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 |
|---|---|---|---|---|---|---|---|---|
[
"6^\\circ"
] | [
"skywork"
] | 206d584e4400f8df53be06189a5ca13248ae2e83ba421388d0cf4f7a137266b9 | [
{
"content": "Given triangle $ABC$ and a point $P$ inside it, $\\angle BAP=18^\\circ$, $\\angle CAP=30^\\circ$, $\\angle ACP=48^\\circ$, and $AP=BC$. If $\\angle BCP=x^\\circ$, find $x$.",
"role": "user"
}
] | Given triangle $ABC$ and a point $P$ inside it, $\angle BAP=18^\circ$, $\angle CAP=30^\circ$, $\angle ACP=48^\circ$, and $AP=BC$. If $\angle BCP=x^\circ$, find $x$. | "[\"6^\\\\circ\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2250, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16222"}] | {
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} |
[
"\\frac{2 \\sqrt{7}}{7}"
] | [
"skywork"
] | 9e1b8d3cee851b393d4ab7675cab458b9686474fec3f659afe69e66a31b474c1 | [
{
"content": "9. (16 points) As shown in Figure 1, let the base of the pyramid $E-ABCD$ be a rhombus, and $\\angle ABC=60^{\\circ}, AB=EC=2$, $AE=BE=\\sqrt{2}$.\n(1) Prove: Plane $EAB \\perp$ Plane $ABCD$;\n(2) Find the cosine value of the dihedral angle $A-EC-D$.\n\n保留了原文的换行和格式。",
"role": "user"
}
] | 9. (16 points) As shown in Figure 1, let the base of the pyramid $E-ABCD$ be a rhombus, and $\angle ABC=60^{\circ}, AB=EC=2$, $AE=BE=\sqrt{2}$.
(1) Prove: Plane $EAB \perp$ Plane $ABCD$;
(2) Find the cosine value of the dihedral angle $A-EC-D$.
保留了原文的换行和格式。 | "[\"\\\\frac{2 \\\\sqrt{7}}{7}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2253, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16223"}] | {
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} |
[
"3000"
] | [
"skywork"
] | 29ca3d92930115fd06a23acadb5e9026ab0f5507268ddfbd8a573da2b24c72da | [
{
"content": "4. On one of the sides of a triangle, 60 points are taken, and on another - 50. (These points are distinct from the vertices of the triangle.) Each vertex at the base is connected by straight line segments to the points taken on the opposite side. How many intersection points of these segments are... | 4. On one of the sides of a triangle, 60 points are taken, and on another - 50. (These points are distinct from the vertices of the triangle.) Each vertex at the base is connected by straight line segments to the points taken on the opposite side. How many intersection points of these segments are formed in this case? | "[\"3000\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2261, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "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:16224"}] | {
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} |
[
"8 - 4\\sqrt{2}"
] | [
"skywork"
] | 6f5bfab81e01edb5bec3de8971a61d940e46e0441ef5903ba2b04aa01c420bf4 | [
{
"content": "The triangle $\\triangle ABC$ is an isosceles triangle where $AB = 4\\sqrt{2}$ and $\\angle B$ is a right angle. If $I$ is the incenter of $\\triangle ABC,$ then what is $BI$?\n\nExpress your answer in the form $a + b\\sqrt{c},$ where $a,$ $b,$ and $c$ are integers, and $c$ is not divisible by any... | The triangle $\triangle ABC$ is an isosceles triangle where $AB = 4\sqrt{2}$ and $\angle B$ is a right angle. If $I$ is the incenter of $\triangle ABC,$ then what is $BI$?
Express your answer in the form $a + b\sqrt{c},$ where $a,$ $b,$ and $c$ are integers, and $c$ is not divisible by any perfect square other than $1... | "[\"8 - 4\\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2259, "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:16225"}] | {
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} |
[
"\\frac{1}{54}"
] | [
"skywork"
] | faacd9345372cec64b4dfa8f21c7c3473263c494da52d6cb3df6d7ae5c2d7d9d | [
{
"content": "Hello.\n\nSuppose $a$, $b$, $c$ are real numbers such that $a+b+c = 0$ and $a^{2}+b^{2}+c^{2} = 1$.\nProve that $a^{2}b^{2}c^{2}\\leq \\frac{1}{54}$ and determine the cases of equality.",
"role": "user"
}
] | Hello.
