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 |
|---|---|---|---|---|---|---|---|---|
[
"95"
] | [
"skywork"
] | d3f4e28a9f2448ab8ead8527ff3d4c65108c7bd53458004f7de3432b2bc8f2ab | [
{
"content": "In the figure, $\\angle A$, $\\angle B$, and $\\angle C$ are right angles. If $\\angle AEB = 40^\\circ$ and $\\angle BED = \\angle BDE$, then $\\angle CDE =$\n\n$\\text{(A)}\\ 75^\\circ \\qquad \\text{(B)}\\ 80^\\circ \\qquad \\text{(C)}\\ 85^\\circ \\qquad \\text{(D)}\\ 90^\\circ \\qquad \\text{... | In the figure, $\angle A$, $\angle B$, and $\angle C$ are right angles. If $\angle AEB = 40^\circ$ and $\angle BED = \angle BDE$, then $\angle CDE =$
$\text{(A)}\ 75^\circ \qquad \text{(B)}\ 80^\circ \qquad \text{(C)}\ 85^\circ \qquad \text{(D)}\ 90^\circ \qquad \text{(E)}\ 95^\circ$ | "[\"95\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 1616, "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:15604"}] | {
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} |
[
"2025"
] | [
"skywork"
] | 8888e33045b79680d615b4d37080977a6b5ef7946af87beaba9932dc0cef5085 | [
{
"content": "A square has been divided into $2022$ rectangles with no two of them having a common interior point. What is the maximal number of distinct lines that can be determined by the sides of these rectangles?",
"role": "user"
}
] | A square has been divided into $2022$ rectangles with no two of them having a common interior point. What is the maximal number of distinct lines that can be determined by the sides of these rectangles? | "[\"2025\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1610, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15605"}, {"dataset": "skywork", "extra_inf... | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1, 2, 3"
] | [
"skywork"
] | ea80b43ade432a43aa6d4eb08b10495db5c77e527ed1feb12b82f91865b7fba2 | [
{
"content": "Example 1 Find all non-right triangles $ABC$ such that\n$$\n\\begin{array}{l}\n\\tan A \\cdot \\tan B \\cdot \\tan C \\\\\n\\leqslant[\\tan A]+[\\tan B]+[\\tan C],\n\\end{array}\n$$\n\nwhere $[x]$ denotes the greatest integer not exceeding the real number $x$. (2009, Nanjing University Independent... | Example 1 Find all non-right triangles $ABC$ such that
$$
\begin{array}{l}
\tan A \cdot \tan B \cdot \tan C \\
\leqslant[\tan A]+[\tan B]+[\tan C],
\end{array}
$$
where $[x]$ denotes the greatest integer not exceeding the real number $x$. (2009, Nanjing University Independent Admission Examination) | "[\"1, 2, 3\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1609, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15606"}] | {
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} |
[
"1061_{9}"
] | [
"skywork"
] | 8a9666b570a596e214427f8a432398b0de7f265c2c33c47b45fe51fae20dc5c6 | [
{
"content": "Add $175_{9} + 714_{9} + 61_9$. Express your answer in base $9$.",
"role": "user"
}
] | Add $175_{9} + 714_{9} + 61_9$. Express your answer in base $9$. | "[\"1061_{9}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1643, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15607"}] | {
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"label_correctness_independently_verified": false,
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} |
[
"50"
] | [
"skywork"
] | 7da633b41d02a85a9dc538586c5411006b3ee2e43600f01944175835c9983395 | [
{
"content": "Given $a \\in \\mathbb{R}$, the function $f(x) = ax^3 - 3x^2$, and $x = 2$ is an extreme point of the function $y = f(x)$.\n\n1. Find the value of $a$.\n2. Find the extreme values of the function $f(x)$ in the interval $[-1, 5]$.",
"role": "user"
}
] | Given $a \in \mathbb{R}$, the function $f(x) = ax^3 - 3x^2$, and $x = 2$ is an extreme point of the function $y = f(x)$.
1. Find the value of $a$.
2. Find the extreme values of the function $f(x)$ in the interval $[-1, 5]$. | "[\"50\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1563, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15608"}] | {
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} |
[
"5\\leqslantx\\leqslant10"
] | [
"skywork"
] | a9df11ef495e4a7685264cd69532cc24143a91c8421a51aa836c2c6e42afc836 | [
{
"content": "2.14. Solve the equation\n\n$$\n\\sqrt{x+3-4 \\sqrt{x-1}}+\\sqrt{x+8-6 \\sqrt{x-1}}=1\n$$",
"role": "user"
}
] | 2.14. Solve the equation
$$
\sqrt{x+3-4 \sqrt{x-1}}+\sqrt{x+8-6 \sqrt{x-1}}=1
$$ | "[\"5\\\\leqslantx\\\\leqslant10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1633, "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:15609"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"539"
] | [
"skywork"
] | a3cd18c00909e83788998c4cacfd8b17ab9038e3b54c1c2d6ce49aca32a16c3d | [
{
"content": "The formula for converting a Fahrenheit temperature $F$ to the corresponding Celsius temperature $C$ is $C = \\frac{5}{9}(F-32).$ An integer Fahrenheit temperature is converted to Celsius, rounded to the nearest integer, converted back to Fahrenheit, and again rounded to the nearest integer. For h... | The formula for converting a Fahrenheit temperature $F$ to the corresponding Celsius temperature $C$ is $C = \frac{5}{9}(F-32).$ An integer Fahrenheit temperature is converted to Celsius, rounded to the nearest integer, converted back to Fahrenheit, and again rounded to the nearest integer. For how many integer Fahrenh... | "[\"539\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 1621, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15610"}, {"dataset": "skywork", "extra_i... | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"skywork"
] | a3d9a3e5c47e0b9ed3ec55e46e84b1adad322bf32ea2eba02b87b4e80f236260 | [
{
"content": "What is $(3+3+5)\\div2 - 1\\div2$ in simplest terms?",
"role": "user"
}
] | What is $(3+3+5)\div2 - 1\div2$ in simplest terms? | "[\"5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1642, "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:15611"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3\\mathrm{~}"
] | [
"skywork"
] | 9b29443caef624aba0db1ef92df656ffe6c250f5b5e8d24e8295f47dddcf6c3b | [
{
"content": "18. The total weight of a box, 20 plates and 30 cups is $4.8 \\mathrm{~kg}$. The total weight of the box, 40 plates and 50 cups is $8.4 \\mathrm{~kg}$. What is the total weight of the box, 10 plates and 20 cups?\nA $3 \\mathrm{~kg}$\nB $3.2 \\mathrm{~kg}$\nC $3.6 \\mathrm{~kg}$\nD $4 \\mathrm{~kg}... | 18. The total weight of a box, 20 plates and 30 cups is $4.8 \mathrm{~kg}$. The total weight of the box, 40 plates and 50 cups is $8.4 \mathrm{~kg}$. What is the total weight of the box, 10 plates and 20 cups?
A $3 \mathrm{~kg}$
B $3.2 \mathrm{~kg}$
C $3.6 \mathrm{~kg}$
D $4 \mathrm{~kg}$
E $4.2 \mathrm{~kg}$ | "[\"3\\\\mathrm{~}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1637, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15612"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2}"
] | [
"skywork"
] | 4dfd55b48722e84bf7dc1b5c4ef9577417741bd5374b3b1cfa9d4bb36d61a939 | [
{
"content": "4. [8] Each segment with endpoints at the vertices of a regular 100-gon was painted - red if there is an even number of vertices between its endpoints, and blue otherwise (in particular, all sides of the 100-gon are red). Numbers were placed at the vertices, the sum of whose squares is 1, and on t... | 4. [8] Each segment with endpoints at the vertices of a regular 100-gon was painted - red if there is an even number of vertices between its endpoints, and blue otherwise (in particular, all sides of the 100-gon are red). Numbers were placed at the vertices, the sum of whose squares is 1, and on the segments - the prod... | "[\"\\\\frac{1}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1594, "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:15613"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\left( 0, \\frac{1}{4} \\right)"
] | [
"skywork"
] | 9d579e1e960cf396765e9ffeca474671220dfbd99f156c7b1f7aa9333dce8f5e | [
{
"content": "Find the focus of the the parabola $y = x^2.$",
"role": "user"
}
] | Find the focus of the the parabola $y = x^2.$ | "[\"\\\\left( 0, \\\\frac{1}{4} \\\\right)\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1597, "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:15614"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1653"
] | [
"skywork"
] | 2bebc7189c3910b94f5ac98cc6fe7fb57d2b44f1a96e44b947f7e8dbf6dee217 | [
{
"content": "3. What is the greatest value that the sum of the first $n$ terms of the arithmetic progression $113,109,105, \\ldots$ can take?\n\n#",
"role": "user"
}
] | 3. What is the greatest value that the sum of the first $n$ terms of the arithmetic progression $113,109,105, \ldots$ can take?
