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{\\sqrt[4]{450}}{5}"
] | [
"skywork"
] | ab2bad06ef01e7771cedfae845a6b0ebfe519f63096c73416ff7d38ff5bbde87 | [
{
"content": "9. $[\\mathbf{7}]$ Let $x(t)$ be a solution to the differential equation\n$$\n\\left(x+x^{\\prime}\\right)^{2}+x \\cdot x^{\\prime \\prime}=\\cos t\n$$\nwith $x(0)=x^{\\prime}(0)=\\sqrt{\\frac{2}{5}}$. Compute $x\\left(\\frac{\\pi}{4}\\right)$.",
"role": "user"
}
] | 9. $[\mathbf{7}]$ Let $x(t)$ be a solution to the differential equation
$$
\left(x+x^{\prime}\right)^{2}+x \cdot x^{\prime \prime}=\cos t
$$
with $x(0)=x^{\prime}(0)=\sqrt{\frac{2}{5}}$. Compute $x\left(\frac{\pi}{4}\right)$. | "[\"\\\\frac{\\\\sqrt[4]{450}}{5}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 223, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14262"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{4\\sqrt{3}}{3}"
] | [
"skywork"
] | dadee9385476762677e6ac1b07e19cd40db838a834e9bb3aafb6b49e7f888e7f | [
{
"content": "8. Given $a, b, c \\in \\mathbf{R}_{+}, a^{2}+b^{2}+c^{2}=1$. Let\n$$\nM=\\max \\left\\{a+\\frac{1}{b}, b+\\frac{1}{c}, c+\\frac{1}{a}\\right\\},\n$$\n\nthen the minimum value of $M$ is . $\\qquad$",
"role": "user"
}
] | 8. Given $a, b, c \in \mathbf{R}_{+}, a^{2}+b^{2}+c^{2}=1$. Let
$$
M=\max \left\{a+\frac{1}{b}, b+\frac{1}{c}, c+\frac{1}{a}\right\},
$$
then the minimum value of $M$ is . $\qquad$ | "[\"\\\\frac{4\\\\sqrt{3}}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 212, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14263"}] | {
"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
} |
[
"109"
] | [
"skywork"
] | 6e7349a88e7f005b68568410ad5113a6ce4a4655f78b9a78521f45a7250398d9 | [
{
"content": "An arithmetic progression, commonly referred to as an A.P., is a sequence in which each term, starting from the second, is equal to the sum of the previous term and a fixed value \\( r \\) called the common difference or the ratio of the progression. For example, the sequence below is an arithmeti... | An arithmetic progression, commonly referred to as an A.P., is a sequence in which each term, starting from the second, is equal to the sum of the previous term and a fixed value \( r \) called the common difference or the ratio of the progression. For example, the sequence below is an arithmetic progression with the f... | "[\"109\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 202, "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:14264"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"118"
] | [
"skywork"
] | fbb02e6ef09b0e78a6e0dc8076a3c294adbe64d2911e7512efb39680106ed7d3 | [
{
"content": "# 1. Task 1.1 \n\nTimur and Alexander are counting the trees growing around their house. Both are moving in the same direction but start counting from different trees. What is the total number of trees growing around the house if the tree that Timur called the 12th, Alexander counted as $33-\\math... | # 1. Task 1.1
Timur and Alexander are counting the trees growing around their house. Both are moving in the same direction but start counting from different trees. What is the total number of trees growing around the house if the tree that Timur called the 12th, Alexander counted as $33-\mathrm{m}$, and the tree that... | "[\"118\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 207, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:14265"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{97}{200}"
] | [
"skywork"
] | da73a92f510b087bfa39e72a3de064a52b492b9a42e2982337de30e68c464d0c | [
{
"content": "Alexio has 200 cards numbered 1-200, inclusive, and places them in a box. Alexio then chooses a card from the box at random. What is the probability that the number on the card he chooses is a multiple of 4, 5, or 7? Express your answer as a common fraction.",
"role": "user"
}
] | Alexio has 200 cards numbered 1-200, inclusive, and places them in a box. Alexio then chooses a card from the box at random. What is the probability that the number on the card he chooses is a multiple of 4, 5, or 7? Express your answer as a common fraction. | "[\"\\\\frac{97}{200}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 238, "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:14266"}] | {
"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
} |
[
"1260"
] | [
"skywork"
] | ef0c82a2b5e3b53a971ec97713433fb342969cb9f870406409b0c07dc3d5f8e7 | [
{
"content": "A math conference is hosting a series of lectures by seven distinct lecturers. Dr. Smith's lecture depends on Dr. Jones’s lecture, and additionally, Dr. Brown's lecture depends on Dr. Green’s lecture. How many valid orders can these seven lecturers be scheduled, given these dependencies?",
"ro... | A math conference is hosting a series of lectures by seven distinct lecturers. Dr. Smith's lecture depends on Dr. Jones’s lecture, and additionally, Dr. Brown's lecture depends on Dr. Green’s lecture. How many valid orders can these seven lecturers be scheduled, given these dependencies? | "[\"1260\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 222, "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:14267"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"P(x,y,z) = x^2 + y^2 + z^2 + 2xyz"
] | [
"skywork"
] | ae96f109f3ebbf55b410c5d59d4e8a93e220940f9b36995ced9d0b80313e4527 | [
{
"content": "Determine if there exists a (three-variable) polynomial $P(x,y,z)$ with integer coefficients satisfying the following property: a positive integer $n$ is [i]not[/i] a perfect square if and only if there is a triple $(x,y,z)$ of positive integers such that $P(x,y,z) = n$.",
"role": "user"
}
] | Determine if there exists a (three-variable) polynomial $P(x,y,z)$ with integer coefficients satisfying the following property: a positive integer $n$ is [i]not[/i] a perfect square if and only if there is a triple $(x,y,z)$ of positive integers such that $P(x,y,z) = n$. | "[\"P(x,y,z) = x^2 + y^2 + z^2 + 2xyz\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 215, "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:14268"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | c6566119d5c774a3f9b6bc4358d850c649b9fb7c93ab347052607bde8d08e67f | [
{
"content": "A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains 100 cans, how many rows does it contain?",
"role": "user"
}
] | A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains 100 cans, how many rows does it contain? | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 225, "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:14269"}] | {
"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
} |
[
"B"
] | [
"skywork"
] | c45dbfb968b3daed0983b8a58e6869eab2065d38936df015819887e98764efbe | [
{
"content": "Suppose that\n\\[\\frac{2x}{3}-\\frac{x}{6}\\]\nis an integer. Which of the following statements must be true about $x$?\n$\\mathrm{(A)}\\ \\text{It is negative.}\\\\\\mathrm{(B)}\\ \\text{It is even, but not necessarily a multiple of 3.}\\\\\\mathrm{(C)}\\ \\text{It is a multiple of 3, but not ne... | Suppose that
\[\frac{2x}{3}-\frac{x}{6}\]
is an integer. Which of the following statements must be true about $x$?
$\mathrm{(A)}\ \text{It is negative.}\\\mathrm{(B)}\ \text{It is even, but not necessarily a multiple of 3.}\\\mathrm{(C)}\ \text{It is a multiple of 3, but not necessarily even.}\\\mathrm{(D)}\ \text{It i... | "[\"B\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 219, "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:14271"}] | {
"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"
] | c9904f1b3a3ce2f540f11a763c0908198b45d83a641ddea175926df8f32f9f7e | [
{
"content": "3 [\n\nFrom one point, two tangents are drawn to a circle. The length of each tangent is 12, and the distance between the points of tangency is 14.4. Find the radius of the circle.\n\n#",
"role": "user"
}
] | 3 [
From one point, two tangents are drawn to a circle. The length of each tangent is 12, and the distance between the points of tangency is 14.4. Find the radius of the circle.
# | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 240, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14272"}] | {
"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
} |
[
"D"
] | [
"skywork"
] | b0e2ee0e70ced060dd6b1b46ed33a174aa5cced1efebda3cbe7f9030e7926a0f | [
{
"content": "$2 \\cdot 110$ To make $p=x^{4}+6 x^{3}+11 x^{2}+3 x+31$ a perfect square of an integer, the number of integer values of $x$ is\n(A) 4.\n(B) 3.\n(C) 2.\n(D) 1.\n(E) 0.\n(16th American High School Mathematics Examination, 1965)",
"role": "user"
}
] | $2 \cdot 110$ To make $p=x^{4}+6 x^{3}+11 x^{2}+3 x+31$ a perfect square of an integer, the number of integer values of $x$ is
(A) 4.
(B) 3.
(C) 2.
(D) 1.
(E) 0.
(16th American High School Mathematics Examination, 1965) | "[\"D\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 237, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14273"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 3d1baed6c0801e0110163e08d089437fe52f338403a82e626d5018f6c165f081 | [
{
"content": "[ [tangents drawn from one point] [ Midline of a triangle $\\quad$]\n\nA circle of radius 1 is inscribed in triangle $ABC$, where $\\cos \\angle B=0.8$. This circle touches the midline of triangle $ABC$, parallel to side $AC$. Find the side $AC$.",
"role": "user"
}
] | [ [tangents drawn from one point] [ Midline of a triangle $\quad$]
A circle of radius 1 is inscribed in triangle $ABC$, where $\cos \angle B=0.8$. This circle touches the midline of triangle $ABC$, parallel to side $AC$. Find the side $AC$. | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 221, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14274"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2{,}042{,}220"
] | [
"skywork"
] | f40360686a442652a8bc11f4876b629c66f7d094d2f290de470f32084c1e822d | [
{
"content": "Points $A_1, A_2, \\ldots, A_{2022}$ are chosen on a plane so that no three of them are collinear. Consider all angles $A_iA_jA_k$ for distinct points $A_i, A_j, A_k$. What largest possible number of these angles can be equal to $90^\\circ$?\n\n[i]Proposed by Anton Trygub[/i]",
"role": "user"
... | Points $A_1, A_2, \ldots, A_{2022}$ are chosen on a plane so that no three of them are collinear. Consider all angles $A_iA_jA_k$ for distinct points $A_i, A_j, A_k$. What largest possible number of these angles can be equal to $90^\circ$?
