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 |
|---|---|---|---|---|---|---|---|---|
[
"18"
] | [
"skywork"
] | a2f5583e7c590a591ee163834239878c59387e9e326ef8eab09214ea2c3a74f2 | [
{
"content": "1. The integer parts of two finite decimals are 7 and 10, respectively. Therefore, the number of possible integer values for the product of these two finite decimals is $(\\quad)$.\n(A) 16\n(B) 17\n(C) 18\n(D) 19",
"role": "user"
}
] | 1. The integer parts of two finite decimals are 7 and 10, respectively. Therefore, the number of possible integer values for the product of these two finite decimals is $(\quad)$.
(A) 16
(B) 17
(C) 18
(D) 19 | "[\"18\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107474, "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:117439"}] | {
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[
"4"
] | [
"skywork"
] | 09dac2c5b32e5f9db8307562df338e59f51b70e70acd12f9a7873bee842e9ba2 | [
{
"content": "## Task 4 - 060614\n\nIn a house, exactly the following tenants live: Albrecht, Becker, Conrad, Dietrich, Ermler, Fritsche, Geißler, Hamann, Ilgner, Keies, Lorenz, Männig, Nolte, Oswald, Richter, and Pätzold.\n\nOn the ground floor and in each floor, exactly two tenants live, and the following is ... | ## Task 4 - 060614
In a house, exactly the following tenants live: Albrecht, Becker, Conrad, Dietrich, Ermler, Fritsche, Geißler, Hamann, Ilgner, Keies, Lorenz, Männig, Nolte, Oswald, Richter, and Pätzold.
On the ground floor and in each floor, exactly two tenants live, and the following is known:
Albrechts live two... | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107478, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117440"}] | {
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[
"3"
] | [
"skywork"
] | 5766cf654fe3d30fb1e1b6944f6a5402c0382e60c46d5c5c1e5a1eaf5218296d | [
{
"content": "15 A finite set of points $M$ on the plane satisfies: for any two points $A, B$ in $M$, there must exist a third point $C$ such that $\\triangle A B C$ is an equilateral triangle. Find the maximum number of elements in $M$.",
"role": "user"
}
] | 15 A finite set of points $M$ on the plane satisfies: for any two points $A, B$ in $M$, there must exist a third point $C$ such that $\triangle A B C$ is an equilateral triangle. Find the maximum number of elements in $M$. | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107489, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117441"}] | {
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[
"n+1"
] | [
"skywork"
] | 3bcaaa066bba126bf5e030d75b190230ceb05ba54baa8463a0082a72904ae3f1 | [
{
"content": "5. Given the set $S=\\{1,2,3, \\cdots, 2 n, 2 n+1\\}$, a subset $T$ of which has the property that for any three elements $x, y, z$, $x+y \\neq z$, then the maximum number of elements in $T$ is $\\qquad$.",
"role": "user"
}
] | 5. Given the set $S=\{1,2,3, \cdots, 2 n, 2 n+1\}$, a subset $T$ of which has the property that for any three elements $x, y, z$, $x+y \neq z$, then the maximum number of elements in $T$ is $\qquad$. | "[\"n+1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107479, "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:117442"}] | {
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[
"88"
] | [
"skywork"
] | 4832e5c23404a1ca636e22e8e029d41133144f7f218105c8842b05c94663bcb2 | [
{
"content": "3. Given the sequence $\\left\\{a_{n}\\right\\}$ satisfies\n$$\na_{n+1}=a_{n}+a_{n-1}(n \\geqslant 2) \\text {. }\n$$\n\nIf $a_{7}=8$, then $a_{1}+a_{2}+\\cdots+a_{10}=$ $\\qquad$",
"role": "user"
}
] | 3. Given the sequence $\left\{a_{n}\right\}$ satisfies
$$
a_{n+1}=a_{n}+a_{n-1}(n \geqslant 2) \text {. }
$$
If $a_{7}=8$, then $a_{1}+a_{2}+\cdots+a_{10}=$ $\qquad$ | "[\"88\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107462, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117443"}] | {
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} |
[
"\\frac{4}{9}"
] | [
"skywork"
] | dcd604d53c044816bc01702d112932d58f3c10a2bedda440d4e6f8b566cd3a17 | [
{
"content": "The sequence $\\left\\{x_{n}\\right\\}$ satisfies $x_{1}=1$, and for any $n \\in \\mathbb{Z}^{+}$, it holds that $x_{n+1}=x_{n}+3 \\sqrt{x_{n}}+\\frac{n}{\\sqrt{x_{n}}}$. Find the value of $\\lim _{n \\rightarrow+\\infty} \\frac{n^{2}}{x_{n}}$.",
"role": "user"
}
] | The sequence $\left\{x_{n}\right\}$ satisfies $x_{1}=1$, and for any $n \in \mathbb{Z}^{+}$, it holds that $x_{n+1}=x_{n}+3 \sqrt{x_{n}}+\frac{n}{\sqrt{x_{n}}}$. Find the value of $\lim _{n \rightarrow+\infty} \frac{n^{2}}{x_{n}}$. | "[\"\\\\frac{4}{9}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107493, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117444"}] | {
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} |
[
"-\\sqrt{3}"
] | [
"skywork"
] | f916030857e31ee04218490eaf04efb56904b802954aedd5ce3667cf1f37a8d7 | [
{
"content": "## Problem Statement\n\nCalculate the limit of the numerical sequence:\n\n$\\lim _{n \\rightarrow \\infty} \\frac{n^{2}-\\sqrt{3 n^{5}-7}}{\\left(n^{2}-n \\cos n+1\\right) \\sqrt{n}}$",
"role": "user"
}
] | ## Problem Statement
Calculate the limit of the numerical sequence:
$\lim _{n \rightarrow \infty} \frac{n^{2}-\sqrt{3 n^{5}-7}}{\left(n^{2}-n \cos n+1\right) \sqrt{n}}$ | "[\"-\\\\sqrt{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107508, "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:117445"}] | {
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} |
[
"5"
] | [
"skywork"
] | ce63106901975d6517f6017e53645303aea959e6dfd5bb8c23da28cd2b3f7e3d | [
{
"content": "9.5. At competitions, an athlete's performance is evaluated by 7 judges, each of whom gives a score (an integer from 0 to 10). To obtain the final score, the best and worst scores from the judges are discarded, and the arithmetic mean is calculated. If the average score were calculated based on al... | 9.5. At competitions, an athlete's performance is evaluated by 7 judges, each of whom gives a score (an integer from 0 to 10). To obtain the final score, the best and worst scores from the judges are discarded, and the arithmetic mean is calculated. If the average score were calculated based on all seven scores, the at... | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107492, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117447"}] | {
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} |
[
"5"
] | [
"skywork"
] | b63835232ac2a64dc86a4f28ea8c619757822c0f192b151d26ac01bb4f9f998f | [
{
"content": "# 2. Option 1.\n\nTourists Vitya and Pasha are walking from city A to city B at equal speeds, while tourists Katya and Masha are walking from city B to city A at equal speeds. Vitya met Masha at 12:00, Pasha met Masha at 15:00, and Vitya met Katya at 14:00. How many hours after noon did Pasha meet... | # 2. Option 1.