Suppose $a$, $b$, $c$ are real numbers such that $a+b+c = 0$ and $a^{2}+b^{2}+c^{2} = 1$.
Prove that $a^{2}b^{2}c^{2}\leq \frac{1}{54}$ and determine the cases of equality. | "[\" \\\\frac{1}{54} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2263, "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:16226"}] | {
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} |
[
"12"
] | [
"skywork"
] | 8e1462a077087cf84f52b6deb5fcb5745bf6d46a6edeae88761a2f9ceaab0f86 | [
{
"content": "Barbara, Edward, Abhinav, and Alex took turns writing this test. Working alone, they could finish it in $10$, $9$, $11$, and $12$ days, respectively. If only one person works on the test per day, and nobody works on it unless everyone else has spent at least as many days working on it, how many da... | Barbara, Edward, Abhinav, and Alex took turns writing this test. Working alone, they could finish it in $10$, $9$, $11$, and $12$ days, respectively. If only one person works on the test per day, and nobody works on it unless everyone else has spent at least as many days working on it, how many days (an integer) did it... | "[\"12\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2262, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16227"}, {"dataset": "skywork", "extra_... | {
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} |
[
"1003"
] | [
"skywork"
] | 8a63b891038a8fa97777f05aa4b2d4ccfe2cc275c1786958291d24edab1eb779 | [
{
"content": "G87 (47-2, 塞黑) Let $P$ be a regular 2006-gon. If an end of a diagonal of $P$ divides the boundary of $P$ into two parts, each containing an odd number of sides of $P$, then the diagonal is called a \"good edge\". It is stipulated that each side of $P$ is a \"good edge\".\n\nGiven 2003 non-intersec... | G87 (47-2, 塞黑) Let $P$ be a regular 2006-gon. If an end of a diagonal of $P$ divides the boundary of $P$ into two parts, each containing an odd number of sides of $P$, then the diagonal is called a "good edge". It is stipulated that each side of $P$ is a "good edge".
Given 2003 non-intersecting diagonals inside $P$ th... | "[\"1003\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2248, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16228"}] | {
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} |
[
"11"
] | [
"skywork"
] | 54eaf9654b9b7a746000c0527203768e3cca4f544d26266f41b2ba736b021bcc | [
{
"content": "How many perfect cubes are between 1000 and 10000?",
"role": "user"
}
] | How many perfect cubes are between 1000 and 10000? | "[\"11\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2285, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "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:16229"}] | {
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"reference_present": true
} |
[
"\\frac{3}{128}"
] | [
"skywork"
] | 810f1cd2cf59dfb06965427d669343e03b3d45f183a78165b779c339a3e65f0a | [
{
"content": "In a geometric sequence with five terms $t_{1}, t_{2}, t_{3}, t_{4}, t_{5}$, each term is positive and $t_{1}>t_{2}$. If the sum of the first two terms is $\\frac{15}{2}$ and the sum of the squares of the first two terms is $\\frac{153}{4}$, what is the value of $t_{5}$ ?\n\n(A geometric sequence ... | In a geometric sequence with five terms $t_{1}, t_{2}, t_{3}, t_{4}, t_{5}$, each term is positive and $t_{1}>t_{2}$. If the sum of the first two terms is $\frac{15}{2}$ and the sum of the squares of the first two terms is $\frac{153}{4}$, what is the value of $t_{5}$ ?
(A geometric sequence is a sequence in which eac... | "[\"\\\\frac{3}{128}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2256, "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:16231"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"31"
] | [
"skywork"
] | 4aac2f6b3b6469c413cf20f72b7feeaec469f6928e6a9a73751c3f62f28b535d | [
{
"content": "Suppose you have two bank cards for making purchases: a debit card and a credit card. Today you decided to buy airline tickets worth 20,000 rubles. If you pay for the purchase with the credit card (the credit limit allows it), you will have to repay the bank within $\\mathrm{N}$ days to stay withi... | Suppose you have two bank cards for making purchases: a debit card and a credit card. Today you decided to buy airline tickets worth 20,000 rubles. If you pay for the purchase with the credit card (the credit limit allows it), you will have to repay the bank within $\mathrm{N}$ days to stay within the grace period in w... | "[\"31\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2252, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:16232"}] | {
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"reference_present": true
} |
[
"n"
] | [
"skywork"
] | 4ecce25bdb1305fef301ad66823cfd4b0afe2e5e4388ea1d63ded67fbccb25d1 | [
{
"content": "Anjanan A.\n\nAll possible non-empty subsets are taken from the set of numbers $1,2,3, \\ldots, n$. For each subset, the reciprocal of the product of all its numbers is taken. Find the sum of all such reciprocal values.",
"role": "user"
}
] | Anjanan A.