# | "[\"1653\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1626, "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:15615"}] | {
"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
} |
[
"a = 1"
] | [
"skywork"
] | fd27a0aa91238fccdb8184c48b23b9b46adb928042642fde422bef380b0b185a | [
{
"content": "a) Find at least two functions $f: \\mathbb{R}^+ \\rightarrow \\mathbb{R}^+$ such that $$\\displaystyle{2f(x^2)\\geq xf(x) + x,}$$ for all $x \\in \\mathbb{R}^+.$\n\nb) Let $f: \\mathbb{R}^+ \\rightarrow \\mathbb{R}^+$ be a function such that $$\\displaystyle{2f(x^2)\\geq xf(x) + x,}$$ for all $... | a) Find at least two functions $f: \mathbb{R}^+ \rightarrow \mathbb{R}^+$ such that $$\displaystyle{2f(x^2)\geq xf(x) + x,}$$ for all $x \in \mathbb{R}^+.$
b) Let $f: \mathbb{R}^+ \rightarrow \mathbb{R}^+$ be a function such that $$\displaystyle{2f(x^2)\geq xf(x) + x,}$$ for all $x \in \mathbb{R}^+.$ Show that $ f(... | "[\" a = 1 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1604, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15616"}] | {
"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
} |
[
"(-2,2)"
] | [
"skywork"
] | 18c05198c9ebc51e5c48ec66e57c601d0ddeafd2945d0bbd6f932d7542f3caf8 | [
{
"content": "Example 11. Find the domain of the function\n\n\\[\nf(x)=\\log \\left(4-x^{2}\\right)\n\\]",
"role": "user"
}
] | Example 11. Find the domain of the function
\[
f(x)=\log \left(4-x^{2}\right)
\] | "[\"(-2,2)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1635, "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:15617"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"S(n) = \\left\\lfloor \\frac{n}{2} \\right\\rfloor \\left\\lceil \\frac{n}{2} \\right\\rceil"
] | [
"skywork"
] | 2153c6f14d4b407283d50d0660cd726b76a1337a5ac77bae95e959ba39fa636d | [
{
"content": "Let $n$ be a fixed positive integer. To any choice of real numbers satisfying \\[0\\le x_{i}\\le 1,\\quad i=1,2,\\ldots, n,\\] there corresponds the sum \\[\\sum_{1\\le i<j\\le n}|x_{i}-x_{j}|.\\] Let $S(n)$ denote the largest possible value of this sum. Find $S(n)$.",
"role": "user"
}
] | Let $n$ be a fixed positive integer. To any choice of real numbers satisfying \[0\le x_{i}\le 1,\quad i=1,2,\ldots, n,\] there corresponds the sum \[\sum_{1\le i<j\le n}|x_{i}-x_{j}|.\] Let $S(n)$ denote the largest possible value of this sum. Find $S(n)$. | "[\"S(n) = \\\\left\\\\lfloor \\\\frac{n}{2} \\\\right\\\\rfloor \\\\left\\\\lceil \\\\frac{n}{2} \\\\right\\\\rceil\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1627, "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:15618"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"-\\frac{1}{2}"
] | [
"skywork"
] | f05d22abf4619a0b098f063bf7afcad95720b024a08bb4b9aa6d2a55261d0b9a | [
{
"content": "Given a sequence $\\{a_n\\}$ satisfying $a_1=1$, $a_2=3$, if $|a_{n+1}-a_n|=2^n$ $(n\\in\\mathbb{N}^*)$, and the sequence $\\{a_{2n-1}\\}$ is increasing while $\\{a_{2n}\\}$ is decreasing, then $\\lim\\limits_{n\\to\\infty} \\frac{a_{2n-1}}{a_{2n}}=$ ______.",
"role": "user"
}
] | Given a sequence $\{a_n\}$ satisfying $a_1=1$, $a_2=3$, if $|a_{n+1}-a_n|=2^n$ $(n\in\mathbb{N}^*)$, and the sequence $\{a_{2n-1}\}$ is increasing while $\{a_{2n}\}$ is decreasing, then $\lim\limits_{n\to\infty} \frac{a_{2n-1}}{a_{2n}}=$ ______. | "[\"-\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1624, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15619"}] | {
"all_reference_components_parse": true,
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"reference_components": 1,
"reference_present": true
} |
[
"m"
] | [
"skywork"
] | d23042c08b7a1619ab17616b11ebb8671e1240a94312185de5cfca1793dc869a | [
{
"content": "Find all positive integers $m$ with the next property:\nIf $d$ is a positive integer less or equal to $m$ and it isn't coprime to $m$ , then there exist positive integers $a_{1}, a_{2}$,. . ., $a_{2019}$ (where all of them are coprimes to $m$) such that\n$m+a_{1}d+a_{2}d^{2}+\\cdot \\cdot \\cdot+a... | Find all positive integers $m$ with the next property:
If $d$ is a positive integer less or equal to $m$ and it isn't coprime to $m$ , then there exist positive integers $a_{1}, a_{2}$,. . ., $a_{2019}$ (where all of them are coprimes to $m$) such that
$m+a_{1}d+a_{2}d^{2}+\cdot \cdot \cdot+a_{2019}d^{2019}$
is a perfe... | "[\" m \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1612, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15620"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"skywork"
] | e1c9175bb9611d36cee4cee5346affb0bfdd8c832c1a544dca90cb1af1cb1a12 | [
{
"content": "5. [5 points] Given the numbers $\\log _{\\left(\\frac{x}{2}-1\\right)^{2}}\\left(\\frac{x}{2}-\\frac{1}{4}\\right), \\log _{\\sqrt{x-\\frac{11}{4}}}\\left(\\frac{x}{2}-1\\right), \\log _{\\frac{x}{2}-\\frac{1}{4}}\\left(x-\\frac{11}{4}\\right)^{2}$. For which $x$ are two of these numbers equal, a... | 5. [5 points] Given the numbers $\log _{\left(\frac{x}{2}-1\right)^{2}}\left(\frac{x}{2}-\frac{1}{4}\right), \log _{\sqrt{x-\frac{11}{4}}}\left(\frac{x}{2}-1\right), \log _{\frac{x}{2}-\frac{1}{4}}\left(x-\frac{11}{4}\right)^{2}$. For which $x$ are two of these numbers equal, and the third one greater than them by 1? | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1615, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:15621"}] | {
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[
"7"
] | [
"skywork"
] | 87019ad90d15851607244e20b8d1403474a68f8658a9fe48b99c24139954fd71 | [
{
"content": "You are out walking and see a group of rhinoceroses (which each have two horns and four legs) and triceratopses (which each have three horns and four legs). If you count 31 horns and 48 legs, how many triceratopses are there?",
"role": "user"
}
] | You are out walking and see a group of rhinoceroses (which each have two horns and four legs) and triceratopses (which each have three horns and four legs). If you count 31 horns and 48 legs, how many triceratopses are there? | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1631, "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:15622"}] | {
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} |
[
"529"
] | [
"skywork"
] | 2a71de3d2f04496723d1b94daf5eb1e71eee6e56e38b6821d08286cfcaa2c9a3 | [
{
"content": "Suppose that $y = \\frac34x$ and $x^y = y^x$ . The quantity $x + y$ can be expressed as a rational number $\\frac {r}{s}$ , where $r$ and $s$ are relatively prime positive integers. Find $r + s$ .",
"role": "user"
}
] | Suppose that $y = \frac34x$ and $x^y = y^x$ . The quantity $x + y$ can be expressed as a rational number $\frac {r}{s}$ , where $r$ and $s$ are relatively prime positive integers. Find $r + s$ . | "[\"529\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 1625, "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:15623"}, {"dataset": "skywork", "extra_inf... | {
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[
"\\frac{1}{2}"
] | [
"skywork"
] | 808401836f88da4212efcc9c355fe48f38236dfcbea13b653b40686b80b8a4ff | [
{
"content": "If $\\mathbf{a}$ and $\\mathbf{b}$ are two unit vectors with an angle of $\\frac{\\pi}{4}$ between them, compute the volume of the parallelepiped generated by $\\mathbf{a},$ $\\mathbf{a} + \\mathbf{b} \\times \\mathbf{a},$ and $\\mathbf{b}.$",
"role": "user"
}
] | If $\mathbf{a}$ and $\mathbf{b}$ are two unit vectors with an angle of $\frac{\pi}{4}$ between them, compute the volume of the parallelepiped generated by $\mathbf{a},$ $\mathbf{a} + \mathbf{b} \times \mathbf{a},$ and $\mathbf{b}.$ | "[\"\\\\frac{1}{2}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1629, "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:15624"}] | {
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} |
[
"2<x<5 \\text{ or } x<-3"
] | [
"skywork"
] | b5d94a5dd80fefbd387928511da3288b64224c91b24136611af7bdec06d23449 | [
{
"content": "2. Solve the inequality $\\frac{x^{2}-2 x-15}{x-2}<0$ ,",
"role": "user"
}
] | 2. Solve the inequality $\frac{x^{2}-2 x-15}{x-2}<0$ , | "[\"2<x<5 \\\\text{ or } x<-3\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1639, "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:15625"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"29"
] | [
"skywork"
] | fb5aac69f89f1af9e6014aba6a329b7b5007da5869d07ae7bf381d12b7ce4282 | [
{
"content": "1. Among the triangles with side lengths being consecutive natural numbers and a perimeter not exceeding 100, the number of acute triangles is $\\qquad$ .",
"role": "user"
}
] | 1. Among the triangles with side lengths being consecutive natural numbers and a perimeter not exceeding 100, the number of acute triangles is $\qquad$ . | "[\"29\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1636, "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:15626"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\alpha+\\beta=2"
] | [
"skywork"
] | e9c38cbc1fe56b527361408a6300ae3fd296bf7e8629e1e4d9e298efe1411269 | [
{
"content": "$4 \\cdot 103$ real numbers $\\alpha, \\beta$ satisfy the system of equations\n$$\n\\left\\{\\begin{array}{l}\n\\alpha^{3}-3 \\alpha^{2}+5 \\alpha-17=0 \\\\\n\\beta^{3}-3 \\beta^{2}+5 \\beta+11=0 .\n\\end{array}\\right.\n$$\n\nFind $\\alpha+\\beta$.",
"role": "user"
}
] | $4 \cdot 103$ real numbers $\alpha, \beta$ satisfy the system of equations
$$
\left\{\begin{array}{l}
\alpha^{3}-3 \alpha^{2}+5 \alpha-17=0 \\
\beta^{3}-3 \beta^{2}+5 \beta+11=0 .
