(m)$ is a perfect square.",
"role": "user"
}
] | Find all functions $f:\mathbb{N}\to \mathbb{N}$ so that for every natural numbers $m,n$ :$f(n)+2mn+f(m)$ is a perfect square. | "[\"f(n) = (n + 2\\\\ell)^2 - 2\\\\ell^2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1382, "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:15388"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"9950"
] | [
"skywork"
] | ab14158c162c573b602908ade311afe5969528c063cb88de48fded9140f022b9 | [
{
"content": "What is the largest four-digit number whose digits add up to 23?",
"role": "user"
}
] | What is the largest four-digit number whose digits add up to 23? | "[\"9950\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1409, "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:15389"}] | {
"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
} |
[
"10"
] | [
"skywork"
] | cfdd0433f22c498b0ce60842368c2c67c651e79ed9c8b9e322f36204a620c1ce | [
{
"content": "There are 11 children sitting in a circle playing a game. They are numbered clockwise from 1 to 11. The game starts with child number 1, and each child has to say a two-digit number. The number they say cannot have a digit sum of 6 or 9, and no child can repeat a number that has already been said.... | There are 11 children sitting in a circle playing a game. They are numbered clockwise from 1 to 11. The game starts with child number 1, and each child has to say a two-digit number. The number they say cannot have a digit sum of 6 or 9, and no child can repeat a number that has already been said. The game continues un... | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1383, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:15390"}] | {
"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"
] | 9b15a141eb169c5d5fb91b0568c1cdd45f23b36a61e6b4a224fe0e5e7efa7b96 | [
{
"content": "The TV station continuously plays 5 advertisements, consisting of 3 different commercial advertisements and 2 different Olympic promotional advertisements. The requirements are that the last advertisement must be an Olympic promotional advertisement, and the 2 Olympic promotional advertisements ca... | The TV station continuously plays 5 advertisements, consisting of 3 different commercial advertisements and 2 different Olympic promotional advertisements. The requirements are that the last advertisement must be an Olympic promotional advertisement, and the 2 Olympic promotional advertisements can be played consecutiv... | "[\"36\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1391, "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:15391"}] | {
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[
"12"
] | [
"skywork"
] | 44e99affb541c054f006c40990e5113a76e4331f5cf29956b1a2c4172ce79e82 | [
{
"content": "The lines tangent to a circle with center $O$ at points $A$ and $B$ intersect at point $M$. Find the chord $AB$ if the segment $MO$ is divided by it into segments equal to 2 and 18.",
"role": "user"
}
] | The lines tangent to a circle with center $O$ at points $A$ and $B$ intersect at point $M$. Find the chord $AB$ if the segment $MO$ is divided by it into segments equal to 2 and 18. | "[\"12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1396, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:15392"}] | {
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} |
[
"80"
] | [
"skywork"
] | 7aa56f7156a95d88b04bc6942e7fec4b5bb889f3679a5357c28e62ff10622a3d | [
{
"content": "The two diagonals of a rhombus have lengths with ratio $3 : 4$ and sum $56$. What is the perimeter of the rhombus?",
"role": "user"
}
] | The two diagonals of a rhombus have lengths with ratio $3 : 4$ and sum $56$. What is the perimeter of the rhombus? | "[\"80\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1406, "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:15393"}] | {
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"reference_components": 1,
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[
"350"
] | [
"skywork"
] | 360316224963c84780ac66798be201a0662dae61edc615c7cd09c67979fc1898 | [
{
"content": "2. how many seven-digit numbers are there for which the product of the digits is equal to $45^{3}$?\n\n## Solution:",
"role": "user"
}
] | 2. how many seven-digit numbers are there for which the product of the digits is equal to $45^{3}$?