[i]Proposed by Anton Trygub[/i] | "[\" 2{,}042{,}220 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 235, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14275"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"8"
] | [
"skywork"
] | cb6243e4127fc50adcfcd567393467b42923d7c2a4358c70f0bed7c9c0677cbc | [
{
"content": "7.009. $\\left(N^{\\frac{1}{\\log _{2} N}} \\cdot N^{\\frac{1}{\\log _{4} N}} \\cdot N^{\\frac{1}{\\log _{8} N}} \\cdots N^{\\frac{1}{\\log _{64} N}}\\right)^{\\frac{1}{15}}$ (the bases of the logarithms are consecutive natural powers of the number 2).",
"role": "user"
}
] | 7.009. $\left(N^{\frac{1}{\log _{2} N}} \cdot N^{\frac{1}{\log _{4} N}} \cdot N^{\frac{1}{\log _{8} N}} \cdots N^{\frac{1}{\log _{64} N}}\right)^{\frac{1}{15}}$ (the bases of the logarithms are consecutive natural powers of the number 2). | "[\"8\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 230, "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:14276"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | d4d2676ecb8dcd1c4327b0d9176d57a62bf9de31d36fe4cc2cc91f3d1e321d19 | [
{
"content": "Example 9 For a finite set $A$, function $f: N \\rightarrow A$ has only the following property: if $i, j \\in N, |H| i-j |$ is a prime number, then $f(i) \\neq f(j)$. How many elements does set $A$ have at least?",
"role": "user"
}
] | Example 9 For a finite set $A$, function $f: N \rightarrow A$ has only the following property: if $i, j \in N, |H| i-j |$ is a prime number, then $f(i) \neq f(j)$. How many elements does set $A$ have at least? | "[\"4\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 229, "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:14277"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"11"
] | [
"skywork"
] | dda69def6bbc0d814beb98398d95d39f9d44d1a555a5a9f7c34525d8460861a4 | [
{
"content": "$2 \\cdot 62$ Given 1990 piles of stones, each consisting of $1, 2, \\cdots, 1990$ stones, in each round, you are allowed to pick any number of piles and remove the same number of stones from these piles. How many rounds are needed at minimum to remove all the stones?",
"role": "user"
}
] | $2 \cdot 62$ Given 1990 piles of stones, each consisting of $1, 2, \cdots, 1990$ stones, in each round, you are allowed to pick any number of piles and remove the same number of stones from these piles. How many rounds are needed at minimum to remove all the stones? | "[\"11\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 232, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14278"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | c915220cffae9ed37d10878fe0d39edbdddf9dbb0d8e829a5698c89ae50b1dcc | [
{
"content": "A food factory regularly purchases flour. It is known that the factory needs 6 tons of flour per day, the price of each ton of flour is 1800 yuan, and the storage and other costs for flour are an average of 3 yuan per ton per day. Each time flour is purchased, a shipping fee of 900 yuan is require... | A food factory regularly purchases flour. It is known that the factory needs 6 tons of flour per day, the price of each ton of flour is 1800 yuan, and the storage and other costs for flour are an average of 3 yuan per ton per day. Each time flour is purchased, a shipping fee of 900 yuan is required. How often should th... | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 245, "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:14279"}] | {
"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
} |
[
"12"
] | [
"skywork"
] | cee744bbb810ff1a6b7ad36345da15e60ef6081467d87e0bfe8957a02c20820d | [
{
"content": "There are two circles: one with center at point \\( A \\) and radius 6, and the other with center at point \\( B \\) and radius 3. Their common internal tangent touches the circles respectively at points \\( C \\) and \\( D \\). The lines \\( AB \\) and \\( CD \\) intersect at point \\( E \\). Fin... | There are two circles: one with center at point \( A \) and radius 6, and the other with center at point \( B \) and radius 3. Their common internal tangent touches the circles respectively at points \( C \) and \( D \). The lines \( AB \) and \( CD \) intersect at point \( E \). Find the length of \( CD \), given that... | "[\"12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 231, "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:14280"}] | {
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[
"112"
] | [
"skywork"
] | bdeb97ccdf5b47627f820e90e82f8605babd93fc79d9187f90de05697a3a2c02 | [
{
"content": "In the equation $\\frac{1}{7} + \\frac{7}{x} = \\frac{16}{x} + \\frac{1}{16}$, what is the value of $x$?",
"role": "user"
}
] | In the equation $\frac{1}{7} + \frac{7}{x} = \frac{16}{x} + \frac{1}{16}$, what is the value of $x$? | "[\"112\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 256, "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:14282"}] | {
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[
"m>4-2 \\sqrt{2}"
] | [
"skywork"
] | 2546fc902343515d3f1a07ab1b342a71ea94a46ce5fa828cf3d923f1039b5905 | [
{
"content": "Five. (This question is worth 20 points) Given an odd function $f(x)$ defined on $(-\\infty, 0) \\cup(0,+\\infty)$, and it is an increasing function on $(0, +\\infty)$, with $f(1)=0$. Also, the function\n$g(\\theta)=\\sin ^{2} \\theta+m \\cos \\theta-2 m, \\theta \\in\\left[0, \\frac{\\pi}{2}\\rig... | Five. (This question is worth 20 points) Given an odd function $f(x)$ defined on $(-\infty, 0) \cup(0,+\infty)$, and it is an increasing function on $(0, +\infty)$, with $f(1)=0$. Also, the function
$g(\theta)=\sin ^{2} \theta+m \cos \theta-2 m, \theta \in\left[0, \frac{\pi}{2}\right]$, and the sets
$M, N$ satisfy $M=\... | "[\"m>4-2 \\\\sqrt{2}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 214, "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:14283"}] | {
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[
"145"
] | [
"skywork"
] | bd9167f37f836e1f7a8058ce8f295f8ad153ba086e655f2b0413574d1b9958f2 | [
{
"content": "A natural number is a [i]factorion[/i] if it is the sum of the factorials of each of its decimal digits. For example, $145$ is a factorion because $145 = 1! + 4! + 5!$.\nFind every 3-digit number which is a factorion.",
"role": "user"
}
] | A natural number is a [i]factorion[/i] if it is the sum of the factorials of each of its decimal digits. For example, $145$ is a factorion because $145 = 1! + 4! + 5!$.
Find every 3-digit number which is a factorion. | "[\"145\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 248, "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:14284"}] | {
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[
"\\frac{5}{16}"
] | [
"skywork"
] | 2fde389e4411e9409ade4dd15244f9113da3a65fd5a44cd066a1d721f6efdaff | [
{
"content": "In the Cartesian coordinate system $xOy$, the parametric equation of curve $C_{1}$ is $\\begin{cases}x=a\\cos \\varphi \\\\ y=b\\sin \\varphi\\end{cases} (a > b > 0,$ $\\varphi$ is the parameter), and the point $M(2, \\sqrt{3})$ on curve $C1$ corresponds to the parameter $\\varphi= \\frac{\\pi}{3}... | In the Cartesian coordinate system $xOy$, the parametric equation of curve $C_{1}$ is $\begin{cases}x=a\cos \varphi \\ y=b\sin \varphi\end{cases} (a > b > 0,$ $\varphi$ is the parameter), and the point $M(2, \sqrt{3})$ on curve $C1$ corresponds to the parameter $\varphi= \frac{\pi}{3}$. Using $O$ as the pole and the po... | "[\"\\\\frac{5}{16}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 206, "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:14285"}] | {
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[
"13"
] | [
"skywork"
] | 84b5ed998b20802d5a586795a885e89c029e89f8abc7a10c6aa87b2a35846727 | [
{
"content": "Let $S$ be the set of complex numbers of the form $x + yi,$ where $x$ and $y$ are real numbers, such that\n\\[\\frac{1}{2} \\le x \\le \\frac{\\sqrt{2}}{2}.\\]Find the smallest positive integer $m$ such that for all positive integers $n \\ge m,$ there exists a complex number $z \\in S$ such that $... | Let $S$ be the set of complex numbers of the form $x + yi,$ where $x$ and $y$ are real numbers, such that
\[\frac{1}{2} \le x \le \frac{\sqrt{2}}{2}.\]Find the smallest positive integer $m$ such that for all positive integers $n \ge m,$ there exists a complex number $z \in S$ such that $z^n = 1.$ | "[\"13\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 227, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14286"}] | {
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[
"6"
] | [
"skywork"
] | 1214cd0f8f9335927f6372933bbf9da49d88da9b6372998d9671f5684e2ae0a9 | [
{
"content": "If $a,b,c$ are non-negative integers less than $7$ such that \\begin{align*}\na+2b+3c&\\equiv 0\\pmod 7,\\\\\n2a+3b+c&\\equiv 4\\pmod 7,\\\\\n3a+b+2c&\\equiv 4\\pmod 7,\n\\end{align*}then determine the remainder when $abc$ is divided by $7$.",
"role": "user"
}
] | If $a,b,c$ are non-negative integers less than $7$ such that \begin{align*}
a+2b+3c&\equiv 0\pmod 7,\\
2a+3b+c&\equiv 4\pmod 7,\\
3a+b+2c&\equiv 4\pmod 7,
\end{align*}then determine the remainder when $abc$ is divided by $7$. | "[\"6\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 249, "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:14287"}] | {
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[
"-1"
] | [
"skywork"
] | a7b012e09306ee8fe05fb0e1a4c353b7fc5dbf5bd9365ae2fecc03a3b9c662cb | [
{
"content": "When simplified, $\\log{8} \\div \\log{\\frac{1}{8}}$ becomes:",
"role": "user"
}
] | When simplified, $\log{8} \div \log{\frac{1}{8}}$ becomes: | "[\"-1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 233, "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:14288"}] | {
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[
"194"
] | [
"skywork"
] | 8f8cfa6ce09cbb26044d220b3af11e792514ed9aee44ec5c6faacfb76be2d47d | [
{
"content": "The increasing sequence of positive integers $a_1,a_2,a_3,\\cdots$ has the property that\n\\[a_{n+2}=a_n+a_{n+1} \\text{ for all } n\\ge 1.\\]\nIf $a_7=120$, then $a_8$ is\n$\\text{(A) } 128\\quad \\text{(B) } 168\\quad \\text{(C) } 193\\quad \\text{(D) } 194\\quad \\text{(E) } 210$",
"role":... | The increasing sequence of positive integers $a_1,a_2,a_3,\cdots$ has the property that
\[a_{n+2}=a_n+a_{n+1} \text{ for all } n\ge 1.\]
If $a_7=120$, then $a_8$ is