Tourists Vitya and Pasha are walking from city A to city B at equal speeds, while tourists Katya and Masha are walking from city B to city A at equal speeds. Vitya met Masha at 12:00, Pasha met Masha at 15:00, and Vitya met Katya at 14:00. How many hours after noon did Pasha meet Katya? | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107500, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117448"}] | {
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"reference_present": true
} |
[
"\\frac{1+\\sqrt{5}}{2}"
] | [
"skywork"
] | 81546383596d80880eac7d286a64a162178b170b4d5776b039ff43e16ca9c931 | [
{
"content": "6. Find all triples of positive reals $(x, y, z)$ that satisfy the system\n\n$$\n2 x \\sqrt{x+1}-y(y+1)=1\n$$\n\n$$\n\\begin{aligned}\n& 2 y \\sqrt{y+1}-z(z+1)=1 \\\\\n& 2 z \\sqrt{z+1}-x(x+1)=1\n\\end{aligned}\n$$",
"role": "user"
}
] | 6. Find all triples of positive reals $(x, y, z)$ that satisfy the system
$$
2 x \sqrt{x+1}-y(y+1)=1
$$
$$
\begin{aligned}
& 2 y \sqrt{y+1}-z(z+1)=1 \\
& 2 z \sqrt{z+1}-x(x+1)=1
\end{aligned}
$$ | "[\"\\\\frac{1+\\\\sqrt{5}}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107494, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117449"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3795"
] | [
"skywork"
] | dd0add3c317e00379fdb708a2086286d650db8f33e5d482c7df345d310d426c5 | [
{
"content": "The Hoopers, coached by Coach Loud, have 15 players. George and Alex are the two players who refuse to play together in the same lineup. Additionally, if George plays, another player named Sam refuses to play. How many starting lineups of 6 players can Coach Loud create, provided the lineup does n... | The Hoopers, coached by Coach Loud, have 15 players. George and Alex are the two players who refuse to play together in the same lineup. Additionally, if George plays, another player named Sam refuses to play. How many starting lineups of 6 players can Coach Loud create, provided the lineup does not include both George... | "[\"3795\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107502, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:117450"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{n(n+1)}{2}-1"
] | [
"skywork"
] | 516b7c4c753a34cc593e9acc36448585d6f5c6057981e314c603d46636ace52a | [
{
"content": "Hunter 591 placed $n(n \\geqslant 2)$ nets at different positions on a number line, the initial positions of the nets are denoted as $a_{1}, a_{2}$, $\\cdots, a_{n}$. There is a bug between each pair of adjacent nets, and each net moves in the positive or negative direction at speeds $v_{1}, v_{2}... | Hunter 591 placed $n(n \geqslant 2)$ nets at different positions on a number line, the initial positions of the nets are denoted as $a_{1}, a_{2}$, $\cdots, a_{n}$. There is a bug between each pair of adjacent nets, and each net moves in the positive or negative direction at speeds $v_{1}, v_{2}, \cdots, v_{n}$. If two... | "[\"\\\\frac{n(n+1)}{2}-1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107488, "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:117451"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"505"
] | [
"skywork"
] | 731bf1bad857ed82abacb5d4201c711c0bb501aba2c7fde5c0d7b230e2f2c4dc | [
{
"content": "What is the largest number of integers that we can choose from the set $\\{1, 2, 3, \\ldots, 2017\\}$ such that the difference between any two of them is not a prime number?",
"role": "user"
}
] | What is the largest number of integers that we can choose from the set $\{1, 2, 3, \ldots, 2017\}$ such that the difference between any two of them is not a prime number? | "[\"505\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107511, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:117452"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"-\\frac{1}{3}"
] | [
"skywork"
] | 4999abc502ba040187f65a75bc69ab9c68266429f6a1568b1e28fb473c99adc5 | [
{
"content": "Determine the common rational root \\( k \\) of the following polynomial equations which is not integral:\n\\[45x^4 + ax^3 + bx^2 + cx + 8 = 0\\]\n\\[8x^5 + dx^4 + ex^3 + fx^2 + gx + 45 = 0\\]\nThis root \\( k \\) is assumed to be a negative non-integer.",
"role": "user"
}
] | Determine the common rational root \( k \) of the following polynomial equations which is not integral:
\[45x^4 + ax^3 + bx^2 + cx + 8 = 0\]
\[8x^5 + dx^4 + ex^3 + fx^2 + gx + 45 = 0\]
This root \( k \) is assumed to be a negative non-integer. | "[\"-\\\\frac{1}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107487, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117453"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"a \\in \\left(0, \\frac{1}{2}\\right]"
] | [
"skywork"
] | 1772c01ac405d1ed0fddd0e9d28404810f4946fd7c4e5a1e445c77bc9198f49d | [
{
"content": "9. (16 points) Given points $A(1,0), B(0,-2)$, and $O$ as the origin, a moving point $C$ satisfies:\n$$\n\\overrightarrow{O C}=\\alpha \\overrightarrow{O A}+\\beta \\overrightarrow{O B}(\\alpha, \\beta \\in \\mathbf{R}, \\alpha-2 \\beta=1) \\text {. }\n$$\n\nLet the trajectory of point $C$ interse... | 9. (16 points) Given points $A(1,0), B(0,-2)$, and $O$ as the origin, a moving point $C$ satisfies:
$$
\overrightarrow{O C}=\alpha \overrightarrow{O A}+\beta \overrightarrow{O B}(\alpha, \beta \in \mathbf{R}, \alpha-2 \beta=1) \text {. }
$$
Let the trajectory of point $C$ intersect the hyperbola $\frac{x^{2}}{a^{2}}-\... | "[\"a \\\\in \\\\left(0, \\\\frac{1}{2}\\\\right]\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107501, "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:117454"}] | {
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} |
[
"k=6,3, \\frac{10}{3}"
] | [
"skywork"
] | 09bfb3c997060668968e566477cdc6805fa1b3e089f8098eef8ae6c3b11e2f10 | [
{
"content": "Five. (Full marks 25 points) Let the quadratic equation in $x$ be $\\left(k^{2}-6 k+8\\right) x^{2}+\\left(2 k^{2}-6 k-4\\right) x+k^{2}=4$ with both roots being integers. Find all real values of $k$ that satisfy the condition.\n\n---\n\nTranslate the above text into English, please retain the ori... | Five. (Full marks 25 points) Let the quadratic equation in $x$ be $\left(k^{2}-6 k+8\right) x^{2}+\left(2 k^{2}-6 k-4\right) x+k^{2}=4$ with both roots being integers. Find all real values of $k$ that satisfy the condition.
---
Translate the above text into English, please retain the original text's line breaks and f... | "[\"k=6,3, \\\\frac{10}{3}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107523, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117455"}] | {
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} |
[
"2^100 - 2^87"
] | [
"skywork"
] | d71bede35ad13c3a1a4ddab3dac1023f8990d154dc3ae74032c4e165ca2f2a13 | [
{
"content": "The set \\( M \\) is a subset of the set \\( A = \\{1, 2, \\cdots, 100\\} \\), and \\( M \\) contains at least one square number or cube number. Find the number of such subsets \\( M \\).",
"role": "user"
}
] | The set \( M \) is a subset of the set \( A = \{1, 2, \cdots, 100\} \), and \( M \) contains at least one square number or cube number. Find the number of such subsets \( M \). | "[\"2^100 - 2^87\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 107499, "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:117456"}] | {
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[
"7"
] | [
"skywork"
] | 4b7ced12d2d7d04f497c819107914fd672a1d5b804650a0852a08a736ece0a2e | [
{
"content": "Tompsongo A.K.\n\nIn a certain kingdom, there were 32 knights. Some of them were vassals of others (a vassal could have only one suzerain, and the suzerain was always richer than his vassal). A knight who had at least four vassals bore the title of baron. What is the maximum number of barons that ... | Tompsongo A.K.
In a certain kingdom, there were 32 knights. Some of them were vassals of others (a vassal could have only one suzerain, and the suzerain was always richer than his vassal). A knight who had at least four vassals bore the title of baron. What is the maximum number of barons that could be under these con... | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107496, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117458"}] | {
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[
"77"
] | [
"skywork"
] | 49696e61d233987949ae3cc0575da5f49cecff3b76bc372bfcdc2e40cc921fcf | [
{
"content": "It is now 3:00:00 PM, as read on a 12-hour digital clock. In 315 hours, 58 minutes, and 16 seconds, the time will be $X:Y:Z$. What is the value of $X + Y + Z$?",
"role": "user"
}
] | It is now 3:00:00 PM, as read on a 12-hour digital clock. In 315 hours, 58 minutes, and 16 seconds, the time will be $X:Y:Z$. What is the value of $X + Y + Z$? | "[\"77\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107515, "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:117459"}] | {
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[
"\\frac{1}{\\pi}"
] | [
"skywork"
] | cd759d1448415404683a052e4e9991989dee8cc6f12bdda6c2a9c7fed1afc695 | [
{
"content": "A cube with side length $100cm$ is filled with water and has a hole through which the water drains into a cylinder of radius $100cm.$ If the water level in the cube is falling at a rate of $1 \\frac{cm}{s} ,$ how fast is the water level in the cylinder rising?",
"role": "user"
}
] | A cube with side length $100cm$ is filled with water and has a hole through which the water drains into a cylinder of radius $100cm.$ If the water level in the cube is falling at a rate of $1 \frac{cm}{s} ,$ how fast is the water level in the cylinder rising? | "[\"\\\\frac{1}{\\\\pi}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107510, "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:117460"}] | {
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[
"7414"
] | [
"skywork"
] | df0c02846cc5b4c5287f867219a4479fc514bf2a8c7561493edd2c3a4a3e3bf4 | [
{
"content": "What is the nearest integer to \\((3+\\sqrt{2})^6\\)?",
"role": "user"
}
] | What is the nearest integer to \((3+\sqrt{2})^6\)? | "[\"7414\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107526, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117461"}] | {
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[
"510"
] | [
"skywork"
] | 4c823a5759a5a9487384a2616d06e15e2e8bc5fabc453339fa283e36231f46d5 | [
{
"content": "1. Given the set\n$$\nM=\\left\\{x|5-| 2 x-3 \\mid \\in \\mathbf{N}_{+}\\right\\} \\text {. }\n$$\n\nThen the number of all non-empty proper subsets of $M$ is ( ).\n(A) 254\n(B) 255\n(C) 510\n(D) 511",
"role": "user"
}
] | 1. Given the set
$$
M=\left\{x|5-| 2 x-3 \mid \in \mathbf{N}_{+}\right\} \text {. }
$$
Then the number of all non-empty proper subsets of $M$ is ( ).
(A) 254
(B) 255
(C) 510
(D) 511 | "[\"510\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107507, "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:117462"}] | {
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[
"180"
] | [
"skywork"
] | 3e9d83c64dd6fe5dd1b9c799a4439e5ab9eb2219c70ac55335842fb28e174fa2 | [
{
"content": "11. (20 points) Given non-zero complex numbers $x, y$ satisfy $y^{2}\\left(x^{2}-x y+y^{2}\\right)+x^{3}(x-y)=0$.\nFind the value of $\\sum_{m=0}^{29} \\sum_{n=0}^{29} x^{18 m n} y^{-18 m n}$.",
"role": "user"
}
] | 11. (20 points) Given non-zero complex numbers $x, y$ satisfy $y^{2}\left(x^{2}-x y+y^{2}\right)+x^{3}(x-y)=0$.
Find the value of $\sum_{m=0}^{29} \sum_{n=0}^{29} x^{18 m n} y^{-18 m n}$. | "[\"180\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107505, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117463"}] | {
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[
"946"
] | [
"skywork"
] | 31a9c59e16dea2b4ffa1378884ecf0263b75280b4e1d5f5bb0d8e5d2a7dc4ead | [
{
"content": "Find the number of elements in the first $64$ rows of Pascal's Triangle that are divisible by $4$.\n\n$\\mathrm{(A)}\\,256\\quad\\mathrm{(B)}\\,496\\quad\\mathrm{(C)}\\,512\\quad\\mathrm{(D)}\\,640\\quad\\mathrm{(E)}\\,796 \\\\\n\\quad\\mathrm{(F)}\\,946\\quad\\mathrm{(G)}\\,1024\... | Find the number of elements in the first $64$ rows of Pascal's Triangle that are divisible by $4$.
