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 |
|---|---|---|---|---|---|---|---|---|
[
"\\ln2"
] | [
"skywork"
] | 069f808d2a2002e671ffa567e3c305d746ce9bef82a509a69646d44f1731dbb8 | [
{
"content": "1. [3] Let $f$ be a differentiable real-valued function defined on the positive real numbers. The tangent lines to the graph of $f$ always meet the $y$-axis 1 unit lower than where they meet the function. If $f(1)=0$, what is $f(2)$ ?",
"role": "user"
}
] | 1. [3] Let $f$ be a differentiable real-valued function defined on the positive real numbers. The tangent lines to the graph of $f$ always meet the $y$-axis 1 unit lower than where they meet the function. If $f(1)=0$, what is $f(2)$ ? | "[\"\\\\ln2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108515, "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:118435"}] | {
"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
} |
[
"871"
] | [
"skywork"
] | 352b1700f7be9f6e42607eb389f804664a75a2f61708300407df7c638ec8c28b | [
{
"content": "Given a family of sets \\(\\{A_{1}, A_{2}, \\ldots, A_{n}\\}\\) that satisfies the following conditions:\n(1) Each set \\(A_{i}\\) contains exactly 30 elements;\n(2) For any \\(1 \\leq i < j \\leq n\\), the intersection \\(A_{i} \\cap A_{j}\\) contains exactly 1 element;\n(3) The intersection \\(A... | Given a family of sets \(\{A_{1}, A_{2}, \ldots, A_{n}\}\) that satisfies the following conditions:
(1) Each set \(A_{i}\) contains exactly 30 elements;
(2) For any \(1 \leq i < j \leq n\), the intersection \(A_{i} \cap A_{j}\) contains exactly 1 element;
(3) The intersection \(A_{1} \cap A_{2} \cap \ldots \cap A_{n} =... | "[\"871\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108507, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118436"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"x\\in(-2,-\\frac{1}{3}]\\cup(8,\\infty)"
] | [
"skywork"
] | 1622d3289a0122709224ee6cfb05cf5522263b56b34c677b056a1c34c53e8a97 | [
{
"content": "\\section*{Problem 1 - 111241}\n\nAll real numbers \\(x\\) are to be specified for which the expression\n\n\\[\n\\frac{2 x}{|x-3|-5}+\\frac{1}{x+2}\n\\]\n\nexists, and among these, all \\(x\\) are to be determined that satisfy the following inequality (2):\n\n\\[\n\\frac{2 x}{|x-3|-5}+\\frac{1}{x+... | \section*{Problem 1 - 111241}
All real numbers \(x\) are to be specified for which the expression
\[
\frac{2 x}{|x-3|-5}+\frac{1}{x+2}
\]
exists, and among these, all \(x\) are to be determined that satisfy the following inequality (2):
\[
\frac{2 x}{|x-3|-5}+\frac{1}{x+2} \geq 1
\] | "[\"x\\\\in(-2,-\\\\frac{1}{3}]\\\\cup(8,\\\\infty)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108514, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118437"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-\\frac{3}{2}"
] | [
"skywork"
] | f5823303cf5ec12dddbd339fbd10596d3f7aa3177c04a9d3a5848f7cf6c74897 | [
{
"content": "A straight line joins the points $(-1,1)$ and $(3,9)$. Its $x$-intercept is:",
"role": "user"
}
] | A straight line joins the points $(-1,1)$ and $(3,9)$. Its $x$-intercept is: | "[\"-\\\\frac{3}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108520, "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:118438"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | b2f91b6ad5c69a4c52ac9012029604f0445cacb7e6b38280d6794e2d1ed4d883 | [
{
"content": "14. The first term of the sequence $\\left\\{a_{n}\\right\\}$ is 2, the sum of the first $n$ terms is $S_{n}$, and $\\left\\{S_{n}\\right\\}$ is a geometric sequence with a common ratio of $\\frac{1}{3}$.\n(1) Find the general formula for the sequence $\\left\\{a_{n}\\right\\}$;\n(2) Let $b_{n}=a_... | 14. The first term of the sequence $\left\{a_{n}\right\}$ is 2, the sum of the first $n$ terms is $S_{n}$, and $\left\{S_{n}\right\}$ is a geometric sequence with a common ratio of $\frac{1}{3}$.
(1) Find the general formula for the sequence $\left\{a_{n}\right\}$;
(2) Let $b_{n}=a_{n} S_{n}$, find the sum of all terms... | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108483, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118439"}] | {
"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
} |
[
"1944"
] | [
"skywork"
] | f370f5d839bb0603222ce5156da3996c22355c255a30f12b2e9799098db2ac5f | [
{
"content": "12. Find the smallest natural number greater than 1 that is at least 600 times greater than each of its prime divisors.",
"role": "user"
}
] | 12. Find the smallest natural number greater than 1 that is at least 600 times greater than each of its prime divisors. | "[\"1944\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108522, "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:118440"}] | {
"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"
] | fdd64c0d2874f3b93e1901b75200b1f4f6b5e9dcc5eef729b74783979bd8deb7 | [
{
"content": "There is a point source of light in an empty universe. What is the minimum number of solid balls (of any size) one must place in space so that any light ray emanating from the light source intersects at least one ball?",
"role": "user"
}
] | There is a point source of light in an empty universe. What is the minimum number of solid balls (of any size) one must place in space so that any light ray emanating from the light source intersects at least one ball? | "[\"4\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108518, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118442"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.5R^{2}(\\pi+\\sqrt{3})"
] | [
"skywork"
] | f818b8ee981b939cc8b4dbb13894a4e1afe7cce81909f78748da66a296771e5c | [
{
"content": "1.45. In a circle of radius $R$, two parallel chords are drawn on opposite sides of the center, one of which subtends an arc of $60^{\\circ}$, the other an arc of $120^{\\circ}$. Find the area of the part of the circle enclosed between the chords.",
"role": "user"
}
] | 1.45. In a circle of radius $R$, two parallel chords are drawn on opposite sides of the center, one of which subtends an arc of $60^{\circ}$, the other an arc of $120^{\circ}$. Find the area of the part of the circle enclosed between the chords. | "[\"0.5R^{2}(\\\\pi+\\\\sqrt{3})\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108534, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:118443"}] | {
"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
} |
[
"56"
] | [
"skywork"
] | 518512769fd098459863f81ad1f55917f64dee562aaf79ccf4840cabddc034e9 | [
{
"content": "(4) Let $M$ be the set of midpoints of all edges of a cube. Then the number of planes that pass through and only through 3 points in $M$ is ( ).\n(A) 56\n(B) 81\n(C) 136\n(D) 145",
"role": "user"
}
] | (4) Let $M$ be the set of midpoints of all edges of a cube. Then the number of planes that pass through and only through 3 points in $M$ is ( ).
(A) 56
(B) 81
(C) 136
(D) 145 | "[\"56\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108519, "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:118444"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"132"
] | [
"skywork"
] | 2fe6aa87f61b1dd6308cc733d4c2930c74a48b038035d91e5e5e8bdf03a439b0 | [
{
"content": "Šárka enjoys celebrating, so in addition to birthdays, she came up with antibirthdays: the date of the antibirthday is created by swapping the day and month numbers in the birth date. She was born on 8.11., so her antibirthday is on 11.8. Her mother cannot celebrate her antibirthday: she was born ... | Šárka enjoys celebrating, so in addition to birthdays, she came up with antibirthdays: the date of the antibirthday is created by swapping the day and month numbers in the birth date. She was born on 8.11., so her antibirthday is on 11.8. Her mother cannot celebrate her antibirthday: she was born on 23.7., her antibirt... | "[\"132\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108511, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118445"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\text{odd}"
] | [
"skywork"
] | 16f3faaec4544a54b44d1031b7710c6139a2fd6d143eaf4f8bad505437fbd1e6 | [
{
"content": "Let $f(x)$ be an odd function. Is $f(f(x))$ even, odd, or neither?\n\nEnter \"odd\", \"even\", or \"neither\".",
"role": "user"
}
] | Let $f(x)$ be an odd function. Is $f(f(x))$ even, odd, or neither?
Enter "odd", "even", or "neither". | "[\"\\\\text{odd}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108536, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:118446"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"p(x, y) = \\frac{(x+y)^2 + 3x + y}{2}"
] | [
"skywork"
] | 38b620e39d75be5ef6bfe02382f38cd275d13449c37273c96fa4c8cba00626c4 | [
{
"content": "Does there exist a second-degree polynomial $p(x, y)$ in two variables such that every non-negative integer $ n $ equals $p(k,m)$ for one and only one ordered pair $(k,m)$ of non-negative integers?\n\n[i]Proposed by Finland.[/i]",
"role": "user"
}
] | Does there exist a second-degree polynomial $p(x, y)$ in two variables such that every non-negative integer $ n $ equals $p(k,m)$ for one and only one ordered pair $(k,m)$ of non-negative integers?