$\text{(A) } 128\quad \text{(B) } 168\quad \text{(C) } 193\quad \text{(D) } 194\quad \text{(E) } 210$ | "[\"194\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 244, "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:14289"}] | {
"all_reference_components_parse": true,
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"reference_components": 1,
"reference_present": true
} |
[
"94^\\circ"
] | [
"skywork"
] | fee92217ba20c35883719bee235b3c1782ad488dc3fac094706c9a1704afbf74 | [
{
"content": "In an acute triangle $ABC$, we define $D$ is the projection of $A$ on the side $BC$, and $M$ is the mid-point of $AC$. Take a point $P$ on the line segment $BM$ such that $\\angle PAM=\\angle MBA$. If we have $\\angle BAP=41^{\\circ}$ and $\\angle PDB=115^{\\circ}$, find the $\\angle BAC$.",
"... | In an acute triangle $ABC$, we define $D$ is the projection of $A$ on the side $BC$, and $M$ is the mid-point of $AC$. Take a point $P$ on the line segment $BM$ such that $\angle PAM=\angle MBA$. If we have $\angle BAP=41^{\circ}$ and $\angle PDB=115^{\circ}$, find the $\angle BAC$. | "[\"94^\\\\circ\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 246, "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:14290"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"8.4"
] | [
"skywork"
] | 1f03224207f75cd5abe81b08dfa11a4b65394b585c7229266350bb2542f97a1b | [
{
"content": "Three children need to cover a distance of 84 kilometers using two bicycles. Walking, they cover 5 kilometers per hour, while bicycling they cover 20 kilometers per hour. How long will it take for all three to reach the destination if only one child can ride a bicycle at a time?",
"role": "use... | Three children need to cover a distance of 84 kilometers using two bicycles. Walking, they cover 5 kilometers per hour, while bicycling they cover 20 kilometers per hour. How long will it take for all three to reach the destination if only one child can ride a bicycle at a time? | "[\"8.4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 242, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14291"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"a=3, b=4, c=7"
] | [
"skywork"
] | d706080e137729534f0a69d733b97879ea004a478c6964bce216a021ecf2ce9f | [
{
"content": "Five. (25 points) Given positive integers $a$, $b$, $c$ satisfying $a<b<c$, and $\\frac{1}{a-1}+\\frac{1}{b-1}+\\frac{1}{c-1}=1$. Find the values of $a$, $b$, and $c$.\n\n untranslated part:\n\n将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。\n\n---\n\nFive. (25 points) Given positive integers $a$, $b$, $c$ sat... | Five. (25 points) Given positive integers $a$, $b$, $c$ satisfying $a<b<c$, and $\frac{1}{a-1}+\frac{1}{b-1}+\frac{1}{c-1}=1$. Find the values of $a$, $b$, and $c$.
untranslated part:
将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。
---
Five. (25 points) Given positive integers $a$, $b$, $c$ satisfying $a<b<c$, and $\frac{1}{a-... | "[\"a=3, b=4, c=7\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 262, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14292"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"T_{405}(1211,-805)"
] | [
"skywork"
] | 26fdc70b02bb81263b23a120d31dcc24c83d4a9ec13306d3a02705624f58dde7 | [
{
"content": "## Task B-1.4.\n\nThe length of $\\overline{A B}$ is sequentially divided from vertex $A$ by points $T_{1}, T_{2}, T_{3}, \\ldots, T_{2016}$ into 2017 equal parts. If the coordinates of points $T_{3}(5,-1)$ and $T_{4}(8,-3)$ are known, determine the coordinates of points $A$ and $B$. Can the diffe... | ## Task B-1.4.
The length of $\overline{A B}$ is sequentially divided from vertex $A$ by points $T_{1}, T_{2}, T_{3}, \ldots, T_{2016}$ into 2017 equal parts. If the coordinates of points $T_{3}(5,-1)$ and $T_{4}(8,-3)$ are known, determine the coordinates of points $A$ and $B$. Can the difference in coordinates for a... | "[\"T_{405}(1211,-805)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 209, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14293"}] | {
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} |
[
"\\text{all } k"
] | [
"skywork"
] | e0b967d1dad58f16e0e780a5de1674e8a417ef67c365e3f4693056c54364816b | [
{
"content": "Consider an infinite white plane divided into square cells. For which $k$ it is possible to paint a positive finite number of cells black so that on each horizontal, vertical and diagonal line of cells there is either exactly $k$ black cells or none at all?\n\nA. Dinev, K. Garov, N Belukhov",
... | Consider an infinite white plane divided into square cells. For which $k$ it is possible to paint a positive finite number of cells black so that on each horizontal, vertical and diagonal line of cells there is either exactly $k$ black cells or none at all?
A. Dinev, K. Garov, N Belukhov | "[\"\\\\text{all } k\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 247, "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:14294"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2310"
] | [
"skywork"
] | 3200fe7bea79e5944931df83916aa8c5977ea4b0f067e4ddad85d51315bb28c1 | [
{
"content": "Task 1. All different products of two different factors from the first five prime numbers are formed. Calculate the square root of the product of the square roots of the obtained products.",
"role": "user"
}
] | Task 1. All different products of two different factors from the first five prime numbers are formed. Calculate the square root of the product of the square roots of the obtained products. | "[\"2310\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 250, "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:14295"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 22bfbe3a964f2ea0989af66be0a437907b170322e73b953c5d905441be86586e | [
{
"content": "Charlie plans to sell bananas for forty cents and apples for fifty cents at his fruit stand, but Dave accidentally reverses the prices. After selling all their fruit they earn a dollar more than they would have with the original prices. How many more bananas than apples did they sell?\n\n$\\mathrm... | Charlie plans to sell bananas for forty cents and apples for fifty cents at his fruit stand, but Dave accidentally reverses the prices. After selling all their fruit they earn a dollar more than they would have with the original prices. How many more bananas than apples did they sell?
$\mathrm{(A) \ } 2 \qquad \mathrm... | "[\"10\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 251, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14296"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"2\\sqrt{3}+\\sqrt{5}"
] | [
"skywork"
] | c21b786f106a0a7e4b3699b846764dde78790f0a6ea591ad39c52395ff50bdd1 | [
{
"content": "4. Given $A(0,0), B(1,0), C(0,2), D(3,3)$, point $P$ is any point in the plane, then the minimum value of $|P A|+|P B|+|P C|+|P D|$ is $\\qquad$.",
"role": "user"
}
] | 4. Given $A(0,0), B(1,0), C(0,2), D(3,3)$, point $P$ is any point in the plane, then the minimum value of $|P A|+|P B|+|P C|+|P D|$ is $\qquad$. | "[\"2\\\\sqrt{3}+\\\\sqrt{5}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 254, "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:14297"}] | {
"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
} |
[
"n^2 - 1"
] | [
"skywork"
] | 4ee19d83619478b1c78a2c42759e5a56c7fa549d320ce420ed4e5cc833e0f6b1 | [
{
"content": "From a $n\\times (n-1)$ rectangle divided into unit squares, we cut the [i]corner[/i], which consists of the first row and the first column. (that is, the corner has $2n-2$ unit squares). For the following, when we say [i]corner[/i] we reffer to the above definition, along with rotations and symme... | From a $n\times (n-1)$ rectangle divided into unit squares, we cut the [i]corner[/i], which consists of the first row and the first column. (that is, the corner has $2n-2$ unit squares). For the following, when we say [i]corner[/i] we reffer to the above definition, along with rotations and symmetry. Consider an infini... | "[\" n^2 - 1 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 226, "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:14298"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 3721018843b7f47b67dec318fcfa58aa6b04f42dbb51c2a7e388a1ceb0668e3c | [
{
"content": "The equations of $L_1$ and $L_2$ are $y=mx$ and $y=nx$, respectively. Suppose $L_1$ makes twice as large of an angle with the horizontal (measured counterclockwise from the positive x-axis ) as does $L_2$, and that $L_1$ has 4 times the slope of $L_2$. If $L_1$ is not horizontal, then $mn$ is",
... | The equations of $L_1$ and $L_2$ are $y=mx$ and $y=nx$, respectively. Suppose $L_1$ makes twice as large of an angle with the horizontal (measured counterclockwise from the positive x-axis ) as does $L_2$, and that $L_1$ has 4 times the slope of $L_2$. If $L_1$ is not horizontal, then $mn$ is | "[\"2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 252, "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:14299"}] | {
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} |
[
"2 \\text{ mm}"
] | [
"skywork"
] | 8ef5ad17afaf186b03deb03baf4be72982d52baa066e0cc0146197185e242c76 | [
{
"content": "Let $M$ be the intersection of the diagonals of a cyclic quadrilateral $ABCD$. Find the length of $AD$, if it is known that $AB=2$ mm , $BC = 5$ mm, $AM = 4$ mm, and $\\frac{CD}{CM}= 0.6$.",
"role": "user"
}
] | Let $M$ be the intersection of the diagonals of a cyclic quadrilateral $ABCD$. Find the length of $AD$, if it is known that $AB=2$ mm , $BC = 5$ mm, $AM = 4$ mm, and $\frac{CD}{CM}= 0.6$. | "[\"2 \\\\text{ mm}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 257, "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:14300"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"1480"
] | [
"skywork"
] | d9b76be885e71fd517b806239cdaea1b75a9998e6aa904bb104d75f31fba9728 | [
{
"content": "## Aufgabe 1 - 290831\n\nEine Aufgabe des bedeutenden englischen Naturwissenschaftlers Isaak Newton (1643 bis 1727) lautet:\n\nEin Kaufmann besaß eine gewisse Geldsumme.\n\nIm ersten Jahr verbrauchte er davon 100 Pfund; zum Rest gewann er durch seine Arbeit ein Drittel desselben dazu.\n\nIm zweite... | ## Aufgabe 1 - 290831
Eine Aufgabe des bedeutenden englischen Naturwissenschaftlers Isaak Newton (1643 bis 1727) lautet:
Ein Kaufmann besaß eine gewisse Geldsumme.