$\mathrm{(A)}\,256\quad\mathrm{(B)}\,496\quad\mathrm{(C)}\,512\quad\mathrm{(D)}\,640\quad\mathrm{(E)}\,796 \\
\quad\mathrm{(F)}\,946\quad\mathrm{(G)}\,1024\quad\mathrm{(H)}\,1134\quad\mathrm{(I)}\,1256\q... | "[\"946\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107518, "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:117464"}] | {
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} |
[
"39"
] | [
"skywork"
] | 37bff3c3d4a87efff2023f35dc342be22b3ffa3acec0aa42b3fa4549602f13f5 | [
{
"content": "Example 2 Given\n$$\n\\begin{array}{l}\n\\frac{1}{1 \\times \\sqrt{2}+2 \\sqrt{1}}+\\frac{1}{2 \\sqrt{3}+3 \\sqrt{2}}+\\cdots+ \\\\\n\\frac{1}{n \\sqrt{n+1}+(n+1) \\sqrt{n}}\n\\end{array}\n$$\n\nis greater than $\\frac{19}{20}$ and less than $\\frac{20}{21}$. Then the difference between the maximu... | Example 2 Given
$$
\begin{array}{l}
\frac{1}{1 \times \sqrt{2}+2 \sqrt{1}}+\frac{1}{2 \sqrt{3}+3 \sqrt{2}}+\cdots+ \\
\frac{1}{n \sqrt{n+1}+(n+1) \sqrt{n}}
\end{array}
$$
is greater than $\frac{19}{20}$ and less than $\frac{20}{21}$. Then the difference between the maximum and minimum values of the positive integer $n... | "[\"39\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107513, "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:117465"}] | {
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[
"24"
] | [
"skywork"
] | 5485ce469d64485a09a0488776d97d43f1ac9952cee73d5f6c27ac9312f6db09 | [
{
"content": "4. The regular octagon $A B C D E F G H$ is inscribed in a circle. Points $P$ and $Q$ are on the circle, with $P$ between $C$ and $D$, such that $A P Q$ is an equilateral triangle. It is possible to inscribe a regular $n$-sided polygon, one of whose sides is $P D$, in the circle. What is the value... | 4. The regular octagon $A B C D E F G H$ is inscribed in a circle. Points $P$ and $Q$ are on the circle, with $P$ between $C$ and $D$, such that $A P Q$ is an equilateral triangle. It is possible to inscribe a regular $n$-sided polygon, one of whose sides is $P D$, in the circle. What is the value of $n$ ? | "[\"24\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107512, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117466"}] | {
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[
"\\dfrac {2^{101}-2048}{3}"
] | [
"skywork"
] | 213ce08952dc9da2ec657d6fb7324edbf99262dd426f18f89598964e26f02f0f | [
{
"content": "Given that the geometric sequence $\\{a_n\\}$ is an increasing sequence, and $a_5^2=a_{10}$, $2(a_n+a_{n+2})=5a_{n+1}$, where $n\\in\\mathbb{N}^*$. \n(Ⅰ) Find $a_n$; \n(Ⅱ) Let $c_n=1-(-1)^na_n$, the solution set of the inequality $c_k \\geqslant 2014$ $(1\\leqslant k\\leqslant 100,k\\in\\mathbb{... | Given that the geometric sequence $\{a_n\}$ is an increasing sequence, and $a_5^2=a_{10}$, $2(a_n+a_{n+2})=5a_{n+1}$, where $n\in\mathbb{N}^*$.
(Ⅰ) Find $a_n$;
(Ⅱ) Let $c_n=1-(-1)^na_n$, the solution set of the inequality $c_k \geqslant 2014$ $(1\leqslant k\leqslant 100,k\in\mathbb{N}^*)$ is $M$, find the sum of al... | "[\"\\\\dfrac {2^{101}-2048}{3}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 107498, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117467"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\pi a^2"
] | [
"skywork"
] | 397a9484a6b6ee5c5f04ed6dda49bebc6e2645287c201331ea41c19146a307b6 | [
{
"content": "Let $a$ be positive numbers.For $|x|\\leq a,$ find the maximum and minimum value of $\\int_{x-a}^{x+a}\\sqrt{4a^{2}-t^{2}}\\ dt.$",
"role": "user"
}
] | Let $a$ be positive numbers.For $|x|\leq a,$ find the maximum and minimum value of $\int_{x-a}^{x+a}\sqrt{4a^{2}-t^{2}}\ dt.$ | "[\"\\\\pi a^2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107519, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117468"}] | {
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[
"\\frac{1}{\\sqrt{2}}"
] | [
"skywork"
] | de28cdc396318f4815d7d832c6f5c673329f96f4136539228f71b6dd6f44b4e6 | [
{
"content": "52. On the plane, a square $A B C D$ is given. Find the minimum of the ratio $\\frac{O A+O C}{O B+O D}$, where $O$ is an arbitrary point on the plane.",
"role": "user"
}
] | 52. On the plane, a square $A B C D$ is given. Find the minimum of the ratio $\frac{O A+O C}{O B+O D}$, where $O$ is an arbitrary point on the plane. | "[\"\\\\frac{1}{\\\\sqrt{2}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107520, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:117469"}] | {
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[
"The only solution is \\((a, b, c, d) = (5, -3, 2, 3)\\)."
] | [
"skywork"
] | 95bb3257c090d46138dc618a8c98bf6762f8391e89067a47ada9de31ea97852d | [
{
"content": "Find all ordered 4-tuples of integers $(a, b, c, d)$ (not necessarily distinct) satisfying the following system of equations: $a^{2}-b^{2}-c^{2}-d^{2} =c-b-2$, $2 a b =a-d-32$, $2 a c =28-a-d$, $2 a d =b+c+31$.",
"role": "user"
}
] | Find all ordered 4-tuples of integers $(a, b, c, d)$ (not necessarily distinct) satisfying the following system of equations: $a^{2}-b^{2}-c^{2}-d^{2} =c-b-2$, $2 a b =a-d-32$, $2 a c =28-a-d$, $2 a d =b+c+31$. | "[\"The only solution is \\\\((a, b, c, d) = (5, -3, 2, 3)\\\\).\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 107524, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117470"}] | {
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} |
[
"68"
] | [
"skywork"
] | cdb1955d634df30d36624fd66f5488fc67b96e3559db855f8035d88b78102711 | [
{
"content": "Use the Horner's method to calculate the value of the polynomial $f(x) = 2x^5 + 5x^3 - x^2 + 9x + 1$ when $x = 3$. What is the value of $v_3$ in the third step?",
"role": "user"
}
] | Use the Horner's method to calculate the value of the polynomial $f(x) = 2x^5 + 5x^3 - x^2 + 9x + 1$ when $x = 3$. What is the value of $v_3$ in the third step? | "[\"68\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107509, "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:117471"}] | {
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} |
[
"4^{\\frac{n-1}{4}} - (-1)^{\\frac{n-1}{4}}"
] | [
"skywork"
] | 6f7d485bacb8d6844cc2e4761265d8db8600d2b2886f9ee98653a4d786bfa1be | [
{
"content": "A plane geometric figure of $n$ sides with the vertices $A_1,A_2,A_3,\\dots, A_n$ ($A_i$ is adjacent to $A_{i+1}$ for every $i$ integer where $1\\leq i\\leq n-1$ and $A_n$ is adjacent to $A_1$) is called [i]brazilian[/i] if:\nI - The segment $A_jA_{j+1}$ is equal to $(\\sqrt{2})^{j-1}$, for every ... | A plane geometric figure of $n$ sides with the vertices $A_1,A_2,A_3,\dots, A_n$ ($A_i$ is adjacent to $A_{i+1}$ for every $i$ integer where $1\leq i\leq n-1$ and $A_n$ is adjacent to $A_1$) is called [i]brazilian[/i] if:
I - The segment $A_jA_{j+1}$ is equal to $(\sqrt{2})^{j-1}$, for every $j$ with $1\leq j\leq n-1$.... | "[\"4^{\\\\frac{n-1}{4}} - (-1)^{\\\\frac{n-1}{4}}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107504, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117472"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{8\\sqrt{2}}{3}"
] | [
"skywork"
] | 1d12efe400179066fe64e03a07256aa85315e84899503cd851a5e1b777d85048 | [
{
"content": "A line passes through point $Q(\\frac{1}{3}, \\frac{4}{3})$ and intersects the hyperbola $x^{2}- \\frac{y^{2}}{4}=1$ at points $A$ and $B$. Point $Q$ is the midpoint of chord $AB$.\n\n1. Find the equation of the line containing $AB$.\n2. Find the length of $|AB|$.",
"role": "user"
}
] | A line passes through point $Q(\frac{1}{3}, \frac{4}{3})$ and intersects the hyperbola $x^{2}- \frac{y^{2}}{4}=1$ at points $A$ and $B$. Point $Q$ is the midpoint of chord $AB$.