[i]Proposed by Finland.[/i] | "[\" p(x, y) = \\\\frac{(x+y)^2 + 3x + y}{2} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108516, "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:118447"}] | {
"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
} |
[
"9"
] | [
"skywork"
] | b4ae94e524e8a1a5cef7ca6b1f694227be8568e5b67f9a9c0077607673ba0cf6 | [
{
"content": "2. If $\\frac{1-\\cos \\theta}{4+\\sin ^{2} \\theta}=\\frac{1}{2}$, then $\\left(4+\\cos ^{3} \\theta\\right) \\cdot\\left(3+\\sin ^{3} \\theta\\right)=$",
"role": "user"
}
] | 2. If $\frac{1-\cos \theta}{4+\sin ^{2} \theta}=\frac{1}{2}$, then $\left(4+\cos ^{3} \theta\right) \cdot\left(3+\sin ^{3} \theta\right)=$ | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108521, "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:118448"}] | {
"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"
] | cd6d8b699919f63c4cdc65058ccd4ffb72fcfe7d88c38119001bf8b68d53bb20 | [
{
"content": "Juan and Mary play a two-person game in which the winner gains 2 points and the loser loses 1 point.\nIf Juan won exactly 3 games and Mary had a final score of 5 points, how many games did they play?\n\n$\\textbf{(A)}\\ 7 \\qquad \\textbf{(B)}\\ 8 \\qquad \\textbf{(C)}\\ 4 \\qquad \\textbf{(D)}\\ ... | Juan and Mary play a two-person game in which the winner gains 2 points and the loser loses 1 point.
If Juan won exactly 3 games and Mary had a final score of 5 points, how many games did they play?
$\textbf{(A)}\ 7 \qquad \textbf{(B)}\ 8 \qquad \textbf{(C)}\ 4 \qquad \textbf{(D)}\ 5 \qquad \textbf{(E)}\ 11$ | "[\"7\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108524, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:118449"}] | {
"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
} |
[
"\\arccos \\frac{\\sqrt{15}}{5} \\text{ or } \\arccos \\frac{\\sqrt{7}}{7}"
] | [
"skywork"
] | bbf16d328343febe8eace2b634c99708cdbc63dc11dfb43bc66b6cb853f47b0b | [
{
"content": "3. (20 points) As shown in Figure 1, in rectangle $ABCD$, $AB = \\sqrt{3}$, $BC = a$. Also, $PA \\perp$ plane $ABCD$, $PA = 4$.\n(1) If there exists a point $Q$ on side $BC$ such that $PQ \\perp QD$, find the range of values for $a$;\n(2) When there is exactly one point $Q$ on $BC$ such that $PQ \... | 3. (20 points) As shown in Figure 1, in rectangle $ABCD$, $AB = \sqrt{3}$, $BC = a$. Also, $PA \perp$ plane $ABCD$, $PA = 4$.
(1) If there exists a point $Q$ on side $BC$ such that $PQ \perp QD$, find the range of values for $a$;
(2) When there is exactly one point $Q$ on $BC$ such that $PQ \perp QD$, find the angle be... | "[\"\\\\arccos \\\\frac{\\\\sqrt{15}}{5} \\\\text{ or } \\\\arccos \\\\frac{\\\\sqrt{7}}{7}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108494, "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:118450"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{11 - \\sqrt{13}}{2}"
] | [
"skywork"
] | b85d5b3a3ef9dbe9bb209e8a7127334ff3b4c4e7657c27601098fc4ede46baf8 | [
{
"content": "Let $f(x) = x^2 + 6x + c$ for all real numbers $x$, where $c$ is some real number. For what values of $c$ does $f(f(x))$ have exactly $3$ distinct real roots?",
"role": "user"
}
] | Let $f(x) = x^2 + 6x + c$ for all real numbers $x$, where $c$ is some real number. For what values of $c$ does $f(f(x))$ have exactly $3$ distinct real roots? | "[\"\\\\frac{11 - \\\\sqrt{13}}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108525, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118451"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | ae43ccd5267886ae9b4a0f680be998fedff03a3e77d5f8870c1897b74aa931e6 | [
{
"content": "How many distinct four-digit even numbers can be formed using the digits 0, 1, 2, 3?",
"role": "user"
}
] | How many distinct four-digit even numbers can be formed using the digits 0, 1, 2, 3? | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108526, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:118452"}] | {
"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
} |
[
"401"
] | [
"skywork"
] | 78419e5f24323db7f103edb69ea1f01b5e08f3eae35fb9e009c56a9672e54dd1 | [
{
"content": "A set \\( A \\) consists of 40 elements chosen from \\(\\{1, 2, \\ldots, 50\\}\\), and \\( S \\) is the sum of all elements in the set \\( A \\). How many distinct values can \\( S \\) take?",
"role": "user"
}
] | A set \( A \) consists of 40 elements chosen from \(\{1, 2, \ldots, 50\}\), and \( S \) is the sum of all elements in the set \( A \). How many distinct values can \( S \) take? | "[\"401\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108532, "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:118454"}] | {
"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
} |
[
"7043"
] | [
"skywork"
] | 6a1a095ffa0167261226f6ef204cb0753888312eb75450089e268060378aabbb | [
{
"content": "What is the largest prime factor of the sum of $1579$ and $5464$?",
"role": "user"
}
] | What is the largest prime factor of the sum of $1579$ and $5464$? | "[\"7043\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108550, "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:118455"}] | {
"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
} |
[
"P"
] | [
"skywork"
] | 11506a7cba9c88108b86521646b28a9c834f1bbf73b43c9d56322a9482884443 | [
{
"content": "A plane rectangular grid is given and a “rational point” is defined as a point $(x, y)$ where $x$ and $y$ are both rational numbers. Let $A,B,A',B'$ be four distinct rational points. Let $P$ be a point such that $\\frac{A'B'}{AB}=\\frac{B'P}{BP} = \\frac{PA'}{PA}.$ In other words, the triangles $A... | A plane rectangular grid is given and a “rational point” is defined as a point $(x, y)$ where $x$ and $y$ are both rational numbers. Let $A,B,A',B'$ be four distinct rational points. Let $P$ be a point such that $\frac{A'B'}{AB}=\frac{B'P}{BP} = \frac{PA'}{PA}.$ In other words, the triangles $ABP, A'B'P$ are directly o... | "[\" P \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108509, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118457"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"54"
] | [
"skywork"
] | 97b2172153569573d82144ef3981342ce4b6c580109921b54327bee0b46f4bbd | [
{
"content": "13.144. The sum of all even two-digit numbers is divisible by one of them without a remainder. The quotient obtained differs from the divisor only in the order of the digits, and the sum of its digits is 9. What two-digit number was the divisor?",
"role": "user"
}
] | 13.144. The sum of all even two-digit numbers is divisible by one of them without a remainder. The quotient obtained differs from the divisor only in the order of the digits, and the sum of its digits is 9. What two-digit number was the divisor? | "[\"54\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108527, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:118458"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"26"
] | [
"skywork"
] | 3d2839828489df9552b88bb4bb3d02ffc8c49ed880137f2c088f05259f2d407a | [
{
"content": "What is the smallest positive integer that satisfies the congruence $5x \\equiv 17 \\pmod{31}$?",
"role": "user"
}
] | What is the smallest positive integer that satisfies the congruence $5x \equiv 17 \pmod{31}$? | "[\"26\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108549, "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:118459"}] | {
"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"
] | 03e2ab65380b77050db8ca2788e0b49f86cc74f58e77140d40ab55a5b1f63147 | [
{
"content": "1. Find all values of $p$, for each of which the numbers $-p-8$, $3 \\cdot \\sqrt{p}$, and $p-7$ are the first, second, and third terms, respectively, of some geometric progression.",
"role": "user"
}
] | 1. Find all values of $p$, for each of which the numbers $-p-8$, $3 \cdot \sqrt{p}$, and $p-7$ are the first, second, and third terms, respectively, of some geometric progression. | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108541, "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:118460"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2\\sqrt{2}"
] | [
"skywork"
] | 7c28db3fc5089381773c718d3bccc2b8f6fe7d60e8cf1174e7957da0ae8222a4 | [
{
"content": "(10) The sum of the maximum and minimum values of the function $y=\\sin x+\\sqrt{2+\\cos ^{2} x}$ is\n\n保留了源文本的换行和格式。",
"role": "user"
}
] | (10) The sum of the maximum and minimum values of the function $y=\sin x+\sqrt{2+\cos ^{2} x}$ is
保留了源文本的换行和格式。 | "[\"2\\\\sqrt{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108531, "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:118461"}] | {
"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{60}{13}"
] | [
"skywork"
] | c0e46bd83210bcbf3094ff3151d040516060e362a19d6d802201f778bbd6a2cf | [
{
"content": "Find the minimum value of $\\sqrt{x^2+y^2}$ if $5x+12y=60$.",
"role": "user"
}
] | Find the minimum value of $\sqrt{x^2+y^2}$ if $5x+12y=60$. | "[\"\\\\frac{60}{13}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108546, "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:118462"}] | {
"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
} |
[
"252"
] | [
"skywork"
] | 97e8d3ce223bb7c7a218cd55a7c98145204189f59c14da7a32eed664fbe87693 | [
{
"content": "The NIMO problem writers have invented a new chess piece called the *Oriented Knight*. This new chess piece has a limited number of moves: it can either move two squares to the right and one square upward or two squares upward and one square to the right. How many ways can the knight move from t... | The NIMO problem writers have invented a new chess piece called the *Oriented Knight*. This new chess piece has a limited number of moves: it can either move two squares to the right and one square upward or two squares upward and one square to the right. How many ways can the knight move from the bottom-left square ... | "[\"252\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108537, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118463"}] | {
"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
} |
[
"96"
] | [
"skywork"
] | 0d0a96088b9680e25fa529e1f2a5c1b36bcb2e26f21f7d6f74cf4ac182bdf0ce | [
{