\end{array}\right.
$$
Find $\alpha+\beta$. | "[\"\\\\alpha+\\\\beta=2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1630, "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:15627"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"12"
] | [
"skywork"
] | 534399029f9fcc0cb7e5de68babd730878769b12d4cce842fca47608d150dee2 | [
{
"content": "6. Given that the three sides of triangle $A B C$ are all positive integers, if $\\angle A=2 \\angle B$, and $C A=9$, then the minimum possible value of $B C$ is $\\qquad$ .",
"role": "user"
}
] | 6. Given that the three sides of triangle $A B C$ are all positive integers, if $\angle A=2 \angle B$, and $C A=9$, then the minimum possible value of $B C$ is $\qquad$ . | "[\"12\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1638, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15628"}] | {
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} |
[
"3124"
] | [
"skywork"
] | e55a36b866b401359d1a51072de75dcbbe0d086736e2f386964e8e42ffabe51d | [
{
"content": "What is the greatest integer less than or equal to \\[\\frac{5^{80} + 3^{80}}{5^{75} + 3^{75}}?\\]",
"role": "user"
}
] | What is the greatest integer less than or equal to \[\frac{5^{80} + 3^{80}}{5^{75} + 3^{75}}?\] | "[\"3124\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1655, "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:15629"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3\\pi}{8}"
] | [
"skywork"
] | 49d15552cfd3d7734880df923eb6f66b5d0bc4db8415001cf58cdca4ab69e869 | [
{
"content": "Given the function $f(x) = 2\\sin x\\cos x - 2\\sin^2 x + 1$, determine the smallest positive value of $\\varphi$ such that the graph of $f(x)$ shifted to the right by $\\varphi$ units is symmetric about the y-axis.",
"role": "user"
}
] | Given the function $f(x) = 2\sin x\cos x - 2\sin^2 x + 1$, determine the smallest positive value of $\varphi$ such that the graph of $f(x)$ shifted to the right by $\varphi$ units is symmetric about the y-axis. | "[\"\\\\frac{3\\\\pi}{8}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1632, "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:15630"}] | {
"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"
] | 8f4ad0bc6b7a9472767b420c3dc581eebf9776c1494910efa68eee6bc4941c2e | [
{
"content": "5. Given real numbers $x, y$ satisfy $x+y=1$. Then, the maximum value of $\\left(x^{3}+1\\right)\\left(y^{3}+1\\right)$ is",
"role": "user"
}
] | 5. Given real numbers $x, y$ satisfy $x+y=1$. Then, the maximum value of $\left(x^{3}+1\right)\left(y^{3}+1\right)$ is | "[\"4\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1640, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15631"}, {"dataset": "skywork", "extra_inf... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{8\\sqrt{3}}{3}"
] | [
"skywork"
] | 4f14db9cd2a9a4f93c765444ca3ba4f0bf5e331cf2126e55daff086e0a527ed9 | [
{
"content": "Given triangle $\\triangle ABC$, $A=120^{\\circ}$, $D$ is a point on side $BC$, $AD\\bot AC$, and $AD=2$. Calculate the possible area of $\\triangle ABC$.",
"role": "user"
}
] | Given triangle $\triangle ABC$, $A=120^{\circ}$, $D$ is a point on side $BC$, $AD\bot AC$, and $AD=2$. Calculate the possible area of $\triangle ABC$. | "[\"\\\\frac{8\\\\sqrt{3}}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1622, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15632"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3\\pi}{2}"
] | [
"skywork"
] | e6fd22773bc5c5b6c21a47feb283f60f1638533008898dc9a7cf61c1c77ca3ff | [
{
"content": "If the function $f(x)=\\sin \\left( \\frac{x+\\varphi}{3}\\right)$ is an even function, determine the value of $\\varphi$.",
"role": "user"
}
] | If the function $f(x)=\sin \left( \frac{x+\varphi}{3}\right)$ is an even function, determine the value of $\varphi$. | "[\"\\\\frac{3\\\\pi}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1634, "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:15633"}] | {
"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
} |
[
"1080"
] | [
"skywork"
] | 3c2a92cf0614bdf78062599ea96ce91e460a89819332cae2d5919581c0c65f67 | [
{
"content": "(Answer in numbers) \nFrom 5 different storybooks and 4 different math books, 4 books are to be selected and given to 4 students, one book per student. How many different ways are there to: \n(1) Select 2 storybooks and 2 math books? \n(2) Ensure one specific storybook and one specific math boo... | (Answer in numbers)
From 5 different storybooks and 4 different math books, 4 books are to be selected and given to 4 students, one book per student. How many different ways are there to:
(1) Select 2 storybooks and 2 math books?
(2) Ensure one specific storybook and one specific math book are among the selected?... | "[\"1080\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1606, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:15634"}] | {
"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, \\infty)"
] | [
"skywork"
] | ec09501083061c9308447c9071bea4c083cb01b9dbf3bce385cd82de19472424 | [
{
"content": "Determine all sets of real numbers $S$ such that:\n\n[list]\n[*] $1$ is the smallest element of $S$,\n[*] for all $x,y\\in S$ such that $x>y$, $\\sqrt{x^2-y^2}\\in S$\n[/list]",
"role": "user"
}
] | Determine all sets of real numbers $S$ such that:
[list]
[*] $1$ is the smallest element of $S$,
[*] for all $x,y\in S$ such that $x>y$, $\sqrt{x^2-y^2}\in S$
[/list] | "[\"[1, \\\\infty)\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 1648, "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:15635"}] | {
"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"
] | [
"skywork"
] | 38dbfe4cb35dd605e2d8fc76cf4618bbfee9da2961545dfafc2ea45373d4d161 | [
{
"content": "13.383 Several workers complete a job in 14 days. If there were 4 more people and each worked 1 hour longer per day, then the same job would be done in 10 days. If there were still 6 more people and each worked 1 hour longer per day, then this\njob would be completed in 7 days. How many workers we... | 13.383 Several workers complete a job in 14 days. If there were 4 more people and each worked 1 hour longer per day, then the same job would be done in 10 days. If there were still 6 more people and each worked 1 hour longer per day, then this
job would be completed in 7 days. How many workers were there and how many h... | "[\"20\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1617, "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:15636"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"128\\sqrt{15}"
] | [
"skywork"
] | 4e767e2a22ed8d6e739d5b95d1a151b6f9c3b574f1b825bb0919f2f33e99b673 | [
{
"content": "A net for hexagonal pyramid is constructed by placing a triangle with side lengths $x$ , $x$ , and $y$ on each side of a regular hexagon with side length $y$ . What is the maximum volume of the pyramid formed by the net if $x+y=20$ ?",
"role": "user"
}
] | A net for hexagonal pyramid is constructed by placing a triangle with side lengths $x$ , $x$ , and $y$ on each side of a regular hexagon with side length $y$ . What is the maximum volume of the pyramid formed by the net if $x+y=20$ ? | "[\"128\\\\sqrt{15}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1647, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15637"}, {"dataset": "skywork", "extra_inf... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"skywork"
] | 26a865c676ca2939fc80310ac6d53cd177326292501844c44616692338e81d9c | [
{
"content": "At the \"Lukomorye\" station, they sell cards for one, five, and twenty rides. All cards cost a whole number of gold coins. Five cards for one ride are more expensive than one card for five rides, and four cards for five rides are more expensive than one card for twenty rides. It turned out that t... | At the "Lukomorye" station, they sell cards for one, five, and twenty rides. All cards cost a whole number of gold coins. Five cards for one ride are more expensive than one card for five rides, and four cards for five rides are more expensive than one card for twenty rides. It turned out that the cheapest way for 33 b... | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1641, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15638"}] | {
"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"
] | f1eb7207631f2f943edba064f8843ec495642846d7c50e329cc8ca426da2335a | [
{
"content": "Given a circle $\\omega$ with radius $1$. Let $T$ be a set of triangles good, if the following conditions apply:\n(a) the circumcircle of each triangle in the set $T$ is $\\omega$;\n(b) The interior of any two triangles in the set $T$ has no common point.\nFind all positive real numbers $t$, for w... | Given a circle $\omega$ with radius $1$. Let $T$ be a set of triangles good, if the following conditions apply:
(a) the circumcircle of each triangle in the set $T$ is $\omega$;
(b) The interior of any two triangles in the set $T$ has no common point.