1. Find the equation of the line containing $AB$.
2. Find the length of $|AB|$. | "[\"\\\\frac{8\\\\sqrt{2}}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107514, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "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:117473"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | 5063848fd10299ffbcd43c2c6b65bc9b1751c35662202ff58335c1deacfb5c51 | [
{
"content": "61. A shape made of building blocks, when viewed from the front is $\\square$, and when viewed from the side is $\\square$. If this shape is made using $n$ identical cubic blocks, then how many possible values can $n$ have?",
"role": "user"
}
] | 61. A shape made of building blocks, when viewed from the front is $\square$, and when viewed from the side is $\square$. If this shape is made using $n$ identical cubic blocks, then how many possible values can $n$ have? | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107525, "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:117475"}] | {
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[
"43"
] | [
"skywork"
] | 39346d4853741fb76225cec74ad8bd1a24d65d4593eac6b5cada34dea3a1c53d | [
{
"content": "For certain real values of $a, b, c,$ and $d,$ the equation $x^4+ax^3+bx^2+cx+d=0$ has four non-real roots. The product of two of these roots is $7-3i$ and the sum of the other two roots is $5-2i,$ where $i^2 = -1.$ Find $b.$",
"role": "user"
}
] | For certain real values of $a, b, c,$ and $d,$ the equation $x^4+ax^3+bx^2+cx+d=0$ has four non-real roots. The product of two of these roots is $7-3i$ and the sum of the other two roots is $5-2i,$ where $i^2 = -1.$ Find $b.$ | "[\"43\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107522, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117476"}] | {
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[
"12"
] | [
"skywork"
] | 4e092cc879ee72338573edbf34950ad7b30b5d80b7b8761add9f8a37e1d39dc2 | [
{
"content": "Problem 5. (6 points) Peter has $n^{3}$ unit white cubes, from which he wants to assemble a cube $n \\times n \\times n$ with a completely white surface. How many of the faces of the unit cubes does Emil need to color to prevent Peter? Solve the problem for:\na) (2 points) $n=2$;\nb) (4 points) $n... | Problem 5. (6 points) Peter has $n^{3}$ unit white cubes, from which he wants to assemble a cube $n \times n \times n$ with a completely white surface. How many of the faces of the unit cubes does Emil need to color to prevent Peter? Solve the problem for:
a) (2 points) $n=2$;
b) (4 points) $n=3$. | "[\"12\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107517, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117477"}] | {
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[
"\\arccos(\\sqrt{3}-1);\\frac{\\pi}{2}-\\arccos(\\sqrt{3}-1)"
] | [
"skywork"
] | 974701d19d8383c2ac6e028f43457d4a7cdab68f4d488f4fea34bda42f74cc9e | [
{
"content": "12.266. The base of the pyramid is an equilateral triangle. Two lateral faces are perpendicular to the plane of the base. The sum of two unequal plane angles at the vertex is $\\frac{\\pi}{2}$. Find these angles.",
"role": "user"
}
] | 12.266. The base of the pyramid is an equilateral triangle. Two lateral faces are perpendicular to the plane of the base. The sum of two unequal plane angles at the vertex is $\frac{\pi}{2}$. Find these angles. | "[\"\\\\arccos(\\\\sqrt{3}-1);\\\\frac{\\\\pi}{2}-\\\\arccos(\\\\sqrt{3}-1)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107527, "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:117478"}] | {
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[
"2001"
] | [
"skywork"
] | 381bce9d1c3fc34f9c1ddec9a10102f3433f8dee54c051ed2abf4da37c11802b | [
{
"content": "A robot colors natural numbers starting from 1 in ascending order according to the following rule: any natural number that can be expressed as the sum of two composite numbers is colored red; those that do not meet this requirement are colored yellow. For example, 23 can be expressed as the sum of... | A robot colors natural numbers starting from 1 in ascending order according to the following rule: any natural number that can be expressed as the sum of two composite numbers is colored red; those that do not meet this requirement are colored yellow. For example, 23 can be expressed as the sum of two composite numbers... | "[\"2001\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107529, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117479"}] | {
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[
"18"
] | [
"skywork"
] | af9977962da681e5dce6031d3e0999caa5b62abb96120e242189d5a0f6adf5ac | [
{
"content": "1. The diagram shows a shape made from ten squares of side-length $1 \\mathrm{~cm}$, joined edge to edge.\nWhat is the length of its perimeter, in centimetres?\nA 14\nB 18\nC 30\nD 32\nE 40",
"role": "user"
}
] | 1. The diagram shows a shape made from ten squares of side-length $1 \mathrm{~cm}$, joined edge to edge.
What is the length of its perimeter, in centimetres?
A 14
B 18
C 30
D 32
E 40 | "[\"18\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107530, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117480"}] | {
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[
"\\textbf{(C)}4"
] | [
"skywork"
] | 10855e14a7d61901889e98a0199e5ba76be9a909d7955b5d706e351dd6951550 | [
{
"content": "What is the tens digit in the sum $7!+8!+9!+...+2006!$\n$\\textbf{(A) } 1\\qquad \\textbf{(B) } 3\\qquad \\textbf{(C) } 4\\qquad \\textbf{(D) } 6\\qquad \\textbf{(E) } 9$",
"role": "user"
}
] | What is the tens digit in the sum $7!+8!+9!+...+2006!$
$\textbf{(A) } 1\qquad \textbf{(B) } 3\qquad \textbf{(C) } 4\qquad \textbf{(D) } 6\qquad \textbf{(E) } 9$ | "[\"\\\\textbf{(C)}4\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 107544, "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:117481"}] | {
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[
"0.209"
] | [
"skywork"
] | 97285f9ee02c7b20e7b5e75d299b26b713cb74bd314fc563b54bede773bb7fcd | [
{
"content": "Two concentric circles have radii $3$ and $5$. Two points on the outer circle are chosen independently and uniformly at random. What is the probability that the chord joining the two points intersects the inner circle?",
"role": "user"
}
] | Two concentric circles have radii $3$ and $5$. Two points on the outer circle are chosen independently and uniformly at random. What is the probability that the chord joining the two points intersects the inner circle? | "[\"0.209\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 107542, "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:117483"}] | {
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[
"26"
] | [
"skywork"
] | a9e570e2b2ebd0bc5b252fc467f8e591ec24cdb5fe8962138970d493ea8963d1 | [
{
"content": "Flat Albert and his buddy Mike are watching the game on Sunday afternoon. Albert is drinking lemonade from a two-dimensional cup which is an isosceles triangle whose height and base measure 9 cm and 6 cm; the opening of the cup corresponds to the base, which points upwards. Every minute after the ... | Flat Albert and his buddy Mike are watching the game on Sunday afternoon. Albert is drinking lemonade from a two-dimensional cup which is an isosceles triangle whose height and base measure 9 cm and 6 cm; the opening of the cup corresponds to the base, which points upwards. Every minute after the game begins, the follo... | "[\"26\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107521, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117484"}] | {
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[
"142857"
] | [
"skywork"
] | 1a5dd37e70c870ca51c24d7e58097dd973b82b4c31263406ca754688329c6056 | [
{
"content": "Find the least natural number whose last digit is 7 such that it becomes 5 times larger when this last digit is carried to the beginning of the number.",
"role": "user"
}
] | Find the least natural number whose last digit is 7 such that it becomes 5 times larger when this last digit is carried to the beginning of the number. | "[\"142857\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107548, "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:117485"}] | {
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"reference_components": 1,
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} |
[
"300\\pi"
] | [
"skywork"
] | 63968581ab862a7ba1e3b8ae87455a731f53feb6bf0ecf84e120457d95d064e8 | [
{
"content": "The area of the base of a hemisphere is $100\\pi$. What is the total surface area of the hemisphere? Express your answer in terms of $\\pi$.",
"role": "user"
}
] | The area of the base of a hemisphere is $100\pi$. What is the total surface area of the hemisphere? Express your answer in terms of $\pi$. | "[\"300\\\\pi\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107535, "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:117486"}] | {
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[
"10"
] | [
"skywork"
] | 128490fef874aee669b38285df738b6397c40be35d415dcf7a367d6fda2d5023 | [
{
"content": "There are six rock specimens with weights of 8.5 kg, 6 kg, 4 kg, 4 kg, 3 kg, and 2 kg. They need to be distributed into three backpacks such that the heaviest backpack is as light as possible. What is the weight of the rock specimens in the heaviest backpack?",
"role": "user"
}
] | There are six rock specimens with weights of 8.5 kg, 6 kg, 4 kg, 4 kg, 3 kg, and 2 kg. They need to be distributed into three backpacks such that the heaviest backpack is as light as possible. What is the weight of the rock specimens in the heaviest backpack? | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107546, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117487"}] | {
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[
"\\frac{3 \\cdot 2013^2}{2}"
] | [
"skywork"
] | 8cea9159aca86542e7ff7f45ff9fe529d203bf69d8d2839333907ac0bb83a47e | [
{
"content": "Numbers $0$ and $2013$ are written at two opposite vertices of a cube. Some real numbers are to be written at the remaining $6$ vertices of the cube. On each edge of the cube the difference between the numbers at its endpoints is written. When is the sum of squares of the numbers written on the ed... | Numbers $0$ and $2013$ are written at two opposite vertices of a cube. Some real numbers are to be written at the remaining $6$ vertices of the cube. On each edge of the cube the difference between the numbers at its endpoints is written. When is the sum of squares of the numbers written on the edges minimal? | "[\"\\\\frac{3 \\\\cdot 2013^2}{2}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107534, "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:117489"}] | {
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[
"15000"
] | [
"skywork"
] | b7d0203e86b78927c2e484549cc17406582973a185541f75e5a24459f851dd54 | [
{
"content": "A workshop produces a type of instrument with a fixed cost of $7500. Each additional unit of the instrument requires an additional investment of $100. The total revenue function is given by: $H(x) = \\begin{cases} 400x - x^2, (0 \\leq x \\leq 200) \\\\ 40000, (x > 200) \\end{cases}$, where $x$ is ... | A workshop produces a type of instrument with a fixed cost of $7500. Each additional unit of the instrument requires an additional investment of $100. The total revenue function is given by: $H(x) = \begin{cases} 400x - x^2, (0 \leq x \leq 200) \\ 40000, (x > 200) \end{cases}$, where $x$ is the monthly production volum... | "[\"15000\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107531, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117490"}] | {
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[
"256"
] | [
"skywork"
] | c90b91ccb19b34d5482f4179d539eb72cb145e872f435c099816aaa8407c90cd | [
{
"content": "Given the binomial $(ax+b)^{n}=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+…+a_{n}x^{n}(a，b∈R，n∈N^{*})$.\n\n(1) When $a=b=1$, $n=6$, find:\n ① The value of $a_{1}+a_{2}+a_{3}+…+a_{n}$.\n ② The value of $a_{1}+2a_{2}+3a_{3}+…+na_{n}$.\n\n(2) When $a=1$, $b=- \\sqrt {3}$, $n=8$, find the value of $(a_{0}+a... | Given the binomial $(ax+b)^{n}=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+…+a_{n}x^{n}(a，b∈R，n∈N^{*})$.
(1) When $a=b=1$, $n=6$, find:
① The value of $a_{1}+a_{2}+a_{3}+…+a_{n}$.
② The value of $a_{1}+2a_{2}+3a_{3}+…+na_{n}$.
