answers listlengths 1 1 | datasets listlengths 1 1 | id stringlengths 64 64 | messages listlengths 1 1 | prompt stringlengths 10 3.97k | reference_answer_raw stringlengths 9 3.95k | source stringclasses 11
values | source_records stringlengths 283 1.44k | verifiability dict |
|---|---|---|---|---|---|---|---|---|
[
"\\frac{1}{\\left(\\frac{n+1}{2}\\right)^2}"
] | [
"skywork"
] | ad1a5fc6d4f125b4a88d5fae34b3f44c6fc167e57c88479829b4152baf902a33 | [
{
"content": "A $100 \\times100$ chessboard has a non-negative real number in each of its cells. A chessboard is [b]balanced[/b] if and only if the numbers sum up to one for each column of cells as well as each row of cells. Find the largest positive real number $x$ so that, for any balanced chessboard, we can ... | A $100 \times100$ chessboard has a non-negative real number in each of its cells. A chessboard is [b]balanced[/b] if and only if the numbers sum up to one for each column of cells as well as each row of cells. Find the largest positive real number $x$ so that, for any balanced chessboard, we can find $100$ cells of it ... | "[\" \\\\frac{1}{\\\\left(\\\\frac{n+1}{2}\\\\right)^2} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1923, "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:15912"}] | {
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[
"465"
] | [
"skywork"
] | 7a4c89333b42e42290cb2c9ff3d24a43cb8ebbe9656fc1db78cc4a666178a95a | [
{
"content": "Ninety-four bricks, each measuring $4''\\times10''\\times19'',$ are to be stacked one on top of another to form a tower 94 bricks tall. Each brick can be oriented so it contributes $4''\\,$ or $10''\\,$ or $19''\\,$ to the total height of the tower. How many different tower heights can be achieved... | Ninety-four bricks, each measuring $4''\times10''\times19'',$ are to be stacked one on top of another to form a tower 94 bricks tall. Each brick can be oriented so it contributes $4''\,$ or $10''\,$ or $19''\,$ to the total height of the tower. How many different tower heights can be achieved using all ninety-four of t... | "[\"465\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1940, "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:15913"}, {"dataset": "skywork", "extra_... | {
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[
"12560"
] | [
"skywork"
] | ea1f5528bd24a04850abead3277258da8cd60bd3191cdba4c8b7261c71ca103d | [
{
"content": "1. The expression $1000 \\sin 10^{\\circ} \\cos 20^{\\circ} \\cos 30^{\\circ} \\cos 40^{\\circ}$ can be simplified as $a \\sin b^{\\circ}$, where $a$ and $b$ are positive integers with $0<b<90$. Find the value of $100 a+b$.",
"role": "user"
}
] | 1. The expression $1000 \sin 10^{\circ} \cos 20^{\circ} \cos 30^{\circ} \cos 40^{\circ}$ can be simplified as $a \sin b^{\circ}$, where $a$ and $b$ are positive integers with $0<b<90$. Find the value of $100 a+b$. | "[\"12560\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1920, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15914"}] | {
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[
"\\frac{8}{3}"
] | [
"skywork"
] | 3f2b42230212b5f5ef8d21838bb631b06641c86fe9dc57639440190679e0825c | [
{
"content": "Given that $x$ is a root of the equation $x^{2}+x-6=0$, simplify $\\frac{x-1}{\\frac{2}{{x-1}}-1}$ and find its value.",
"role": "user"
}
] | Given that $x$ is a root of the equation $x^{2}+x-6=0$, simplify $\frac{x-1}{\frac{2}{{x-1}}-1}$ and find its value. | "[\"\\\\frac{8}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1935, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15915"}] | {
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[
"4026"
] | [
"skywork"
] | d39d713bf940c5f295e2d02af6895d163b7ef309682a3c40d77e9b9bfafc580a | [
{
"content": "3. If $\\left\\{a_{n}\\right\\}$ is an arithmetic sequence, the first term $a_{1}>0$, and\n$$\na_{2013}+a_{2014}>0, a_{2013} a_{2014}<0,\n$$\nthen the largest natural number $n$ for which $a_{n}>0$ is ( ).\n(A) 4025\n(B) 4026\n(C) 4027\n(D) 4028",
"role": "user"
}
] | 3. If $\left\{a_{n}\right\}$ is an arithmetic sequence, the first term $a_{1}>0$, and
$$
a_{2013}+a_{2014}>0, a_{2013} a_{2014}<0,
$$
then the largest natural number $n$ for which $a_{n}>0$ is ( ).
(A) 4025
(B) 4026
(C) 4027
(D) 4028 | "[\"4026\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1934, "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:15917"}] | {
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[
"61"
] | [
"skywork"
] | bd336dd07893b8ddc57af62e195c3299f2271c2e68b06f273d7574a624c2773b | [
{
"content": "Natasha has more than $\\$1$ but less than $\\$10$ worth of dimes. When she puts her dimes in stacks of 3, she has 1 left over. When she puts them in stacks of 4, she has 1 left over. When she puts them in stacks of 5, she also has 1 left over. How many dimes does Natasha have?",
"role": "user... | Natasha has more than $\$1$ but less than $\$10$ worth of dimes. When she puts her dimes in stacks of 3, she has 1 left over. When she puts them in stacks of 4, she has 1 left over. When she puts them in stacks of 5, she also has 1 left over. How many dimes does Natasha have? | "[\"61\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1938, "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:15918"}] | {
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"reference_present": true
} |
[
"202"
] | [
"skywork"
] | 309c314d945368d5e3b26b862b1526c8d3d5d15c0705b9362aa1007d9b498f5c | [
{
"content": "3. In $5, 8, 15, 18, 25, 28, \\cdots, 2008, 2015$, there are $\\qquad$ numbers whose digit sum is even (the digit sum of 138 is $1+3+8=12$)",
"role": "user"
}
] | 3. In $5, 8, 15, 18, 25, 28, \cdots, 2008, 2015$, there are $\qquad$ numbers whose digit sum is even (the digit sum of 138 is $1+3+8=12$) | "[\"202\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1937, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15920"}] | {
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} |
[
"21"
] | [
"skywork"
] | 0b8319189a726583ae201d87551f5780bdb79ebd217dc3d57eda14228e761441 | [
{
"content": "Example 6 As shown in Figure $3, \\odot O$ has a diameter whose length is the largest integer root of the quadratic equation in $x$\n$$\nx^{2}+2(k-2) x+k\n$$\n$=0$ (where $k$ is an integer). $P$ is a point outside $\\odot O$. A tangent $PA$ and a secant $PBC$ are drawn from point $P$ to $\\odot O$... | Example 6 As shown in Figure $3, \odot O$ has a diameter whose length is the largest integer root of the quadratic equation in $x$
$$
x^{2}+2(k-2) x+k
$$
$=0$ (where $k$ is an integer). $P$ is a point outside $\odot O$. A tangent $PA$ and a secant $PBC$ are drawn from point $P$ to $\odot O$, with $A$ being the point of... | "[\"21\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1926, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15921"}] | {
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[
"\\frac{5}{2}"
] | [
"skywork"
] | e8a9d24bea92d8ed84c7c4287aed42c68fb77e0113c14db859f9b2350c3d58bc | [
{
"content": "Find $\\frac{\\frac{1}{3} + \\frac{1}{4}}{ \\frac{2}{5} - \\frac{1}{6}}$. Express your answer as a fraction in simplest form.",
"role": "user"
}
] | Find $\frac{\frac{1}{3} + \frac{1}{4}}{ \frac{2}{5} - \frac{1}{6}}$. Express your answer as a fraction in simplest form. | "[\"\\\\frac{5}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1970, "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:15922"}] | {
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} |
[
"34"
] | [
"skywork"
] | 5e2590765a93ef141e5a060226b03d3bbb878fa0da90a2ffd6eee242a849edff | [
{
"content": "What is the smallest positive integer that leaves a remainder of 4 when divided by 5 and a remainder of 6 when divided by 7?",
"role": "user"
}
] | What is the smallest positive integer that leaves a remainder of 4 when divided by 5 and a remainder of 6 when divided by 7? | "[\"34\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1965, "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:15923"}] | {
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[
"71"
] | [
"skywork"
] | 553c1815c6f9e6b84c3acf766c6969b02f539423ace7a7775c7d832617491285 | [
{
"content": "The complex numbers $z$ and $w$ satisfy $z^{13} = w,$ $w^{11} = z,$ and the imaginary part of $z$ is $\\sin{\\frac{m\\pi}{n}}$ , for relatively prime positive integers $m$ and $n$ with $m<n.$ Find $n.$",
"role": "user"
}
] | The complex numbers $z$ and $w$ satisfy $z^{13} = w,$ $w^{11} = z,$ and the imaginary part of $z$ is $\sin{\frac{m\pi}{n}}$ , for relatively prime positive integers $m$ and $n$ with $m<n.$ Find $n.$ | "[\"71\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 1945, "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:15924"}, {"dataset": "skywork", "extra_inf... | {
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"reference_components": 1,
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} |
[
"60"
] | [
"skywork"
] | d590dff2bd908c14de9e4786bf31cd4c349e713bb2152dc3433a81378ac6c578 | [
{
"content": "11.2. On the board, the expression $\\frac{a}{b} \\cdot \\frac{c}{d} \\cdot \\frac{e}{f}$ is written, where $a, b, c, d, e, f$ are natural numbers. If the number $a$ is increased by 1, then the value of this expression increases by 3. If in the original expression the number $c$ is increased by 1,... | 11.2. On the board, the expression $\frac{a}{b} \cdot \frac{c}{d} \cdot \frac{e}{f}$ is written, where $a, b, c, d, e, f$ are natural numbers. If the number $a$ is increased by 1, then the value of this expression increases by 3. If in the original expression the number $c$ is increased by 1, then its value increases b... | "[\"60\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1943, "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:15925"}] | {
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} |
[
"-\\frac{1}{2}"
] | [
"skywork"
] | f9294feb1522686140455385171995f6ff2edb758da615d417742871775c064b | [
{
"content": "Suppose that $\\alpha$ is inversely proportional to $\\beta$. If $\\alpha = 4$ when $\\beta = 9$, find $\\alpha$ when $\\beta = -72$.",
"role": "user"
}
] | Suppose that $\alpha$ is inversely proportional to $\beta$. If $\alpha = 4$ when $\beta = 9$, find $\alpha$ when $\beta = -72$. | "[\"-\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1959, "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:15926"}] | {
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"reference_present": true
} |
[
"12"
] | [
"skywork"
] | 8dbf99a9a22875274a62562d6acb3c8cce89a7c29cf4b2c7438f0f59d7634232 | [
{
"content": "\\section*{Task 2 - 330922}\n\nTo mill a quantity of grain, two milling machines \\(A\\) and \\(B\\) can be used. Each milling machine processes the same amount in the same time.\n\nIf machine \\(A\\) is used for 8 hours first and then only machine \\(B\\) is used, \\(B\\) would need exactly 18 mo... | \section*{Task 2 - 330922}
To mill a quantity of grain, two milling machines \(A\) and \(B\) can be used. Each milling machine processes the same amount in the same time.