"content": "Senators Sernie Banders and Cedric \"Ced\" Truz of OMOrica are running for the office of Price Dent. The election works as follows: There are $66$ states, each composed of many adults and $2017$ children, with only the latter eligible to vote. On election day, the children each cast their vote wit... | Senators Sernie Banders and Cedric "Ced" Truz of OMOrica are running for the office of Price Dent. The election works as follows: There are $66$ states, each composed of many adults and $2017$ children, with only the latter eligible to vote. On election day, the children each cast their vote with equal probability to B... | "[\"96\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108529, "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:118464"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"skywork"
] | 3b63552c8e654b54147c3029f44bac07cae3d433bd75f6d75ada555854a92550 | [
{
"content": "How many pairs of positive integers $(a, b)$ with $a \\leq b$ satisfy $\\frac{1}{a} + \\frac{1}{b} = \\frac{1}{6}$?",
"role": "user"
}
] | How many pairs of positive integers $(a, b)$ with $a \leq b$ satisfy $\frac{1}{a} + \frac{1}{b} = \frac{1}{6}$? | "[\"5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108548, "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:118465"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"skywork"
] | 8c08d6c7c238264f55b1dce5bf949399be4dd683ea842e43676fe2fb35689561 | [
{
"content": "The angle can be represented by the two uppercase letters on its sides and the vertex letter. The angle in the diagram $\\angle A O B$ symbol (\"$\\angle$\" represents angle) can also be represented by $\\angle O$ (when there is only one angle). In the triangle $\\mathrm{ABC}$ below, given $\\angl... | The angle can be represented by the two uppercase letters on its sides and the vertex letter. The angle in the diagram $\angle A O B$ symbol ("$\angle$" represents angle) can also be represented by $\angle O$ (when there is only one angle). In the triangle $\mathrm{ABC}$ below, given $\angle B A O = \angle C A O$, $\an... | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108539, "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:118466"}] | {
"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
} |
[
"1344"
] | [
"skywork"
] | 6ff204e9f9469bdc1c56821487d802bc76210575e25fc07fa8e7f9f2f45ca03a | [
{
"content": "1. On an island, there are two tribes: the tribe of knights, who always tell the truth, and the tribe of liars, who always lie. On the main holiday, 2017 islanders sat around a large round table. Each islander said the phrase: \"my neighbors are from the same tribe.\" It turned out that two liars ... | 1. On an island, there are two tribes: the tribe of knights, who always tell the truth, and the tribe of liars, who always lie. On the main holiday, 2017 islanders sat around a large round table. Each islander said the phrase: "my neighbors are from the same tribe." It turned out that two liars made a mistake and accid... | "[\"1344\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108533, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118467"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2\\sqrt{145}"
] | [
"skywork"
] | 1715b6db14b46ae3f3cae05b166c0d2d982f51bd47b8ad2b6d0d346de9b192f5 | [
{
"content": "Let $ABC$ be a triangle with $AB=13$, $BC=14$, and $CA=15$. The incircle of $ABC$ meets $BC$ at $D$. Line $AD$ meets the circle through $B$, $D$, and the reflection of $C$ over $AD$ at a point $P\\neq D$. Compute $AP$.\n\n[i]2020 CCA Math Bonanza Tiebreaker Round #4[/i]",
"role": "user"
}
] | Let $ABC$ be a triangle with $AB=13$, $BC=14$, and $CA=15$. The incircle of $ABC$ meets $BC$ at $D$. Line $AD$ meets the circle through $B$, $D$, and the reflection of $C$ over $AD$ at a point $P\neq D$. Compute $AP$.
[i]2020 CCA Math Bonanza Tiebreaker Round #4[/i] | "[\"2\\\\sqrt{145}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108542, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118468"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"skywork"
] | e5bb9f06fa603f67dee535c872d2d0e33f1b0f010d81591d656558cfbdd2b0f0 | [
{
"content": "The sum \n\\[ \\sum_{k=0}^{\\infty} \\frac{2^{k}}{5^{2^{k}}+1}\\]\ncan be written in the form $\\frac{p}{q}$ where $p$ and $q$ are relatively prime positive integers. Find $p+q$.",
"role": "user"
}
] | The sum
\[ \sum_{k=0}^{\infty} \frac{2^{k}}{5^{2^{k}}+1}\]
can be written in the form $\frac{p}{q}$ where $p$ and $q$ are relatively prime positive integers. Find $p+q$. | "[\"5\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108554, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118470"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | 4c9fcafaacb8875a8a45144285d1f61048bc983fdda0c4906fb7bf754679c54d | [
{
"content": "52. There are 2018 balls in a box, numbered $1, 2, 3, \\ldots, 2018$. Now, 1616 balls are drawn from the box and their numbers are multiplied. Find the units digit of the product.",
"role": "user"
}
] | 52. There are 2018 balls in a box, numbered $1, 2, 3, \ldots, 2018$. Now, 1616 balls are drawn from the box and their numbers are multiplied. Find the units digit of the product. | "[\"0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108552, "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:118471"}] | {
"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
} |
[
"1006"
] | [
"skywork"
] | 3d33129ac36e29a9a037851d79c051812d4e0144c2fd16c559eefba0ec812202 | [
{
"content": "Let $n$ be a positive integer, $[x]$ be the greatest integer not exceeding the real number $x$, and $\\{x\\}=x-[x]$.\n(1) Find all positive integers $n$ that satisfy\n$$\n\\sum_{k=1}^{2013}\\left[\\frac{k n}{2013}\\right]=2013+n\n$$\n\n(2) Find all positive integers $n$ that maximize $\\sum_{k=1}^... | Let $n$ be a positive integer, $[x]$ be the greatest integer not exceeding the real number $x$, and $\{x\}=x-[x]$.
(1) Find all positive integers $n$ that satisfy
$$
\sum_{k=1}^{2013}\left[\frac{k n}{2013}\right]=2013+n
$$
(2) Find all positive integers $n$ that maximize $\sum_{k=1}^{2013}\left\{\frac{k n}{2013}\right... | "[\"1006\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108540, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118472"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"48"
] | [
"skywork"
] | 9a142c13af286148fbdeef9e2c921b9e9b94c8586ee9d93117dc4966198e2cbd | [
{
"content": "How many square units are in the area of the parallelogram with vertices at (0, 0), (6, 0), (2, 8) and (8, 8)?",
"role": "user"
}
] | How many square units are in the area of the parallelogram with vertices at (0, 0), (6, 0), (2, 8) and (8, 8)? | "[\"48\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108565, "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:118473"}] | {
"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{28}{53}"
] | [
"skywork"
] | df7dbde938a74abb03ed3c895b6e185abf80d28d72b439c04cf840730794172e | [
{
"content": "[ Inscribed and Circumscribed Circles ] [ Inscribed Angle Subtended by a Diameter ]\n\nA circle with radius 1 is circumscribed around triangle $A P K$. The extension of side $A P$ beyond vertex $P$ intercepts a segment $B K$ from the tangent to the circle at vertex $K$, and $B K$ is equal to 7. Fi... | [ Inscribed and Circumscribed Circles ] [ Inscribed Angle Subtended by a Diameter ]
A circle with radius 1 is circumscribed around triangle $A P K$. The extension of side $A P$ beyond vertex $P$ intercepts a segment $B K$ from the tangent to the circle at vertex $K$, and $B K$ is equal to 7. Find the area of triangle ... | "[\"\\\\frac{28}{53}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108535, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:118475"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"18 \\pi"
] | [
"skywork"
] | 0b3e95cb9d8ae9c33e215f9504a6ad22e8673a8b191e10fe0a463fdf6889227d | [
{
"content": "Alice is sitting in a teacup ride with infinitely many layers of spinning disks. The largest disk has radius 5. Each succeeding disk has its center attached to a point on the circumference of the previous disk and has a radius equal to $2 / 3$ of the previous disk. Each disk spins around its cente... | Alice is sitting in a teacup ride with infinitely many layers of spinning disks. The largest disk has radius 5. Each succeeding disk has its center attached to a point on the circumference of the previous disk and has a radius equal to $2 / 3$ of the previous disk. Each disk spins around its center (relative to the dis... | "[\"18 \\\\pi\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108551, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118476"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\text{No}"
] | [
"skywork"
] | aa2ce120e91c012a9580b17a53008950ace3398d69bd66ccd1ac83abafc23478 | [
{
"content": "A physicist encounters $2015$ atoms called usamons. Each usamon either has one electron or zero electrons, and the physicist can't tell the difference. The physicist's only tool is a diode. The physicist may connect the diode from any usamon $A$ to any other usamon $B$. (This connection is direct... | A physicist encounters $2015$ atoms called usamons. Each usamon either has one electron or zero electrons, and the physicist can't tell the difference. The physicist's only tool is a diode. The physicist may connect the diode from any usamon $A$ to any other usamon $B$. (This connection is directed.) When she does so,... | "[\"\\\\text{No}\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 108545, "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:118477"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"A"
] | [
"skywork"
] | f4d591d91406d3703446abb9c4e0b8d41046e44d8af17b4cd84b58f1c95a80e5 | [
{
"content": "7.53 In $\\triangle A B C$, if $2 \\sin A \\cos B=\\sin C$, then this triangle is\n(A) an isosceles triangle.\n(B) a right triangle.\n(C) a scalene triangle.\n(D) an equilateral triangle.\n(Anhui Province Wuhu City Junior High School Mathematics Competition, 1990)",
"role": "user"
}
] | 7.53 In $\triangle A B C$, if $2 \sin A \cos B=\sin C$, then this triangle is
(A) an isosceles triangle.