Im ersten Jahr verbrauchte er davon 100 Pfund; zum Rest gewann er durch seine Arbeit ein Drittel desselben dazu.
Im zweiten Jahr verbrauchte er wiederum... | "[\"1480\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 253, "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:14301"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | f819ee30564cf48b1da16e9a8f8fa5d202bc23d2c9da873feb96a2a0a84eee61 | [
{
"content": "Find the remainder of $4^{18}+5^{17}$ when divided by 3.\n\n#",
"role": "user"
}
] | Find the remainder of $4^{18}+5^{17}$ when divided by 3.
# | "[\"0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 269, "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:14302"}] | {
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} |
[
"\\[\n\\boxed{(10,10,1), (10,1,10), (1,10,10)}\n\\]"
] | [
"skywork"
] | cb5011d1473010911c0febc43b2a20ec4df8129684034ce8a530559088d9ef48 | [
{
"content": "Solve the equation $a^3 + b^3 + c^3 = 2001$ in positive integers.",
"role": "user"
}
] | Solve the equation $a^3 + b^3 + c^3 = 2001$ in positive integers. | "[\"\\\\[\\n\\\\boxed{(10,10,1), (10,1,10), (1,10,10)}\\n\\\\]\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 268, "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:14303"}] | {
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"reference_components": 1,
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} |
[
"1"
] | [
"skywork"
] | c637d63d766c46f3c33c4768bea031788d78e714650959783be29513fd39a579 | [
{
"content": "Let $f(x)$ be the function defined for $x\\geq 0$ which satisfies the following conditions.\r\n(a) $f(x)=\\begin{cases}x \\ \\ \\ \\ \\ \\ \\ \\ ( 0\\leq x<1) \\\\ 2-x \\ \\ \\ (1\\leq x <2) \\end{cases}$ \r\n\r\n(b) $f(x+2n)=f(x) \\ (n=1,2,\\cdots)$\r\n\r\nFind $\\lim_{n\\to\\infty}\\int_{0}^{2n}... | Let $f(x)$ be the function defined for $x\geq 0$ which satisfies the following conditions.
(a) $f(x)=\begin{cases}x \ \ \ \ \ \ \ \ ( 0\leq x<1) \\ 2-x \ \ \ (1\leq x <2) \end{cases}$
(b) $f(x+2n)=f(x) \ (n=1,2,\cdots)$
Find $\lim_{n\to\infty}\int_{0}^{2n}f(x)e^{-x}\ dx.$ | "[\"1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 239, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14304"}] | {
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} |
[
"1 + \\sqrt{3}"
] | [
"skywork"
] | 8df3c113c9fb290aa0c6e5870727163d340e7d05e88de87f6d7381d5f8f96874 | [
{
"content": "Let $x$ and $y$ be positive real numbers. Find the minimum value of\n\\[\\frac{\\sqrt{(x^2 + y^2)(3x^2 + y^2)}}{xy}.\\]",
"role": "user"
}
] | Let $x$ and $y$ be positive real numbers. Find the minimum value of
\[\frac{\sqrt{(x^2 + y^2)(3x^2 + y^2)}}{xy}.\] | "[\"1 + \\\\sqrt{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 276, "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:14305"}] | {
"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\\sqrt{2} - 1)\\pi"
] | [
"skywork"
] | 5ed2668c89fcede75f00967bbe3efb9fab8c37be26bb4bddd075a77a2b13b582 | [
{
"content": "The diagram shows a square \\(PQRS\\) with edges of length 1, and four arcs, each of which is a quarter of a circle. Arc \\(TRU\\) has center \\(P\\); arc \\(VPW\\) has center \\(R\\); arc \\(UV\\) has center \\(S\\); and arc \\(WT\\) has center \\(Q\\). What is the length of the perimeter of the ... | The diagram shows a square \(PQRS\) with edges of length 1, and four arcs, each of which is a quarter of a circle. Arc \(TRU\) has center \(P\); arc \(VPW\) has center \(R\); arc \(UV\) has center \(S\); and arc \(WT\) has center \(Q\). What is the length of the perimeter of the shaded region?
A) 6
B) \((2 \sqrt{2} ... | "[\"(2\\\\sqrt{2} - 1)\\\\pi\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 259, "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:14306"}] | {
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"reference_components": 1,
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} |
[
"196"
] | [
"skywork"
] | 64b387a9b24c81412d0777e5055d3d12d23ae5562222fc1dc38cb172c15e8a92 | [
{
"content": "Problem 4. (4 points) A chess piece moves 8 or 9 squares in a horizontal or vertical direction on a $15 \\times 15$ board, with each square being visited at most once. What is the maximum number of squares the piece can visit? (There is no restriction on which square the piece starts from.)",
... | Problem 4. (4 points) A chess piece moves 8 or 9 squares in a horizontal or vertical direction on a $15 \times 15$ board, with each square being visited at most once. What is the maximum number of squares the piece can visit? (There is no restriction on which square the piece starts from.) | "[\"196\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 275, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14307"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 046bd526021a6fd3891739bedf5bc6d5e292336f08747bf6c7055aa1d609d34b | [
{
"content": "Problem 8.5. A field was partially planted with corn, oats, and millet. If the remaining part is completely planted with millet, then millet will occupy half of the entire field. If the remaining part is equally divided between oats and corn, then oats will occupy half of the entire field. By what... | Problem 8.5. A field was partially planted with corn, oats, and millet. If the remaining part is completely planted with millet, then millet will occupy half of the entire field. If the remaining part is equally divided between oats and corn, then oats will occupy half of the entire field. By what factor will the amoun... | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 255, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:14308"}] | {
"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
} |
[
"24x^2-6x+3"
] | [
"skywork"
] | c20e7deca789ceb611b758b2b19730c3f7331bc5c6717dfef7663cc7e1f90b8d | [
{
"content": "Expand the following expression: $3(8x^2-2x+1)$.",
"role": "user"
}
] | Expand the following expression: $3(8x^2-2x+1)$. | "[\"24x^2-6x+3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 278, "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:14309"}] | {
"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
} |
[
"52"
] | [
"skywork"
] | 7709af02e229575aa5c2cce4de357a991aa455bcbe1e74cc75270da60017fb92 | [
{
"content": "A container in the shape of a right circular cone is 12 inches tall and its base has a 5-inch radius. The liquid that is sealed inside is 9 inches deep when the cone is held with its point down and its base horizontal. When the liquid is held with its point up and its base horizontal, the liquid i... | A container in the shape of a right circular cone is 12 inches tall and its base has a 5-inch radius. The liquid that is sealed inside is 9 inches deep when the cone is held with its point down and its base horizontal. When the liquid is held with its point up and its base horizontal, the liquid is $m-n\sqrt[3]{p},$ ... | "[\"52\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 258, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:14310"}, {"dataset": "skywork", "extra_inf... | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"83161"
] | [
"skywork"
] | 1fd7494c4094d2d338b0862038acd8bc3c80d45e0cefaebf96bd7bb724c0cbe9 | [
{
"content": "2. Determine the smallest natural number that is divisible by 13, and when divided by the numbers $2,3, \\ldots, 11,12$ leaves a remainder of 1.",
"role": "user"
}
] | 2. Determine the smallest natural number that is divisible by 13, and when divided by the numbers $2,3, \ldots, 11,12$ leaves a remainder of 1. | "[\"83161\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 271, "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:14311"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"skywork"
] | ceaf522c7b11e3eeca4e548fb9a3d54b3868821b6ce0e27ecdc166685acd3a1e | [
{
"content": "How many roots does the equation\n\n$$\n\\overbrace{f(f(\\ldots f}^{10 \\text{ times } f}(x) \\ldots)) + \\frac{1}{2} = 0\n$$\n\nhave, where \\( f(x) = |x| - 1 \\)?",
"role": "user"
}
] | How many roots does the equation
$$
\overbrace{f(f(\ldots f}^{10 \text{ times } f}(x) \ldots)) + \frac{1}{2} = 0
$$
have, where \( f(x) = |x| - 1 \)? | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 261, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14312"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{2}{3}"
] | [
"skywork"
] | 74e6d2fbd8966379a54a8faf9b994b537b400cef4ce69ae06df5e56a199e16dd | [
{
"content": "Let $ABC$ be a triangle such that $|AB|=7$, $|BC|=8$, $|AC|=6$. Let $D$ be the midpoint of side $[BC]$. If the circle through $A$, $B$ and $D$ cuts $AC$ at $A$ and $E$, what is $|AE|$?\n\n$ \n\\textbf{(A)}\\ \\dfrac 23\n\\qquad\\textbf{(B)}\\ 1\n\\qquad\\textbf{(C)}\\ \\dfrac 32\n\\qquad\\textbf{(... | Let $ABC$ be a triangle such that $|AB|=7$, $|BC|=8$, $|AC|=6$. Let $D$ be the midpoint of side $[BC]$. If the circle through $A$, $B$ and $D$ cuts $AC$ at $A$ and $E$, what is $|AE|$?