Find all positive real numbers $t$, for which for each positive inte... | "[\"6\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1651, "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:15639"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"(-\\infty,-1)\\cup(1,+\\infty)"
] | [
"skywork"
] | 3c4ec6a9040c1991e7d7cf80a97be519cadc28d0fe6085431f1fae46a36644d6 | [
{
"content": "2. Let $f(x)$ be an odd function defined on $(-\\infty, 0) \\cup(0,+\\infty)$. When $x>0$, $x f^{\\prime}(x)<0$ and $f(1)=0$. Then the solution set of the inequality $x f(x)<0$ is $\\qquad$.",
"role": "user"
}
] | 2. Let $f(x)$ be an odd function defined on $(-\infty, 0) \cup(0,+\infty)$. When $x>0$, $x f^{\prime}(x)<0$ and $f(1)=0$. Then the solution set of the inequality $x f(x)<0$ is $\qquad$. | "[\"(-\\\\infty,-1)\\\\cup(1,+\\\\infty)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1646, "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:15640"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"(3;\\frac{3}{2}),(6;3)"
] | [
"skywork"
] | bc3766edabc1cfe1d0d60d2d8bb6ac8fa1ae55c90b7f1245c9931890934d41b7 | [
{
"content": "6.242. $\\left\\{\\begin{array}{l}\\sqrt{\\frac{3 x-2 y}{2 x}}+\\sqrt{\\frac{2 x}{3 x-2 y}}=2, \\\\ x^{2}-18=2 y(4 y-9) .\\end{array}\\right.$",
"role": "user"
}
] | 6.242. $\left\{\begin{array}{l}\sqrt{\frac{3 x-2 y}{2 x}}+\sqrt{\frac{2 x}{3 x-2 y}}=2, \\ x^{2}-18=2 y(4 y-9) .\end{array}\right.$ | "[\"(3;\\\\frac{3}{2}),(6;3)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1659, "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:15641"}] | {
"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"
] | 66c80bdd963fd879bbdee72ada7de6161a263f7c9e684bce3f64a97267d78224 | [
{
"content": "6. Let the side length of a regular $n$-sided polygon be $a$, and the longest and shortest diagonals be $b$ and $c$ respectively. If $a=b-c$, then $n=$ $\\qquad$",
"role": "user"
}
] | 6. Let the side length of a regular $n$-sided polygon be $a$, and the longest and shortest diagonals be $b$ and $c$ respectively. If $a=b-c$, then $n=$ $\qquad$ | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1662, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15642"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | c4dcc22eb5c130e0b7e86254c1e369c22aaf50003941de7bf463202bbbf3280c | [
{
"content": "7. Given $a=2 \\sin 45^{\\circ}+1, b=2 \\cos 45^{\\circ}-1$. Then the value of the algebraic expression $\\left(\\frac{a^{2}+b^{2}}{2 a b}-1\\right) \\div\\left(\\frac{a^{2}-b^{2}}{a^{2} b+a b^{2}}\\right)$ is",
"role": "user"
}
] | 7. Given $a=2 \sin 45^{\circ}+1, b=2 \cos 45^{\circ}-1$. Then the value of the algebraic expression $\left(\frac{a^{2}+b^{2}}{2 a b}-1\right) \div\left(\frac{a^{2}-b^{2}}{a^{2} b+a b^{2}}\right)$ is | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1656, "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:15643"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{216}{25}"
] | [
"skywork"
] | 22f527b114f6a8f6317fc5baed09dde8c77c659b56d0a26547b2cdaf1dddfcc0 | [
{
"content": "1. In the acute triangle $\\triangle ABC$, the altitude $CE$ from $AB$ intersects with the altitude $BD$ from $AC$ at point $H$. The circle with diameter $DE$ intersects $AB$ and $AC$ at points $F$ and $G$, respectively. $FG$ intersects $AH$ at point $K$. Given $BC=25$, $BD=20$, $BE=7$, find the l... | 1. In the acute triangle $\triangle ABC$, the altitude $CE$ from $AB$ intersects with the altitude $BD$ from $AC$ at point $H$. The circle with diameter $DE$ intersects $AB$ and $AC$ at points $F$ and $G$, respectively. $FG$ intersects $AH$ at point $K$. Given $BC=25$, $BD=20$, $BE=7$, find the length of $AK$. | "[\"\\\\frac{216}{25}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1650, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15644"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"28/3"
] | [
"skywork"
] | 647523dcb13fba1096aae191590cf15302872803b15af14d4ef3c689d209687c | [
{
"content": "Triangle \\(ABC\\) has a right angle at \\(B\\), with \\(AB = 3\\) and \\(BC = 4\\). If \\(D\\) and \\(E\\) are points on \\(AC\\) and \\(BC\\), respectively, such that \\(CD = DE = \\frac{5}{3}\\), find the perimeter of quadrilateral \\(ABED\\).",
"role": "user"
}
] | Triangle \(ABC\) has a right angle at \(B\), with \(AB = 3\) and \(BC = 4\). If \(D\) and \(E\) are points on \(AC\) and \(BC\), respectively, such that \(CD = DE = \frac{5}{3}\), find the perimeter of quadrilateral \(ABED\). | "[\"28/3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1623, "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:15645"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2}"
] | [
"skywork"
] | 8c343264c450925a3eb70b3f425c4bb8fdd71b38f4b1612d9e65e4a20e5e7839 | [
{
"content": "A container holds one liter of wine, and another holds one liter of water. From the first container, we pour one deciliter into the second container and mix thoroughly. Then, we pour one deciliter of the mixture back into the first container. Calculate the limit of the amount of wine in the first ... | A container holds one liter of wine, and another holds one liter of water. From the first container, we pour one deciliter into the second container and mix thoroughly. Then, we pour one deciliter of the mixture back into the first container. Calculate the limit of the amount of wine in the first container if this proc... | "[\"\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1652, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15646"}] | {
"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"
] | 82503ef9584c54aa46e790630770f23f8e12be12755369918ff3925e5fb5c886 | [
{
"content": "Given positive integers $a, b,$ and $c$ with $a + b + c = 20$.\nDetermine the number of possible integer values for $\\frac{a + b}{c}.$",
"role": "user"
}
] | Given positive integers $a, b,$ and $c$ with $a + b + c = 20$.
Determine the number of possible integer values for $\frac{a + b}{c}.$ | "[\"6\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1660, "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:15647"}] | {
"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"
] | 157368b4b2a55153f7ca32231ca756bb1d50e02e3d9858353c33182c5cbe9726 | [
{
"content": "Evaluate the determinant of the given matrix:\n\\[\n\\begin{vmatrix} \\sin \\theta \\sin \\phi & \\sin \\theta \\cos \\phi & \\cos \\theta \\\\ \\cos \\phi & -\\sin \\phi & 0 \\\\ -\\cos \\theta \\sin \\phi & -\\cos \\theta \\cos \\phi & \\sin \\theta \\end{vmatrix}\n\\]",
"role": "user"
}
] | Evaluate the determinant of the given matrix:
\[
\begin{vmatrix} \sin \theta \sin \phi & \sin \theta \cos \phi & \cos \theta \\ \cos \phi & -\sin \phi & 0 \\ -\cos \theta \sin \phi & -\cos \theta \cos \phi & \sin \theta \end{vmatrix}
\] | "[\"-1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1672, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:15648"}] | {
"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
} |
[
"g(x)=f(x)"
] | [
"skywork"
] | 9972cb8aa0ac2ce6f446e07c170827e51f69b06a3504554e261876c50592a10c | [
{
"content": "9. (16 points) Given the function\n$$\nf(x)=a x^{2}+b x+c(a \\neq 0) \\text {, }\n$$\n$g(x)$ is a quadratic function, and it always holds that\n$$\nf(g(x))=g(f(x)) .\n$$\n\nFind $g(x)$.",
"role": "user"
}
] | 9. (16 points) Given the function
$$
f(x)=a x^{2}+b x+c(a \neq 0) \text {, }
$$
$g(x)$ is a quadratic function, and it always holds that
$$
f(g(x))=g(f(x)) .
$$
Find $g(x)$. | "[\"g(x)=f(x)\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1644, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:15649"}] | {
"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"
] | ea0aa1aafb04869b24ec1262f70e45e9e2990e75b433276443cb7a20234afb89 | [
{
"content": "The sum of the first $n$ terms in the infinite geometric sequence $\\left\\{1,\\frac{1}{3},\\frac{1}{9},\\frac{1}{27},\\dots \\right\\}$ is $\\frac{121}{81}$. Find $n$.",
"role": "user"
}
] | The sum of the first $n$ terms in the infinite geometric sequence $\left\{1,\frac{1}{3},\frac{1}{9},\frac{1}{27},\dots \right\}$ is $\frac{121}{81}$. Find $n$. | "[\"5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1678, "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:15650"}] | {
"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
} |
[
"341/1024"
] | [
"skywork"
] | 51a3a376f3f93a514e932d1ef5a92ade49a4cfd60cb797248afb52692260d94e | [
{
"content": "For a positive integer $n$ , let $v(n)$ denote the largest integer $j$ such that $n$ is divisible by $2^j$ . Let $a$ and $b$ be chosen uniformly and independently at random from among the integers between 1 and 32, inclusive. What is the probability that $v(a) > v(b)$ ?",
"role"... | For a positive integer $n$ , let $v(n)$ denote the largest integer $j$ such that $n$ is divisible by $2^j$ . Let $a$ and $b$ be chosen uniformly and independently at random from among the integers between 1 and 32, inclusive. What is the probability that $v(a) > v(b)$ ? | "[\"341/1024\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1666, "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:15651"}, {"dataset": "skywork", "extra_inf... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"50"
] | [
"skywork"
] | 38a8a3da11e1261d15ad55ad9ff78b1203e6c95d3f36963860cd9ac2e053dcf6 | [
{
"content": "Variant 8.1.4. Dima and Seryozha were picking berries from a raspberry bush, on which 450 berries grew. Seryozha alternated actions while picking berries: he put one berry in the basket and ate the next one. Dima also alternated: he put two berries in the basket and ate the next one. It is known t... | Variant 8.1.4. Dima and Seryozha were picking berries from a raspberry bush, on which 450 berries grew. Seryozha alternated actions while picking berries: he put one berry in the basket and ate the next one. Dima also alternated: he put two berries in the basket and ate the next one. It is known that Seryozha picks ber... | "[\"50\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1664, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15652"}] | {
"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
} |
[
"-159\\frac{1}{2}"
] | [
"skywork"
] | 487e14c89b79fb1d4532005e01d5375fda3318eb81c9be78692e91c78908911d | [
{
"content": "Calculate:<br/>$(1)4.7+\\left(-2.5\\right)-\\left(-5.3\\right)-7.5$;<br/>$(2)18+48\\div \\left(-2\\right)^{2}-\\left(-4\\right)^{2}\\times 5$;<br/>$(3)-1^{4}+\\left(-2\\right)^{2}\\div 4\\times [5-\\left(-3\\right)^{2}]$;<br/>$(4)(-19\\frac{15}{16})×8$ (Solve using a simple method).",