## Solution: | "[\"350\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1387, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15394"}] | {
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"plain_numeric_reference": true,
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[
"227"
] | [
"skywork"
] | 27f64a5e975e59637de354d9c8fc956faca9db46e9ceeb1366645b441d36dc3f | [
{
"content": "The incircle $\\omega$ of triangle $ABC$ is tangent to $\\overline{BC}$ at $X$. Let $Y \\neq X$ be the other intersection of $\\overline{AX}$ with $\\omega$. Points $P$ and $Q$ lie on $\\overline{AB}$ and $\\overline{AC}$, respectively, so that $\\overline{PQ}$ is tangent to $\\omega$ at $Y$. Assu... | The incircle $\omega$ of triangle $ABC$ is tangent to $\overline{BC}$ at $X$. Let $Y \neq X$ be the other intersection of $\overline{AX}$ with $\omega$. Points $P$ and $Q$ lie on $\overline{AB}$ and $\overline{AC}$, respectively, so that $\overline{PQ}$ is tangent to $\omega$ at $Y$. Assume that $AP = 3$, $PB = 4$, $AC... | "[\"227\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 1386, "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:15395"}, {"dataset": "skywork", "extra_... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"60"
] | [
"skywork"
] | 32527a4d943809c8786af89f9cc96c428aa149cdb79b28b8c2d39149a079b0e2 | [
{
"content": "4. Ivica, on the excursion, spends half of his money and an additional 10 kuna every day. In four days, he spends all his money. How much money did Ivica have?",
"role": "user"
}
] | 4. Ivica, on the excursion, spends half of his money and an additional 10 kuna every day. In four days, he spends all his money. How much money did Ivica have? | "[\"60\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1414, "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:15396"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2^{90}-1"
] | [
"skywork"
] | 35262baf0c89ca3fa18e45c7603efb43a88c10a41bb71fd16b7eb8968cacdc2b | [
{
"content": "Example 2 (1996 National High School League Question) The number of proper subsets of the set $\\left\\{x \\left\\lvert\\,-1 \\leqslant \\log _{\\frac{1}{x}} 10<-\\frac{1}{2}\\right., x \\in \\mathbf{N}_{+}\\right\\}$ is $\\qquad$ .",
"role": "user"
}
] | Example 2 (1996 National High School League Question) The number of proper subsets of the set $\left\{x \left\lvert\,-1 \leqslant \log _{\frac{1}{x}} 10<-\frac{1}{2}\right., x \in \mathbf{N}_{+}\right\}$ is $\qquad$ . | "[\"2^{90}-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1377, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:15397"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"155"
] | [
"skywork"
] | c4f8bcef95c422237376038db1885dcaa0cf00f7b0488844b1e4dd1f5611741b | [
{
"content": "2. The cities $A$ and $B$ are $106 \\mathrm{~km}$ apart. At noon, from city $A$, Antonio set off on a bicycle heading towards $B$ at a constant speed of $30 \\mathrm{~km} / \\mathrm{h}$. Half an hour later, from city $B$, Bojan set off on foot heading towards $A$ at a constant speed of $5 \\mathrm... | 2. The cities $A$ and $B$ are $106 \mathrm{~km}$ apart. At noon, from city $A$, Antonio set off on a bicycle heading towards $B$ at a constant speed of $30 \mathrm{~km} / \mathrm{h}$. Half an hour later, from city $B$, Bojan set off on foot heading towards $A$ at a constant speed of $5 \mathrm{~km} / \mathrm{h}$. At th... | "[\"155\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1389, "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:15398"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"802"
] | [
"skywork"
] | f98dacdc7c08dde0522550a72f3b837ddd36567d8d853b8d51963b86e9c91acc | [
{
"content": "For each positive integer $n$, let $f(n) = n^4 - 360n^2 + 400$. What is the sum of all values of $f(n)$ that are prime numbers?",
"role": "user"
}
] | For each positive integer $n$, let $f(n) = n^4 - 360n^2 + 400$. What is the sum of all values of $f(n)$ that are prime numbers? | "[\"802\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1395, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:15399"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"77"
] | [
"skywork"
] | 56c3e0a3aaa4d8ce45b35b7e3b7a0b7fb176e58dcb4837dbd6e38b107fd521f8 | [
{
"content": "Five integers have an average of 69. The middle integer (the median) is 83 . The most frequently occurring integer (the mode) is 85 . The range of the five integers is 70 . What is the second smallest of the five integers?\n(A) 77\n(B) 15\n(C) 50\n(D) 55\n(E) 49",
"role": "user"
}
] | Five integers have an average of 69. The middle integer (the median) is 83 . The most frequently occurring integer (the mode) is 85 . The range of the five integers is 70 . What is the second smallest of the five integers?
(A) 77
(B) 15
(C) 50
(D) 55
(E) 49 | "[\"77\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1405, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15400"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt[4]{8}+2"
] | [
"skywork"
] | b7eed6295817e0048844c879c919034376725cfd4f166e4f4aeb5d4538c38665 | [
{
"content": "5. Place eight balls with a radius of 1 in two layers inside a cylinder, such that each ball is tangent to its four adjacent balls, and is also tangent to one base and the side of the cylinder. Then the height of this cylinder is $\\qquad$ .",
"role": "user"
}
] | 5. Place eight balls with a radius of 1 in two layers inside a cylinder, such that each ball is tangent to its four adjacent balls, and is also tangent to one base and the side of the cylinder. Then the height of this cylinder is $\qquad$ . | "[\"\\\\sqrt[4]{8}+2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1385, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15401"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{4}{3}"
] | [
"skywork"
] | 923f6cd3fb9c807d675ac1fa227dca4c7003f847919eeea79386f2d9fdf89194 | [
{
"content": "A regular hexagon is inscribed in a circle and another regular hexagon is circumscribed about the same circle. What is the ratio of the area of the larger hexagon to the area of the smaller hexagon? Express your answer as a common fraction.",
"role": "user"
}
] | A regular hexagon is inscribed in a circle and another regular hexagon is circumscribed about the same circle. What is the ratio of the area of the larger hexagon to the area of the smaller hexagon? Express your answer as a common fraction. | "[\"\\\\frac{4}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1403, "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:15402"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
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