If machine \(A\) is used for 8 hours first and then only machine \(B\) is used, \(B\) would need exactly 18 more hours to complete the entire grain... | "[\"12\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1933, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:15927"}] | {
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} |
[
"26.14"
] | [
"skywork"
] | 7ce52388e77606d63bc9d26b3e469c7ebecdb30c4cd800a2379f48ed9b627faa | [
{
"content": "The average age of 40 sixth-graders is 12. The average age of 30 of their teachers is 45. What is the average age of all these sixth-graders and their teachers?",
"role": "user"
}
] | The average age of 40 sixth-graders is 12. The average age of 30 of their teachers is 45. What is the average age of all these sixth-graders and their teachers? | "[\"26.14\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1971, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15928"}] | {
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"reference_components": 1,
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} |
[
"16"
] | [
"skywork"
] | 68430f190757f7c860b6f2068add44847633fc74f9ba3620f0ed731029671e61 | [
{
"content": "A $7 \\times 7$ board is either empty or contains an invisible $2 \\times 2$ ship placed \"on the cells.\" Detectors can be placed on certain cells of the board and then activated simultaneously. An activated detector signals if its cell is occupied by the ship. What is the minimum number of detec... | A $7 \times 7$ board is either empty or contains an invisible $2 \times 2$ ship placed "on the cells." Detectors can be placed on certain cells of the board and then activated simultaneously. An activated detector signals if its cell is occupied by the ship. What is the minimum number of detectors needed to guarantee d... | "[\"16\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1946, "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:15929"}] | {
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} |
[
"3\\sqrt{2}"
] | [
"skywork"
] | ec942b1e2833083244c074b337f1092c95bb4cdf90eb17b41b3effd19fb8c5e5 | [
{
"content": "In triangle $ABC$, $AB = 8$, $AC = 17$, and $BC = 15$. Let $I$ be the incenter. The incircle of triangle $ABC$ touches sides $BC$, $AC$, and $AB$ at $D$, $E$, and $F$, respectively. Find the length of $BI$.",
"role": "user"
}
] | In triangle $ABC$, $AB = 8$, $AC = 17$, and $BC = 15$. Let $I$ be the incenter. The incircle of triangle $ABC$ touches sides $BC$, $AC$, and $AB$ at $D$, $E$, and $F$, respectively. Find the length of $BI$. | "[\"3\\\\sqrt{2}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1949, "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:15930"}] | {
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} |
[
"25"
] | [
"skywork"
] | 4991ed5c096750c2ea90d1486dbd6d93642e0b73e38e33779187195248df4a7d | [
{
"content": "The plane is divided into unit cells, and each of the cells is painted in one of two given colors. Find the minimum possible number of cells in a figure consisting of entire cells which contains each of the $16$ possible colored $2\\times2$ squares.",
"role": "user"
}
] | The plane is divided into unit cells, and each of the cells is painted in one of two given colors. Find the minimum possible number of cells in a figure consisting of entire cells which contains each of the $16$ possible colored $2\times2$ squares. | "[\"25\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1951, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15931"}] | {
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} |
[
"e^{\\frac {100}{3}}"
] | [
"skywork"
] | 70c6de58f18cca3598ba7574e744d26dfb6e2609d9d629d46f729f1a0868a52d | [
{
"content": "Given a sequence $\\{a_n\\}$ that satisfies $\\frac {\\ln a_{1}}{3} \\cdot \\frac {\\ln a_{2}}{6} \\cdot \\frac {\\ln a_{3}}{9} \\cdot \\ldots \\cdot \\frac {\\ln a_{n}}{3n} = \\frac {3n}{2} (n \\in \\mathbb{N}^{*})$, calculate the value of $a_{10}$.",
"role": "user"
}
] | Given a sequence $\{a_n\}$ that satisfies $\frac {\ln a_{1}}{3} \cdot \frac {\ln a_{2}}{6} \cdot \frac {\ln a_{3}}{9} \cdot \ldots \cdot \frac {\ln a_{n}}{3n} = \frac {3n}{2} (n \in \mathbb{N}^{*})$, calculate the value of $a_{10}$. | "[\"e^{\\\\frac {100}{3}}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1950, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15932"}] | {
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"2n-2"
] | [
"skywork"
] | 359d5c7fcaab2a6636777ac710ef3f2ed2d573d428f05599c028ea9ae3d14bd0 | [
{
"content": "3. Suppose that each of $n$ people knows exactly one piece of information, and all $n$ pieces are different. Every time person $A$ phones person $B, A$ tells $B$ everything he knows, while $B$ tells $A$ nothing. What is the minimum of phone calls between pairs of people needed for everyone to know... | 3. Suppose that each of $n$ people knows exactly one piece of information, and all $n$ pieces are different. Every time person $A$ phones person $B, A$ tells $B$ everything he knows, while $B$ tells $A$ nothing. What is the minimum of phone calls between pairs of people needed for everyone to know everything? | "[\"2n-2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1948, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15933"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"201"
] | [
"skywork"
] | f8ae927722d533c0c2a91ada64b9bb59d7938378ad6bc4b27578eee3c868215e | [
{
"content": "If a computer executes the following program:\n1. Initial values \\( x = 3 \\), \\( S = 0 \\)\n2. \\( x = x + 2 \\)\n3. \\( S = S + x \\)\n4. If \\( S \\geq 10000 \\), go to step 5; otherwise, repeat from step 2\n5. Print \\( x \\)\n6. Stop\n\nWhat value will be printed by step 5?",
"role": "u... | If a computer executes the following program:
1. Initial values \( x = 3 \), \( S = 0 \)
2. \( x = x + 2 \)
3. \( S = S + x \)
4. If \( S \geq 10000 \), go to step 5; otherwise, repeat from step 2
5. Print \( x \)
6. Stop
What value will be printed by step 5? | "[\"201\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1960, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "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:15934"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\varnothing"
] | [
"skywork"
] | 84c7952c92f405747c4341032db3193d48f65311fa88901978d31ada968212f8 | [
{
"content": "3. Given $p_{1}, p_{2}, \\cdots, p_{2015}$ are the first 2015 prime numbers in ascending order, let $m=p_{1} p_{2} \\cdots p_{2015}$. Then the set of positive integer solutions for the indeterminate equation\n$$\n(2 x-y-z)(2 y-z-x)(2 z-x-y)=m\n$$\n\nis $\\qquad$ .",
"role": "user"
}
] | 3. Given $p_{1}, p_{2}, \cdots, p_{2015}$ are the first 2015 prime numbers in ascending order, let $m=p_{1} p_{2} \cdots p_{2015}$. Then the set of positive integer solutions for the indeterminate equation
$$
(2 x-y-z)(2 y-z-x)(2 z-x-y)=m
$$
is $\qquad$ . | "[\"\\\\varnothing\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1962, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15935"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac 13"
] | [
"skywork"
] | 2d27b4872a2d5d5368e37184f8c163968a3be7c0e122a9f2e0bb91a47b0fe017 | [
{
"content": "Express as a common fraction: $0.\\overline5+0.\\overline1-0.\\overline3$",
"role": "user"
}
] | Express as a common fraction: $0.\overline5+0.\overline1-0.\overline3$ | "[\"\\\\frac 13\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1978, "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:15936"}] | {
"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
} |
[
"290"
] | [
"skywork"
] | e67bff2e652e1301b7d27a02b507dd2379bf6bc4bdad38133ccfadeaf914a56c | [
{
"content": "12. Let the equation $x y=6(x+y)$ have all positive integer solutions $\\left(x_{1}, y_{1}\\right),\\left(x_{2}, y_{2}\\right), \\cdots,\\left(x_{n}, y_{n}\\right)$, then $\\sum_{k=1}^{n}\\left(x_{k}+y_{k}\\right)=$\n$\\qquad$ .",
"role": "user"
}
] | 12. Let the equation $x y=6(x+y)$ have all positive integer solutions $\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right), \cdots,\left(x_{n}, y_{n}\right)$, then $\sum_{k=1}^{n}\left(x_{k}+y_{k}\right)=$
$\qquad$ . | "[\"290\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1952, "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:15937"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | f7d441c0f32a87cc0c8bc4cbf2932e4e53a033f08627b88895acad50e171b430 | [
{
"content": "For real numbers $x$, let \n\\[P(x)=1+\\cos(x)+i\\sin(x)-\\cos(2x)-i\\sin(2x)+\\cos(3x)+i\\sin(3x)\\]\nwhere $i = \\sqrt{-1}$. For how many values of $x$ with $0\\leq x<2\\pi$ does \n\\[P(x)=0?\\]",
"role": "user"
}
] | For real numbers $x$, let
\[P(x)=1+\cos(x)+i\sin(x)-\cos(2x)-i\sin(2x)+\cos(3x)+i\sin(3x)\]
where $i = \sqrt{-1}$. For how many values of $x$ with $0\leq x<2\pi$ does
\[P(x)=0?\] | "[\"0\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1968, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:15938"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | 49f57c1f0121cd61e836d70b2e27e58301fc9008221c10e2b9434b47d69b4c3b | [
{
"content": "10.4.1. (12 points) Find all pairs of integers $(x, y)$ that are solutions to the equation\n\n$$\n7 x y-13 x+15 y-37=0 \\text {. }\n$$\n\nIn your answer, indicate the sum of the found values of $x$.",
"role": "user"
}
] | 10.4.1. (12 points) Find all pairs of integers $(x, y)$ that are solutions to the equation
$$
7 x y-13 x+15 y-37=0 \text {. }
$$
In your answer, indicate the sum of the found values of $x$. | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1974, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15939"}] | {
"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
} |
[
"4022"
] | [
"skywork"
] | 9c19b25e7c2173b8433ce957ce41fed252f29bb833ce0666b5c6afc30e1bb13d | [
{
"content": "5. The number $S$ is the result of the following sum:\n\n$$\n1+10+19+28+37+\\cdots+10^{2013} .\n$$\n\nIf the number $S$ is written out, how many times does the digit ' 5 ' appear in the result?",
"role": "user"
}
] | 5. The number $S$ is the result of the following sum:
$$
1+10+19+28+37+\cdots+10^{2013} .