(B) a right triangle.
(C) a scalene triangle.
(D) an equilateral triangle.
(Anhui Province Wuhu City Junior High School Mathematics Competition, 1990) | "[\"A\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108558, "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:118479"}] | {
"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
} |
[
"99"
] | [
"skywork"
] | 6b14d55fd86d4fb41d1b3d7de040460c95cdd92b7e6ff08f8a45f26adae10e5d | [
{
"content": "Define $a_k = (k^2 + 1)k!$ and $b_k = a_1 + a_2 + a_3 + \\cdots + a_k$. Let \\[\\frac{a_{100}}{b_{100}} = \\frac{m}{n}\\] where $m$ and $n$ are relatively prime natural numbers. Find $n - m$.",
"role": "user"
}
] | Define $a_k = (k^2 + 1)k!$ and $b_k = a_1 + a_2 + a_3 + \cdots + a_k$. Let \[\frac{a_{100}}{b_{100}} = \frac{m}{n}\] where $m$ and $n$ are relatively prime natural numbers. Find $n - m$. | "[\"99\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108557, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:118480"}] | {
"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
} |
[
"240"
] | [
"skywork"
] | cf1a3c22a6a3556f2470d117209a5b04fbf21f6c1824e0453d0840dd7e292d84 | [
{
"content": "Let \\( T \\) be a trapezoid with two right angles and side lengths \\( 4, 4, 5 \\), and \\( \\sqrt{17} \\). Two line segments are drawn, connecting the midpoints of opposite sides of \\( T \\) and dividing \\( T \\) into 4 regions. If the difference between the areas of the largest and smallest o... | Let \( T \) be a trapezoid with two right angles and side lengths \( 4, 4, 5 \), and \( \sqrt{17} \). Two line segments are drawn, connecting the midpoints of opposite sides of \( T \) and dividing \( T \) into 4 regions. If the difference between the areas of the largest and smallest of these regions is \( d \), compu... | "[\"240\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108547, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:118481"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"skywork"
] | 3d8748429b7c104efc06b39fa83dc963d27b058cabb207b34673b9c30a05b68f | [
{
"content": "Given the equation $x^{2}-px+q=0$ ($p > 0, q > 0$) with two distinct roots $x_{1}$, $x_{2}$, and the fact that $x_{1}$, $x_{2}$, and $-2$ can be appropriately sorted to form an arithmetic sequence as well as a geometric sequence, find the value of $p \\times q$.",
"role": "user"
}
] | Given the equation $x^{2}-px+q=0$ ($p > 0, q > 0$) with two distinct roots $x_{1}$, $x_{2}$, and the fact that $x_{1}$, $x_{2}$, and $-2$ can be appropriately sorted to form an arithmetic sequence as well as a geometric sequence, find the value of $p \times q$. | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108543, "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:118482"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\pi}{3}"
] | [
"skywork"
] | 41ff9e83b0952e7aecad0b0fdfec1cfcac97e444e6136c734163c20112dfa21e | [
{
"content": "If the direction vector of line $l$ is $\\overrightarrow{d}=(1,\\sqrt{3})$, then the inclination angle of line $l$ is ______.",
"role": "user"
}
] | If the direction vector of line $l$ is $\overrightarrow{d}=(1,\sqrt{3})$, then the inclination angle of line $l$ is ______. | "[\"\\\\frac{\\\\pi}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108556, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118483"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | d779b00d1e23e9302acb727326e2afb47699001e8cf5404332afc7532a972d32 | [
{
"content": "14. There are 5 different books: three on mathematics and two on physics. In how many ways can two books be selected: one on mathematics and one on physics?",
"role": "user"
}
] | 14. There are 5 different books: three on mathematics and two on physics. In how many ways can two books be selected: one on mathematics and one on physics? | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108568, "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:118484"}] | {
"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
} |
[
"486"
] | [
"skywork"
] | b1827d8f76b34d910b52edbc0b64d2c1310113bc4a5c20839497a6283999e265 | [
{
"content": "Lynne is tiling her long and narrow rectangular front hall. The hall is 2 tiles wide and 13 tiles long. She is going to use exactly 11 black tiles and exactly 15 white tiles. Determine the number of distinct ways of tiling the hall so that no two black tiles are adjacent (that is, share an edge).\... | Lynne is tiling her long and narrow rectangular front hall. The hall is 2 tiles wide and 13 tiles long. She is going to use exactly 11 black tiles and exactly 15 white tiles. Determine the number of distinct ways of tiling the hall so that no two black tiles are adjacent (that is, share an edge).
## PART B
For each q... | "[\"486\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108559, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118485"}] | {
"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
} |
[
"(m,n) = (1,1), (43,13), (49,37)"
] | [
"skywork"
] | 3d0a786ea805604c17f1598d4741a6725acbf4e504a14f6fce4196d651c50008 | [
{
"content": "Find all pairs $(m,n)$ of positive odd integers, such that $n \\mid 3m+1$ and $m \\mid n^2+3$.",
"role": "user"
}
] | Find all pairs $(m,n)$ of positive odd integers, such that $n \mid 3m+1$ and $m \mid n^2+3$. | "[\"(m,n) = (1,1), (43,13), (49,37)\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108569, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118486"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"25"
] | [
"skywork"
] | 3e8e533b9d12e236c3e4485cb65084a9b3f65ba0a74bdeb05a21db2ade5df0d7 | [
{
"content": "10. (10 points) Xiao Ming and Xiao Hua are in Class 6 (1), which has between 20 and 30 students, and each student has a unique birthday. Xiao Ming says: “The number of students older than me is twice the number of students younger than me.” Xiao Hua says: “The number of students older than me is t... | 10. (10 points) Xiao Ming and Xiao Hua are in Class 6 (1), which has between 20 and 30 students, and each student has a unique birthday. Xiao Ming says: “The number of students older than me is twice the number of students younger than me.” Xiao Hua says: “The number of students older than me is three times the number ... | "[\"25\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108555, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118487"}] | {
"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{872}{1000}"
] | [
"skywork"
] | 5a5cf83ca2e81c0404b8399c3c63f70b906b5c9a7e9b23450252f4e4efe1a9d2 | [
{
"content": "Each of the $6$ sides and the $9$ diagonals of a regular hexagon are randomly and independently colored red, blue, or green with equal probability. What is the probability that there will be a triangle whose vertices are among the vertices of the hexagon such that all of its sides have the same co... | Each of the $6$ sides and the $9$ diagonals of a regular hexagon are randomly and independently colored red, blue, or green with equal probability. What is the probability that there will be a triangle whose vertices are among the vertices of the hexagon such that all of its sides have the same color?