$
\textbf{(A)}\ \dfrac 23
\qquad\textbf{(B)}\ 1
\qquad\textbf{(C)}\ \dfrac 32
\qquad\textbf{(D)}\ 2
\qquad\textbf{(E)}\ 3
$ | "[\"\\\\frac{2}{3}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 260, "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:14313"}] | {
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} |
[
"(0,0), (\\sqrt{22}, \\sqrt{22}), (-\\sqrt{22}, -\\sqrt{22}), (\\sqrt{20}, -\\sqrt{20}), (-\\sqrt{20}, \\sqrt{20}), \\left( \\frac{-3 + \\sqrt{5}}{2} y, \\pm 2\\sqrt{3 + \\sqrt{5}} \\right), \\left( \\frac{-3 - \\sqrt{5}}{2} y, \\pm 2\\sqrt{3 - \\sqrt{5}} \\right)"
] | [
"skywork"
] | eec6b26b1a1ae9a93726c21f332686562ef43ff11d21b351133f507d038edb47 | [
{
"content": "Find all real pairs $(x,y)$ that solve the system of equations \\begin{align} x^5 &= 21x^3+y^3\n\\\\ y^5 &= x^3+21y^3. \\end{align}",
"role": "user"
}
] | Find all real pairs $(x,y)$ that solve the system of equations \begin{align} x^5 &= 21x^3+y^3
\\ y^5 &= x^3+21y^3. \end{align} | "[\" (0,0), (\\\\sqrt{22}, \\\\sqrt{22}), (-\\\\sqrt{22}, -\\\\sqrt{22}), (\\\\sqrt{20}, -\\\\sqrt{20}), (-\\\\sqrt{20}, \\\\sqrt{20}), \\\\left( \\\\frac{-3 + \\\\sqrt{5}}{2} y, \\\\pm 2\\\\sqrt{3 + \\\\sqrt{5}} \\\\right), \\\\left( \\\\frac{-3 - \\\\sqrt{5}}{2} y, \\\\pm 2\\\\sqrt{3 - \\\\sqrt{5}} \\\\right) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 284, "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:14314"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 1ceb19520cda6c45f08ebc1792d1c876905903aeea7c038b548cd3101eb4940f | [
{
"content": "4. Solve the equation\n\n$$\nx^{2018}+\\frac{1}{x^{2018}}=1+x^{2019}\n$$",
"role": "user"
}
] | 4. Solve the equation
$$
x^{2018}+\frac{1}{x^{2018}}=1+x^{2019}
$$ | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 272, "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:14315"}] | {
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[
"[\\frac{(n+1)(n+3)(2n+1)}{24}]"
] | [
"skywork"
] | 2a28355da3848cdca01167686663e307ef24d4137f399922c9a3ce30f4854d11 | [
{
"content": "How many triangles are there whose sides are integers not greater than a given $n$?",
"role": "user"
}
] | How many triangles are there whose sides are integers not greater than a given $n$? | "[\"[\\\\frac{(n+1)(n+3)(2n+1)}{24}]\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 266, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:14316"}] | {
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[
"b,2"
] | [
"skywork"
] | 19dbf5b3db709f7e131d70080fba8ac7a9d59b6677ee7b0913d7a0d3619718fe | [
{
"content": "Problem 10. (6 points)\n\nArtyom is planning to get a consumer loan from a bank in the amount of 65 thousand rubles for a term of 1 year. Which of the following interest calculation options, in your opinion, would be the most beneficial for Artyom in the case where the principal is repaid at the e... | Problem 10. (6 points)
Artyom is planning to get a consumer loan from a bank in the amount of 65 thousand rubles for a term of 1 year. Which of the following interest calculation options, in your opinion, would be the most beneficial for Artyom in the case where the principal is repaid at the end of the loan term in o... | "[\"b,2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 274, "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:14317"}] | {
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[
"10.5"
] | [
"skywork"
] | bc0551c877426a14fd76d56b64ddfb91ee25d47fe738e15fd3134cb229154640 | [
{
"content": "On the board, an example of dividing two positive numbers was given. David noticed that if he increased the dividend by two and the divisor by seven, the quotient would remain unchanged.\n\nBy how much would the divisor need to increase so that increasing the dividend by three would again result i... | On the board, an example of dividing two positive numbers was given. David noticed that if he increased the dividend by two and the divisor by seven, the quotient would remain unchanged.
By how much would the divisor need to increase so that increasing the dividend by three would again result in the same quotient?
(M... | "[\"10.5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 263, "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:14318"}] | {
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[
"\\lfloor n / 2\\rfloor+1"
] | [
"skywork"
] | 4511ed318501967019f184820b90ff80275af749c1015e810240b1bba1528e67 | [
{
"content": "For each positive real number $\\alpha$, define $$ \\lfloor\\alpha \\mathbb{N}\\rfloor:=\\{\\lfloor\\alpha m\\rfloor \\mid m \\in \\mathbb{N}\\} $$ Let $n$ be a positive integer. A set $S \\subseteq\\{1,2, \\ldots, n\\}$ has the property that: for each real $\\beta>0$, $$ \\text { if } S \\subsete... | For each positive real number $\alpha$, define $$ \lfloor\alpha \mathbb{N}\rfloor:=\{\lfloor\alpha m\rfloor \mid m \in \mathbb{N}\} $$ Let $n$ be a positive integer. A set $S \subseteq\{1,2, \ldots, n\}$ has the property that: for each real $\beta>0$, $$ \text { if } S \subseteq\lfloor\beta \mathbb{N}\rfloor \text {, t... | "[\"\\\\lfloor n / 2\\\\rfloor+1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 273, "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:14319"}] | {
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[
"72"
] | [
"skywork"
] | dd999efa3f4381312e3984ada91776ef0df30a34aab17df45937c4d9d24f5c84 | [
{
"content": "In a set of 100 numbers. If one number is removed, the median of the remaining numbers will be 78. If another number is removed, the median of the remaining numbers will be 66. Find the median of the entire set.\n\n#",
"role": "user"
}
] | In a set of 100 numbers. If one number is removed, the median of the remaining numbers will be 78. If another number is removed, the median of the remaining numbers will be 66. Find the median of the entire set.
# | "[\"72\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 267, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14320"}] | {
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[
"33"
] | [
"skywork"
] | bab94a26175f90b77c0f85cb63449b45f5138a7e36aab5f5027f19c605e8f165 | [
{
"content": "(7) The sum of all positive integers $n$ that satisfy $\\frac{1}{4}<\\sin \\frac{\\pi}{n}<\\frac{1}{3}$ is $\\qquad$",
"role": "user"
}
] | (7) The sum of all positive integers $n$ that satisfy $\frac{1}{4}<\sin \frac{\pi}{n}<\frac{1}{3}$ is $\qquad$ | "[\"33\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 277, "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:14321"}] | {
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[
"80"
] | [
"skywork"
] | edb43c5864f8dd61a134c7ceab8f5206d65856dcb422fd91d6cefe52a01e6f36 | [
{
"content": "If \n$$\\sum_{k=1}^{40} \\left( \\sqrt{1 + \\frac{1}{k^{2}} + \\frac{1}{(k + 1)^{2}}}\\right) = a + \\frac {b}{c}$$\nwhere $a, b, c \\in \\mathbb{N}, b < c, gcd(b,c) =1 ,$ then what is the value of $a+ b ?$",
"role": "user"
}
] | If
$$\sum_{k=1}^{40} \left( \sqrt{1 + \frac{1}{k^{2}} + \frac{1}{(k + 1)^{2}}}\right) = a + \frac {b}{c}$$
where $a, b, c \in \mathbb{N}, b < c, gcd(b,c) =1 ,$ then what is the value of $a+ b ?$ | "[\"80\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 281, "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:14322"}, {"dataset": "skywork", "extra_info... | {
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[
"\\frac{18839183877670041942218307147122500601235}{4769168484048619242209570178451249271212}\\approx0.3950203"
] | [
"skywork"
] | 44db32843f1fda1cea8679b3595afd399ed8a5673eb6ca957aef142ba405147d | [
{
"content": "35. [25] Let $P$ denote the set of all subsets of $\\{1, \\ldots, 23\\}$. A subset $S \\subseteq P$ is called good if whenever $A, B$ are sets in $S$, the set $(A \\backslash B) \\cup(B \\backslash A)$ is also in $S$. (Here, $A \\backslash B$ denotes the set of all elements in $A$ that are not in ... | 35. [25] Let $P$ denote the set of all subsets of $\{1, \ldots, 23\}$. A subset $S \subseteq P$ is called good if whenever $A, B$ are sets in $S$, the set $(A \backslash B) \cup(B \backslash A)$ is also in $S$. (Here, $A \backslash B$ denotes the set of all elements in $A$ that are not in $B$, and $B \backslash A$ deno... | "[\"\\\\frac{18839183877670041942218307147122500601235}{4769168484048619242209570178451249271212}\\\\approx0.3950203\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 288, "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:14323"}] | {
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[
"\\frac{24\\sqrt{10}-15}{41}"
] | [
"skywork"
] | 946f6dbca8e02ed1b81b651c96da582073c5f4438ef24748316e9bdfdaa4f1c0 | [
{
"content": "16. The radius of $\\odot O$ is $R$, and the radius of $\\odot O_{1}$ is $r (R > r)$. The two circles are externally tangent at $A$. $OD$ is tangent to $\\odot O_{1}$ at $D$, and $O_{1}E$ is tangent to $\\odot O$ at $E$. $B$ and $C$ are the midpoints of $OE$ and $O_{1}D$, respectively. (1) Prove t... | 16. The radius of $\odot O$ is $R$, and the radius of $\odot O_{1}$ is $r (R > r)$. The two circles are externally tangent at $A$. $OD$ is tangent to $\odot O_{1}$ at $D$, and $O_{1}E$ is tangent to $\odot O$ at $E$. $B$ and $C$ are the midpoints of $OE$ and $O_{1}D$, respectively. (1) Prove that points $B$, $A$, and $... | "[\"\\\\frac{24\\\\sqrt{10}-15}{41}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 265, "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:14324"}] | {
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[
"6"
] | [
"skywork"
] | 2fc631b8f78ee2eeef4ad53d825d583c8f1cd088037eb43aabf67a2d5709d837 | [
{