"role": ... | Calculate:<br/>$(1)4.7+\left(-2.5\right)-\left(-5.3\right)-7.5$;<br/>$(2)18+48\div \left(-2\right)^{2}-\left(-4\right)^{2}\times 5$;<br/>$(3)-1^{4}+\left(-2\right)^{2}\div 4\times [5-\left(-3\right)^{2}]$;<br/>$(4)(-19\frac{15}{16})×8$ (Solve using a simple method). | "[\"-159\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1645, "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:15653"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"x\\in(4;5)\\cup(5;\\infty)"
] | [
"skywork"
] | 14c103a50f9585ee3038f404da128ab9fc04b4f5696b16d6962e64f3bdd04563 | [
{
"content": "9.129. $y=\\sqrt{\\frac{x^{2}-1}{(x+3)(x-4)}-1}+\\frac{1}{\\log _{8}(x-4)}$.",
"role": "user"
}
] | 9.129. $y=\sqrt{\frac{x^{2}-1}{(x+3)(x-4)}-1}+\frac{1}{\log _{8}(x-4)}$. | "[\"x\\\\in(4;5)\\\\cup(5;\\\\infty)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1673, "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:15654"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4+2\\sqrt{3}"
] | [
"skywork"
] | ae36462bb682e61ef31f16007db87297d02e7c6d17450e3a8f8ddc06b753e929 | [
{
"content": "If the chord cut by the line $ax-by+2=0$ on the circle $x^{2}+y^{2}+2x-4y+1=0$ is $4$, find the minimum value of $\\dfrac{2}{a}+\\dfrac{3}{b}$.",
"role": "user"
}
] | If the chord cut by the line $ax-by+2=0$ on the circle $x^{2}+y^{2}+2x-4y+1=0$ is $4$, find the minimum value of $\dfrac{2}{a}+\dfrac{3}{b}$. | "[\"4+2\\\\sqrt{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1667, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:15655"}] | {
"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
} |
[
"3268"
] | [
"skywork"
] | 65225c04755a8b9d3afde8c2329baf16b8f1a54f1c310e88b13b941eba6e8e6c | [
{
"content": "What is the least common multiple of the numbers 1056 and 792, and then add 100 to your result?",
"role": "user"
}
] | What is the least common multiple of the numbers 1056 and 792, and then add 100 to your result? | "[\"3268\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1701, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15656"}] | {
"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 + 1774x + 235"
] | [
"skywork"
] | 221ef4227278e488178d602a548a9e34e5f2950b0116b6d40475ab99ac638c75 | [
{
"content": "Find the quadratic function $f(x) = x^2 + ax + b$ such that\n\\[\\frac{f(f(x) + x)}{f(x)} = x^2 + 1776x + 2010.\\]",
"role": "user"
}
] | Find the quadratic function $f(x) = x^2 + ax + b$ such that
\[\frac{f(f(x) + x)}{f(x)} = x^2 + 1776x + 2010.\] | "[\"x^2 + 1774x + 235\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1671, "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:15657"}] | {
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[
"8"
] | [
"skywork"
] | c7fb11db756efd174b9d3786fc5ec1d8d6b3176975dda7d36440ec87d01fe14d | [
{
"content": "3. The equation $(x-a)(x-8)-1=0$ has two integer roots, then\n$$\na=\n$$\n.",
"role": "user"
}
] | 3. The equation $(x-a)(x-8)-1=0$ has two integer roots, then
$$
a=
$$
. | "[\"8\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1676, "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:15658"}] | {
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[
"245"
] | [
"skywork"
] | 4329f4c19ac0ab90d810460a6f3d658f8dfd2a89356e9e863099e686289782a8 | [
{
"content": "At a gathering of $30$ people, there are $20$ people who all know each other and $10$ people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur within the group?",
"role": "user"
}
] | At a gathering of $30$ people, there are $20$ people who all know each other and $10$ people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur within the group? | "[\"245\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1661, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15659"}] | {
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"reference_components": 1,
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} |
[
"C"
] | [
"skywork"
] | 4d251969e25e22272075f512ba9f1c03ce7368978ff1fb4ba74dda5aed05b295 | [
{
"content": "4. Given the planar vector $(1,1)$. Then the planar vector $\\left(\\frac{1-\\sqrt{3}}{2}, \\frac{1+\\sqrt{3}}{2}\\right)$ is obtained by transforming the vector $(1,1)$ through $(\\quad)$.\n(A) clockwise rotation by $60^{\\circ}$\n(B) clockwise rotation by $120^{\\circ}$\n(C) counterclockwise rot... | 4. Given the planar vector $(1,1)$. Then the planar vector $\left(\frac{1-\sqrt{3}}{2}, \frac{1+\sqrt{3}}{2}\right)$ is obtained by transforming the vector $(1,1)$ through $(\quad)$.
(A) clockwise rotation by $60^{\circ}$
(B) clockwise rotation by $120^{\circ}$
(C) counterclockwise rotation by $60^{\circ}$
(D) counterc... | "[\"C\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1680, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15660"}] | {
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[
"\\frac{3 \\sqrt{2}}{2}"
] | [
"skywork"
] | 232cff1c06668272f1fc1444954bbe6ac0e6b720da7a68c3fbb9000948900ce2 | [
{
"content": "In the rectangular coordinate system $(xOy)$, there is an ellipse $(C)$: $\\frac{x^{2}}{a^{2}}+ \\frac{y^{2}}{b^{2}}=1 (a > b > 0)$ with an eccentricity $e=\\frac{\\sqrt{2}}{2}$. Also, point $P(2,1)$ is on the ellipse $(C)$.\n\n1. Find the equation of the ellipse $(C)$.\n2. If points $A$ and $B$ a... | In the rectangular coordinate system $(xOy)$, there is an ellipse $(C)$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ with an eccentricity $e=\frac{\sqrt{2}}{2}$. Also, point $P(2,1)$ is on the ellipse $(C)$.
1. Find the equation of the ellipse $(C)$.
2. If points $A$ and $B$ are both on the ellipse $(C)$,... | "[\"\\\\frac{3 \\\\sqrt{2}}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1665, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15661"}] | {
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} |
[
"64"
] | [
"skywork"
] | 9df5f106d344f77c9dd9a2e864bcdbb7e713fd30c4b60b3b7b0f989ebfa2f532 | [
{
"content": "The area of the smallest square that will contain a circle of radius 4 is what?",
"role": "user"
}
] | The area of the smallest square that will contain a circle of radius 4 is what? | "[\"64\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1685, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15662"}] | {
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} |
[
"4082"
] | [
"skywork"
] | e3bfa00a80c387d96b4a1b45e8b5282fb8cbb952ab0eb7cb675074576472239b | [
{
"content": "Let $ABC$ be a triangle with $AB=5$, $BC=7$, $CA=8$, and circumcircle $\\omega$. Let $P$ be a point inside $ABC$ such that $PA:PB:PC=2:3:6$. Let rays $\\overrightarrow{AP}$, $\\overrightarrow{BP}$, and $\\overrightarrow{CP}$ intersect $\\omega$ again at $X$, $Y$, and $Z$, respectively. The area of... | Let $ABC$ be a triangle with $AB=5$, $BC=7$, $CA=8$, and circumcircle $\omega$. Let $P$ be a point inside $ABC$ such that $PA:PB:PC=2:3:6$. Let rays $\overrightarrow{AP}$, $\overrightarrow{BP}$, and $\overrightarrow{CP}$ intersect $\omega$ again at $X$, $Y$, and $Z$, respectively. The area of $XYZ$ can be expressed in ... | "[\"4082\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1663, "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:15663"}] | {
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[
"x = \\frac{\\pi}{4}"
] | [
"skywork"
] | 4371565d29ed1da8025b23bae2c53c801cc4c5556678d0527469beefd32185d9 | [
{
"content": "Find, with proof, all real numbers $ x \\in \\lbrack 0, \\frac {\\pi}{2} \\rbrack$, such that $ (2 \\minus{} \\sin 2x)\\sin (x \\plus{} \\frac {\\pi}{4}) \\equal{} 1$.",
"role": "user"
}
] | Find, with proof, all real numbers $ x \in \lbrack 0, \frac {\pi}{2} \rbrack$, such that $ (2 \minus{} \sin 2x)\sin (x \plus{} \frac {\pi}{4}) \equal{} 1$. | "[\" x = \\\\frac{\\\\pi}{4} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1674, "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:15664"}] | {
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[
"(-\\frac{5}{2}, -2] \\cup \\{-1\\}"
] | [
"skywork"
] | 90f798ee53ae0ec9198990d7b24ed0a32eb40eedaab5a118384cb7e2b62bd8a3 | [
{
"content": "It is given the equation $x^2+px+1=0$, with roots $x_1$ and $x_2$;\n\n(a) find a second-degree equation with roots $y_1,y_2$ satisfying the conditions $y_1=x_1(1-x_1)$, $y_2=x_2(1-x_2)$;\n(b) find all possible values of the real parameter $p$ such that the roots of the new equation lies between $-... | It is given the equation $x^2+px+1=0$, with roots $x_1$ and $x_2$;
(a) find a second-degree equation with roots $y_1,y_2$ satisfying the conditions $y_1=x_1(1-x_1)$, $y_2=x_2(1-x_2)$;
(b) find all possible values of the real parameter $p$ such that the roots of the new equation lies between $-2$ and $1$. | "[\"(-\\\\frac{5}{2}, -2] \\\\cup \\\\{-1\\\\}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1658, "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:15665"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"150"
] | [
"skywork"
] | 6fc1b036e02c161d13ff63cce9306cc4d317d0e83f2b86c0a5f8447295e93f97 | [
{
"content": "In quadrilateral $ABCD, BC=8, CD=12, AD=10,$ and $m\\angle A= m\\angle B = 60^\\circ.$ Given that $AB = p + \\sqrt{q},$ where $p$ and $q$ are positive integers, find $p+q.$",
"role": "user"
}
] | In quadrilateral $ABCD, BC=8, CD=12, AD=10,$ and $m\angle A= m\angle B = 60^\circ.$ Given that $AB = p + \sqrt{q},$ where $p$ and $q$ are positive integers, find $p+q.$ | "[\"150\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 1681, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15666"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | e4003f0f0bb51db5b6a42a2c95a4ab469493cc9e5a86231a79fa6f184be188e7 | [
{
"content": "We have that $\\lceil x \\rceil - \\lfloor x \\rfloor = 0.$ Then, what is $\\lceil x \\rceil - x$?",
"role": "user"
}
] | We have that $\lceil x \rceil - \lfloor x \rfloor = 0.$ Then, what is $\lceil x \rceil - x$? | "[\"0\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1698, "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:15667"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9876524130"
] | [
"skywork"
] | 36eb3bb4a5f5438c6fbadab381cb551ccb5eb19464119eb23fdd328e50d86ede | [
{
"content": "## Task 25/66\n\nWhat is the largest multiple of 11 in which none of the digits occurs more than once?",
"role": "user"
}
] | ## Task 25/66
What is the largest multiple of 11 in which none of the digits occurs more than once? | "[\"9876524130\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1699, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15668"}] | {
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} |
[
"\\frac{3+\\sqrt{3}}{2}"
] | [
"skywork"
] | e4d7c6de72ed02b89ac83955743bbd894e3b12c3178dfa1a84c13d92d02c299d | [
{
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$, respectively, and $(2a-c)\\cos B=b\\cos C$.\n(I) Find the measure of angle $B$;\n(II) If $\\cos A=\\frac{\\sqrt{2}}{2}$ and $a=2$, find the area of $\\triangle ABC$.",
"role": "user"
}
] | In $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$, respectively, and $(2a-c)\cos B=b\cos C$.