A) $\frac{3}{4}$
... | "[\"\\\\frac{872}{1000}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108561, "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:118488"}] | {
"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
} |
[
"20.5"
] | [
"skywork"
] | 1ecda9bfa58a8f14829e377ee6a205b39f24dbc28a14568039410d535319d255 | [
{
"content": "A penny, nickel, dime, and quarter are simultaneously flipped. What is the expected value of the amount of the coins which come up heads? Express your answer in cents, rounded to the nearest tenth of a cent.",
"role": "user"
}
] | A penny, nickel, dime, and quarter are simultaneously flipped. What is the expected value of the amount of the coins which come up heads? Express your answer in cents, rounded to the nearest tenth of a cent. | "[\"20.5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108564, "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:118490"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3}{2}"
] | [
"skywork"
] | a54af7785fb1a920773170bacc57c5e5e765c0435add2deb4d03b073166d762d | [
{
"content": "1. Given the function $f(x)=\\frac{x^{2}}{1+x^{2}}$. Then, $f\\left(\\frac{1}{2004}\\right)+f(1)+f(2004)=$ $\\qquad$ .",
"role": "user"
}
] | 1. Given the function $f(x)=\frac{x^{2}}{1+x^{2}}$. Then, $f\left(\frac{1}{2004}\right)+f(1)+f(2004)=$ $\qquad$ . | "[\"\\\\frac{3}{2}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108571, "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:118492"}] | {
"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^{4033}"
] | [
"skywork"
] | ed07c5d92caf4a8f841571f5067986732b12832c2ded79a43afc02695d846107 | [
{
"content": "8. Given that $S$ is an infinite subset of the set of positive integers, satisfying that for any $a, b, c \\in S, a b c \\in S$, the elements of $S$ are arranged in ascending order to form the sequence $\\left\\{a_{n}\\right\\}$, and it is known that $a_{1}=2, a_{2031}=2^{4061}$, then $a_{2017}=$ ... | 8. Given that $S$ is an infinite subset of the set of positive integers, satisfying that for any $a, b, c \in S, a b c \in S$, the elements of $S$ are arranged in ascending order to form the sequence $\left\{a_{n}\right\}$, and it is known that $a_{1}=2, a_{2031}=2^{4061}$, then $a_{2017}=$ $\qquad$ . | "[\"2^{4033}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108566, "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:118493"}] | {
"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
} |
[
"8\\sqrt{1008}"
] | [
"skywork"
] | d02dd06f3d6c9af62afd9358b1df67d914fc9e4bb3e52cedb93938de7e14cfe5 | [
{
"content": "Rectangle $EFGH$ has area $2016$. An ellipse with area $2016\\pi$ passes through $E$ and $G$ and has foci at $F$ and $H$. What is the perimeter of the rectangle?",
"role": "user"
}
] | Rectangle $EFGH$ has area $2016$. An ellipse with area $2016\pi$ passes through $E$ and $G$ and has foci at $F$ and $H$. What is the perimeter of the rectangle? | "[\"8\\\\sqrt{1008}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108570, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:118494"}] | {
"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
} |
[
"15880"
] | [
"skywork"
] | 4c9b943fe08829b8351a3ec0c3123fa615e3a4657f3cb369df60bd2b9999d0da | [
{
"content": "Given the integers a and b, where a consists of a sequence of 1986 nines and b consists of a sequence of 1986 fours, calculate the sum of the digits of the base 10 representation of 9ab.",
"role": "user"
}
] | Given the integers a and b, where a consists of a sequence of 1986 nines and b consists of a sequence of 1986 fours, calculate the sum of the digits of the base 10 representation of 9ab. | "[\"15880\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108574, "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:118495"}] | {
"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"
] | 377dcab38f1418756d887b5cc8e56c1540b7cc3d0e7bb66e8cc6743d7edd714f | [
{
"content": "# 4.4. Condition:\n\nIn front of the elevator stand people weighing $130,60,61,65,68,70,79,81,83,87,90,91$ and 95 kg. The elevator's load capacity is 175 kg. What is the minimum number of trips needed to get everyone up?",
"role": "user"
}
] | # 4.4. Condition:
In front of the elevator stand people weighing $130,60,61,65,68,70,79,81,83,87,90,91$ and 95 kg. The elevator's load capacity is 175 kg. What is the minimum number of trips needed to get everyone up? | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108579, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:118496"}] | {
"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
} |
[
"77"
] | [
"skywork"
] | ce4a2acad9a32847c51b08c6fdaf3e2401dcf3b94f22a8f15ffab202acbae00f | [
{
"content": "How many convex polygons are there, each of which has three consecutive vertices at the points $(0 ; 5)$, $(5 ; 5)$, and $(5 ; 0)$, and the coordinates of the other vertices are also non-negative integers?",
"role": "user"
}
] | How many convex polygons are there, each of which has three consecutive vertices at the points $(0 ; 5)$, $(5 ; 5)$, and $(5 ; 0)$, and the coordinates of the other vertices are also non-negative integers? | "[\"77\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108567, "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:118497"}] | {
"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
} |
[
"7744"
] | [
"skywork"
] | 2b044c3519df54b0aedf4b0ade91f17647c25655e5970d49bc7ebf017c76c03f | [
{
"content": "21.12. Find a four-digit number that is a perfect square and has the first two digits the same and the last two digits also the same.",
"role": "user"
}
] | 21.12. Find a four-digit number that is a perfect square and has the first two digits the same and the last two digits also the same. | "[\"7744\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108577, "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:118498"}] | {
"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
} |
[
"1040"
] | [
"skywork"
] | 874f92ae8b7992f2d055a991a49b9aa07a5039f68da2b2dae9b09aa00d9e005b | [
{
"content": "1. (6 points) The calculation result of the expression $2015 \\div\\left(1+\\frac{1}{2}+\\frac{1}{4}+\\frac{1}{8}+\\frac{1}{16}\\right)$ is",
"role": "user"
}
] | 1. (6 points) The calculation result of the expression $2015 \div\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)$ is | "[\"1040\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108588, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:118499"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{3}"
] | [
"skywork"
] | 539c392a22eac3b0a485a8e75e5c57ee4772073ff5c43b5beed09bb721a1fb83 | [
{
"content": "In Mr. Jenkins' 30-student mathematics class, no two students have the same initials, and each student's first name and last name begin with the same letter. Considering the letter ``Y'' as a consonant in this scenario, what is the probability of randomly picking a student whose initials are vowel... | In Mr. Jenkins' 30-student mathematics class, no two students have the same initials, and each student's first name and last name begin with the same letter. Considering the letter ``Y'' as a consonant in this scenario, what is the probability of randomly picking a student whose initials are vowels? Each vowel (A, E, I... | "[\"\\\\frac{1}{3}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108562, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118500"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-1"
] | [
"skywork"
] | cff2ad4583a7fc9217b9767c4cc65cd6e8adcf7cee47cf13b8de66d500d58ce4 | [
{
"content": "Find the solution to $x|x| = 2x+1$ which has the smallest value.",
"role": "user"
}
] | Find the solution to $x|x| = 2x+1$ which has the smallest value. | "[\"-1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108583, "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:118501"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.9651"
] | [
"skywork"
] | dd5122d1ee117f71268f2e331b12255a0865b7ef41f49050cfba1c0ff6eeb5e7 | [
{
"content": "Example 6. Production gives $1 \\%$ of defects. What is the probability that out of 1100 items taken for research, no more than $17$ will be defective?",
"role": "user"
}
] | Example 6. Production gives $1 \%$ of defects. What is the probability that out of 1100 items taken for research, no more than $17$ will be defective? | "[\"0.9651\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108578, "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:118502"}] | {
"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"
] | 0375b8ba3e0a46b4fcbdfe1d73aa0e76e8f7747015f3fe94d73c36a90be221ce | [
{
"content": "10. $1^{1}+2^{2}+3^{3}+4^{4}+5^{5}+6^{6}+7^{7}+8^{8}+9^{9}$ divided by 3 has a remainder of what? Why?",
"role": "user"
}
] | 10. $1^{1}+2^{2}+3^{3}+4^{4}+5^{5}+6^{6}+7^{7}+8^{8}+9^{9}$ divided by 3 has a remainder of what? Why? | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108580, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:118503"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | ce88c913b8def8e334ecbbf76260f6862afd9f2a1c1bd0d0160a43a64b4afb07 | [
{
"content": "B1. Find all natural numbers $n$ whose cube is equal to the sum of the squares of three not necessarily distinct divisors of the number $n$.",
"role": "user"
}
] | B1. Find all natural numbers $n$ whose cube is equal to the sum of the squares of three not necessarily distinct divisors of the number $n$. | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108582, "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:118505"}] | {
"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
} |
[
"60"
] | [
"skywork"
] | 05f0331dcef71ed8a8f1ba47df0578e564edc81596e1b7b2f49c2eeb215adf36 | [
{
"content": "3. Calculate the angle $\\gamma$ in triangle $ABC$, if\n\n$$\n\\frac{1}{a+c}+\\frac{1}{b+c}=\\frac{3}{a+b+c}\n$$\n\nwhere $a, b, c$ are the lengths of the sides of triangle $ABC$ opposite to vertices $A, B, C$ respectively, and $\\gamma$ is the angle at vertex $C$.",
"role": "user"
}
] | 3. Calculate the angle $\gamma$ in triangle $ABC$, if