"content": "In a certain hyperbola, the center is at $(-2,0),$ one focus is at $(-2 + \\sqrt{34},0),$ and one vertex is at $(-5,0).$ The equation of this hyperbola can be written as\n\\[\\frac{(x - h)^2}{a^2} - \\frac{(y - k)^2}{b^2} = 1.\\]Find $h + k + a + b.$",
"role": "user"
}
] | In a certain hyperbola, the center is at $(-2,0),$ one focus is at $(-2 + \sqrt{34},0),$ and one vertex is at $(-5,0).$ The equation of this hyperbola can be written as
\[\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1.\]Find $h + k + a + b.$ | "[\"6\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 292, "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:14325"}] | {
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[
"\\frac{\\sqrt{2}}{2}"
] | [
"skywork"
] | 504e9bb156c0a614a609075a411895a9c1747449861cbd816613cc7ad929f43a | [
{
"content": "In a regular octagon, find the ratio of the length of the shortest diagonal to the longest diagonal. Express your answer as a common fraction in simplest radical form.",
"role": "user"
}
] | In a regular octagon, find the ratio of the length of the shortest diagonal to the longest diagonal. Express your answer as a common fraction in simplest radical form. | "[\"\\\\frac{\\\\sqrt{2}}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 289, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:14326"}] | {
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[
"30"
] | [
"skywork"
] | 1f5a5d60746c0c4a710b46d985dfb14d6397d3d1bc2acc3f8a3672c171bf481e | [
{
"content": "G2.4 Let $d$ and $f$ be positive integers and $a_{1}=0.9$. If $a_{i+1}=a_{i}^{2}$ and $\\prod_{i=1}^{4} a_{i}=\\frac{3^{d}}{f}$, determine the smallest possible value of $d$.",
"role": "user"
}
] | G2.4 Let $d$ and $f$ be positive integers and $a_{1}=0.9$. If $a_{i+1}=a_{i}^{2}$ and $\prod_{i=1}^{4} a_{i}=\frac{3^{d}}{f}$, determine the smallest possible value of $d$. | "[\"30\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 286, "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:14327"}] | {
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} |
[
"\\frac{7}{8}"
] | [
"skywork"
] | 296e2e9edcd48073c13607822b3b0a7d02441b6c30ef561de886ccd02e174387 | [
{
"content": "In a quadrilateral $ABCD$ lying in the plane, $AB=\\sqrt{3}$, $AD=DC=CB=1$. The areas of triangles $ABD$ and $BCD$ are $S$ and $T$ respectively. What is the maximum value of $S^{2} + T^{2}$?",
"role": "user"
}
] | In a quadrilateral $ABCD$ lying in the plane, $AB=\sqrt{3}$, $AD=DC=CB=1$. The areas of triangles $ABD$ and $BCD$ are $S$ and $T$ respectively. What is the maximum value of $S^{2} + T^{2}$? | "[\"\\\\frac{7}{8}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 287, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14328"}] | {
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} |
[
"5"
] | [
"skywork"
] | b50e32a98a219088f5e1d94815fe388571940e55a699ca24c901a1f92905c9d6 | [
{
"content": "KOVSHIN=BOTTLE+GLASS; $\\quad$ TWO KOVSHINS=SEVEN GLASSES; BOTTLE=CUP+TWO GLASSES; $\\quad$ BOTTLE=how many CUPS?",
"role": "user"
}
] | KOVSHIN=BOTTLE+GLASS; $\quad$ TWO KOVSHINS=SEVEN GLASSES; BOTTLE=CUP+TWO GLASSES; $\quad$ BOTTLE=how many CUPS? | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 293, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14329"}] | {
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} |
[
"20"
] | [
"skywork"
] | e2323029dc7c37a355c63b7db1b530fa9faf58c5f2a63d79ac5362e3169ebbe2 | [
{
"content": "In the class, there are 30 students: excellent students, C-grade students, and D-grade students. Excellent students always answer questions correctly, D-grade students always make mistakes, and C-grade students answer the questions given to them strictly in turn, alternating between correct and in... | In the class, there are 30 students: excellent students, C-grade students, and D-grade students. Excellent students always answer questions correctly, D-grade students always make mistakes, and C-grade students answer the questions given to them strictly in turn, alternating between correct and incorrect answers. All s... | "[\"20\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 279, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14330"}] | {
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} |
[
"-1\\leqx\\leq1"
] | [
"skywork"
] | f35bc2a541e5afa0a4cc8c29a30463ec03687477519ba8ffc546deaebacc6aba | [
{
"content": "1.4. Find all real numbers $x$ for which the equality\n\n$$\n|| x|-1|+|| x|+2|=3\n$$\n\nholds.",
"role": "user"
}
] | 1.4. Find all real numbers $x$ for which the equality
$$
|| x|-1|+|| x|+2|=3
$$
holds. | "[\"-1\\\\leqx\\\\leq1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 309, "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:14331"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 82fb869322072e3b3ac99d6d293e653a88c95283ee9072c9404db61fa8e85def | [
{
"content": "A series of lockers, numbered 1 through 100, are all initially closed. Student 1 goes through and opens every locker. Student 3 goes through and \"flips\" every 3rd locker (\"flipping\") a locker means changing its state: if the locker is open he closes it, and if the locker is closed he opens it)... | A series of lockers, numbered 1 through 100, are all initially closed. Student 1 goes through and opens every locker. Student 3 goes through and "flips" every 3rd locker ("flipping") a locker means changing its state: if the locker is open he closes it, and if the locker is closed he opens it). Thus, Student 3 will clo... | "[\"10\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 285, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:14332"}, {"dataset": "skywork", "extra_in... | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"\\frac{16}{3}"
] | [
"skywork"
] | 055bf01c2c664cda04bba89e0a63f961978ac6524bc5d15219237e0ae1615a6f | [
{
"content": "15. Given the ellipse $C: \\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1$ passes through the point $M(0,2)$, and the right focus is $F(2,0)$.\n(1) Write the equation of the ellipse $C$;\n(2) A line $l$ passing through point $F$ intersects the ellipse $C$ at points $A, B$, and intersects the $y$-axis ... | 15. Given the ellipse $C: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ passes through the point $M(0,2)$, and the right focus is $F(2,0)$.
(1) Write the equation of the ellipse $C$;
(2) A line $l$ passing through point $F$ intersects the ellipse $C$ at points $A, B$, and intersects the $y$-axis at point $P$; if $\overrig... | "[\"\\\\frac{16}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 264, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14333"}] | {
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[
"10"
] | [
"skywork"
] | dd2f3b86ab1cb26b9b70b60a4224b253e043419fb3773566136b96cd1207eeed | [
{
"content": "A cyclist traveled from point A to point B, stayed there for 30 minutes, and then returned to A. On the way to B, he overtook a pedestrian, and met him again 2 hours later on his way back. The pedestrian arrived at point B at the same time the cyclist returned to point A. How much time did it take... | A cyclist traveled from point A to point B, stayed there for 30 minutes, and then returned to A. On the way to B, he overtook a pedestrian, and met him again 2 hours later on his way back. The pedestrian arrived at point B at the same time the cyclist returned to point A. How much time did it take the pedestrian to tra... | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 270, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:14334"}] | {
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[
"(3, 6, 0), (3, -6, 0), (3, 4, 2), (3, -2, 2), (3, 2, -2), (3, -4, -2)"
] | [
"skywork"
] | f68b9a3f7aa5b8c2416f1f1e7a022a2d908e5929b56c5de45ccef548c54977f7 | [
{
"content": "Let $x, y$ be integers and $p$ be a prime for which\n\n\\[ x^2-3xy+p^2y^2=12p \\]\nFind all triples $(x,y,p)$.",
"role": "user"
}
] | Let $x, y$ be integers and $p$ be a prime for which
\[ x^2-3xy+p^2y^2=12p \]
Find all triples $(x,y,p)$. | "[\" (3, 6, 0), (3, -6, 0), (3, 4, 2), (3, -2, 2), (3, 2, -2), (3, -4, -2) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 296, "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:14335"}] | {
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} |
[
"\\angle C = 45^{\\circ}, \\angle B = 75^{\\circ}"
] | [
"skywork"
] | 24df680697e38f1d3552ac85e7df6812d7e60849cf3fcb72a29c6e5539d2d0d9 | [
{
"content": "2. In $\\triangle A B C$, $\\angle A=60^{\\circ}$, points $M$, $N$, and $K$ are on sides $B C$, $A C$, and $A B$ respectively, such that $B K=K M=M N=$ $N C$. If $A N=2 A K$, find the measures of $\\angle B$ and $\\angle C$.",
"role": "user"
}
] | 2. In $\triangle A B C$, $\angle A=60^{\circ}$, points $M$, $N$, and $K$ are on sides $B C$, $A C$, and $A B$ respectively, such that $B K=K M=M N=$ $N C$. If $A N=2 A K$, find the measures of $\angle B$ and $\angle C$. | "[\"\\\\angle C = 45^{\\\\circ}, \\\\angle B = 75^{\\\\circ}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 294, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14336"}] | {
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[
"45"
] | [
"skywork"
] | 31c383432daba26a830a88797af929eca8aa4acec6723e5962c13bb914a46ea3 | [
{