(I) Find the measure of angle $B$;
(II) If $\cos A=\frac{\sqrt{2}}{2}$ and $a=2$, find the area of $\triangle ABC$. | "[\"\\\\frac{3+\\\\sqrt{3}}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1657, "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:15669"}] | {
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[
"\\frac{7}{2}"
] | [
"skywork"
] | c53a09fe228ade131069ec97bf3e3512047fd03ae87c23b1ac030430abfd1b6b | [
{
"content": "Let $ABC$ be a triangle with circumcenter $O$ such that $AC=7$. Suppose that the circumcircle of $AOC$ is tangent to $BC$ at $C$ and intersects the line $AB$ at $A$ and $F$. Let $FO$ intersect $BC$ at $E$. Compute $BE$.",
"role": "user"
}
] | Let $ABC$ be a triangle with circumcenter $O$ such that $AC=7$. Suppose that the circumcircle of $AOC$ is tangent to $BC$ at $C$ and intersects the line $AB$ at $A$ and $F$. Let $FO$ intersect $BC$ at $E$. Compute $BE$. | "[\"\\\\frac{7}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1669, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15670"}, {"dataset": "skywork", "extra_in... | {
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[
"\\frac{2 \\sqrt{34}}{17}"
] | [
"skywork"
] | 434c5a920f47676a7f6a3cd24c94833ebd0f78414c17e976ed110311d4590f6a | [
{
"content": "3. In a cube $A B C D-$ $A_{1} B_{1} C_{1} D_{1}$ with edge length 2, $M$ and $N$ are the midpoints of edges $B B_{1}$ and $B_{1} C_{1}$, respectively. If $P$ is a moving point in the plane $D M N$, when the distance from point $P$ to the plane $B C C_{1} B_{1}$ equals the length of $P D$, the ecc... | 3. In a cube $A B C D-$ $A_{1} B_{1} C_{1} D_{1}$ with edge length 2, $M$ and $N$ are the midpoints of edges $B B_{1}$ and $B_{1} C_{1}$, respectively. If $P$ is a moving point in the plane $D M N$, when the distance from point $P$ to the plane $B C C_{1} B_{1}$ equals the length of $P D$, the eccentricity of the traje... | "[\"\\\\frac{2 \\\\sqrt{34}}{17}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1668, "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:15671"}] | {
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} |
[
"\\frac{5 \\sqrt{10}}{3}"
] | [
"skywork"
] | 4aa55eaa135ccf4e65936e46f0ddf9108c645c12af63b430c3ce1da94fce04d9 | [
{
"content": "In the coordinate plane \\(xOy\\), given points \\(A(1,3)\\), \\(B\\left(8 \\frac{1}{3}, 1 \\frac{2}{3}\\right)\\), and \\(C\\left(7 \\frac{1}{3}, 4 \\frac{2}{3}\\right)\\), the extended lines \\(OA\\) and \\(BC\\) intersect at point \\(D\\). Points \\(M\\) and \\(N\\) are on segments \\(OD\\) and... | In the coordinate plane \(xOy\), given points \(A(1,3)\), \(B\left(8 \frac{1}{3}, 1 \frac{2}{3}\right)\), and \(C\left(7 \frac{1}{3}, 4 \frac{2}{3}\right)\), the extended lines \(OA\) and \(BC\) intersect at point \(D\). Points \(M\) and \(N\) are on segments \(OD\) and \(BD\) respectively, with \(OM = MN = BN\). Find ... | "[\"\\\\frac{5 \\\\sqrt{10}}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1694, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15672"}] | {
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[
"16.5"
] | [
"skywork"
] | 2d97c0e1453fa740c38b92f7b3c3e3be5903bc6e827c95ec58a25e72faffba61 | [
{
"content": "The value of $\\frac{150+(150 \\div 10)}{15-5}$ is\n(A) 6\n(B) 3\n(C) 146\n(D) 151.5\n(E) 16.5",
"role": "user"
}
] | The value of $\frac{150+(150 \div 10)}{15-5}$ is
(A) 6
(B) 3
(C) 146
(D) 151.5
(E) 16.5 | "[\"16.5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1703, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15673"}] | {
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[
"84"
] | [
"skywork"
] | 0b304b5d9dc70fafbb736483045acbd2186fce36a90c22810d1ba8ae01b06901 | [
{
"content": "In triangle $ABC$ with $AB=8$ and $AC=10$, the incenter $I$ is reflected across side $AB$ to point $X$ and across side $AC$ to point $Y$. Given that segment $XY$ bisects $AI$, compute $BC^2$. (The incenter is the center of the inscribed circle of triangle .)",
"role": "user"
}
] | In triangle $ABC$ with $AB=8$ and $AC=10$, the incenter $I$ is reflected across side $AB$ to point $X$ and across side $AC$ to point $Y$. Given that segment $XY$ bisects $AI$, compute $BC^2$. (The incenter is the center of the inscribed circle of triangle .) | "[\"84\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1682, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15674"}] | {
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[
"2004002"
] | [
"skywork"
] | 76bd44b0fd67c19f507bd8b191cb4ca205c5ac54b95f230bf1af4fcf1ac1bf5e | [
{
"content": "Determine the value of $$1 \\cdot 2-2 \\cdot 3+3 \\cdot 4-4 \\cdot 5+\\cdots+2001 \\cdot 2002$$",
"role": "user"
}
] | Determine the value of $$1 \cdot 2-2 \cdot 3+3 \cdot 4-4 \cdot 5+\cdots+2001 \cdot 2002$$ | "[\"2004002\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1686, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:15675"}, {"dataset": "skywork", "extra_in... | {
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[
"40"
] | [
"skywork"
] | 76dca189c979a4e565759af1e7bbfe173384ff989b45e72ce7d1eafc9a99cbe0 | [
{
"content": "37. Chihiro accidentally enters a peculiar world of deities. On a night market street, she sees 2020 lanterns with numbers, which are consecutive natural numbers from 1 to 2020. Chihiro picks some lanterns with consecutive numbers and finds that the sum of the numbers on the lanterns she picked is... | 37. Chihiro accidentally enters a peculiar world of deities. On a night market street, she sees 2020 lanterns with numbers, which are consecutive natural numbers from 1 to 2020. Chihiro picks some lanterns with consecutive numbers and finds that the sum of the numbers on the lanterns she picked is exactly 2020. How man... | "[\"40\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1700, "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:15676"}] | {
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} |
[
"\\frac{11}{6}"
] | [
"skywork"
] | ab8fd6c2d6832e3d9406733dc8a26fc1e95eaae964787b97e95c701904f6ad17 | [
{
"content": "In a certain place, four people, $A$, $B$, $C$, and $D$, successively contracted the novel coronavirus, with only $A$ having visited an epidemic area.\n1. If the probabilities of $B$, $C$, and $D$ being infected by $A$ are $\\frac{1}{2}$ each, what is the probability that exactly one of $B$, $C$, ... | In a certain place, four people, $A$, $B$, $C$, and $D$, successively contracted the novel coronavirus, with only $A$ having visited an epidemic area.