$$
If the number $S$ is written out, how many times does the digit ' 5 ' appear in the result? | "[\"4022\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1957, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15940"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{3}"
] | [
"skywork"
] | 5753187c337a8c41cfdc295b9f0fbd3db19bf98f2461b21354f088b3238f2648 | [
{
"content": "1. Given $(1+\\sqrt{3})^{n}=a_{n}+b_{n} \\sqrt{3}$, where $a_{n}$ and $b_{n}$ are integers. Then $\\lim _{n \\rightarrow+\\infty} \\frac{a_{n}}{b_{n}}=$ $\\qquad$\n$(2011$, National High School Mathematics League Sichuan Preliminary Competition)",
"role": "user"
}
] | 1. Given $(1+\sqrt{3})^{n}=a_{n}+b_{n} \sqrt{3}$, where $a_{n}$ and $b_{n}$ are integers. Then $\lim _{n \rightarrow+\infty} \frac{a_{n}}{b_{n}}=$ $\qquad$
$(2011$, National High School Mathematics League Sichuan Preliminary Competition) | "[\"\\\\sqrt{3}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 1964, "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:15941"}] | {
"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
} |
[
"450"
] | [
"skywork"
] | c8514488aa48b11d9500083a7475ec8668116ca8ac5b59506757f4a0e5194aa7 | [
{
"content": "In triangle $ABC,\\,$ angle $C$ is a right angle and the altitude from $C\\,$ meets $\\overline{AB}\\,$ at $D.\\,$ The lengths of the sides of $\\triangle ABC\\,$ are integers, $BD=29^3,\\,$ and $\\cos B=m/n\\,$, where $m\\,$ and $n\\,$ are relatively prime positive integers. Find $m+n.\\,$",
... | In triangle $ABC,\,$ angle $C$ is a right angle and the altitude from $C\,$ meets $\overline{AB}\,$ at $D.\,$ The lengths of the sides of $\triangle ABC\,$ are integers, $BD=29^3,\,$ and $\cos B=m/n\,$, where $m\,$ and $n\,$ are relatively prime positive integers. Find $m+n.\,$ | "[\"450\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 1956, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:15942"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{13}{16},\\frac{17}{16}"
] | [
"skywork"
] | c235c891a824aec8e3c94a67cb7ff6fd9446bfe877bab418c814b33c9ca4e3c0 | [
{
"content": "Example 1 The real solutions to the equation $[2 x]+[3 x]=8 x-\\frac{7}{2}$ are $\\qquad$ .",
"role": "user"
}
] | Example 1 The real solutions to the equation $[2 x]+[3 x]=8 x-\frac{7}{2}$ are $\qquad$ . | "[\"\\\\frac{13}{16},\\\\frac{17}{16}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1953, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15943"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | 0f1cdb052841c734d2207b358aac11e3482ab15951d76ce9497dc9f7eadbf8d2 | [
{
"content": "10.6. Solve in $R$ the equation\n\n$$\n\\sqrt{2 x^{5}+x^{4}+4 x^{3}+2 x^{2}+2 x+1}+\\sqrt{17-2 x+34 x^{2}-4 x^{3}+17 x^{4}-2 x^{5}}=7 x^{2}-8 x+22\n$$",
"role": "user"
}
] | 10.6. Solve in $R$ the equation
$$
\sqrt{2 x^{5}+x^{4}+4 x^{3}+2 x^{2}+2 x+1}+\sqrt{17-2 x+34 x^{2}-4 x^{3}+17 x^{4}-2 x^{5}}=7 x^{2}-8 x+22
$$ | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1976, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:15944"}] | {
"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
} |
[
"1233"
] | [
"skywork"
] | 92689cbef99711c21086f05f5e641e006ac5ed14cdf7c75780b8fb09fd3dac01 | [
{
"content": "1. The number 1232 is divisible by the sum of its digits $1+2+3+2=8$. What is the next number that is divisible by the sum of its digits?",
"role": "user"
}
] | 1. The number 1232 is divisible by the sum of its digits $1+2+3+2=8$. What is the next number that is divisible by the sum of its digits? | "[\"1233\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1967, "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:15945"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3}{4}"
] | [
"skywork"
] | 2ad381515608b45673c8c0b858a1bb25c1cecb8cb52dfc88a00942b8ec8afb1f | [
{
"content": "5. A mouse lives in a circular cage with completely reflective walls. At the edge of this cage, a small flashlight with vertex on the circle whose beam forms an angle of $15^{\\circ}$ is centered at an angle of $37.5^{\\circ}$ away from the center. The mouse will die in the dark. What fraction of ... | 5. A mouse lives in a circular cage with completely reflective walls. At the edge of this cage, a small flashlight with vertex on the circle whose beam forms an angle of $15^{\circ}$ is centered at an angle of $37.5^{\circ}$ away from the center. The mouse will die in the dark. What fraction of the total area of the ca... | "[\"\\\\frac{3}{4}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1955, "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:15946"}] | {
"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
} |
[
"29"
] | [
"skywork"
] | b566e41a7b50cb5031bb129c4a8ba70800fd0b6d5cb49316d82c25e76157d466 | [
{
"content": "Exercise 11. A group of 20 dwarves coming out of the mine sit around a round table to count the gold nuggets each has mined. They make the following observations:\n\n$\\triangleright$ The difference in the number of nuggets between two neighboring dwarves is always 2 or 3.\n\n$\\triangleright$ All... | Exercise 11. A group of 20 dwarves coming out of the mine sit around a round table to count the gold nuggets each has mined. They make the following observations:
$\triangleright$ The difference in the number of nuggets between two neighboring dwarves is always 2 or 3.
$\triangleright$ All the dwarves have mined a di... | "[\"29\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1963, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15947"}] | {
"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
} |
[
"22.5"
] | [
"skywork"
] | 4b04166cf0fc7f43a2b9192d2d535b6df21ecae8efccb7dd228e3e49c1db64d7 | [
{
"content": "A cyclist initially traveled at a speed of 20 km/h. After covering one-third of the distance, the cyclist looked at the clock and decided to increase the speed by 20%. With the new speed, the cyclist traveled the remaining part of the distance. What is the average speed of the cyclist?",
"role... | A cyclist initially traveled at a speed of 20 km/h. After covering one-third of the distance, the cyclist looked at the clock and decided to increase the speed by 20%. With the new speed, the cyclist traveled the remaining part of the distance. What is the average speed of the cyclist? | "[\"22.5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1958, "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:15948"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{33}"
] | [
"skywork"
] | 06734417c439114130e9f68d4358bfad15ced542404eeaf11a08c4718ca71009 | [
{
"content": "[ Law of Sines [Trigonometric Ratios in a Right Triangle]\n\nThe hypotenuse $A B$ of the right triangle $A B C$ is 9, and the leg $B C$ is 3. A point $M$ is taken on the hypotenuse such that $A M: M B=1: 2$. Find $C M$.\n\n#",
"role": "user"
}
] | [ Law of Sines [Trigonometric Ratios in a Right Triangle]
The hypotenuse $A B$ of the right triangle $A B C$ is 9, and the leg $B C$ is 3. A point $M$ is taken on the hypotenuse such that $A M: M B=1: 2$. Find $C M$.
# | "[\"\\\\sqrt{33}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1966, "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:15949"}] | {
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[
"9"
] | [
"skywork"
] | 3fc9aa82445a6565c65a609789b9b1bb3acc67e7d1742b2cc9dd1f02dcc96b01 | [
{
"content": "At the round table, $10$ people are sitting, some of them are knights, and the rest are liars (knights always say pride, and liars always lie) . It is clear thath I have at least one knight and at least one liar. \nWhat is the largest number of those sitting at the table can say: ''Both of my nei... | At the round table, $10$ people are sitting, some of them are knights, and the rest are liars (knights always say pride, and liars always lie) . It is clear thath I have at least one knight and at least one liar.