$$
\frac{1}{a+c}+\frac{1}{b+c}=\frac{3}{a+b+c}
$$
where $a, b, c$ are the lengths of the sides of triangle $ABC$ opposite to vertices $A, B, C$ respectively, and $\gamma$ is the angle at vertex $C$. | "[\"60\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108573, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:118506"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-2^{50}"
] | [
"skywork"
] | 2209a289000907449f9853eb5c5031d294b1e6a768d2875254b27d60b0f75169 | [
{
"content": "[ Sums of numerical sequences and series of differences ] Pascal's Triangle and the Binomial Theorem Complex numbers help solve tasks_\n\nUsing the expansion $(1+i)^{n}$ by the Binomial Theorem, find:\n\na) $C_{100}^{0}-C_{100}^{2}+C_{100}^{4}-\\ldots+C_{100}^{100}$\n\nb) $C_{99}^{1}-C_{99}^{3}+C_... | [ Sums of numerical sequences and series of differences ] Pascal's Triangle and the Binomial Theorem Complex numbers help solve tasks_
Using the expansion $(1+i)^{n}$ by the Binomial Theorem, find:
a) $C_{100}^{0}-C_{100}^{2}+C_{100}^{4}-\ldots+C_{100}^{100}$
b) $C_{99}^{1}-C_{99}^{3}+C_{99}^{5}-\ldots-C_{99}^{99}$. | "[\"-2^{50}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108575, "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:118507"}] | {
"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
} |
[
"984"
] | [
"skywork"
] | a2d9beb8ad5e7dd813ac45f1036fa3f453c08c61a5caa0ec9e7d8ef0f1548fa4 | [
{
"content": "Task 3. (15 points) The bases $AB$ and $CD$ of trapezoid $ABCD$ are 41 and 24, respectively, and its diagonals are perpendicular to each other. Find the scalar product of vectors $\\overrightarrow{AD}$ and $\\overrightarrow{BC}$.",
"role": "user"
}
] | Task 3. (15 points) The bases $AB$ and $CD$ of trapezoid $ABCD$ are 41 and 24, respectively, and its diagonals are perpendicular to each other. Find the scalar product of vectors $\overrightarrow{AD}$ and $\overrightarrow{BC}$. | "[\"984\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108597, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118508"}] | {
"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
} |
[
"4769280"
] | [
"skywork"
] | fa7da58750880e5ca41a97097948edc6e37257f222c6f2cb2f09afd10fbb6d3e | [
{
"content": "Among a group of 120 people, some pairs are friends. A *weak quartet* is a set of four people containing exactly one pair of friends. What is the maximum possible number of weak quartets ?",
"role": "user"
}
] | Among a group of 120 people, some pairs are friends. A *weak quartet* is a set of four people containing exactly one pair of friends. What is the maximum possible number of weak quartets ? | "[\"4769280\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108581, "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:118509"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"42.78"
] | [
"skywork"
] | 2adef32af9db469d6eafbf0cd5133451db7a98d1f0cac2110eb84f97ee6a569f | [
{
"content": "John drove continuously from 8:30 a.m. until 2:15 p.m. of the same day and covered a distance of 246 miles. What was his average speed in miles per hour?",
"role": "user"
}
] | John drove continuously from 8:30 a.m. until 2:15 p.m. of the same day and covered a distance of 246 miles. What was his average speed in miles per hour? | "[\"42.78\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108613, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118510"}] | {
"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
} |
[
"1442/2016"
] | [
"skywork"
] | da4b32464e616d20cb173b7133612c0fbac1ad454b5491887f1abae70768dae0 | [
{
"content": "Danielle picks a positive integer \\(1 \\leq n \\leq 2016\\) uniformly at random. What is the probability that \\(\\operatorname{gcd}(n, 2015)=1\\)?",
"role": "user"
}
] | Danielle picks a positive integer \(1 \leq n \leq 2016\) uniformly at random. What is the probability that \(\operatorname{gcd}(n, 2015)=1\)? | "[\"1442/2016\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108594, "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:118511"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"(x^{2}+3x+2)(x+3)=(x+1)(x^{2}+5x+6)"
] | [
"skywork"
] | 63d3bb33f362b0b9fea1ae35d1c16a60b917cfb0d3fa08bd6b279b8135bc096b | [
{
"content": "1. Instead of the ellipsis signs, insert such numbers so that the expression $\\left(x^{2}+\\ldots \\times x+2\\right) \\times(x+3)=(x+\\ldots) \\times\\left(x^{2}+\\ldots \\times x+6\\right)$ becomes an identity.",
"role": "user"
}
] | 1. Instead of the ellipsis signs, insert such numbers so that the expression $\left(x^{2}+\ldots \times x+2\right) \times(x+3)=(x+\ldots) \times\left(x^{2}+\ldots \times x+6\right)$ becomes an identity. | "[\"(x^{2}+3x+2)(x+3)=(x+1)(x^{2}+5x+6)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108576, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118513"}] | {
"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
} |
[
"2048"
] | [
"skywork"
] | e168c00c35fe5aaa55030bf0a0027441eed4a61443a894b04d304df0075a9920 | [
{
"content": "Remove all perfect squares from the sequence of positive integers \\(1, 2, 3, \\cdots\\) to get a new sequence. What is the 2003rd term of this new sequence?",
"role": "user"
}
] | Remove all perfect squares from the sequence of positive integers \(1, 2, 3, \cdots\) to get a new sequence. What is the 2003rd term of this new sequence? | "[\"2048\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108603, "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:118515"}] | {
"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"
] | a3f7b892434103d7e05f1ed2ffd4000a4b993e7ba9ca305d6ecd87bdd9b718ec | [
{
"content": "Given a function $f(x)$ defined on $R$ such that $f(2x+2)=-f(2x)$. If $f(x)=4x+3$ when $x\\in(\\frac{1}{2},\\frac{5}{4})$, then $f(2023)=\\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | Given a function $f(x)$ defined on $R$ such that $f(2x+2)=-f(2x)$. If $f(x)=4x+3$ when $x\in(\frac{1}{2},\frac{5}{4})$, then $f(2023)=\_\_\_\_\_\_$. | "[\"-7\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108586, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118516"}] | {
"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
} |
[
"783"
] | [
"skywork"
] | b57422c99019007b784f2abe383880382b3945ccb99bc7f256ca9d1ba220ab11 | [
{
"content": "What is the smallest multiple of 29 whose last two digits in base 10 are 29 and whose sum of digits is 29?",
"role": "user"
}
] | What is the smallest multiple of 29 whose last two digits in base 10 are 29 and whose sum of digits is 29? | "[\"783\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108607, "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:118517"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"40"
] | [
"skywork"
] | 5d3221e9dfd3e9fef42cb0e8593fe5a198f118c9816c8f03bf051c481819ac7b | [
{
"content": "39. Find a two-digit number that has the following properties:\n\na) if the desired number is multiplied by 2 and 1 is added to the product, the result is a perfect square;\n\nb) if the desired number is multiplied by 3 and 1 is added to the product, the result is a perfect square.",
"role": "... | 39. Find a two-digit number that has the following properties:
a) if the desired number is multiplied by 2 and 1 is added to the product, the result is a perfect square;
b) if the desired number is multiplied by 3 and 1 is added to the product, the result is a perfect square. | "[\"40\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108593, "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:118518"}] | {
"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
} |
[
"125"
] | [
"skywork"
] | d0e466d4aafc1cba12c6f1433083c26a90d067d37822e7feb4dd7e060732b1ab | [
{
"content": "One dimension of a cube is increased by $1$, another is decreased by $1$, and the third is left unchanged. The volume of the new rectangular solid is $5$ less than that of the cube. What was the volume of the cube?",
"role": "user"
}
] | One dimension of a cube is increased by $1$, another is decreased by $1$, and the third is left unchanged. The volume of the new rectangular solid is $5$ less than that of the cube. What was the volume of the cube? | "[\"125\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108602, "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:118519"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | 6451eb8ce472870a60939ec15baf871ab0302f03718477291890a0df840c3ba5 | [
{
"content": "What is the value of $\\sqrt{3! \\cdot 3!}$ expressed as a positive integer?",
"role": "user"
}
] | What is the value of $\sqrt{3! \cdot 3!}$ expressed as a positive integer? | "[\"6\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108612, "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:118520"}] | {
"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
} |
[
"34999"
] | [
"skywork"
] | 98cf00b0c5d836fd128e51b867d73f3a0878feafdf1497ecce2945bb8758f19d | [
{
"content": "Let $S = \\{10^n + 1000: n = 0, 1, \\dots\\}$. Compute the largest positive integer not expressible as the sum of (not necessarily distinct) elements of $S$.\n\n[i]Proposed by Ankan Bhattacharya[/i]",
"role": "user"
}
] | Let $S = \{10^n + 1000: n = 0, 1, \dots\}$. Compute the largest positive integer not expressible as the sum of (not necessarily distinct) elements of $S$.
[i]Proposed by Ankan Bhattacharya[/i] | "[\"34999\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108598, "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:118521"}] | {
"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
} |
[
"33"
] | [
"skywork"
] | 0b31c2ec87ea4435cd744cae82d79cdf9606eb49b12d87658fc6fa38ace39f23 | [
{
"content": "Example 2. Find the smallest positive integer $n$, such that in any 9-vertex and $n$-edge graph with edges colored in two colors, there must exist a monochromatic triangle.\n(33rd IMO, Problem 3)",
"role": "user"
}
] | Example 2. Find the smallest positive integer $n$, such that in any 9-vertex and $n$-edge graph with edges colored in two colors, there must exist a monochromatic triangle.