1. If the probabilities of $B$, $C$, and $D$ being infected by $A$ are $\frac{1}{2}$ each, what is the probability that exactly one of $B$, $C$, and $D$ is infected with... | "[\"\\\\frac{11}{6}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1670, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:15678"}] | {
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[
"17,280"
] | [
"skywork"
] | f55cf80c6905e8283343e4c91e44a8173ab991196a068e730ef2be1d7b488ae3 | [
{
"content": "In how many ways can I arrange 4 different math books and 6 different history books on my bookshelf, if I require a math book on both ends and all history books must be together?",
"role": "user"
}
] | In how many ways can I arrange 4 different math books and 6 different history books on my bookshelf, if I require a math book on both ends and all history books must be together? | "[\"17,280\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1705, "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:15679"}] | {
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[
"95210"
] | [
"skywork"
] | 02c09b74ec2fe55a6a97793efa51f979ebbb8e55d3778b3851067c9fc946b709 | [
{
"content": "9. In the five-digit number abcde, $a, b, c, d, e$ represent its ten-thousands, thousands, hundreds, tens, and units place values, respectively. If $\\mathrm{d}>\\mathrm{e}, \\mathrm{c}>\\mathrm{d}+\\mathrm{e}, \\mathrm{b}>\\mathrm{c}+\\mathrm{d}+\\mathrm{e}, \\mathrm{a}>\\mathrm{b}+\\mathrm{c}+\\... | 9. In the five-digit number abcde, $a, b, c, d, e$ represent its ten-thousands, thousands, hundreds, tens, and units place values, respectively. If $\mathrm{d}>\mathrm{e}, \mathrm{c}>\mathrm{d}+\mathrm{e}, \mathrm{b}>\mathrm{c}+\mathrm{d}+\mathrm{e}, \mathrm{a}>\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e}$. Then, the la... | "[\"95210\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1679, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15680"}] | {
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[
"895"
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"skywork"
] | 90efe7a0682dc8a41a9961b9653998be98dee51ced2d82e371580280db67ad23 | [
{
"content": "Devah draws a row of 1000 equally spaced dots on a sheet of paper. She goes through the dots from left to right, one by one, checking if the midpoint between the current dot and some remaining dot to its left is also a remaining dot. If so, she erases the current dot. How many dots does Devah e... | Devah draws a row of 1000 equally spaced dots on a sheet of paper. She goes through the dots from left to right, one by one, checking if the midpoint between the current dot and some remaining dot to its left is also a remaining dot. If so, she erases the current dot. How many dots does Devah end up erasing? | "[\"895\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1704, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15681"}] | {
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[
"168"
] | [
"skywork"
] | 1677b7144ae5db329cea587fa1a4a11aee4b3564b00edecd92267063576c4a35 | [
{
"content": "472. For which number and for which natural $a$ are the fractions reducible:\na) $\\frac{a^{4}+a^{3}-a^{2}+a+1}{a^{2}-1}$;\nb) $\\frac{a^{4}+6 a^{3}+15 a^{2}+18 a+8}{a^{4}+6 a^{3}+13 a^{2}+12 a+3}$?\n\n473 $3^{\\circ}$. Let $a$ and $b$ be natural numbers, where $a > b$, and the number $a$ is divid... | 472. For which number and for which natural $a$ are the fractions reducible:
a) $\frac{a^{4}+a^{3}-a^{2}+a+1}{a^{2}-1}$;
b) $\frac{a^{4}+6 a^{3}+15 a^{2}+18 a+8}{a^{4}+6 a^{3}+13 a^{2}+12 a+3}$?
473 $3^{\circ}$. Let $a$ and $b$ be natural numbers, where $a > b$, and the number $a$ is divided by the number $b$ with a r... | "[\"168\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1677, "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:15682"}] | {
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[
"[\\sqrt{15}-1,+\\infty)"
] | [
"skywork"
] | 28fe54c5c067a67162edfcae0cee59b60ecb8ea5dee118766dc697865e9b12c0 | [
{
"content": "3. Let points $A$ and $B$ lie on the parabola $y^{2}=6 x$ and the circle $\\odot C:(x-4)^{2}+y^{2}=1$, respectively. Then the range of $|A B|$ is $\\qquad$ .",
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}
] | 3. Let points $A$ and $B$ lie on the parabola $y^{2}=6 x$ and the circle $\odot C:(x-4)^{2}+y^{2}=1$, respectively. Then the range of $|A B|$ is $\qquad$ . | "[\"[\\\\sqrt{15}-1,+\\\\infty)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1688, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:15683"}, {"dataset": "skywork", "extra_in... | {
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[
"71"
] | [
"skywork"
] | c7ea9a2d0721877727fe9fdc1d4c9cdad1d91657ba6617af5111296020c1c526 | [
{
"content": "Let $P(x) = x^2 - 3x - 7$ , and let $Q(x)$ and $R(x)$ be two quadratic polynomials also with the coefficient of $x^2$ equal to $1$ . David computes each of the three sums $P + Q$ , $P + R$ , and $Q + R$ and is surprised to find that each pair of these sums has a common root, and these three common... | Let $P(x) = x^2 - 3x - 7$ , and let $Q(x)$ and $R(x)$ be two quadratic polynomials also with the coefficient of $x^2$ equal to $1$ . David computes each of the three sums $P + Q$ , $P + R$ , and $Q + R$ and is surprised to find that each pair of these sums has a common root, and these three common roots are distinct. I... | "[\"71\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 1675, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:15684"}, {"dataset": "skywork", "extra_in... | {
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[
"\\frac{1}{4}"
] | [
"skywork"
] | 8a4faf86c99d6184424ae74c8b1bcd8b0da756fb17316384b59ba3aedf5cea5b | [
{
"content": "Problem 2. On the sides of a square with side 1, points $K$, $L$, $M$, and $N$ are marked such that segment $K M$ is parallel to two of the square's sides, and segment $L N$ is parallel to the other two sides. Segment $K L$ cuts off a triangle from the square with a perimeter of 1. What is the are... | Problem 2. On the sides of a square with side 1, points $K$, $L$, $M$, and $N$ are marked such that segment $K M$ is parallel to two of the square's sides, and segment $L N$ is parallel to the other two sides. Segment $K L$ cuts off a triangle from the square with a perimeter of 1. What is the area of the triangle cut ... | "[\"\\\\frac{1}{4}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1696, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15685"}] | {
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[
"258"
] | [
"skywork"
] | dc0356f1cbf312dcef10f51c60e3491cd11491c3129d221ed5219a1db53e2a89 | [
{
"content": "A teacher was leading a class of four perfectly logical students. The teacher chose a set $S$ of four integers and gave a different number in $S$ to each student. Then the teacher announced to the class that the numbers in $S$ were four consecutive two-digit positive integers, that some number in ... | A teacher was leading a class of four perfectly logical students. The teacher chose a set $S$ of four integers and gave a different number in $S$ to each student. Then the teacher announced to the class that the numbers in $S$ were four consecutive two-digit positive integers, that some number in $S$ was divisible by $... | "[\"258\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 1683, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15686"}, {"dataset": "skywork", "extra_... | {
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[
"49"
] | [
"skywork"
] | 068973dea1c29a35965cf7ee27fad9286624290a07d2c124b56d811453d302aa | [
{
"content": "Rubanov I.S.\n\nWhat is the maximum finite number of roots that the equation\n\n$$\n\\left|x-a_{1}\\right|+. .+|x-a 50|=\\left|x-b_{1}\\right|+. .+|x-b 50|\n$$\n\ncan have, where $a_{1}, a_{2}, \\ldots, a_{50}, b_{1}, b_{2}, \\ldots, b_{50}$ are distinct numbers?",
"role": "user"
}
] | Rubanov I.S.
What is the maximum finite number of roots that the equation
$$
\left|x-a_{1}\right|+. .+|x-a 50|=\left|x-b_{1}\right|+. .+|x-b 50|
$$
can have, where $a_{1}, a_{2}, \ldots, a_{50}, b_{1}, b_{2}, \ldots, b_{50}$ are distinct numbers? | "[\"49\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1695, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:15687"}, {"dataset": "skywork", "extra_in... | {
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[
"\\sqrt[10]{10}"
] | [
"skywork"
] | 06efd3989ea998901b7dfa7d71b04913d6dbb87a35866858b87f5c219e09c73b | [
{
"content": "7.191. $\\log _{10} x+\\log _{\\sqrt{10}} x+\\log _{\\sqrt[3]{10}} x+\\ldots+\\log _{\\sqrt[1]{10}} x=5.5$.",
"role": "user"
}
] | 7.191. $\log _{10} x+\log _{\sqrt{10}} x+\log _{\sqrt[3]{10}} x+\ldots+\log _{\sqrt[1]{10}} x=5.5$. | "[\"\\\\sqrt[10]{10}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1691, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15688"}] | {
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[
"17"
] | [
"skywork"
] | fba5714e3fc6b8025e809823ae60d976d60fb79b5cad56c7e73d518f19ccecaa | [
{
"content": "This game is played on an $8 \\times 8$ chessboard with two kings. The columns are numbered from $A$ to $H$ from left to right, and the rows are numbered from 1 to 8 from bottom to top. The white king plays first and starts at the bottom left (at $A 1$), the black king starts at $A8$. The goal of ... | This game is played on an $8 \times 8$ chessboard with two kings. The columns are numbered from $A$ to $H$ from left to right, and the rows are numbered from 1 to 8 from bottom to top. The white king plays first and starts at the bottom left (at $A 1$), the black king starts at $A8$. The goal of the white king is to re... | "[\"17\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1697, "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:15689"}] | {
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[
"55"
] | [
"skywork"
] | 0d945bf34544e0b7106c56646b336b6c6bb36f509486340941c616c03618e518 | [
{
"content": "At the end of 1994, Walter was half as old as his grandmother. The sum of the years in which they were born was 3838. How old will Walter be at the end of 1999?",
"role": "user"
}
] | At the end of 1994, Walter was half as old as his grandmother. The sum of the years in which they were born was 3838. How old will Walter be at the end of 1999? | "[\"55\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1716, "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:15690"}] | {