(2) When $a=1$, $b=- \sqrt {3}$, $n=8$, find the value of $(a_{0}+a_{2}+a_{4}+a_{6}+a_{8})^{2}-(... | "[\"256\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107536, "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:117491"}] | {
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[
"2\\arcsin\\frac{1}{\\sqrt{5}}"
] | [
"skywork"
] | 4d4ff39518c69ec6b842877b25d810bb9660e7f92e5da0275124da974fa62049 | [
{
"content": "10,11\n\nThe base of an inclined parallelepiped is a rectangle $A B C D$; $A A 1, B B 1, C C 1$ and $D D 1$ are the lateral edges. A sphere with center at point $O$ touches the edges $B C, A 1 B 1$ and $D D 1$ at points $B, A 1$ and $D 1$, respectively. Find $\\angle A 1 O B$, if $A D=4$, and the ... | 10,11
The base of an inclined parallelepiped is a rectangle $A B C D$; $A A 1, B B 1, C C 1$ and $D D 1$ are the lateral edges. A sphere with center at point $O$ touches the edges $B C, A 1 B 1$ and $D D 1$ at points $B, A 1$ and $D 1$, respectively. Find $\angle A 1 O B$, if $A D=4$, and the height of the parallelepi... | "[\"2\\\\arcsin\\\\frac{1}{\\\\sqrt{5}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107540, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117492"}] | {
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[
"12"
] | [
"skywork"
] | 26ed3a1fea76c40fde457de3fc9a2f4f4b279c521b15b035177b64e8ac726dd9 | [
{
"content": "4. How many different right-angled triangles exist, one of the legs of which is equal to $\\sqrt{2016}$, and the other leg and the hypotenuse are expressed as natural numbers\n\nANSWER: 12.",
"role": "user"
}
] | 4. How many different right-angled triangles exist, one of the legs of which is equal to $\sqrt{2016}$, and the other leg and the hypotenuse are expressed as natural numbers
ANSWER: 12. | "[\"12\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107538, "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:117493"}] | {
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"reference_present": true
} |
[
"2^k \\text{ for } k \\in \\mathbb{Z}_{>0}"
] | [
"skywork"
] | 4483adc39091730d699c7e59958d4a7db0147b591d77df3d3c474ea346197c16 | [
{
"content": "We call a natural number venerable if the sum of all its divisors, including $1$, but not including the number itself, is $1$ less than this number. Find all the venerable numbers, some exact degree of which is also venerable.",
"role": "user"
}
] | We call a natural number venerable if the sum of all its divisors, including $1$, but not including the number itself, is $1$ less than this number. Find all the venerable numbers, some exact degree of which is also venerable. | "[\"2^k \\\\text{ for } k \\\\in \\\\mathbb{Z}_{>0}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107537, "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:117494"}] | {
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} |
[
"106"
] | [
"skywork"
] | 11703ce1787fee31e1238bede2236c88598aa8dfbea86d67bb1e565ac17c2abe | [
{
"content": "12. (IMO-20-1) The last three digits of the numbers $1978^{n}$ and $1978^{m}$ are equal. Find the positive integers $n$ and $m$ such that $n+m$ is minimized, where $n>m \\geqslant 1$.",
"role": "user"
}
] | 12. (IMO-20-1) The last three digits of the numbers $1978^{n}$ and $1978^{m}$ are equal. Find the positive integers $n$ and $m$ such that $n+m$ is minimized, where $n>m \geqslant 1$. | "[\"106\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107552, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117495"}] | {
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"reference_components": 1,
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[
"3024"
] | [
"skywork"
] | ca49efc0259b2595911e93985d06033fd6fe224ce1abc5f883775ae2752625d2 | [
{
"content": "Consider a fictional country where license plates are made using an extended Rotokas alphabet with fourteen letters: A, E, G, I, K, M, O, P, R, S, T, U, V, Z. License plates are six letters long and must start with G, end with M, and not contain the letters S, T, or Z. Additionally, no letters may... | Consider a fictional country where license plates are made using an extended Rotokas alphabet with fourteen letters: A, E, G, I, K, M, O, P, R, S, T, U, V, Z. License plates are six letters long and must start with G, end with M, and not contain the letters S, T, or Z. Additionally, no letters may repeat. How many such... | "[\"3024\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107541, "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:117496"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"75"
] | [
"skywork"
] | cdf8495ba0d79e96ddaf2d2f70ef4d0a362fd1590612b603c88a6c2aff41f0ac | [
{
"content": "Let $E$ be a three-dimensional ellipsoid. For a plane $p$, let $E(p)$ be the projection of $E$ onto the plane $p$. The minimum and maximum areas of $E(p)$ are $9 \\pi$ and $25 \\pi$, and there exists a $p$ where $E(p)$ is a circle of area $16 \\pi$. If $V$ is the volume of $E$, compute $V / \\pi$.... | Let $E$ be a three-dimensional ellipsoid. For a plane $p$, let $E(p)$ be the projection of $E$ onto the plane $p$. The minimum and maximum areas of $E(p)$ are $9 \pi$ and $25 \pi$, and there exists a $p$ where $E(p)$ is a circle of area $16 \pi$. If $V$ is the volume of $E$, compute $V / \pi$. | "[\"75\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107539, "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:117497"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac {12}{5}"
] | [
"skywork"
] | 7bb7d9a6c6a8ea44cd06e546ccd1a75f51cb3f2be69f44a4c202c361f714f15b | [
{
"content": "Given that in the rectangular coordinate system $(xOy)$, the origin is the pole and the positive semi-axis of $x$ is the polar axis to establish a polar coordinate system, the polar coordinate equation of the conic section $(C)$ is $p^{2}= \\frac {12}{3+\\sin ^{2}\\theta }$, the fixed point $A(0,-... | Given that in the rectangular coordinate system $(xOy)$, the origin is the pole and the positive semi-axis of $x$ is the polar axis to establish a polar coordinate system, the polar coordinate equation of the conic section $(C)$ is $p^{2}= \frac {12}{3+\sin ^{2}\theta }$, the fixed point $A(0,- \sqrt {3})$, $F\_{1}$, $... | "[\"\\\\frac {12}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107532, "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:117498"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3^{n-1}-2^{n-1}"
] | [
"skywork"
] | fae3f175b3adc71117e36ebbc0d26a41145925817840d78130e5d45312b14f9c | [
{
"content": "## Task A-4.4.\n\nIn a football club, there are $n$ players who have jerseys with mutually distinct numbers from 1 to $n$. At the end of the season, the player with number 1 retires. The management selects one of the remaining players to sell to another club, while the remaining $n-2$ players rece... | ## Task A-4.4.
In a football club, there are $n$ players who have jerseys with mutually distinct numbers from 1 to $n$. At the end of the season, the player with number 1 retires. The management selects one of the remaining players to sell to another club, while the remaining $n-2$ players receive jerseys with mutuall... | "[\"3^{n-1}-2^{n-1}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107547, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117499"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 5cd8b8e4353027efd6cd94d28dcc10124e99fc5e3cecc63d09b0c5b003042baf | [
{
"content": "9. $\\tan 20^{\\circ} \\csc 60^{\\circ}\\left(\\csc 10^{\\circ}-1\\right)=$",
"role": "user"
}
] | 9. $\tan 20^{\circ} \csc 60^{\circ}\left(\csc 10^{\circ}-1\right)=$ | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107557, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117500"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20, -5"
] | [
"skywork"
] | 6392997637292f4ba4e622d8c04c326bff80902d61df9431a72116102ff678a9 | [
{
"content": "The values of $a$ in the equation: $\\log_{10}(a^2 - 15a) = 2$ are:",
"role": "user"
}
] | The values of $a$ in the equation: $\log_{10}(a^2 - 15a) = 2$ are: | "[\"20, -5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107550, "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:117501"}] | {
"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}{3}"
] | [
"skywork"
] | edbf915faa321d3c5f75b9290d8a13929e1e2091a3528557daa4b7b9695db389 | [
{
"content": "A three-digit natural number $abc$ is termed a \"convex number\" if and only if the digits $a$, $b$, and $c$ (representing the hundreds, tens, and units place, respectively) satisfy $a < b$ and $c < b$. Given that $a$, $b$, and $c$ belong to the set $\\{5, 6, 7, 8, 9\\}$ and are distinct from one ... | A three-digit natural number $abc$ is termed a "convex number" if and only if the digits $a$, $b$, and $c$ (representing the hundreds, tens, and units place, respectively) satisfy $a < b$ and $c < b$. Given that $a$, $b$, and $c$ belong to the set $\{5, 6, 7, 8, 9\}$ and are distinct from one another, find the probabil... | "[\"\\\\frac {1}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107551, "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:117502"}] | {
"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
} |
[
"2011"
] | [
"skywork"
] | 6c9e477c4ad0c1a8a58c81ecd8ccd84b286e560a1e825dc3e5bd77190d931170 | [
{
"content": "Given that $x$ and $y$ are positive integers, and $x^2 - y^2 = 53$, find the value of $x^3 - y^3 - 2(x + y) + 10$.",
"role": "user"
}
] | Given that $x$ and $y$ are positive integers, and $x^2 - y^2 = 53$, find the value of $x^3 - y^3 - 2(x + y) + 10$. | "[\"2011\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107558, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:117503"}] | {
"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
} |
[
"58"
] | [
"skywork"
] | 3650a7c0ec4a874cf4ad5dacb4046dca0eea7a21c7fa10e15906abed76584cce | [
{
"content": "Suppose $N=1+11+101+1001+10001+\\ldots+1 \\overbrace{000 \\ldots 0000}^{50 \\text { zeroes }}$.\n\nWhen $N$ is calculated and written as a single integer, the sum of its digits is\n(A) 58\n(B) 99\n(C) 55\n(D) 50\n(E) 103",
"role": "user"
}
] | Suppose $N=1+11+101+1001+10001+\ldots+1 \overbrace{000 \ldots 0000}^{50 \text { zeroes }}$.