(33rd IMO, Problem 3) | "[\"33\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108605, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:118522"}] | {
"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"
] | 5132064a0d1351045f3b39ac22c90b9fd59559b6c083e6344e02b7971ac2660e | [
{
"content": "Given the function $f(x)=-\\frac{1}{3}x^{3}+bx^{2}+cx+bc$ has an extreme value of $-\\frac{4}{3}$ at $x=1$, find the value of $b$.",
"role": "user"
}
] | Given the function $f(x)=-\frac{1}{3}x^{3}+bx^{2}+cx+bc$ has an extreme value of $-\frac{4}{3}$ at $x=1$, find the value of $b$. | "[\"-1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108590, "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:118523"}] | {
"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"
] | 53ba63058fe02713c36095c0090282886a5f9110d39d3ca6ba8c5c534b071505 | [
{
"content": "Given a regular hexagon, a circle is drawn circumscribing it and another circle is drawn inscribing it. The ratio of the area of the larger circle to the area of the smaller circle can be written in the form $\\frac{m}{n}$ , where m and n are relatively prime positive integers. Compute $m + n$.",
... | Given a regular hexagon, a circle is drawn circumscribing it and another circle is drawn inscribing it. The ratio of the area of the larger circle to the area of the smaller circle can be written in the form $\frac{m}{n}$ , where m and n are relatively prime positive integers. Compute $m + n$. | "[\" 7 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108599, "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:118524"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"28"
] | [
"skywork"
] | 8c84d3a09411a752517685bbe36b9c43bbc5c36e972981d45c51ee831eac1752 | [
{
"content": "There are 2021 balls in a crate, numbered from 1 to 2021. Erica calculates the digit sum for each ball. For example, the digit sum of 2021 is 5, since \\(2+0+2+1=5\\). Balls with equal digit sums have the same color and balls with different digit sums have different colors. How many different colo... | There are 2021 balls in a crate, numbered from 1 to 2021. Erica calculates the digit sum for each ball. For example, the digit sum of 2021 is 5, since \(2+0+2+1=5\). Balls with equal digit sums have the same color and balls with different digit sums have different colors. How many different colors of balls are there in... | "[\"28\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108589, "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:118525"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{3}"
] | [
"skywork"
] | c58f50f6f6d256c4e38514757577e2a67ce421cfc84f2487aa01a95957291641 | [
{
"content": "9. [6] Segments $A A^{\\prime}, B B^{\\prime}$, and $C C^{\\prime}$, each of length 2, all intersect at a point $O$. If $\\angle A O C^{\\prime}=\\angle B O A^{\\prime}=$ $\\angle C O B^{\\prime}=60^{\\circ}$, find the maximum possible value of the sum of the areas of triangles $A O C^{\\prime}, B... | 9. [6] Segments $A A^{\prime}, B B^{\prime}$, and $C C^{\prime}$, each of length 2, all intersect at a point $O$. If $\angle A O C^{\prime}=\angle B O A^{\prime}=$ $\angle C O B^{\prime}=60^{\circ}$, find the maximum possible value of the sum of the areas of triangles $A O C^{\prime}, B O A^{\prime}$, and $C O B^{\prim... | "[\"\\\\sqrt{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108592, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118526"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"16"
] | [
"skywork"
] | 7d8534c2c596ad7813c141aea6323a03a3fbd6f3bb66fb21b2aa2b6840aca0df | [
{
"content": "9. The lateral face of a regular triangular pyramid $S A B C$ is inclined to the base plane $A B C$ at an angle $\\alpha=\\operatorname{arctg} \\frac{3}{4}$. Points $M, N, K$ are the midpoints of the sides of the base $A B C$. Triangle $M N K$ is the lower base of a right prism. The edges of the u... | 9. The lateral face of a regular triangular pyramid $S A B C$ is inclined to the base plane $A B C$ at an angle $\alpha=\operatorname{arctg} \frac{3}{4}$. Points $M, N, K$ are the midpoints of the sides of the base $A B C$. Triangle $M N K$ is the lower base of a right prism. The edges of the upper base of the prism in... | "[\"16\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108600, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118527"}] | {
"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
} |
[
"388"
] | [
"skywork"
] | d2862daa6478d3390911a0e20d6e7b01a363d815d3a6fcb2e80cb551d895e260 | [
{
"content": "Example 7. (IMO-20-3)\nLet $f, g: Z^{+} \\rightarrow Z^{+}$ be strictly increasing functions, and $f\\left(Z^{+}\\right) \\cup g\\left(Z^{+}\\right)=Z^{+}, f\\left(Z^{+}\\right) \\cap g\\left(Z^{+}\\right)=\\phi$, $g(n)=f[f(n)]+1$. Find $f(240)$. Here $Z^{+}$ is the set of positive integers.",
... | Example 7. (IMO-20-3)
Let $f, g: Z^{+} \rightarrow Z^{+}$ be strictly increasing functions, and $f\left(Z^{+}\right) \cup g\left(Z^{+}\right)=Z^{+}, f\left(Z^{+}\right) \cap g\left(Z^{+}\right)=\phi$, $g(n)=f[f(n)]+1$. Find $f(240)$. Here $Z^{+}$ is the set of positive integers. | "[\"388\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108591, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:118528"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"13"
] | [
"skywork"
] | 319a32a59e6fba9eb32c3c3303b76af5e3d347d5c81b5a1f77f12fad0a478ab9 | [
{
"content": "Given an ellipse $C$: $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 (a > b > 0)$, where the upper vertex of $C$ is $A$, and the two foci are $F_{1}$ and $F_{2}$, with an eccentricity of $\\frac{1}{2}$. A line passing through $F_{1}$ and perpendicular to $AF_{2}$ intersects $C$ at points $D$ and $E$, wh... | Given an ellipse $C$: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$, where the upper vertex of $C$ is $A$, and the two foci are $F_{1}$ and $F_{2}$, with an eccentricity of $\frac{1}{2}$. A line passing through $F_{1}$ and perpendicular to $AF_{2}$ intersects $C$ at points $D$ and $E$, where $|DE| = 6$. Find the ... | "[\"13\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108585, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118530"}] | {
"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{18 \\sqrt{7}}{7}"
] | [
"skywork"
] | 762d6055dfb337fe2708dad6e1a47326e007c777055e1721febe1749ff718ad4 | [
{
"content": "16. Through the center $O$ of the equilateral $\\triangle A B C$, draw a line intersecting $A B$ and $A C$ at points $D$ and $E$ respectively. If $D O=3, C E=2$, then the side length of the equilateral triangle is $\\qquad$ .",
"role": "user"
}
] | 16. Through the center $O$ of the equilateral $\triangle A B C$, draw a line intersecting $A B$ and $A C$ at points $D$ and $E$ respectively. If $D O=3, C E=2$, then the side length of the equilateral triangle is $\qquad$ . | "[\"\\\\frac{18 \\\\sqrt{7}}{7}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 108615, "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:118531"}] | {
"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
} |
[
"8"
] | [
"skywork"
] | 293a51c6ad1ea67d8a143c0731ece1b555db089c2f1aa5e9e106950e154a707b | [
{
"content": "10. Determine the units digit of $(2!+2)(3!+3)(4!+2)(5!+3) \\cdots(2018!+2)(2019!+3)$.",
"role": "user"
}
] | 10. Determine the units digit of $(2!+2)(3!+3)(4!+2)(5!+3) \cdots(2018!+2)(2019!+3)$. | "[\"8\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108618, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118532"}] | {
"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
} |
[
"675"
] | [
"skywork"
] | b70d28399acf92d7ed1a567512b53fde92755f3a0cabaad18cccc62ae254b832 | [
{
"content": "2. 47 If $a<b<c<d<e$ are consecutive positive integers, $b+c+d$ is a perfect square, and $a+b+c+d+e$ is a perfect cube, what is the minimum value of $c$?",
"role": "user"
}
] | 2. 47 If $a<b<c<d<e$ are consecutive positive integers, $b+c+d$ is a perfect square, and $a+b+c+d+e$ is a perfect cube, what is the minimum value of $c$? | "[\"675\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108619, "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:118533"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"skywork"
] | 8838d7ae52547206a2c1e893c92217a476e9aeb06bde1af8f8b93f3000019d65 | [
{
"content": "For each permutation $(a_1,a_2,\\dots,a_{11})$ of the numbers $1,2,3,4,5,6,7,8,9,10,11$, we can determine at least $k$ of $a_i$s when we get $(a_1+a_3, a_2+a_4,a_3+a_5,\\dots,a_8+a_{10},a_9+a_{11})$. $k$ can be at most ?\n\n$ \\textbf{(A)}\\ 11 \\qquad \\textbf{(B)}\\ 6 \\qquad \\textbf{(C)}\\ 5 \... | For each permutation $(a_1,a_2,\dots,a_{11})$ of the numbers $1,2,3,4,5,6,7,8,9,10,11$, we can determine at least $k$ of $a_i$s when we get $(a_1+a_3, a_2+a_4,a_3+a_5,\dots,a_8+a_{10},a_9+a_{11})$. $k$ can be at most ?