"content": "In $\\triangle{ABC}$ with $AB = 12$ , $BC = 13$ , and $AC = 15$ , let $M$ be a point on $\\overline{AC}$ such that the incircles of $\\triangle{ABM}$ and $\\triangle{BCM}$ have equal radii. Then $\\frac{AM}{CM} = \\frac{p}{q}$ , where $p$ and $q$ are relatively prime positive integers. Find $p + q... | In $\triangle{ABC}$ with $AB = 12$ , $BC = 13$ , and $AC = 15$ , let $M$ be a point on $\overline{AC}$ such that the incircles of $\triangle{ABM}$ and $\triangle{BCM}$ have equal radii. Then $\frac{AM}{CM} = \frac{p}{q}$ , where $p$ and $q$ are relatively prime positive integers. Find $p + q$ . | "[\"45\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 302, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14338"}, {"dataset": "skywork", "extra_inf... | {
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} |
[
"10"
] | [
"skywork"
] | 45ca768265a22e813fa9a98939e9f785d99c190b7cbb77df4176ef17bc79151e | [
{
"content": "Points $A$, $B$, and $C$ form an isosceles triangle with $AB = AC$. Points $M$, $N$, and $O$ are the midpoints of sides $AB$, $BC$, and $CA$ respectively. Find the number of noncongruent triangles that can be drawn using any three of these six points as vertices.",
"role": "user"
}
] | Points $A$, $B$, and $C$ form an isosceles triangle with $AB = AC$. Points $M$, $N$, and $O$ are the midpoints of sides $AB$, $BC$, and $CA$ respectively. Find the number of noncongruent triangles that can be drawn using any three of these six points as vertices. | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 290, "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:14339"}] | {
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"reference_components": 1,
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} |
[
"15"
] | [
"skywork"
] | a7e45e7ea8582997da5d2f20787437587ba29487d85a025805be0b274038973d | [
{
"content": "In Cologne, there were three brothers who had 9 containers of wine. The first container had a capacity of 1 quart, the second contained 2 quarts, with each subsequent container holding one more quart than the previous one, so the last container held 9 quarts. The task is to divide the wine equally... | In Cologne, there were three brothers who had 9 containers of wine. The first container had a capacity of 1 quart, the second contained 2 quarts, with each subsequent container holding one more quart than the previous one, so the last container held 9 quarts. The task is to divide the wine equally among the three broth... | "[\"15\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 301, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14340"}] | {
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[
"70"
] | [
"skywork"
] | 02f4a828e3fb10a020d418a7d155452fd2154ac53d8d4931e4a3b1268caab21e | [
{
"content": "At HappyTails Training Center, cats can learn to do three tricks: jump, fetch, and spin. Of the cats at the center:\n- 40 cats can jump\n- 25 cats can fetch\n- 30 cats can spin\n- 15 cats can jump and fetch\n- 10 cats can fetch and spin\n- 12 cats can jump and spin\n- 5 cats can do all three\n- 7 ... | At HappyTails Training Center, cats can learn to do three tricks: jump, fetch, and spin. Of the cats at the center:
- 40 cats can jump
- 25 cats can fetch
- 30 cats can spin
- 15 cats can jump and fetch
- 10 cats can fetch and spin
- 12 cats can jump and spin
- 5 cats can do all three
- 7 cats can do none
How many cat... | "[\"70\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 297, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14341"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"802"
] | [
"skywork"
] | 0a4dd92f078d91bee7b1e2f026b62b40b947d21d8559d72f57c607eef1659512 | [
{
"content": "An infinite geometric series has sum 2005. A new series, obtained by squaring each term of the original series, has 10 times the sum of the original series. The common ratio of the original series is $\\frac mn$ where $m$ and $n$ are relatively prime integers. Find $m+n.$",
"role": "user"
}
... | An infinite geometric series has sum 2005. A new series, obtained by squaring each term of the original series, has 10 times the sum of the original series. The common ratio of the original series is $\frac mn$ where $m$ and $n$ are relatively prime integers. Find $m+n.$ | "[\"802\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 295, "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:14342"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"63"
] | [
"skywork"
] | 2482eb951fd2880c2a254b4cee8b1a1c5a2ae83d2aa116a88959156d530b7c43 | [
{
"content": "Given the set \\( A = \\{x \\mid (x-2)(x-6) \\geqslant 3, x \\in \\mathbf{Z}, 0 \\leqslant x \\leq 7\\} \\), find the number of non-empty subsets of \\( A \\).",
"role": "user"
}
] | Given the set \( A = \{x \mid (x-2)(x-6) \geqslant 3, x \in \mathbf{Z}, 0 \leqslant x \leq 7\} \), find the number of non-empty subsets of \( A \). | "[\"63\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 298, "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:14343"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"637"
] | [
"skywork"
] | f80330b272e8a19d1702a6ebaa47bdd2cd7437b7f00307572cde922adeef1962 | [
{
"content": "5. Consider the set $S=\\{1,2, \\cdots, 10\\}$ and all its non-empty subsets. If the number of even numbers in a non-empty subset is no less than the number of odd numbers, then this subset is called a \"good subset\". Therefore, the number of good subsets is ( ) .\n(A) 631\n(B) 633\n(C) 635\n(D) ... | 5. Consider the set $S=\{1,2, \cdots, 10\}$ and all its non-empty subsets. If the number of even numbers in a non-empty subset is no less than the number of odd numbers, then this subset is called a "good subset". Therefore, the number of good subsets is ( ) .
(A) 631
(B) 633
(C) 635
(D) 637 | "[\"637\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 300, "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:14344"}] | {
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} |
[
"28"
] | [
"skywork"
] | 57c45d030f92608e52b43ab64916fbad614b5b54cc407aca5b5ed3636889b01a | [
{
"content": "Alice refuses to sit next to either Bob or Carla. Derek refuses to sit next to Eric. How many ways are there for the five of them to sit in a row of $5$ chairs under these conditions?",
"role": "user"
}
] | Alice refuses to sit next to either Bob or Carla. Derek refuses to sit next to Eric. How many ways are there for the five of them to sit in a row of $5$ chairs under these conditions? | "[\"28\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 308, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:14345"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"44"
] | [
"skywork"
] | f9bcf2e050fda0615ab5c04d991e2482f762bb0b50a1fab95e049a0f051e594a | [
{
"content": "Find the smallest positive integer $n$ for which the expansion of $(xy-3x+7y-21)^n$, after like terms have been collected, has at least 1996 terms.",
"role": "user"
}
] | Find the smallest positive integer $n$ for which the expansion of $(xy-3x+7y-21)^n$, after like terms have been collected, has at least 1996 terms. | "[\"44\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 307, "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:14346"}, {"dataset": "skywork", "extra_info... | {
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[
"57"
] | [
"skywork"
] | de48399eb15146dc24d19757f19df0838d58c8e0d84f4d8b3d2c13efce38bf66 | [
{
"content": "A circle with center $O$ has radius 25. Chord $\\overline{AB}$ of length 30 and chord $\\overline{CD}$ of length 14 intersect at point $P$ . The distance between the midpoints of the two chords is 12. The quantity $OP^2$ can be represented as $\\frac{m}{n}$ , where $m$ and $n$ are relatively prime... | A circle with center $O$ has radius 25. Chord $\overline{AB}$ of length 30 and chord $\overline{CD}$ of length 14 intersect at point $P$ . The distance between the midpoints of the two chords is 12. The quantity $OP^2$ can be represented as $\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find ... | "[\"57\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 283, "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:14347"}, {"dataset": "skywork", "extra_info... | {
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} |
[
"\\frac{4}{5}"
] | [
"skywork"
] | 72e7ae981112cd25db070e118dd255363c494b6a9012d32af66879fbffd0e341 | [
{
"content": "4. 47. Let $a, b$ be real numbers, and $x^{4}+a x^{3}+b x^{2}+a x+1=0$ has at least one real root. Try to find the minimum value of $a^{2}+b^{2}$.",
"role": "user"
}
] | 4. 47. Let $a, b$ be real numbers, and $x^{4}+a x^{3}+b x^{2}+a x+1=0$ has at least one real root. Try to find the minimum value of $a^{2}+b^{2}$. | "[\"\\\\frac{4}{5}\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 316, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14348"}] | {
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} |
[
"2k"
] | [
"skywork"
] | 059c362f08c6f3132f18e7969c210397b8329cf4b5729ae8e4ed75ad74a9719f | [
{
"content": "What is the maximum number of axes of symmetry that the union of $k$ segments on a plane can have?",
"role": "user"
}
] | What is the maximum number of axes of symmetry that the union of $k$ segments on a plane can have? | "[\"2k\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 304, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14349"}] | {
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} |
[
"k"
] | [
"skywork"
] | ce2430f3acf8877833cddae5454b242aed7b2336954cd85473f5d608e791743d | [
{
"content": "Given is a piece at the origin of the coordinate plane. Two persons $A,\\ B$ act as following.\nFirst, $A$ marks on a lattice point, on which the piece cannot be anymore put. Then $B$ moves the piece from the point $(x,\\ y)$ to the point $(x+1,\\ y)$ or $(x,\\ y+1)$, a number of $m$ times $(1\\le... | Given is a piece at the origin of the coordinate plane. Two persons $A,\ B$ act as following.