When $N$ is calculated and written as a single integer, the sum of its digits is
(A) 58
(B) 99
(C) 55
(D) 50
(E) 103 | "[\"58\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107553, "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:117504"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{2^{n}+2 \\times(-1)^{n}}{3 \\times 2^{n}}"
] | [
"skywork"
] | f7c1d2be06bd3b03b4e04221e7f20f1a9844008b7d38f77d296b3529f67b4f29 | [
{
"content": "5. A bug crawls along a triangular iron ring, and at each vertex it has an equal chance of crawling to one of the other two vertices. Then the probability that it is back at the starting point after $n$ crawls is\n\n保留源文本的换行和格式，这里的翻译已经按照要求完成。如果需要进一步的帮助或调整，请告知。",
"role": "user"
}
] | 5. A bug crawls along a triangular iron ring, and at each vertex it has an equal chance of crawling to one of the other two vertices. Then the probability that it is back at the starting point after $n$ crawls is
保留源文本的换行和格式，这里的翻译已经按照要求完成。如果需要进一步的帮助或调整，请告知。 | "[\"\\\\frac{2^{n}+2 \\\\times(-1)^{n}}{3 \\\\times 2^{n}}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107555, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117506"}] | {
"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
} |
[
"E"
] | [
"skywork"
] | dd50998b8461cb6caa95174b02dbf13d79773c4d7e80b08ff0c97e96d3901aa1 | [
{
"content": "5. Let $n$ be an integer that is a multiple of 1000 but not of 10000. Which of the following statements is definitely true?\n\n(A) $n / 3$ is a number whose integer part ends with the digits 333 or 666.\n\n(B) $n / 8$ is an integer that ends with the digits 25 or 75.\n\n(C) $n / 125$ is an integer... | 5. Let $n$ be an integer that is a multiple of 1000 but not of 10000. Which of the following statements is definitely true?
(A) $n / 3$ is a number whose integer part ends with the digits 333 or 666.
(B) $n / 8$ is an integer that ends with the digits 25 or 75.
(C) $n / 125$ is an integer that ends with the digits 8... | "[\"E\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107554, "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:117507"}] | {
"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
} |
[
"f(n)=[\\log_{2}n]+1"
] | [
"skywork"
] | 63c44d07401fa20346157caef2d342a78bf599406e7b04c844b50ea8963e5d06 | [
{
"content": "$7 \\cdot 111$ Let $S=\\{1,2, \\cdots, n\\}, n \\geqslant 2, F=\\left\\{A_{1}, A_{2}, \\cdots, A_{t}\\right\\}$, where $A_{i} \\subset S, i=1,2, \\cdots, t$. If for any $x, y \\in S$, there exists $A_{i} \\in F$, such that $\\mid A_{i} \\cap$ $\\{x, y\\} \\mid=1$, then $F$ is said to distinguish $... | $7 \cdot 111$ Let $S=\{1,2, \cdots, n\}, n \geqslant 2, F=\left\{A_{1}, A_{2}, \cdots, A_{t}\right\}$, where $A_{i} \subset S, i=1,2, \cdots, t$. If for any $x, y \in S$, there exists $A_{i} \in F$, such that $\mid A_{i} \cap$ $\{x, y\} \mid=1$, then $F$ is said to distinguish $S$. If $S \subset U A_{i}$, then $F$ is s... | "[\"f(n)=[\\\\log_{2}n]+1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107545, "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:117508"}] | {
"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
} |
[
"48"
] | [
"skywork"
] | c55101630acc17aca4b89a9498edc773535dc63b764706fe7b099d6d165b6fa4 | [
{
"content": "Five positive integers (not necessarily all different) are written on five cards. Boris calculates the sum of the numbers on every pair of cards. He obtains only three different totals: 57, 70, and 83. What is the largest integer on any card?",
"role": "user"
}
] | Five positive integers (not necessarily all different) are written on five cards. Boris calculates the sum of the numbers on every pair of cards. He obtains only three different totals: 57, 70, and 83. What is the largest integer on any card? | "[\"48\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107574, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117509"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | 01016b6539c495d8bb505c7e72c777fa50c0a25e98b8ff0986d2205095dafce4 | [
{
"content": "The first term of a sequence is equal to $3^{2012}$. Each subsequent term is equal to the sum of the digits of the previous term. Find the 10th term.",
"role": "user"
}
] | The first term of a sequence is equal to $3^{2012}$. Each subsequent term is equal to the sum of the digits of the previous term. Find the 10th term. | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107566, "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:117510"}] | {
"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
} |
[
"61"
] | [
"skywork"
] | d8b4f959653d7c39d9832db99fea023a2305debc8705a75b6f1a575175946b4c | [
{
"content": "5. If the distances from the center of the ellipse to the focus, the endpoint of the major axis, the endpoint of the minor axis, and the directrix are all positive integers, then the minimum value of the sum of these four distances is $\\qquad$ .",
"role": "user"
}
] | 5. If the distances from the center of the ellipse to the focus, the endpoint of the major axis, the endpoint of the minor axis, and the directrix are all positive integers, then the minimum value of the sum of these four distances is $\qquad$ . | "[\"61\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107556, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117511"}] | {
"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
} |
[
"2018"
] | [
"skywork"
] | e6b4a5b546bb5f0c49a2398fc98c6a9c4fdbe7c8a6d1be78fd9b0a4912c22e2f | [
{
"content": "If $x=2018$, then the expression $x^{2}+2 x-x(x+1)$ equals\n(A) -2018\n(B) 2018\n(C) 10090\n(D) -10090\n(E) 4039",
"role": "user"
}
] | If $x=2018$, then the expression $x^{2}+2 x-x(x+1)$ equals
(A) -2018
(B) 2018
(C) 10090
(D) -10090
(E) 4039 | "[\"2018\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107567, "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:117512"}] | {
"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"
] | 2f0318e0d692ab94f4144d0f12ff7307eccd1b96d704da3c0687175735cc3288 | [
{
"content": "3. The three points $A, B, C$ form a triangle. $A B=4, B C=5 A C=6$. Let the angle bisector of $\\angle A$ intersect side $B C$ at $D$. Let the foot of the perpendicular from $B$ to the angle bisector of $\\angle A$ be $E$. Let the line through $E$ parallel to $A C$ meet $B C$ at $F$. Compute $D F... | 3. The three points $A, B, C$ form a triangle. $A B=4, B C=5 A C=6$. Let the angle bisector of $\angle A$ intersect side $B C$ at $D$. Let the foot of the perpendicular from $B$ to the angle bisector of $\angle A$ be $E$. Let the line through $E$ parallel to $A C$ meet $B C$ at $F$. Compute $D F$. | "[\"\\\\frac{1}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107549, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117513"}] | {
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[
"0"
] | [
"skywork"
] | c6af2eba7c6755e39950ffd13c5f518526a3d32f6842073ab36e8b359bf10b7e | [
{
"content": "1. Solve the equation $9^{x}+4 \\cdot 3^{x+1}=13$.",
"role": "user"
}
] | 1. Solve the equation $9^{x}+4 \cdot 3^{x+1}=13$. | "[\"0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107585, "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:117516"}] | {
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[
"3\\sqrt{3}\\mathrm{~}"
] | [
"skywork"
] | 4371e9bab0b8b8bfb04155cadaaf2a8b1c96e0e031ef0c368e5241941178b570 | [
{
"content": "10.057. The diagonal of a rectangular trapezoid and its lateral side are equal. Find the length of the midline if the height of the trapezoid is 2 cm and the lateral side is $4 \\mathrm{cm}$.",
"role": "user"
}
] | 10.057. The diagonal of a rectangular trapezoid and its lateral side are equal. Find the length of the midline if the height of the trapezoid is 2 cm and the lateral side is $4 \mathrm{cm}$. | "[\"3\\\\sqrt{3}\\\\mathrm{~}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107559, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117517"}] | {
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[
"-\\frac{4}{3}"
] | [
"skywork"
] | e4b6d0bbe520bd8028a9df249a4fa3e6b07b52b9ef07587b540a30826b70cb71 | [
{
"content": "Charlie noticed his golden ticket was golden in two ways! In addition to being gold, it was a rectangle whose side lengths had ratio the golden ratio $\\varphi = \\tfrac{1+\\sqrt{5}}{2}$. He then folds the ticket so that two opposite corners (vertices connected by a diagonal) coincide and makes a ... | Charlie noticed his golden ticket was golden in two ways! In addition to being gold, it was a rectangle whose side lengths had ratio the golden ratio $\varphi = \tfrac{1+\sqrt{5}}{2}$. He then folds the ticket so that two opposite corners (vertices connected by a diagonal) coincide and makes a sharp crease (the ticket ... | "[\"-\\\\frac{4}{3}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107560, "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:117518"}] | {
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[
"m^{m^{m+2}}"
] | [
"skywork"
] | b27fe536aef8b79ba70095c097aebd487f5306d65089bf712cad5c59e3064ade | [
{
"content": "Let $m \\ge 2$ be an integer. Find the smallest integer $n>m$ such that for any partition of the set $\\{m,m+1,\\cdots,n\\}$ into two subsets, at least one subset contains three numbers $a, b, c$ such that $c=a^{b}$.",
"role": "user"
}
] | Let $m \ge 2$ be an integer. Find the smallest integer $n>m$ such that for any partition of the set $\{m,m+1,\cdots,n\}$ into two subsets, at least one subset contains three numbers $a, b, c$ such that $c=a^{b}$. | "[\" m^{m^{m+2}} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107572, "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:117519"}] | {
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[
"1512"
] | [
"skywork"
] | c6e44056df311b4ee13438ca1222d22e41eeb7c3c51beae986eef42a44cc5ce8 | [
{
"content": "Our football team has 10 members, of which only 3 are strong enough to play offensive lineman, while all other positions can be played by anyone. In how many ways can we choose a starting lineup consisting of a quarterback, a running back, an offensive lineman, and a wide receiver?",
"role": "... | Our football team has 10 members, of which only 3 are strong enough to play offensive lineman, while all other positions can be played by anyone. In how many ways can we choose a starting lineup consisting of a quarterback, a running back, an offensive lineman, and a wide receiver? | "[\"1512\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107563, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117520"}] | {
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} |
[
"\\frac{3}{8} \\sqrt{3} \\mathrm{ab}"
] | [
"skywork"
] | ae26b97aabc2788d1d17af022aae8b6c8c70f414e8f3bd4339c0e991fa3c43df | [
{
"content": "Example 6. Find the maximum value of the area of a triangle inscribed in the ellipse $\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1 \\quad(a>b>0)$.",
"role": "user"
}
] | Example 6. Find the maximum value of the area of a triangle inscribed in the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \quad(a>b>0)$. | "[\"\\\\frac{3}{8} \\\\sqrt{3} \\\\mathrm{ab}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107573, "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:117521"}] | {
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[
"10"
] | [
"skywork"
] | dc4a577dca7074e4033efd9cbda306876cb36a418a783c3715d210bd9c45b044 | [
{
"content": "When 100 is divided by 12 , the remainder is 4 .\n\nWhen 100 is divided by a positive integer $x$, the remainder is 10 .\n\nWhen 1000 is divided by $x$, the remainder is\n(A) 10\n(B) 100\n(C) 0\n(D) 1\n(E) 90",
"role": "user"
}
] | When 100 is divided by 12 , the remainder is 4 .