$ \textbf{(A)}\ 11 \qquad \textbf{(B)}\ 6 \qquad \textbf{(C)}\ 5 \qquad \textbf{(D)}\ 2 \qquad \text... | "[\"5\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108604, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118534"}] | {
"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
} |
[
"\\angle B=80^{\\circ},\\angle C=40^{\\circ}"
] | [
"skywork"
] | 1cd03d0e844e28de1566308d15a79ccde49e4edb96f23a0da625220e8e36b04a | [
{
"content": "Let $ABC$ be a triangle with $\\angle BAC = 60^{\\circ}$. Let $AP$ bisect $\\angle BAC$ and let $BQ$ bisect $\\angle ABC$, with $P$ on $BC$ and $Q$ on $AC$. If $AB + BP = AQ + QB$, what are the angles of the triangle?",
"role": "user"
}
] | Let $ABC$ be a triangle with $\angle BAC = 60^{\circ}$. Let $AP$ bisect $\angle BAC$ and let $BQ$ bisect $\angle ABC$, with $P$ on $BC$ and $Q$ on $AC$. If $AB + BP = AQ + QB$, what are the angles of the triangle? | "[\"\\\\angle B=80^{\\\\circ},\\\\angle C=40^{\\\\circ}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108584, "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:118535"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 12f2bc94aa7594d485486fd867d7f88e3c8cd3dac13bf7be6fd73326fe9bcad1 | [
{
"content": "$100$ stones, each weighs $1$ kg or $10$ kgs or $50$ kgs, weighs $500$ kgs in total. How many values can the number of stones weighing $10$ kgs take?\n\n$ \n\\textbf{(A)}\\ 0\n\\qquad\\textbf{(B)}\\ 1\n\\qquad\\textbf{(C)}\\ 2\n\\qquad\\textbf{(D)}\\ 3\n\\qquad\\textbf{(E)}\\ 4\n$",
"role": "u... | $100$ stones, each weighs $1$ kg or $10$ kgs or $50$ kgs, weighs $500$ kgs in total. How many values can the number of stones weighing $10$ kgs take?
$
\textbf{(A)}\ 0
\qquad\textbf{(B)}\ 1
\qquad\textbf{(C)}\ 2
\qquad\textbf{(D)}\ 3
\qquad\textbf{(E)}\ 4
$ | "[\"1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 108620, "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:118536"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2880"
] | [
"skywork"
] | b9095a184c65cfaf7813d3265c8398d9ce1f5f741088588fb559b160710caeac | [
{
"content": "In how many ways can you arrange 4 different math books and 6 different history books on a shelf if you require there to be a math book on both ends, and additionally, the books must alternate between math and history books starting with a math book?",
"role": "user"
}
] | In how many ways can you arrange 4 different math books and 6 different history books on a shelf if you require there to be a math book on both ends, and additionally, the books must alternate between math and history books starting with a math book? | "[\"2880\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 108624, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118537"}] | {
"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
} |
[
"\\arcsin\\frac{1}{k}\\sqrt{\\frac{1+\\sqrt{1+4k^2}}{2}},\\pi-\\arcsin\\frac{1}{k}\\sqrt{\\frac{1+\\sqrt{1+4k^2}}{2}}"
] | [
"skywork"
] | 0ce2ca8619140f1fb6be4456309fbe9a6624ad20913a963dcd625240fef3dce5 | [
{
"content": "12.403 The ratio of the radius of the circle circumscribed around a trapezoid to the radius of the circle inscribed in it is $\\boldsymbol{k}$. Find the angles of the trapezoid and the permissible values of $k$.",
"role": "user"
}
] | 12.403 The ratio of the radius of the circle circumscribed around a trapezoid to the radius of the circle inscribed in it is $\boldsymbol{k}$. Find the angles of the trapezoid and the permissible values of $k$. | "[\"\\\\arcsin\\\\frac{1}{k}\\\\sqrt{\\\\frac{1+\\\\sqrt{1+4k^2}}{2}},\\\\pi-\\\\arcsin\\\\frac{1}{k}\\\\sqrt{\\\\frac{1+\\\\sqrt{1+4k^2}}{2}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108611, "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:118538"}] | {
"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
} |
[
"-101"
] | [
"skywork"
] | 47508f43cbade2152a206a26b7ac165e8f9160792d14080dda7e7aff4fa63539 | [
{
"content": "The product of two consecutive negative integers is 2550. What is the sum of the two integers?",
"role": "user"
}
] | The product of two consecutive negative integers is 2550. What is the sum of the two integers? | "[\"-101\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108633, "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:118539"}] | {
"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{5}{4}"
] | [
"skywork"
] | 63f0aadcd534e659b42549ef24e9a50b2e5aa9eaa0df8ada7382292f3a5a7aef | [
{
"content": "The real numbers $a,$ $b,$ $c,$ and $d$ satisfy\n\\[a^2 + b^2 + c^2 + 1 = d + \\sqrt{a + b + c - d}.\\]Find $d.$",
"role": "user"
}
] | The real numbers $a,$ $b,$ $c,$ and $d$ satisfy
\[a^2 + b^2 + c^2 + 1 = d + \sqrt{a + b + c - d}.\]Find $d.$ | "[\"\\\\frac{5}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108625, "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:118540"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | 4d51a6a57fa733756b4bfd00f7714d6dd4d66b7ba3bf9e65213bce7290da8ae3 | [
{
"content": "When a positive integer $N$ is divided by 60 , the remainder is 49 . When $N$ is divided by 15 , the remainder is\n(A) 0\n(B) 3\n(C) 4\n(D) 5\n(E) 8\n\n## Part B: Each correct answer is worth 6.",
"role": "user"
}
] | When a positive integer $N$ is divided by 60 , the remainder is 49 . When $N$ is divided by 15 , the remainder is
(A) 0
(B) 3
(C) 4
(D) 5
(E) 8
## Part B: Each correct answer is worth 6. | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108621, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118543"}] | {
"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
} |
[
"2B"
] | [
"skywork"
] | 5160e265441396653dab5fc4a55cd889c0725aabb5775a4989b7bc6e8dd675b1 | [
{
"content": "Let $f(x) = Ax - 2B^2$ and $g(x) = Bx$, where $B \\neq 0$. If $f(g(1)) = 0$, what is $A$ in terms of $B$?",
"role": "user"
}
] | Let $f(x) = Ax - 2B^2$ and $g(x) = Bx$, where $B \neq 0$. If $f(g(1)) = 0$, what is $A$ in terms of $B$? | "[\"2B\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108631, "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:118544"}] | {
"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"
] | 3ae7e6cdb85f1cbe594378fc5f1cb30523ce0da6268362ede15ed3ee076d16e8 | [
{
"content": "7.2. A car, moving at a constant speed, traveled from point A to point B in 3 hours. To reduce the travel time on the return trip, the driver left point B at a speed 25% higher, and upon reaching the midpoint of the journey between A and B, increased the speed by another 20%. How long will the ret... | 7.2. A car, moving at a constant speed, traveled from point A to point B in 3 hours. To reduce the travel time on the return trip, the driver left point B at a speed 25% higher, and upon reaching the midpoint of the journey between A and B, increased the speed by another 20%. How long will the return trip take? | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108617, "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:118545"}] | {
"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
} |
[
"127"
] | [
"skywork"
] | e39999a580aee84e0a1b270fd370a1f8d130e01966e124de809d6e757f2c22dc | [
{
"content": "4. Bear Big and Bear Small have a tree planting competition, within three days, whoever plants more trees wins. On the first day, Bear Big planted 8 more trees than Bear Small, on the second day, Bear Small planted 12 more trees than Bear Big. On the third day, Bear Big planted 130 trees, Bear Sma... | 4. Bear Big and Bear Small have a tree planting competition, within three days, whoever plants more trees wins. On the first day, Bear Big planted 8 more trees than Bear Small, on the second day, Bear Small planted 12 more trees than Bear Big. On the third day, Bear Big planted 130 trees, Bear Small needs to plant at l... | "[\"127\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108596, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:118547"}] | {
"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{2}{5}"
] | [
"skywork"
] | c4c3217d49b0c83e89b0e37c1a2c0ad2b73675651f89a4d19c8f5c6c872c79e7 | [
{
"content": "Calculate the limit\n\n$$\n\\lim _{x \\rightarrow 0}\\left(\\frac{1+x^{2} 2^{x}}{1+x^{2} 5^{x}}\\right)^{1 / \\sin ^{3} x}\n$$",
"role": "user"
}
] | Calculate the limit
$$
\lim _{x \rightarrow 0}\left(\frac{1+x^{2} 2^{x}}{1+x^{2} 5^{x}}\right)^{1 / \sin ^{3} x}
$$ | "[\"\\\\frac{2}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 108639, "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:118548"}] | {
"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{25}{6}"
] | [
"skywork"
] | 52229c529db46f88400566e3320aced5883af8b1371c035d97a0b50cace57623 | [
{
"content": "7. Given a triangle $ABC$. On side $AC$, a point $Q$ is chosen in such a way that the length of the segment $MK$, where $M$ and $K$ are the feet of the perpendiculars dropped from point $Q$ to sides $AB$ and $BC$ respectively, is minimized. In this case, $QM=1$, $QK=\\sqrt{2}$, and $\\angle B=45^{... | 7. Given a triangle $ABC$. On side $AC$, a point $Q$ is chosen in such a way that the length of the segment $MK$, where $M$ and $K$ are the feet of the perpendiculars dropped from point $Q$ to sides $AB$ and $BC$ respectively, is minimized. In this case, $QM=1$, $QK=\sqrt{2}$, and $\angle B=45^{0}$. Find the area of tr... | "[\"\\\\frac{25}{6}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 108608, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:118549"}] | {
"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
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.