What is the largest number of those sitting at the table can say: ''Both of my neighbors are knights '' ?... | "[\"9\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1972, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15950"}] | {
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[
"520"
] | [
"skywork"
] | c8d2baa1bafbd33b7f1c4d59382765e9b485a8d3a53cad434265eeee86c21435 | [
{
"content": "The Crystal Products Factory in the East Sea had an annual output of 100,000 pieces last year, with each crystal product selling for 100 yuan and a fixed cost of 80 yuan. Starting this year, the factory invested 1 million yuan in technology costs and plans to invest an additional 1 million yuan in... | The Crystal Products Factory in the East Sea had an annual output of 100,000 pieces last year, with each crystal product selling for 100 yuan and a fixed cost of 80 yuan. Starting this year, the factory invested 1 million yuan in technology costs and plans to invest an additional 1 million yuan in technology costs each... | "[\"520\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1947, "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:15951"}] | {
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[
"8125"
] | [
"skywork"
] | f632ace28acba45ead7342dd549102e9df9d57b239906adbd04bf8d35f62e5a4 | [
{
"content": "XII OM - II - Task 4\n\nFind the last four digits of the number $ 5^{5555} $.",
"role": "user"
}
] | XII OM - II - Task 4
Find the last four digits of the number $ 5^{5555} $. | "[\"8125\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1990, "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:15952"}] | {
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[
"\\frac{7 - 3\\sqrt{3}}{11}"
] | [
"skywork"
] | 1652bbdf7ff75297e3348b682584f4d38303ca2ae499389a199ecc2644033b7e | [
{
"content": "In the triangle \\(ABC\\), it is known that \\(AB=BC\\) and \\(\\angle BAC=45^\\circ\\). The line \\(MN\\) intersects side \\(AC\\) at point \\(M\\), and side \\(BC\\) at point \\(N\\). Given that \\(AM=2 \\cdot MC\\) and \\(\\angle NMC=60^\\circ\\), find the ratio of the area of triangle \\(MNC\\... | In the triangle \(ABC\), it is known that \(AB=BC\) and \(\angle BAC=45^\circ\). The line \(MN\) intersects side \(AC\) at point \(M\), and side \(BC\) at point \(N\). Given that \(AM=2 \cdot MC\) and \(\angle NMC=60^\circ\), find the ratio of the area of triangle \(MNC\) to the area of quadrilateral \(ABNM\). | "[\"\\\\frac{7 - 3\\\\sqrt{3}}{11}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1961, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15953"}] | {
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[
"17^\\circ"
] | [
"skywork"
] | 038d76bec004fa1478c0b1ca376d769d671a1bb88d75d5af594d568c32c73220 | [
{
"content": "The complement of an angle is $5^{\\circ}$ more than four times the angle. What is the number of degrees in the measure of the angle?",
"role": "user"
}
] | The complement of an angle is $5^{\circ}$ more than four times the angle. What is the number of degrees in the measure of the angle? | "[\"17^\\\\circ\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1988, "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:15954"}] | {
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[
"3"
] | [
"skywork"
] | 70c6593fb6d6b6245b6cad9b532ad41a3e5425d0e3fd56388b92b2122d247788 | [
{
"content": "3. In $\\triangle A B C$, $\\angle C=90^{\\circ}, \\angle A$ and $\\angle B$ are bisected and intersect at point $P$, and $P E \\perp A B$ at point $E$. If $B C=2, A C=3$,\nthen $A E \\cdot E B=$ $\\qquad$",
"role": "user"
}
] | 3. In $\triangle A B C$, $\angle C=90^{\circ}, \angle A$ and $\angle B$ are bisected and intersect at point $P$, and $P E \perp A B$ at point $E$. If $B C=2, A C=3$,
then $A E \cdot E B=$ $\qquad$ | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1977, "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:15955"}] | {
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[
"\\frac{1}{12}"
] | [
"skywork"
] | 5e7c1b8c4fc4b4b57b25eacf748cf1f3bdec70f085dcd9b681ca4f62d8f9fa65 | [
{
"content": "What is the maximum value of $\\frac{(2^t-3t)t}{4^t}$ for real values of $t?$\n$\\textbf{(A)}\\ \\frac{1}{16} \\qquad\\textbf{(B)}\\ \\frac{1}{15} \\qquad\\textbf{(C)}\\ \\frac{1}{12} \\qquad\\textbf{(D)}\\ \\frac{1}{10} \\qquad\\textbf{(E)}\\ \\frac{1}{9}$",
"role": "user"
}
] | What is the maximum value of $\frac{(2^t-3t)t}{4^t}$ for real values of $t?$
$\textbf{(A)}\ \frac{1}{16} \qquad\textbf{(B)}\ \frac{1}{15} \qquad\textbf{(C)}\ \frac{1}{12} \qquad\textbf{(D)}\ \frac{1}{10} \qquad\textbf{(E)}\ \frac{1}{9}$ | "[\"\\\\frac{1}{12}\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 1983, "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:15956"}] | {
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[
"\\frac{n(n^2 + 1)}{2}"
] | [
"skywork"
] | 39c9f8d77152563c3bf0b629f5117edbe8877658f98dfcef2e08bdfceb417d8e | [
{
"content": "A $n$ by $n$ magic square contains numbers from $1$ to $n^2$ such that the sum of every row and every column is the same. What is this sum?",
"role": "user"
}
] | A $n$ by $n$ magic square contains numbers from $1$ to $n^2$ such that the sum of every row and every column is the same. What is this sum? | "[\"\\\\frac{n(n^2 + 1)}{2}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1982, "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:15957"}] | {
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[
"2019"
] | [
"skywork"
] | 34029c6e03aca22c0c0c0214ed96473087f94ba689f7ed11b89e9b7466e47cae | [
{
"content": "14. The function $f(x)$ defined on $\\mathbf{R}$ satisfies $\\left\\{\\begin{array}{l}f(x+2016) \\leqslant f(x)+2016, \\\\ f(x+2017) \\geqslant f(x)+2017,\\end{array}\\right.$ and $f(1)=2$. Let $a_{n}=f(n)\\left(n \\in \\mathbf{N}^{*}\\right)$, then $a_{2018}=$ $\\qquad$",
"role": "user"
}
] | 14. The function $f(x)$ defined on $\mathbf{R}$ satisfies $\left\{\begin{array}{l}f(x+2016) \leqslant f(x)+2016, \\ f(x+2017) \geqslant f(x)+2017,\end{array}\right.$ and $f(1)=2$. Let $a_{n}=f(n)\left(n \in \mathbf{N}^{*}\right)$, then $a_{2018}=$ $\qquad$ | "[\"2019\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1980, "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:15958"}] | {
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[
"6"
] | [
"skywork"
] | dea50279e1a56efd5e9b9adf5c91528b0acce401d8f6d4557408f2c23eabe866 | [
{
"content": "What is the GCD of all numbers of the form $i \\times(i+1) \\times(i+2)$ with $i \\geq 1$ (we are looking for the greatest common divisor of all these numbers).",
"role": "user"
}
] | What is the GCD of all numbers of the form $i \times(i+1) \times(i+2)$ with $i \geq 1$ (we are looking for the greatest common divisor of all these numbers). | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1987, "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:15959"}] | {
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[
"89"
] | [
"skywork"
] | 4c19b067648f72b50b7be0455db1103b3cab04edb7a8f21fe182e2d6f7e0a489 | [
{
"content": "26. (5 points)\nIn Muyangyang's candy jar, there are 10 identical chocolate beans. Each time, 1 or 2 beans can be taken out. To take out all 10 chocolate beans, there are $\\qquad$ different ways.",
"role": "user"
}
] | 26. (5 points)
In Muyangyang's candy jar, there are 10 identical chocolate beans. Each time, 1 or 2 beans can be taken out. To take out all 10 chocolate beans, there are $\qquad$ different ways. | "[\"89\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1984, "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:15960"}] | {
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[
"2^n"
] | [
"skywork"
] | 61492393a08172463b559778bf4886c0997bcaeac92df6c85a78948959024ec7 | [
{
"content": "Consider a $ n \\times n$ checkerboard with $ n > 1, n \\in \\mathbb{N}.$ How many possibilities are there to put $ 2n \\minus{} 2$ identical pebbles on the checkerboard (each on a different field/place) such that no two pebbles are on the same checkerboard diagonal. Two pebbles are on the same ch... | Consider a $ n \times n$ checkerboard with $ n > 1, n \in \mathbb{N}.$ How many possibilities are there to put $ 2n \minus{} 2$ identical pebbles on the checkerboard (each on a different field/place) such that no two pebbles are on the same checkerboard diagonal. Two pebbles are on the same checkerboard diagonal if the... | "[\" 2^n \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1979, "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:15961"}] | {
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[
"\\sqrt{-k};-1<k<0"
] | [
"skywork"
] | 0abf34328baf3fe456353b3b20d7e067defb5168ce8b58c40c6ca48c8968968f | [
{
"content": "12.279. The cosine of the angle between two adjacent lateral faces of a regular quadrilateral pyramid is $k$. Find the cosine of the angle between a lateral face and the plane of the base and the permissible values of $k$.",
"role": "user"
}
] | 12.279. The cosine of the angle between two adjacent lateral faces of a regular quadrilateral pyramid is $k$. Find the cosine of the angle between a lateral face and the plane of the base and the permissible values of $k$. | "[\"\\\\sqrt{-k};-1<k<0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1969, "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:15962"}] | {
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[
"32"
] | [
"skywork"
] | ba0ddfafaed824d21c333413171187575ed2646557a2c233d492c61069028090 | [
{
"content": "Let $f(x)=\\sum_{k=2}^{10}(\\lfloor kx \\rfloor -k \\lfloor x \\rfloor)$, where $\\lfloor r \\rfloor$ denotes the greatest integer less than or equal to $r$. How many distinct values does $f(x)$ assume for $x \\ge 0$?",
"role": "user"
}
] | Let $f(x)=\sum_{k=2}^{10}(\lfloor kx \rfloor -k \lfloor x \rfloor)$, where $\lfloor r \rfloor$ denotes the greatest integer less than or equal to $r$. How many distinct values does $f(x)$ assume for $x \ge 0$? | "[\"32\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1999, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15963"}] | {
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[
"3680\\mathrm{~}^{2}"
] | [
"skywork"
] | ccefdf6940a14c3f5dbd8d9dda7a9f7c33a687487efba478d2d3c929a0ef11cd | [
{
"content": "7. A rectangular sheet of iron was divided into 2 parts such that the first part was 4 times larger than the second. What is the area of the entire sheet if the first part is $2208 \\mathrm{~cm}^{2}$ larger than the second?",
"role": "user"
}
] | 7. A rectangular sheet of iron was divided into 2 parts such that the first part was 4 times larger than the second. What is the area of the entire sheet if the first part is $2208 \mathrm{~cm}^{2}$ larger than the second? | "[\"3680\\\\mathrm{~}^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2002, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15964"}] | {
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[
"32"
] | [
"skywork"
] | 359952f8b501eae41eca4576e3d76bb3a4d8570dc6b33767382115e947c1c215 | [
{
"content": "2. (8 points) In the figure, two sectors with central angles of $90^{\\circ}$ are placed on the large circle, and the small circle is placed on the two sectors, with all their centers at the same point. If the radius ratio of the small circle, the large circle, and the sectors is 1: 3: 4, then the... | 2. (8 points) In the figure, two sectors with central angles of $90^{\circ}$ are placed on the large circle, and the small circle is placed on the two sectors, with all their centers at the same point. If the radius ratio of the small circle, the large circle, and the sectors is 1: 3: 4, then the shaded area occupies $... | "[\"32\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1986, "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:15965"}] | {
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[
"45"
] | [
"skywork"
] | 31101439c96ef09efcd23d7fe67c143546b3e24db35fac23d55f589a268458d4 | [
{
"content": "The values of $r, s, t$, and $u$ are $2,3,4$, and 5 , but not necessarily in that order. What is the largest possible value of $r \\times s+u \\times r+t \\times r$ ?\n(A) 24\n(B) 45\n(C) 33\n(D) 40\n(E) 49",
"role": "user"
}
] | The values of $r, s, t$, and $u$ are $2,3,4$, and 5 , but not necessarily in that order. What is the largest possible value of $r \times s+u \times r+t \times r$ ?