When 100 is divided by a positive integer $x$, the remainder is 10 .
When 1000 is divided by $x$, the remainder is
(A) 10
(B) 100
(C) 0
(D) 1
(E) 90 | "[\"10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107571, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117522"}] | {
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} |
[
"78"
] | [
"skywork"
] | a2b4e2a1578f4ac131f62440cce43c75296d263edc601792298cbe1b8d3236c7 | [
{
"content": "1. (8 points) The calculation result of the expression $2016 \\times\\left(\\frac{1}{7}-\\frac{5}{6 \\times 8}\\right)$ is",
"role": "user"
}
] | 1. (8 points) The calculation result of the expression $2016 \times\left(\frac{1}{7}-\frac{5}{6 \times 8}\right)$ is | "[\"78\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107588, "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:117523"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"45"
] | [
"skywork"
] | 0b2b5ccace0bccba26a2b93a3a51a2dfd48043bee448ba4f548011748379476c | [
{
"content": "5. In triangle $A B C$, angle $A$ is $75^{\\circ}$, and angle $C$ is $60^{\\circ}$. On the extension of side $A C$ beyond point $C$, segment $C D$ is laid off, equal to half of side $A C$. Find angle $B D C$.",
"role": "user"
}
] | 5. In triangle $A B C$, angle $A$ is $75^{\circ}$, and angle $C$ is $60^{\circ}$. On the extension of side $A C$ beyond point $C$, segment $C D$ is laid off, equal to half of side $A C$. Find angle $B D C$. | "[\"45\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107581, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:117524"}] | {
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"reference_components": 1,
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} |
[
"x_{1,2}=\\frac{-1+\\sqrt{5}}{2}"
] | [
"skywork"
] | 7d0dedf04008ac9d9cabb623d6875dff9e0414b71ea80231f27b21d7c4e3bd51 | [
{
"content": "2. Solve the equation\n\n$$\n\\left(x^{2}+x+2\\right)^{x^{2}+x+1}=9\n$$",
"role": "user"
}
] | 2. Solve the equation
$$
\left(x^{2}+x+2\right)^{x^{2}+x+1}=9
$$ | "[\"x_{1,2}=\\\\frac{-1+\\\\sqrt{5}}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107586, "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:117525"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"12"
] | [
"skywork"
] | 0178df33f8b420a1d558b3261931aed836a735c28bd2b31ce451eb24a1f985df | [
{
"content": "An abundant number is a positive integer such that the sum of its proper divisors is greater than the number itself. Find the smallest abundant number that is not a multiple of 10.",
"role": "user"
}
] | An abundant number is a positive integer such that the sum of its proper divisors is greater than the number itself. Find the smallest abundant number that is not a multiple of 10. | "[\"12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107590, "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:117526"}] | {
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[
"\\frac{X_0}{C}"
] | [
"skywork"
] | 8eaf116a8587acc47507d31468ce314adf4eba91e3874f3c335d77ba0c920bb6 | [
{
"content": "We consider the following game for one person. The aim of the player is to reach a fixed capital $C>2$. The player begins with capital $0<x_0<C$. In each turn let $x$ be the player’s current capital. Define $s(x)$ as follows:\n$$s(x):=\\begin{cases}x&\\text{if }x<1\\\\C-x&\\text{if }C-x<1\\\\1&\\t... | We consider the following game for one person. The aim of the player is to reach a fixed capital $C>2$. The player begins with capital $0<x_0<C$. In each turn let $x$ be the player’s current capital. Define $s(x)$ as follows:
$$s(x):=\begin{cases}x&\text{if }x<1\\C-x&\text{if }C-x<1\\1&\text{otherwise.}\end{cases}$$The... | "[\" \\\\frac{X_0}{C} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107561, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117527"}] | {
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} |
[
"\\frac{225}{64}"
] | [
"skywork"
] | 122c3cb393c5805f4f40e1f721d0b33d29b8c223f58821bd72429d936bf43797 | [
{
"content": "8. A box contains 8 balls of the same size, including three balls numbered 1, three balls numbered 2, and two balls numbered 3. The first ball is randomly drawn from the box and then returned. The second ball is then randomly drawn. Let the product of the numbers on the balls drawn the first and s... | 8. A box contains 8 balls of the same size, including three balls numbered 1, three balls numbered 2, and two balls numbered 3. The first ball is randomly drawn from the box and then returned. The second ball is then randomly drawn. Let the product of the numbers on the balls drawn the first and second times be $\xi$, ... | "[\"\\\\frac{225}{64}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107583, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117528"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{11}{120}"
] | [
"skywork"
] | 2dd09aa6f998a92947ca0203ef1a021ddbaf44301234abb5a0c7d51886b7e55f | [
{
"content": "What is the number halfway between $\\frac{1}{12}$ and $\\frac{1}{10}$?",
"role": "user"
}
] | What is the number halfway between $\frac{1}{12}$ and $\frac{1}{10}$? | "[\"\\\\frac{11}{120}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107606, "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:117529"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2^{99}"
] | [
"skywork"
] | 5dd322a09c956a3d1d30629aa7b7a2eb7cd1f3c5ce5e32f30d5694bb33f79e8a | [
{
"content": "In every row of a grid $100 \\times n$ is written a permutation of the numbers $1,2 \\ldots, 100$. In one move you can choose a row and swap two non-adjacent numbers with difference $1$. Find the largest possible $n$, such that at any moment, no matter the operations made, no two rows may have the... | In every row of a grid $100 \times n$ is written a permutation of the numbers $1,2 \ldots, 100$. In one move you can choose a row and swap two non-adjacent numbers with difference $1$. Find the largest possible $n$, such that at any moment, no matter the operations made, no two rows may have the same permutations. | "[\" 2^{99} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107568, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117530"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"I_{1}>I_{2}"
] | [
"skywork"
] | dd9456a1ece43bb51c0bea25c365a1494d6226d541587555fd353f5556685db1 | [
{
"content": "Example 2. Compare the integrals $I_{1}=\\int_{0}^{1} x d x$ and $I_{2}=\\int_{0}^{1} x^{3} d x$, without calculating them",
"role": "user"
}
] | Example 2. Compare the integrals $I_{1}=\int_{0}^{1} x d x$ and $I_{2}=\int_{0}^{1} x^{3} d x$, without calculating them | "[\"I_{1}>I_{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107584, "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:117531"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{7\\sqrt{2}}{8}"
] | [
"skywork"
] | 9dd284ee20824bad1066e99f6480cbc2d7ca7a38249704ea1ba19f2d87b19121 | [
{
"content": "4. Through the moving point $M$, draw the tangent line $M N$ to the circle $C:(x-2)^{2}+(y-2)^{2}=1$, where $N$ is the point of tangency. If $|M N|=|M O|(O$ is the origin), then the minimum value of $|M N|$ is $\\qquad$ .",
"role": "user"
}
] | 4. Through the moving point $M$, draw the tangent line $M N$ to the circle $C:(x-2)^{2}+(y-2)^{2}=1$, where $N$ is the point of tangency. If $|M N|=|M O|(O$ is the origin), then the minimum value of $|M N|$ is $\qquad$ . | "[\"\\\\frac{7\\\\sqrt{2}}{8}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107575, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:117533"}] | {
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[
"\\[\n\\left(\\frac{n+1}{2}\\right)^2\n\\]"
] | [
"skywork"
] | 995757300a6a9ee061781515a0ef10d7f68e5ee8251265ac47075e690914d7e1 | [
{
"content": "Consider an $n$ -by- $n$ board of unit squares for some odd positive integer $n$ . We say that a collection $C$ of identical dominoes is a maximal grid-aligned configuration on the board if $C$ consists of $(n^2-1)/2$ dominoes where each domino covers exactly two neighboring squares and the domino... | Consider an $n$ -by- $n$ board of unit squares for some odd positive integer $n$ . We say that a collection $C$ of identical dominoes is a maximal grid-aligned configuration on the board if $C$ consists of $(n^2-1)/2$ dominoes where each domino covers exactly two neighboring squares and the dominoes don't overlap: $C$ ... | "[\"\\\\[\\n\\\\left(\\\\frac{n+1}{2}\\\\right)^2\\n\\\\]\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107565, "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:117534"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | 3c19f17cdea55b7ebaf6aa5c0532af65c25e65586620cb2e72f4f65efaccb457 | [
{
"content": "If $x=3, y=2 x$, and $z=3 y$, then the average of $x, y$ and $z$ is\n(A) 6\n(B) 7\n(C) 8\n(D) 9\n(E) 10",
"role": "user"
}
] | If $x=3, y=2 x$, and $z=3 y$, then the average of $x, y$ and $z$ is
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10 | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107598, "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:117535"}] | {
"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
} |
[
"18"
] | [
"skywork"
] | 958c5f438557d70ff29a4bce15c0ccbe9de2a6dd749c197897f0290909c1b468 | [
{
"content": "## 123. Math Puzzle $8 / 75$\n\nYoung Pioneers are painting the $36 \\mathrm{~m}$ long fence of the school grounds. They had planned a certain amount of time for this. However, since they paint $0.20 \\mathrm{~m}$ more of the fence per hour than planned, they will finish two hours earlier.\n\nHow ... | ## 123. Math Puzzle $8 / 75$
Young Pioneers are painting the $36 \mathrm{~m}$ long fence of the school grounds. They had planned a certain amount of time for this. However, since they paint $0.20 \mathrm{~m}$ more of the fence per hour than planned, they will finish two hours earlier.