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[
"486 \\sqrt{3}"
] | [
"skywork"
] | 7138ad718889d5531f1b7f2e8a8e97e045c8bb2f88917331ead631a4c44b8053 | [
{
"content": "What is the area, in square units, of a regular hexagon inscribed in a circle whose area is $324\\pi$ square units? Express your answer in simplest radical form.",
"role": "user"
}
] | What is the area, in square units, of a regular hexagon inscribed in a circle whose area is $324\pi$ square units? Express your answer in simplest radical form. | "[\"486 \\\\sqrt{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1713, "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:15691"}] | {
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[
"41(\\frac{\\sqrt{105}}{55}+\\frac{\\sqrt{3}}{10}+\\frac{3}{22})"
] | [
"skywork"
] | 6356d74729689a3c96b167a2666183063fb41ffcee997b648cab5480b67f8131 | [
{
"content": "A sphere with center at point $O$ passes through the vertices $A, B$, and $C$ of the tetrahedron $A B C D$ and intersects the lines $A D, B D$, and $C D$ at points $K, L$, and $M$ respectively. It is known that $A D=10, B C: B D=3: 2$ and $A B: C D=4 \\sqrt{3}$ $: 11$. The projections of point $O$... | A sphere with center at point $O$ passes through the vertices $A, B$, and $C$ of the tetrahedron $A B C D$ and intersects the lines $A D, B D$, and $C D$ at points $K, L$, and $M$ respectively. It is known that $A D=10, B C: B D=3: 2$ and $A B: C D=4 \sqrt{3}$ $: 11$. The projections of point $O$ onto the planes $A B D... | "[\"41(\\\\frac{\\\\sqrt{105}}{55}+\\\\frac{\\\\sqrt{3}}{10}+\\\\frac{3}{22})\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1684, "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:15692"}] | {
"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
} |
[
"59955"
] | [
"skywork"
] | 6b5c404d8c76094f08fefeb18e91af1cc9f44b6eb0489a02da96add72c84fbe4 | [
{
"content": "For each positive integer $p$, let $b(p)$ denote the unique positive integer $k$ such that $|k-\\sqrt{p}|<\\frac{1}{2}$. For example, $b(6)=2$ and $b(23)=5$. Find $S=\\sum_{p=1}^{2007} b(p)$.",
"role": "user"
}
] | For each positive integer $p$, let $b(p)$ denote the unique positive integer $k$ such that $|k-\sqrt{p}|<\frac{1}{2}$. For example, $b(6)=2$ and $b(23)=5$. Find $S=\sum_{p=1}^{2007} b(p)$. | "[\"59955\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1707, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15693"}] | {
"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
} |
[
"25"
] | [
"skywork"
] | 2c35ef772d643c092d51405791b954e4c05311f431050a1f2b13ce5958dc2bb3 | [
{
"content": "Let $\\triangle XYZ$ have side lengths $XY=15$, $XZ=20$, and $YZ=25$. Inside $\\angle XYZ$, there are two circles: one is tangent to the rays $\\overline{XY}$, $\\overline{XZ}$, and the segment $\\overline{YZ}$, while the other is tangent to the extension of $\\overline{XY}$ beyond $Y$, $\\overlin... | Let $\triangle XYZ$ have side lengths $XY=15$, $XZ=20$, and $YZ=25$. Inside $\angle XYZ$, there are two circles: one is tangent to the rays $\overline{XY}$, $\overline{XZ}$, and the segment $\overline{YZ}$, while the other is tangent to the extension of $\overline{XY}$ beyond $Y$, $\overline{XZ}$, and $\overline{YZ}$. ... | "[\"25\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1711, "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:15694"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"N"
] | [
"skywork"
] | 50e7878fe67b21274074f9b335eb51e6ff20f30daede55788d7a44c84ad3ccda | [
{
"content": "Find all natural numbers $N$ consisting of exactly $1112$ digits (in decimal notation) such that:\n(a) The sum of the digits of $N$ is divisible by $2000$;\n(b) The sum of the digits of $N+1$ is divisible by $2000$;\n(c) $1$ is a digit of $N$.",
"role": "user"
}
] | Find all natural numbers $N$ consisting of exactly $1112$ digits (in decimal notation) such that:
(a) The sum of the digits of $N$ is divisible by $2000$;
(b) The sum of the digits of $N+1$ is divisible by $2000$;
(c) $1$ is a digit of $N$. | "[\" N \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1706, "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:15695"}] | {
"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{\\sqrt{133}}{7}"
] | [
"skywork"
] | 0bdda253cd8a383627e22b209ece744a99b58ff24c7c1d03ef6ed150eb3ddba7 | [
{
"content": "7. Given complex numbers $z_{1}$ and $z_{2}$ satisfy $\\left|z_{1}\\right|=2,\\left|z_{2}\\right|=3$. If the angle between the vectors they correspond to is $60^{\\circ}$, then $\\left|\\frac{z_{1}+z_{2}}{z_{1}-z_{2}}\\right|=$ $\\qquad$ .",
"role": "user"
}
] | 7. Given complex numbers $z_{1}$ and $z_{2}$ satisfy $\left|z_{1}\right|=2,\left|z_{2}\right|=3$. If the angle between the vectors they correspond to is $60^{\circ}$, then $\left|\frac{z_{1}+z_{2}}{z_{1}-z_{2}}\right|=$ $\qquad$ . | "[\"\\\\frac{\\\\sqrt{133}}{7}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1715, "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:15696"}] | {
"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
} |
[
"499"
] | [
"skywork"
] | c46483b694dfcb90a7a9f0658e621e11ea4f66b7e723078e8c541d2e000e7cb3 | [
{
"content": "Given the numbers $1,2,3, \\ldots, 1000$. Find the largest number $m$, such that: no matter which $m$ of these numbers are erased, among the remaining $1000-m$ numbers, there will be two such that one divides the other.",
"role": "user"
}
] | Given the numbers $1,2,3, \ldots, 1000$. Find the largest number $m$, such that: no matter which $m$ of these numbers are erased, among the remaining $1000-m$ numbers, there will be two such that one divides the other. | "[\"499\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1714, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:15697"}] | {
"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}{5}"
] | [
"skywork"
] | 146eaa7ad2bba19849bbab9db05929671237eda10b9fb4420df71d3088ca1d21 | [
{
"content": "1. Solve the equation $2 x^{2}-3 x=2 x \\sqrt{x^{2}-3 x}+1$ in $\\mathbb{R}$.",
"role": "user"
}
] | 1. Solve the equation $2 x^{2}-3 x=2 x \sqrt{x^{2}-3 x}+1$ in $\mathbb{R}$. | "[\"-\\\\frac{1}{5}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1721, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15699"}] | {
"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
} |
[
"13\\sqrt{3}"
] | [
"skywork"
] | c41ae66c94ef9db90df2323861942d2daddc2afdb06326f719d70c139da27f9e | [
{
"content": "If $x,y>0$, $\\log_y(x)+\\log_x(y)=\\frac{10}{3}$ and $xy=144$, then $\\frac{x+y}{2}=$",
"role": "user"
}
] | If $x,y>0$, $\log_y(x)+\log_x(y)=\frac{10}{3}$ and $xy=144$, then $\frac{x+y}{2}=$ | "[\"13\\\\sqrt{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1724, "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:15700"}] | {
"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
} |
[
"25025"
] | [
"skywork"
] | 709aa7ac94e0d03b25b8d4a835031ffacb4529f6e203eb933b74c701bdf71f30 | [
{
"content": "Problem 10.6. Find the largest possible number $A$ having the following property: if the numbers $1,2, \\ldots, 1000$ are ordered in arbitrary way then there exist 50 consecutive numbers with sum not less than $A$.\n\nIvan Landjev",
"role": "user"
}
] | Problem 10.6. Find the largest possible number $A$ having the following property: if the numbers $1,2, \ldots, 1000$ are ordered in arbitrary way then there exist 50 consecutive numbers with sum not less than $A$.
Ivan Landjev | "[\"25025\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1718, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15701"}] | {
"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
} |
[
"143"
] | [
"skywork"
] | eb3f8abcfeafb485dd9a5c3a7d7bb7e78e1dfb7b56e839391125f20ebf4fa6aa | [
{
"content": "180. Find $N=p q$, if $\\varphi(N)=120$, and the numbers $p$ and $q$ are twin prime numbers, i.e., $p-q=2$.",
"role": "user"
}
] | 180. Find $N=p q$, if $\varphi(N)=120$, and the numbers $p$ and $q$ are twin prime numbers, i.e., $p-q=2$. | "[\"143\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1720, "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:15702"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"[1, 3]"
] | [
"skywork"
] | 00f079214d2e667b2f600541eeb72e32cc2a603c67d99e9600055c0021e47310 | [
{
"content": "All sides of a convex hexagon $ABCDEF$ are $1$. Let $M,m$ be the maximum and minimum possible values of three diagonals $AD,BE,CF$. Find the range of $M$, $m$.",
"role": "user"
}
] | All sides of a convex hexagon $ABCDEF$ are $1$. Let $M,m$ be the maximum and minimum possible values of three diagonals $AD,BE,CF$. Find the range of $M$, $m$. | "[\" [1, 3] \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1709, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15704"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"7.5"
] | [
"skywork"
] | 0db51d0793dabe156b3bfa883eb5784ec24f7fe12bbc6d6e42d8bb6d28f8b8e8 | [
{
"content": "In triangle \\(ABC\\), \\(AB = 13\\) and \\(BC = 15\\). On side \\(AC\\), point \\(D\\) is chosen such that \\(AD = 5\\) and \\(CD = 9\\). The angle bisector of the angle supplementary to \\(\\angle A\\) intersects line \\(BD\\) at point \\(E\\). Find \\(DE\\).",
"role": "user"
}
] | In triangle \(ABC\), \(AB = 13\) and \(BC = 15\). On side \(AC\), point \(D\) is chosen such that \(AD = 5\) and \(CD = 9\). The angle bisector of the angle supplementary to \(\angle A\) intersects line \(BD\) at point \(E\). Find \(DE\). | "[\"7.5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1712, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15705"}] | {
"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"
] | e312f7bbaaa36883ac28d9663ef790e7243e471aa9a4cc2096c2085c2d4bc1a0 | [
{
"content": "If the complex number $Z=(1+ai)i$ is an \"equal parts complex number\", determine the value of the real number $a$.",
"role": "user"
}
] | If the complex number $Z=(1+ai)i$ is an "equal parts complex number", determine the value of the real number $a$. | "[\"-1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1719, "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:15706"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
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