(A) 24
(B) 45
(C) 33
(D) 40
(E) 49 | "[\"45\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2006, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15966"}] | {
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[
"33"
] | [
"skywork"
] | 83e17a79e0f57c311976b0d4cb938388b69bec27151ebade7af9c5e7eb5e0ce3 | [
{
"content": "Let $\\star (x)$ be the sum of the digits of a positive integer $x$. $\\mathcal{S}$ is the set of positive integers such that for all elements $n$ in $\\mathcal{S}$, we have that $\\star (n)=15$ and $0\\le n< 10^{8}$. If $m$ is the number of elements in $\\mathcal{S}$, compute $\\star(m)$.",
"... | Let $\star (x)$ be the sum of the digits of a positive integer $x$. $\mathcal{S}$ is the set of positive integers such that for all elements $n$ in $\mathcal{S}$, we have that $\star (n)=15$ and $0\le n< 10^{8}$. If $m$ is the number of elements in $\mathcal{S}$, compute $\star(m)$. | "[\"33\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1992, "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:15967"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"f(x)=1+\\log_{2015}x"
] | [
"skywork"
] | 0effe5226b3ee473dffcd3fb450c1c95add8fe4ff8e63b94fe567404dc32f469 | [
{
"content": "PROBLEM 1. Determine the function $f:(0,+\\infty) \\rightarrow \\mathbb{R}$ with the property:\n\n$$\nf\\left(\\frac{x}{2015}\\right) \\leq \\log _{2015} x \\leq f(x)-1, \\quad \\forall x \\in(0,+\\infty)\n$$",
"role": "user"
}
] | PROBLEM 1. Determine the function $f:(0,+\infty) \rightarrow \mathbb{R}$ with the property:
$$
f\left(\frac{x}{2015}\right) \leq \log _{2015} x \leq f(x)-1, \quad \forall x \in(0,+\infty)
$$ | "[\"f(x)=1+\\\\log_{2015}x\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2000, "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:15968"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"265"
] | [
"skywork"
] | a4dc5d3cb491b87b88d2625103b2068573f63a4195b73f9d6b86b3b7b1ed8edc | [
{
"content": "Find the sum of all integers $0\\le a \\le124$ so that $a^3-2$ is a multiple of $125$.",
"role": "user"
}
] | Find the sum of all integers $0\le a \le124$ so that $a^3-2$ is a multiple of $125$. | "[\"265\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1997, "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:15969"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{8}{9}"
] | [
"skywork"
] | a760eae99f948fe21659fdebc87243ce8d25e17a829e4be9aadbc212b59e1ae1 | [
{
"content": "A chessboard has its squares labeled according to the rule $\\frac{1}{c_i + r_j}$, where $c_i$ is the column number and $r_j$ is the row number. Eight squares are to be chosen such that there is exactly one chosen square in each row and each column. Find the minimum sum of the labels of these eigh... | A chessboard has its squares labeled according to the rule $\frac{1}{c_i + r_j}$, where $c_i$ is the column number and $r_j$ is the row number. Eight squares are to be chosen such that there is exactly one chosen square in each row and each column. Find the minimum sum of the labels of these eight chosen squares. | "[\"\\\\frac{8}{9}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1981, "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:15970"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-1,3,3"
] | [
"skywork"
] | 8ec4937689f372b30af70acb9dd5e5874b095063042043c2f4bf32ca1d0de6f6 | [
{
"content": "Find all roots of the polynomial $x^3-5x^2+3x+9$. Enter your answer as a list of numbers separated by commas. If a root occurs more than once, enter it as many times as its multiplicity.",
"role": "user"
}
] | Find all roots of the polynomial $x^3-5x^2+3x+9$. Enter your answer as a list of numbers separated by commas. If a root occurs more than once, enter it as many times as its multiplicity. | "[\"-1,3,3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2008, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15971"}] | {
"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"
] | 49073a91cec65e2df1b1b46c609081695ecef369cb49bd3d090a94e8ca43755b | [
{
"content": "Find all positive integers $n\\geq1$ such that there exists a pair $(a,b)$ of positive integers, such that $a^2+b+3$ is not divisible by the cube of any prime, and $$n=\\frac{ab+3b+8}{a^2+b+3}.$$",
"role": "user"
}
] | Find all positive integers $n\geq1$ such that there exists a pair $(a,b)$ of positive integers, such that $a^2+b+3$ is not divisible by the cube of any prime, and $$n=\frac{ab+3b+8}{a^2+b+3}.$$ | "[\"2\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 1991, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15972"}] | {
"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{1820\\sqrt{21}}{341}"
] | [
"skywork"
] | 6092d4ce4fe7f10847560ff9cd57b29204bcc5031f2f6f6721e400305e7a4409 | [
{
"content": "## [\n\n The Law of Cosines [Area of a Triangle (using two sides and the included angle).] Quadrilateral $A B C D$ is inscribed in a circle. The lengths of the opposite sides $A B$ and $C D$ are 9 and 4, respectively, $A C=7, B D=8$. Find the area of quadrilateral $A B C D$.\n\n#",
"role": "us... | ## [
The Law of Cosines [Area of a Triangle (using two sides and the included angle).] Quadrilateral $A B C D$ is inscribed in a circle. The lengths of the opposite sides $A B$ and $C D$ are 9 and 4, respectively, $A C=7, B D=8$. Find the area of quadrilateral $A B C D$.
# | "[\"\\\\frac{1820\\\\sqrt{21}}{341}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1973, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15973"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-9"
] | [
"skywork"
] | 19f3c73bb14520c569b40939ed9ee65b4c61e43731ab7f4d97cbf9ac96931efd | [
{
"content": "7. Let $\\left(1+x-x^{2}\\right)^{10}=a_{0}+a_{1} x+\\cdots+a_{20} x^{20}$. Then $a_{0}+a_{1}+2 a_{2}+\\cdots+20 a_{20}=$ $\\qquad$",
"role": "user"
}
] | 7. Let $\left(1+x-x^{2}\right)^{10}=a_{0}+a_{1} x+\cdots+a_{20} x^{20}$. Then $a_{0}+a_{1}+2 a_{2}+\cdots+20 a_{20}=$ $\qquad$ | "[\"-9\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2001, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15974"}] | {
"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
} |
[
"3876"
] | [
"skywork"
] | efdf59ca07781f24535404942661216c40c2710683dfc8f566f32ecdb884cb66 | [
{
"content": "Given the teacher has 30 cookies to distribute among five students so that each student receives at least three cookies, find the number of ways the cookies can be distributed.",
"role": "user"
}
] | Given the teacher has 30 cookies to distribute among five students so that each student receives at least three cookies, find the number of ways the cookies can be distributed. | "[\"3876\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2012, "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:15975"}] | {
"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}{8}"
] | [
"skywork"
] | 1778b0da505a10ec6fbd2639201edd8851e7c923295c742287aead382b3a2cf0 | [
{
"content": "What is the maximum value of $\\frac{(3^t-2t)t}{9^t}$ for real values of $t$?\nA) $\\frac{1}{10}$\nB) $\\frac{1}{12}$\nC) $\\frac{1}{8}$\nD) $\\frac{1}{6}$\nE) $\\frac{1}{4}$",
"role": "user"
}
] | What is the maximum value of $\frac{(3^t-2t)t}{9^t}$ for real values of $t$?
A) $\frac{1}{10}$
B) $\frac{1}{12}$
C) $\frac{1}{8}$
D) $\frac{1}{6}$
E) $\frac{1}{4}$ | "[\"\\\\frac{1}{8}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1998, "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:15976"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3\\sqrt{3}}{4}"
] | [
"skywork"
] | a61654f491af1ec186117904fd2de5d4404372393fe37cfb8dfec7498a44af57 | [
{
"content": "Isosceles triangle $\\triangle{ABC}$ has $\\angle{BAC}=\\angle{ABC}=30^\\circ$ and $AC=BC=2$. If the midpoints of $BC$ and $AC$ are $M$ and $N$, respectively, and the circumcircle of $\\triangle{CMN}$ meets $AB$ at $D$ and $E$ with $D$ closer to $A$ than $E$ is, what is the area of $MNDE$?\n\n[i]2... | Isosceles triangle $\triangle{ABC}$ has $\angle{BAC}=\angle{ABC}=30^\circ$ and $AC=BC=2$. If the midpoints of $BC$ and $AC$ are $M$ and $N$, respectively, and the circumcircle of $\triangle{CMN}$ meets $AB$ at $D$ and $E$ with $D$ closer to $A$ than $E$ is, what is the area of $MNDE$?