First, $A$ marks on a lattice point, on which the piece cannot be anymore put. Then $B$ moves the piece from the point $(x,\ y)$ to the point $(x+1,\ y)$ or $(x,\ y+1)$, a number of $m$ times $(1\leq m\leq k)$. Note that we ma... | "[\" k \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 280, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14350"}] | {
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} |
[
"-1"
] | [
"skywork"
] | c2883f98064e6d053bf7d15670d18063635757248975f2c958a3c368d1ffea96 | [
{
"content": "Evaluate the infinite sum $$\\sum_{n=2}^{\\infty} \\log _{2}\\left(\\frac{1-\\frac{1}{n}}{1-\\frac{1}{n+1}}\\right)$$",
"role": "user"
}
] | Evaluate the infinite sum $$\sum_{n=2}^{\infty} \log _{2}\left(\frac{1-\frac{1}{n}}{1-\frac{1}{n+1}}\right)$$ | "[\"-1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 326, "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:14351"}, {"dataset": "skywork", "extra_info... | {
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} |
[
"15^\\circ"
] | [
"skywork"
] | bd7c812fed942f6960870a411079e7400ed4081e1cb6aed66f7efb03d720140c | [
{
"content": "Let $P$ be a point inside the equilateral triangle $ABC$ such that $6\\angle PBC = 3\\angle PAC = 2\\angle PCA$. Find the measure of the angle $\\angle PBC$ .",
"role": "user"
}
] | Let $P$ be a point inside the equilateral triangle $ABC$ such that $6\angle PBC = 3\angle PAC = 2\angle PCA$. Find the measure of the angle $\angle PBC$ . | "[\"15^\\\\circ\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 324, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14352"}, {"dataset": "skywork", "extra_info... | {
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"reference_components": 1,
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} |
[
"68\\mathrm{C}"
] | [
"skywork"
] | 5d1fe1bad7a3e7d3adfff1ce5ceef68258808d6bfbfabdbbedbcd41ac106fb46 | [
{
"content": "6. (15 points) A metal bar with a temperature of $20^{\\circ} \\mathrm{C}$ was submerged into water taken at a temperature of $100^{\\circ} \\mathrm{C}$. After thermal equilibrium was established, the temperature was found to be $80^{\\circ} \\mathrm{C}$. After this, without removing the first bar... | 6. (15 points) A metal bar with a temperature of $20^{\circ} \mathrm{C}$ was submerged into water taken at a temperature of $100^{\circ} \mathrm{C}$. After thermal equilibrium was established, the temperature was found to be $80^{\circ} \mathrm{C}$. After this, without removing the first bar from the water, another ide... | "[\"68\\\\mathrm{C}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 299, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14353"}] | {
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} |
[
"\\$180"
] | [
"skywork"
] | 0bb76895469cc90662e4fcb4ce57978836eebda92b89f67b792f6f6bcaf81375 | [
{
"content": "Ivan rents a car for $\\$$25 a day and $\\$$0.20 a mile. If he rents it for 4 days and drives it 400 miles, how many dollars does he pay?",
"role": "user"
}
] | Ivan rents a car for $\$$25 a day and $\$$0.20 a mile. If he rents it for 4 days and drives it 400 miles, how many dollars does he pay? | "[\"\\\\$180\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 333, "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:14354"}] | {
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} |
[
"\\frac{24}{7}"
] | [
"skywork"
] | 50278e45204c419781549e1b2fea6f69ea6bfd4cd07d566cfb37d20399e9031b | [
{
"content": "If \\(x\\) and \\(y\\) are positive real numbers such that \\(6x^2 + 12xy + 6y^2 = x^3 + 3x^2 y + 3xy^2\\), find the value of \\(x\\).",
"role": "user"
}
] | If \(x\) and \(y\) are positive real numbers such that \(6x^2 + 12xy + 6y^2 = x^3 + 3x^2 y + 3xy^2\), find the value of \(x\). | "[\"\\\\frac{24}{7}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 311, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14355"}] | {
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[
"105"
] | [
"skywork"
] | 255cadc920e48f714b9a7e1aa01f84b4fd351036b3ea4b42ce95ee89a234c457 | [
{
"content": "10 In the Cartesian coordinate system, given the point set $I=\\{(x, y) \\mid x, y$ are integers, and $0 \\leqslant x \\leqslant 5,0 \\leqslant y \\leqslant 5\\}$, then the number of different positioned squares with vertices from the set $I$ is $\\qquad$.",
"role": "user"
}
] | 10 In the Cartesian coordinate system, given the point set $I=\{(x, y) \mid x, y$ are integers, and $0 \leqslant x \leqslant 5,0 \leqslant y \leqslant 5\}$, then the number of different positioned squares with vertices from the set $I$ is $\qquad$. | "[\"105\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 303, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:14357"}] | {
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} |
[
"10"
] | [
"skywork"
] | 8513e607164e32edd752a26b8f1ee12b4b381df5cfa85e08f3dd76a0ba084db9 | [
{
"content": "SG. 1 If $a$ is the smallest positive integer which gives remainder 1 when divided by 3 and is a multiple of 5, find the value of $a$. (Reference: 1997 FG5.1)",
"role": "user"
}
] | SG. 1 If $a$ is the smallest positive integer which gives remainder 1 when divided by 3 and is a multiple of 5, find the value of $a$. (Reference: 1997 FG5.1) | "[\"10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 332, "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:14358"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 7e20b76ec0589cd360b95488f3d99674d5df71be618137a6a7e29369c00fd2ce | [
{
"content": "Problem 3. Bus stop $B$ is located on a straight highway between stops $A$ and $C$. After some time following departure from $A$, the bus found itself at a point on the highway such that the distance from this point to one of the three stops is equal to the sum of the distances to the other two. A... | Problem 3. Bus stop $B$ is located on a straight highway between stops $A$ and $C$. After some time following departure from $A$, the bus found itself at a point on the highway such that the distance from this point to one of the three stops is equal to the sum of the distances to the other two. After the same amount o... | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 312, "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:14359"}] | {
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"25"
] | [
"skywork"
] | f6e2f91b184c6bba6e9d9f2242139320de29bad4f3ccb8ea20ef099069066986 | [
{
"content": "19. A group of 50 girls sit in a circle. They throw a ball around the circle. Each girl who gets the ball throws it to the girl sitting six places anticlockwise from her, who catches it. Freda catches the ball 100 times. In that time, how many girls never get to catch the ball?\nA 0\nB 8\nC 10\nD ... | 19. A group of 50 girls sit in a circle. They throw a ball around the circle. Each girl who gets the ball throws it to the girl sitting six places anticlockwise from her, who catches it. Freda catches the ball 100 times. In that time, how many girls never get to catch the ball?
A 0
B 8
C 10
D 25
E 40 | "[\"25\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 334, "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:14360"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"168"
] | [
"skywork"
] | 2c1d4a470d48ec8bc9d46f9f6b8dba385f7c101ad31a2ee08d94da7b3c311b2a | [
{
"content": "2. In front of Vasya lies a stack of 15 red, 15 blue, and 15 yellow cards. Vasya needs to choose 15 out of all 45 cards to earn the maximum number of points. Points are awarded as follows: for each red card, Vasya gets one point. For each blue card, Vasya gets a number of points equal to twice the... | 2. In front of Vasya lies a stack of 15 red, 15 blue, and 15 yellow cards. Vasya needs to choose 15 out of all 45 cards to earn the maximum number of points. Points are awarded as follows: for each red card, Vasya gets one point. For each blue card, Vasya gets a number of points equal to twice the number of selected re... | "[\"168\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 320, "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:14361"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"100"
] | [
"skywork"
] | 2fb6099f5bc340d73455184595b79c0328c43abca2a411619357f956d96bbcba | [
{
"content": "8. A parallel beam of light falls normally on a thin lens. Behind the lens, at a distance of $80 \\mathrm{~cm}$ from it, there is a screen on which a circular spot of a certain diameter is visible. If the screen is moved 40 cm, a spot of the same diameter will again be visible on the screen. Deter... | 8. A parallel beam of light falls normally on a thin lens. Behind the lens, at a distance of $80 \mathrm{~cm}$ from it, there is a screen on which a circular spot of a certain diameter is visible. If the screen is moved 40 cm, a spot of the same diameter will again be visible on the screen. Determine the focal length o... | "[\"100\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 318, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14362"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"26.9"
] | [
"skywork"
] | ab878e2446403dfcfae4c650365a4f2bb7a05ba6f61fa688769b7ef59758fcd9 | [
{
"content": "At the beginning of a trip, the mileage odometer read $56,200$ miles. The driver filled the gas tank with $6$ gallons of gasoline. During the trip, the driver filled his tank again with $12$ gallons of gasoline when the odometer read $56,560$. At the end of the trip, the driver filled his tank aga... | At the beginning of a trip, the mileage odometer read $56,200$ miles. The driver filled the gas tank with $6$ gallons of gasoline. During the trip, the driver filled his tank again with $12$ gallons of gasoline when the odometer read $56,560$. At the end of the trip, the driver filled his tank again with $20$ gallons o... | "[\"26.9\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 337, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:14363"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"31"
] | [
"skywork"
] | e9fc2380553542c791f72028b2e31155e4c2c4da1399740448eab1cc994248d6 | [
{
"content": "Given the universal set $U=\\{1, 2, 3, 4, 5, 6, 7, 8\\}$, a set $A=\\{a_1, a_2, a_3, a_4\\}$ is formed by selecting any four elements from $U$, and the set of the remaining four elements is denoted as $\\complement_U A=\\{b_1, b_2, b_3, b_4\\}$. If $a_1+a_2+a_3+a_4 < b_1+b_2+b_3+b_4$, then the num... | Given the universal set $U=\{1, 2, 3, 4, 5, 6, 7, 8\}$, a set $A=\{a_1, a_2, a_3, a_4\}$ is formed by selecting any four elements from $U$, and the set of the remaining four elements is denoted as $\complement_U A=\{b_1, b_2, b_3, b_4\}$. If $a_1+a_2+a_3+a_4 < b_1+b_2+b_3+b_4$, then the number of ways to form set $A$ i... | "[\"31\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 323, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:14364"}] | {
"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
} |
[
"134"
] | [
"skywork"
] | 360b2dc2a79ad011a07bd7ab58656526915bdb4f2e7367e835a3b494e25a0a0d | [
{
"content": "19. How many airplanes? (11th grade, 8 points) The work of the Absent-Minded Scientist involves long business trips, and therefore he often flies on the same airline. This airline has many identical airplanes, and all of them have names. Since the Scientist does not fly every day or even every wee... | 19. How many airplanes? (11th grade, 8 points) The work of the Absent-Minded Scientist involves long business trips, and therefore he often flies on the same airline. This airline has many identical airplanes, and all of them have names. Since the Scientist does not fly every day or even every week, it can be assumed t... | "[\"134\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 291, "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:14365"}, {"dataset": "skywork", "extra_i... | {
"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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