How many hours do they need for ... | "[\"18\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107578, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117536"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\text{True}"
] | [
"skywork"
] | fa08367281eb964459d2ccee1fc03e07270a1afc8fc475d1111d623a706bb1a7 | [
{
"content": "In $7$-gon $A_1A_2A_3A_4A_5A_6A_7$ diagonals $A_1A_3, A_2A_4, A_3A_5, A_4A_6, A_5A_7, A_6A_1$ and $A_7A_2$ are congruent to each other and diagonals $A_1A_4, A_2A_5, A_3A_6, A_4A_7, A_5A_1, A_6A_2$ and $A_7A_3$ are also congruent to each other. Is the polygon necessarily regular?",
"role": "us... | In $7$-gon $A_1A_2A_3A_4A_5A_6A_7$ diagonals $A_1A_3, A_2A_4, A_3A_5, A_4A_6, A_5A_7, A_6A_1$ and $A_7A_2$ are congruent to each other and diagonals $A_1A_4, A_2A_5, A_3A_6, A_4A_7, A_5A_1, A_6A_2$ and $A_7A_3$ are also congruent to each other. Is the polygon necessarily regular? | "[\"\\\\text{True}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107587, "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:117537"}] | {
"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
} |
[
"1720"
] | [
"skywork"
] | c39dfd65418f84ecfd2ed0b072f97116613a67eedba9ade6ca8ea93088739f1c | [
{
"content": "GM Bisain's IQ is so high that he can move around in $10$ dimensional space. He starts at the origin and moves in a straight line away from the origin, stopping after $3$ units. How many lattice points can he land on? A lattice point is one with all integer coordinates.\n\n[i]2019 CCA Math Bonanza... | GM Bisain's IQ is so high that he can move around in $10$ dimensional space. He starts at the origin and moves in a straight line away from the origin, stopping after $3$ units. How many lattice points can he land on? A lattice point is one with all integer coordinates.
[i]2019 CCA Math Bonanza Lightning Round #4.2[/i... | "[\"1720\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107589, "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:117539"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"675 \\text{ dollars}"
] | [
"skywork"
] | 44f824fb6a4ac00433abba21aa87981ed7608407012c3cba8452587c994e8ff0 | [
{
"content": "A two-inch cube $(2\\times 2\\times 2)$ of silver weighs 3 pounds and is worth \\$200. How much is a three-inch cube of silver worth?\n\n$\\textbf{(A)}\\ 300\\text{ dollars} \\qquad \\textbf{(B)}\\ 375\\text{ dollars} \\qquad \\textbf{(C)}\\ 450\\text{ dollars} \\qquad \\textbf{(D)}\\ 560\\text{ ... | A two-inch cube $(2\times 2\times 2)$ of silver weighs 3 pounds and is worth \$200. How much is a three-inch cube of silver worth?
$\textbf{(A)}\ 300\text{ dollars} \qquad \textbf{(B)}\ 375\text{ dollars} \qquad \textbf{(C)}\ 450\text{ dollars} \qquad \textbf{(D)}\ 560\text{ dollars} \qquad \textbf{(E)}\ 675\text{ do... | "[\"675 \\\\text{ dollars}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107591, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117540"}] | {
"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{272}{385}"
] | [
"skywork"
] | 037b8188db4cbd84d86039a1a0620d82e58937c48a61a26a0f8066adfd42f3f9 | [
{
"content": "Point $Q$ is located inside triangle $DEF$ such that angles $QDE, QEF,$ and $QFD$ are all congruent. The sides of the triangle have lengths $DE = 15, EF = 16,$ and $FD = 17.$ Find $\\tan \\angle QDE.$",
"role": "user"
}
] | Point $Q$ is located inside triangle $DEF$ such that angles $QDE, QEF,$ and $QFD$ are all congruent. The sides of the triangle have lengths $DE = 15, EF = 16,$ and $FD = 17.$ Find $\tan \angle QDE.$ | "[\"\\\\frac{272}{385}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107596, "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:117541"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"8"
] | [
"skywork"
] | 363764cb1176c5c5fbdfa37e6bb59067c03d20cf23180f1699e7b920940184e8 | [
{
"content": "13. (5 points)\nThe 5 members of the Sheep Team are participating in a competitive selection match. 2 of them have only a perfect score in \"climbing\", another 2 have only a perfect score in \"jumping\", and 1 person has a perfect score in both \"climbing\" and \"jumping\". Now, 2 people need to ... | 13. (5 points)
The 5 members of the Sheep Team are participating in a competitive selection match. 2 of them have only a perfect score in "climbing", another 2 have only a perfect score in "jumping", and 1 person has a perfect score in both "climbing" and "jumping". Now, 2 people need to be selected from these 5 to ent... | "[\"8\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107604, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117542"}] | {
"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
} |
[
"11"
] | [
"skywork"
] | 3e5d049a0c7d9b09b699e8e1fa664381cba3a7530626dbfced86ee335c83a1e5 | [
{
"content": "3 Let $n$ be a natural number, $f(n)$ be the sum of the digits of $n^{2}+1$ (in decimal), $f_{1}(n)=f(n), f_{k+1}(n)$ $=f\\left(f_{k}(n)\\right)$, then the value of $f_{100}(1990)$ is $\\qquad$.",
"role": "user"
}
] | 3 Let $n$ be a natural number, $f(n)$ be the sum of the digits of $n^{2}+1$ (in decimal), $f_{1}(n)=f(n), f_{k+1}(n)$ $=f\left(f_{k}(n)\right)$, then the value of $f_{100}(1990)$ is $\qquad$. | "[\"11\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107577, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:117544"}] | {
"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
} |
[
"336"
] | [
"skywork"
] | 726310da98d4e5aef2af41fa49f8828105f44a37fea0599482d8412bc31ae5dc | [
{
"content": "15. (15 points) A bag of balls, with red and yellow colors, first 60 balls are taken out, among which there are exactly 56 red balls. Afterwards, each time 18 balls are taken out, there are always 14 red balls, until the last 18 balls are exactly taken out. If the total number of red balls in this... | 15. (15 points) A bag of balls, with red and yellow colors, first 60 balls are taken out, among which there are exactly 56 red balls. Afterwards, each time 18 balls are taken out, there are always 14 red balls, until the last 18 balls are exactly taken out. If the total number of red balls in this pile is exactly four-... | "[\"336\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107594, "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:117545"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-3,(-2;2)"
] | [
"skywork"
] | a323169a0829cb23d29701e8e72558893efd9398a403218750dd3731bba5b4ea | [
{
"content": "253. Given three statements:\n1) the equation $x^{2}-a x+1=0$ has no roots (real);\n2) the equality $|a-2|=2-a$ holds;\n3) the system of equations\n\n$$\n\\left\\{\\begin{array}{l}\nx+y^{2}=a \\\\\nx-\\sin ^{2} y=-3\n\\end{array}\\right.\n$$\n\nhas a unique solution.\n\nFind all values of $a$ for ... | 253. Given three statements:
1) the equation $x^{2}-a x+1=0$ has no roots (real);
2) the equality $|a-2|=2-a$ holds;
3) the system of equations
$$
\left\{\begin{array}{l}
x+y^{2}=a \\
x-\sin ^{2} y=-3
\end{array}\right.
$$
has a unique solution.
Find all values of $a$ for which two of these statements are true and o... | "[\"-3,(-2;2)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107582, "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:117546"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"A"
] | [
"skywork"
] | b2e33457412250cb2f8bc94f7df7cb2f6f5b68965cd2d970e7b00e4fa9529400 | [
{
"content": "4.50 If for all real numbers $x, f(x)=3 x+2$, then the statement “ $|f(x)+4|<a, \\quad b>0$ ” is true under the condition\n(A) $b \\leqslant \\frac{a}{3}$.\n(B) $b>\\frac{a}{3}$.\n(C) $a \\leqslant \\frac{b}{3}$.\n(D) $a>\\frac{b}{3}$.\n(E) This statement is never true.\n(25th American High School... | 4.50 If for all real numbers $x, f(x)=3 x+2$, then the statement “ $|f(x)+4|<a, \quad b>0$ ” is true under the condition
(A) $b \leqslant \frac{a}{3}$.
(B) $b>\frac{a}{3}$.
(C) $a \leqslant \frac{b}{3}$.
(D) $a>\frac{b}{3}$.
(E) This statement is never true.
(25th American High School Mathematics Examination, 1974) | "[\"A\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107576, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117547"}] | {
"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
} |
[
"7066"
] | [
"skywork"
] | d0df8d4e80b6c582999120314d7df7a4b1ca2f0e5f5004d5872ecbc224692734 | [
{
"content": "The sequence $\\left\\{a_{n}\\right\\}$ is defined such that $a_{n}$ is the last digit of the sum $1 + 2 + \\cdots + n$. Let $S_{n}$ be the sum of the first $n$ terms of the sequence $\\left\\{a_{n}\\right\\}$. Calculate $S_{2016}$.",
"role": "user"
}
] | The sequence $\left\{a_{n}\right\}$ is defined such that $a_{n}$ is the last digit of the sum $1 + 2 + \cdots + n$. Let $S_{n}$ be the sum of the first $n$ terms of the sequence $\left\{a_{n}\right\}$. Calculate $S_{2016}$. | "[\"7066\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107602, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:117548"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10^{100}"
] | [
"skywork"
] | 0993fc54dc9f8fff6e015a358cfe4bc84778ebe48cef422196c169ab6e5af0ad | [
{
"content": "2. The integer solution to the equation $(\\lg x)^{\\lg (\\lg x)}=10000$ is $x=$",
"role": "user"
}
] | 2. The integer solution to the equation $(\lg x)^{\lg (\lg x)}=10000$ is $x=$ | "[\"10^{100}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107592, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117549"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
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