[i]2019 CCA Math Bonanza Individu... | "[\"\\\\frac{3\\\\sqrt{3}}{4}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 1995, "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:15977"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"211"
] | [
"skywork"
] | f72cef3ba91430720c259bbeb4578a3f4d8b81d0a8f86cd37d9290521e1df2d1 | [
{
"content": "At a recent math contest, Evan was asked to find $2^{2016} \\pmod{p}$ for a given prime number $p$ with $100 < p < 500$ . Evan has forgotten what the prime $p$ was, but still remembers how he solved it:\n\n\n- Evan first tried taking $2016$ modulo $p - 1$ , but got a value $e$ larger t... | At a recent math contest, Evan was asked to find $2^{2016} \pmod{p}$ for a given prime number $p$ with $100 < p < 500$ . Evan has forgotten what the prime $p$ was, but still remembers how he solved it:
- Evan first tried taking $2016$ modulo $p - 1$ , but got a value $e$ larger than $100$ .
- However, Ev... | "[\"211\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1996, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15978"}] | {
"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{6}{20}"
] | [
"skywork"
] | 318bc092df6eb3a25c067ba657b2b87db767f84ae5466261c82f1836c0e5c734 | [
{
"content": "The numbers 1 through 20 are written on twenty golf balls, with one number on each ball. The golf balls are placed in a box, and one ball is drawn at random. If each ball is equally likely to be drawn, what is the probability that the number on the golf ball drawn is a multiple of 3 ?\n(A) $\\frac... | The numbers 1 through 20 are written on twenty golf balls, with one number on each ball. The golf balls are placed in a box, and one ball is drawn at random. If each ball is equally likely to be drawn, what is the probability that the number on the golf ball drawn is a multiple of 3 ?
(A) $\frac{3}{20}$
(B) $\frac{6}{2... | "[\"\\\\frac{6}{20}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2013, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15980"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\alpha=\\frac{\\pi}{4}"
] | [
"skywork"
] | 230e10d8b2912b1feb6314c6098740b08923fc1f3fc40f6f62368da1fbab3451 | [
{
"content": "3.59. The acute angle of a right triangle is $\\alpha$. Find the ratio of the radius of the inscribed circle to the radius of the circumscribed circle. For what value of $\\alpha$ is this ratio the greatest?",
"role": "user"
}
] | 3.59. The acute angle of a right triangle is $\alpha$. Find the ratio of the radius of the inscribed circle to the radius of the circumscribed circle. For what value of $\alpha$ is this ratio the greatest? | "[\"\\\\alpha=\\\\frac{\\\\pi}{4}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2016, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15981"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{85}{2}"
] | [
"skywork"
] | dac25dd55cc1f3ab364d64fd688fc4e4c693f6a71ea796e855bcc00f37c227c5 | [
{
"content": "Quadrilateral $ABCD$ is inscribed in circle $O$ and has side lengths $AB=5, BC=3, CD=7$, and $DA=9$. Let $X$ and $Y$ be points on $\\overline{BD}$ such that $\\frac{DX}{BD} = \\frac{1}{3}$ and $\\frac{BY}{BD} = \\frac{1}{4}$. Let $E$ be the intersection of line $AX$ and the line through $Y$ parall... | Quadrilateral $ABCD$ is inscribed in circle $O$ and has side lengths $AB=5, BC=3, CD=7$, and $DA=9$. Let $X$ and $Y$ be points on $\overline{BD}$ such that $\frac{DX}{BD} = \frac{1}{3}$ and $\frac{BY}{BD} = \frac{1}{4}$. Let $E$ be the intersection of line $AX$ and the line through $Y$ parallel to $\overline{AD}$. Let ... | "[\"\\\\frac{85}{2}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 1989, "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:15982"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"25"
] | [
"skywork"
] | 026125189ed512821d406e536231d4d0bb009a7a63a10deccbed0979de854902 | [
{
"content": "15$\\cdot$18 Mapping $f:\\{a, b, c, d\\} \\rightarrow\\{1,2,3\\}$. If $10<f(a) \\cdot f(b)$. $f(c) \\cdot f(d)<20$, the number of such mappings is\n(A) 23.\n(B) 24.\n(C) 25.\n(D) 26.\n(2nd \"Hope Cup\" National Mathematics Invitational Competition, 1991)",
"role": "user"
}
] | 15$\cdot$18 Mapping $f:\{a, b, c, d\} \rightarrow\{1,2,3\}$. If $10<f(a) \cdot f(b)$. $f(c) \cdot f(d)<20$, the number of such mappings is
(A) 23.
(B) 24.
(C) 25.
(D) 26.
(2nd "Hope Cup" National Mathematics Invitational Competition, 1991) | "[\"25\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2004, "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:15983"}] | {
"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
} |
[
"476"
] | [
"skywork"
] | e5e0737d9cb46da7c479a74014b787700f999ed6e64a6894164192378112e345 | [
{
"content": "8. Let $\\{a, b, c, d\\}$ be a subset of $\\{1,2, \\cdots, 17\\}$. If 17 divides $(a-b+c-d)$, then $\\{a, b, c, d\\}$ is called a \"good subset\". Then, the number of good subsets is $\\qquad$",
"role": "user"
}
] | 8. Let $\{a, b, c, d\}$ be a subset of $\{1,2, \cdots, 17\}$. If 17 divides $(a-b+c-d)$, then $\{a, b, c, d\}$ is called a "good subset". Then, the number of good subsets is $\qquad$ | "[\"476\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2005, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15984"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"skywork"
] | af3a87f58c4839e0230486a31e02a6588f47c1d707a422c1e5447278e023e932 | [
{
"content": "The polynomial $x^8 - 1$ is factored as\n\\[x^8 - 1 = p_1(x) p_2(x) \\dotsm p_k(x),\\]where each factor $p_i(x)$ is a non-constant polynomial with real coefficients. Find the largest possible value of $k.$",
"role": "user"
}
] | The polynomial $x^8 - 1$ is factored as
\[x^8 - 1 = p_1(x) p_2(x) \dotsm p_k(x),\]where each factor $p_i(x)$ is a non-constant polynomial with real coefficients. Find the largest possible value of $k.$ | "[\"5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2018, "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:15985"}] | {
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[
"1013"
] | [
"skywork"
] | afca03c9a9d4758990e11f15b0f9387f90708f5eb000efc9e0eb850e39c41d44 | [
{
"content": "Find the number of all natural numbers in which each subsequent digit is less than the previous one.",
"role": "user"
}
] | Find the number of all natural numbers in which each subsequent digit is less than the previous one. | "[\"1013\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2003, "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:15986"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2000"
] | [
"skywork"
] | 185690b2ac127564e141088f0a71779e7f80c5d44c3bdaa3450a413df661507f | [
{
"content": "Find the value of\n\\[ \\left\\lfloor \\frac{2002!}{2001! + 2000! + 1999! + \\cdots + 1!} \\right\\rfloor, \\]\nwhere \\(\\lfloor x\\rfloor\\) denotes the greatest integer less than or equal to \\(x\\).",
"role": "user"
}
] | Find the value of
\[ \left\lfloor \frac{2002!}{2001! + 2000! + 1999! + \cdots + 1!} \right\rfloor, \]
where \(\lfloor x\rfloor\) denotes the greatest integer less than or equal to \(x\). | "[\"2000\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2020, "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:15987"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"16"
] | [
"skywork"
] | 7b6757a7f6a181c3a952418d1ef07ac1aafb0e65ce2ed4d2fe4480477cc53df4 | [
{
"content": "Let $a, b, c$ be integers not all the same with $a, b, c\\ge 4$ that satisfy $$4abc = (a + 3) (b + 3) (c + 3).$$\nFind the numerical value of $a + b + c$.",
"role": "user"
}
] | Let $a, b, c$ be integers not all the same with $a, b, c\ge 4$ that satisfy $$4abc = (a + 3) (b + 3) (c + 3).$$
Find the numerical value of $a + b + c$. | "[\"16\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2026, "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:15988"}, {"dataset": "skywork", "extra_inf... | {
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} |
[
"19"
] | [
"skywork"
] | 755215eb1b3cdda9fd82ad47a3af38a8faa4f076bf313dd68969ba816f01e5f1 | [
{
"content": "Hari is obsessed with cubics. He comes up with a cubic with leading coefficient 1, rational coefficients and real roots $0 < a < b < c < 1$. He knows the following three facts: $P(0) = -\\frac{1}{8}$, the roots form a geometric progression in the order $a,b,c$, and \\[ \\sum_{k=1}^{\\infty} (a^k... | Hari is obsessed with cubics. He comes up with a cubic with leading coefficient 1, rational coefficients and real roots $0 < a < b < c < 1$. He knows the following three facts: $P(0) = -\frac{1}{8}$, the roots form a geometric progression in the order $a,b,c$, and \[ \sum_{k=1}^{\infty} (a^k + b^k + c^k) = \dfrac{9}{... | "[\"19\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2010, "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:15989"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"5702887"
] | [
"skywork"
] | 6913c19283e70b6259197ce568496e2ca667f00cbcddd82abf272f0e6248f362 | [
{
"content": "A finite set $\\{a_1, a_2, ... a_k\\}$ of positive integers with $a_1 < a_2 < a_3 < ... < a_k$ is named *alternating* if $i+a$ for $i = 1, 2, 3, ..., k$ is even. The empty set is also considered to be alternating. The number of alternating subsets of $\\{1, 2, 3,..., n\\}$ is denoted by... | A finite set $\{a_1, a_2, ... a_k\}$ of positive integers with $a_1 < a_2 < a_3 < ... < a_k$ is named *alternating* if $i+a$ for $i = 1, 2, 3, ..., k$ is even. The empty set is also considered to be alternating. The number of alternating subsets of $\{1, 2, 3,..., n\}$ is denoted by $A(n)$ .
Develop a metho... | "[\"5702887\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 1985, "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:15990"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"skywork"
] | a5a4efb3d5e726667c1ae0f67cb73e449445359e2e4ced3383e8b31aae0503af | [
{
"content": "Compute the number of real solutions $(x,y,z,w)$ to the system of equations:\n\\begin{align*}\nx &= z+w+zwx, \\\\ \ny &= w+x+wxy, \\\\\nz &= x+y+xyz, \\\\\nw &= y+z+yzw.\n\\end{align*}",
"role": "user"
}
] | Compute the number of real solutions $(x,y,z,w)$ to the system of equations:
\begin{align*}
x &= z+w+zwx, \\
y &= w+x+wxy, \\
z &= x+y+xyz, \\
w &= y+z+yzw.
\end{align*} | "[\"5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2009, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15991"}] | {
"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}{\\sqrt[4]{x^{2}-1}}"
] | [
"skywork"
] | bf3cff7f7bd80d04335b4485195bc32a9c123cf09634601b9e26449d11553c23 | [
{
"content": "2.203. $\\frac{\\sqrt{\\sqrt{\\frac{x-1}{x+1}}+\\sqrt{\\frac{x+1}{x-1}}-2} \\cdot\\left(2 x+\\sqrt{x^{2}-1}\\right)}{\\sqrt{(x+1)^{3}}-\\sqrt{(x-1)^{3}}}$.\n\n2.203. $\\frac{\\sqrt{\\sqrt{\\frac{x-1}{x+1}}+\\sqrt{\\frac{x+1}{x-1}}-2} \\cdot\\left(2 x+\\sqrt{x^{2}-1}\\right)}{\\sqrt{(x+1)^{3}}-\\sq... | 2.203. $\frac{\sqrt{\sqrt{\frac{x-1}{x+1}}+\sqrt{\frac{x+1}{x-1}}-2} \cdot\left(2 x+\sqrt{x^{2}-1}\right)}{\sqrt{(x+1)^{3}}-\sqrt{(x-1)^{3}}}$.
2.203. $\frac{\sqrt{\sqrt{\frac{x-1}{x+1}}+\sqrt{\frac{x+1}{x-1}}-2} \cdot\left(2 x+\sqrt{x^{2}-1}\right)}{\sqrt{(x+1)^{3}}-\sqrt{(x-1)^{3}}}$.
The expression is already in a... | "[\"\\\\frac{1}{\\\\sqrt[4]{x^{2}-1}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2014, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15992"}] | {
"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
} |
[
"2019"
] | [
"skywork"
] | b44a8a0da7b9f62475b19f9a6bbe53419ecf37ac2e97c97d9a03a9c67a3a5500 | [
{
"content": "6. Given $0 \\leqslant m-n \\leqslant 1, 2 \\leqslant m+n \\leqslant 4$. When $m-2 n$ reaches its maximum value, the value of $2019 m+2020 n$ is ( ).\n(A) 2019\n(B) 2020\n(C) 0\n(D) -1",
"role": "user"
}
] | 6. Given $0 \leqslant m-n \leqslant 1, 2 \leqslant m+n \leqslant 4$. When $m-2 n$ reaches its maximum value, the value of $2019 m+2020 n$ is ( ).
(A) 2019
(B) 2020
(C) 0
(D) -1 | "[\"2019\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2022, "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:15993"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"90"
] | [
"skywork"
] | 83dd62aa4fabb3cff320a6a4818ee43b4f43aa4b4232fc4a0b175feb6d1fe715 | [
{
"content": "When \\( \\frac{1}{2222} \\) is expressed as a decimal, what is the sum of the first 50 digits after the decimal point?",
"role": "user"
}
] | When \( \frac{1}{2222} \) is expressed as a decimal, what is the sum of the first 50 digits after the decimal point? | "[\"90\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2032, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:15994"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sin(B+\\frac{\\pi}{6})=\\frac{\\sqrt{3}}{2}"
] | [
"skywork"
] | 47b461cb2275b7d2d80354a2dbb33b5613a40280b4e4413e9c7c344649bdd7fe | [
{
"content": "17 Given that the three interior angles $A, B, C$ of $\\triangle ABC$ are opposite to the sides $a, b, c$ respectively, the vectors $\\vec{m}=(1,1-\\sqrt{3} \\sin A), \\vec{n}=(\\cos A, 1)$, and $\\vec{m} \\perp \\vec{n}$.\n(1) Find the angle $A$;\n(2) If $b+c=\\sqrt{3} a$, find the value of $\\si... | 17 Given that the three interior angles $A, B, C$ of $\triangle ABC$ are opposite to the sides $a, b, c$ respectively, the vectors $\vec{m}=(1,1-\sqrt{3} \sin A), \vec{n}=(\cos A, 1)$, and $\vec{m} \perp \vec{n}$.
(1) Find the angle $A$;
(2) If $b+c=\sqrt{3} a$, find the value of $\sin \left(B+\frac{\pi}{6}\right)$. | "[\"\\\\sin(B+\\\\frac{\\\\pi}{6})=\\\\frac{\\\\sqrt{3}}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 1994, "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:15995"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1000"
] | [
"skywork"
] | 14d2357ea8b9bf1520d9db40fcc144376aa703d7945325cc77792a3c4d2bbc7f | [
{
"content": "1. If $a, b$ are both integers, the equation\n$$\na x^{2}+b x-2008=0\n$$\n\nhas two distinct roots that are prime numbers, then $3 a+b=$ $\\qquad$ (2008, Taiyuan Junior High School Mathematics Competition)",
"role": "user"
}
] | 1. If $a, b$ are both integers, the equation
$$
a x^{2}+b x-2008=0
$$
has two distinct roots that are prime numbers, then $3 a+b=$ $\qquad$ (2008, Taiyuan Junior High School Mathematics Competition) | "[\"1000\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2019, "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:15996"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3}{5}"
] | [
"skywork"
] | 1879780387651750168af9f3e5dbb77dfc6f4276aae71afa34cb23709e06034d | [
{
"content": "Let $\\mathbf{v}$ and $\\mathbf{w}$ be the vectors such that $\\mathbf{v} \\cdot \\mathbf{w} = -3$ and $\\|\\mathbf{w}\\| = 5.$ Find the magnitude of $\\operatorname{proj}_{\\mathbf{w}} \\mathbf{v}.$",
"role": "user"
}
] | Let $\mathbf{v}$ and $\mathbf{w}$ be the vectors such that $\mathbf{v} \cdot \mathbf{w} = -3$ and $\|\mathbf{w}\| = 5.$ Find the magnitude of $\operatorname{proj}_{\mathbf{w}} \mathbf{v}.$ | "[\"\\\\frac{3}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2045, "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:15997"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"24"
] | [
"skywork"
] | e07be042541403d98f67a97a1c2f5d1e3cb5c924e14abd0fe77686fdca0128bb | [
{
"content": "Problem 9.3. All natural numbers from 1 to 1998 inclusive are written 9 times (so that there are 9 ones, 9 twos and so on) in the\ncells of a rectangular table with 9 rows and 1998 collumns, so that the difference between any two elements lying in one and the same column is no greater than 3 . Fin... | Problem 9.3. All natural numbers from 1 to 1998 inclusive are written 9 times (so that there are 9 ones, 9 twos and so on) in the
cells of a rectangular table with 9 rows and 1998 collumns, so that the difference between any two elements lying in one and the same column is no greater than 3 . Find the maximum possible ... | "[\"24\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2021, "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:15998"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac1{216}"
] | [
"skywork"
] | ee7ea8cf9b6b48c6160355aa3a9379d4c879f8c450f62412eab90cb38323fb02 | [
{
"content": "When three standard dice are tossed, the numbers $a,b,c$ are obtained. Find the probability that $abc = 1$.",
"role": "user"
}
] | When three standard dice are tossed, the numbers $a,b,c$ are obtained. Find the probability that $abc = 1$. | "[\"\\\\frac1{216}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2017, "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:15999"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"x\\sinxy=C"
] | [
"skywork"
] | 24944fa7a93f9f327e1e0b25ea1cb6b5c5164001016e23fdc53f0a5d657564a7 | [
{
"content": "Example 1. Solve the differential equation\n\n$$\n(\\sin x y+x y \\cos x y) d x+x^{2} \\cos x y d y=0\n$$",
"role": "user"
}
] | Example 1. Solve the differential equation
$$
(\sin x y+x y \cos x y) d x+x^{2} \cos x y d y=0
$$ | "[\"x\\\\sinxy=C\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2036, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16000"}] | {
"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{17000}{21}"
] | [
"skywork"
] | 66b68d1b0c51adae7c4b348c0b7ae98e7343ed12991e2be13f4daa073d8462f6 | [
{
"content": "Let $x$ be a real number such that\n\\[ x^2 + 8 \\left( \\frac{x}{x-3} \\right)^2 = 53. \\]\nFind all possible values of $y = \\frac{(x - 3)^3 (x + 4)}{2x - 5}.$",
"role": "user"
}
] | Let $x$ be a real number such that
\[ x^2 + 8 \left( \frac{x}{x-3} \right)^2 = 53. \]
Find all possible values of $y = \frac{(x - 3)^3 (x + 4)}{2x - 5}.$ | "[\"\\\\frac{17000}{21}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2007, "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:16001"}] | {
"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
} |
[
"750"
] | [
"skywork"
] | 63f7872b2de78422cf28a95d12f80ebca62831dea88e834cd889e2f26172e8da | [
{
"content": "A ream of paper containing $500$ sheets is $5$ cm thick. Approximately how many sheets of this type of paper would there be in a stack $7.5$ cm high?",
"role": "user"
}
] | A ream of paper containing $500$ sheets is $5$ cm thick. Approximately how many sheets of this type of paper would there be in a stack $7.5$ cm high? | "[\"750\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2042, "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:16002"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"n=1"
] | [
"skywork"
] | 72e460bd61051c314d5de71e2bae974972a79c9b4289b28b1149d40ec4d9ab8e | [
{
"content": "Determine all positive integers $n$ for which the equation \r\n\\[ x^n + (2+x)^n + (2-x)^n = 0 \\] \r\nhas an integer as a solution.",
"role": "user"
}
] | Determine all positive integers $n$ for which the equation
\[ x^n + (2+x)^n + (2-x)^n = 0 \]
has an integer as a solution. | "[\"n=1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2029, "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:16003"}] | {
"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
} |
[
"21"
] | [
"skywork"
] | f5fdce660366cff176d1798039d3ffe910938500f56976128c0bb5727a10602a | [
{
"content": "In a pentagon ABCDE, there is a vertical line of symmetry. Vertex E is moved to \\(E(5,0)\\), while \\(A(0,0)\\), \\(B(0,5)\\), and \\(D(5,5)\\). What is the \\(y\\)-coordinate of vertex C such that the area of pentagon ABCDE becomes 65 square units?",
"role": "user"
}
] | In a pentagon ABCDE, there is a vertical line of symmetry. Vertex E is moved to \(E(5,0)\), while \(A(0,0)\), \(B(0,5)\), and \(D(5,5)\). What is the \(y\)-coordinate of vertex C such that the area of pentagon ABCDE becomes 65 square units? | "[\"21\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2025, "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:16004"}] | {
"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},\\frac{1}{3})"
] | [
"skywork"
] | 964140ec55602a4e28ebaaa725504364e64336b476a1e731f1a225a8746ec093 | [
{
"content": "$\\left\\{\\begin{array}{l}\\frac{1}{4^{x}}+\\frac{1}{27^{y}}=\\frac{5}{6}, \\\\ \\log _{27} y-\\log _{4} x \\geqslant \\frac{1}{6}, \\\\ 27^{y}-4^{x} \\leqslant 1 .\\end{array}\\right.$",
"role": "user"
}
] | $\left\{\begin{array}{l}\frac{1}{4^{x}}+\frac{1}{27^{y}}=\frac{5}{6}, \\ \log _{27} y-\log _{4} x \geqslant \frac{1}{6}, \\ 27^{y}-4^{x} \leqslant 1 .\end{array}\right.$ | "[\"(\\\\frac{1}{2},\\\\frac{1}{3})\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2038, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:16005"}] | {
"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"
] | 273a668b183e3fcd1bf8a9c48f1957dba6c51fce85ba4517ebc73193e2abdbdc | [
{
"content": "Jo and Blair take turns counting. Jo starts by saying 1, and each time Blair follows by saying the last number Jo said plus 2, while Jo says the last number Blair said plus 3. Determine the 20th number said.",
"role": "user"
}
] | Jo and Blair take turns counting. Jo starts by saying 1, and each time Blair follows by saying the last number Jo said plus 2, while Jo says the last number Blair said plus 3. Determine the 20th number said. | "[\"48\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2040, "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:16006"}] | {
"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
} |
[
"75^\\circ"
] | [
"skywork"
] | cc5cd8190ba1892304551e365edd7a40ec784aef8c2dddf9ecf8f165ccf6603d | [
{
"content": "A circle passes through vertex $B$ of the triangle $ABC$, intersects its sides $ AB $and $BC$ at points $K$ and $L$, respectively, and touches the side $ AC$ at its midpoint $M$. The point $N$ on the arc $BL$ (which does not contain $K$) is such that $\\angle LKN = \\angle ACB$. Find $\\angle BAC ... | A circle passes through vertex $B$ of the triangle $ABC$, intersects its sides $ AB $and $BC$ at points $K$ and $L$, respectively, and touches the side $ AC$ at its midpoint $M$. The point $N$ on the arc $BL$ (which does not contain $K$) is such that $\angle LKN = \angle ACB$. Find $\angle BAC $ given that the triangle... | "[\"75^\\\\circ\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2024, "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:16007"}, {"dataset": "skywork", "extra_... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-\\frac{3}{8}"
] | [
"skywork"
] | 6126986b354217b919ccf08c863ca7611d0ef701c2cfca2c2514c3b2bfddb456 | [
{
"content": "If $a^{2}-4a+3=0$, find the value of $\\frac{9-3a}{2a-4} \\div (a+2-\\frac{5}{a-2})$ .",
"role": "user"
}
] | If $a^{2}-4a+3=0$, find the value of $\frac{9-3a}{2a-4} \div (a+2-\frac{5}{a-2})$ . | "[\"-\\\\frac{3}{8}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2031, "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:16008"}] | {
"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
} |
[
"4094"
] | [
"skywork"
] | 6362c3a61f01ca849fb2d053aa564ae9412f02d2d4af94ee42ca1ff81fe67be8 | [
{
"content": "Let $ N$ be the number of ordered pairs of nonempty sets $ \\mathcal{A}$ and $ \\mathcal{B}$ that have the following properties:\r\n\r\n• $ \\mathcal{A} \\cup \\mathcal{B} \\equal{} \\{1,2,3,4,5,6,7,8,9,10,11,12\\}$,\r\n• $ \\mathcal{A} \\cap \\mathcal{B} \\equal{} \\emptyset$,\r\n• The number of ... | Let $ N$ be the number of ordered pairs of nonempty sets $ \mathcal{A}$ and $ \mathcal{B}$ that have the following properties:
• $ \mathcal{A} \cup \mathcal{B} \equal{} \{1,2,3,4,5,6,7,8,9,10,11,12\}$,
• $ \mathcal{A} \cap \mathcal{B} \equal{} \emptyset$,
• The number of elements of $ \mathcal{A}$ is not an elemen... | "[\"4094\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2015, "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:16009"}, {"dataset": "skywork", "extra_... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"AC=BC=\\sqrt{\\frac{5}{2}}"
] | [
"skywork"
] | 45491f7c858650e86f1864689314983c8dbc8081c8a290017ed5ef501c4f1eba | [
{
"content": ".\n\nLet $D$ be the footpoint of the altitude from $B$ in the triangle $A B C$, where $A B=1$. The incentre of triangle $B C D$ coincides with the centroid of triangle $A B C$. Find the lengths of $A C$ and $B C$.",
"role": "user"
}
] | .
Let $D$ be the footpoint of the altitude from $B$ in the triangle $A B C$, where $A B=1$. The incentre of triangle $B C D$ coincides with the centroid of triangle $A B C$. Find the lengths of $A C$ and $B C$. | "[\"AC=BC=\\\\sqrt{\\\\frac{5}{2}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2033, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16010"}, {"dataset": "skywork", "extra_i... | {
"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
} |
[
"4752"
] | [
"skywork"
] | c8bf5825c7e7ea7cc931ea9305a40a2579bbbe2d8853c6fefce511e4d1490a8d | [
{
"content": "On the board are written 5 integers. By adding them in pairs, the following set of 10 numbers was obtained: $5, 8, 9, 13, 14, 14, 15, 17, 18, 23$. Determine which numbers are written on the board. In the answer, write their product.",
"role": "user"
}
] | On the board are written 5 integers. By adding them in pairs, the following set of 10 numbers was obtained: $5, 8, 9, 13, 14, 14, 15, 17, 18, 23$. Determine which numbers are written on the board. In the answer, write their product. | "[\"4752\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2027, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16011"}] | {
"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
} |
[
"8"
] | [
"skywork"
] | b10ad5b09054220ddb13a5407d4c4cdc2156fee68f7d34e14495e36be6124929 | [
{
"content": "Ryan is messing with Brice’s coin. He weights the coin such that it comes up on one side twice as frequently as the other, and he chooses whether to weight heads or tails more with equal probability. Brice flips his modified coin twice and it lands up heads both times. The probability that the coi... | Ryan is messing with Brice’s coin. He weights the coin such that it comes up on one side twice as frequently as the other, and he chooses whether to weight heads or tails more with equal probability. Brice flips his modified coin twice and it lands up heads both times. The probability that the coin lands up heads on th... | "[\" 8 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2023, "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:16012"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"[\\sqrt{3}+\\sqrt{6}, 2 \\sqrt{5}]"
] | [
"skywork"
] | 09deb5ca5ab7acab7202482e8fe9750e4a8d6f513c5e37e26bcf90f2de294532 | [
{
"content": "11. (20 points) Given positive real numbers $a, b$ satisfy $\\frac{1}{a^{2}}+\\frac{4}{b^{2}} \\leqslant 1, a^{2}+2 b^{2} \\leqslant 15$.\nFind the range of $a+b$.",
"role": "user"
}
] | 11. (20 points) Given positive real numbers $a, b$ satisfy $\frac{1}{a^{2}}+\frac{4}{b^{2}} \leqslant 1, a^{2}+2 b^{2} \leqslant 15$.
Find the range of $a+b$. | "[\"[\\\\sqrt{3}+\\\\sqrt{6}, 2 \\\\sqrt{5}]\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2041, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16013"}] | {
"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
} |
[
"3.5"
] | [
"skywork"
] | a5c613ceeb3af7ad9cc6e642e1ac42e046e05174c787680ca607119e905081b9 | [
{
"content": "The Beverage Barn sold $300$ cans of soda to $120$ customers, and every customer bought at least two cans of soda. What is the maximum possible median number of cans of soda bought per customer on that day?\nA) 2.5 \nB) 3.0 \nC) 3.5 \nD) 4.0 \nE) 4.5",
"role": "user"
}
] | The Beverage Barn sold $300$ cans of soda to $120$ customers, and every customer bought at least two cans of soda. What is the maximum possible median number of cans of soda bought per customer on that day?
A) 2.5
B) 3.0
C) 3.5
D) 4.0
E) 4.5 | "[\"3.5\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2043, "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:16014"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
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