All possible non-empty subsets are taken from the set of numbers $1,2,3, \ldots, n$. For each subset, the reciprocal of the product of all its numbers is taken. Find the sum of all such reciprocal values. | "[\"n\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2265, "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:16233"}, {"dataset": "skywork", "extra_inf... | {
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"reference_components": 1,
"reference_present": true
} |
[
"4648"
] | [
"skywork"
] | 9dfef5629d286552a016cb65e9d6e6b9b0fc240ee3c7037120830654fc23523d | [
{
"content": "Compute the number of positive integers less than or equal to $10000$ which are relatively prime to $2014$.",
"role": "user"
}
] | Compute the number of positive integers less than or equal to $10000$ which are relatively prime to $2014$. | "[\"4648\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2277, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:16234"}, {"dataset": "skywork", "extra_inf... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2 \\cdot (2018!)^2"
] | [
"skywork"
] | dc145e5d3af8c2d0884c7b8fa40f51629b25767a7d317860e3ff84ee063b6dcb | [
{
"content": "In how many ways every unit square of a $2018$ x $2018$ board can be colored in red or white such that number of red unit squares in any two rows are distinct and number of red squares in any two columns are distinct.",
"role": "user"
}
] | In how many ways every unit square of a $2018$ x $2018$ board can be colored in red or white such that number of red unit squares in any two rows are distinct and number of red squares in any two columns are distinct. | "[\"2 \\\\cdot (2018!)^2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2268, "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:16235"}, {"dataset": "skywork", "extra_... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"45,45,90"
] | [
"skywork"
] | cbc2b37738ff99027fe71d15f18f928bdb4d9c15c436a7bfe14066cddd059d03 | [
{
"content": "8,9\n\nIn triangle $ABC$, the altitude $AM$ is not less than $BC$, and the altitude $BH$ is not less than $AC$. Find the angles of triangle $ABC$.",
"role": "user"
}
] | 8,9
In triangle $ABC$, the altitude $AM$ is not less than $BC$, and the altitude $BH$ is not less than $AC$. Find the angles of triangle $ABC$. | "[\"45,45,90\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2254, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16236"}] | {
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} |
[
"53"
] | [
"skywork"
] | 23dfc45d56fd11ff48c21a29e6424c59a9fc085c2460f76bd3858edcca809e82 | [
{
"content": "8. If the sequence $\\left\\{a_{n}\\right\\}$ satisfies\n$$\na_{n}=\\left[(2+\\sqrt{3})^{2^{n}}\\right]\\left(n \\in \\mathbf{Z}_{+}\\right),\n$$\n\nthen the last two digits of $a_{2020}$ are $\\qquad$",
"role": "user"
}
] | 8. If the sequence $\left\{a_{n}\right\}$ satisfies
$$
a_{n}=\left[(2+\sqrt{3})^{2^{n}}\right]\left(n \in \mathbf{Z}_{+}\right),
$$
then the last two digits of $a_{2020}$ are $\qquad$ | "[\"53\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2264, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:16237"}] | {
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} |
[
"\\begin{pmatrix}16 & -2 \\\\ 0 & 4 \\end{pmatrix}"
] | [
"skywork"
] | b77caaa7b61e1054f622fba095df6a7dfa62cc4b7f17aa293c5b16f2f47cf3a0 | [
{
"content": "If $\\mathbf{A}^{-1} = \\begin{pmatrix} -4 & 1 \\\\ 0 & 2 \\end{pmatrix},$ then find the inverse of $\\mathbf{A}^2.$",
"role": "user"
}
] | If $\mathbf{A}^{-1} = \begin{pmatrix} -4 & 1 \\ 0 & 2 \end{pmatrix},$ then find the inverse of $\mathbf{A}^2.$ | "[\"\\\\begin{pmatrix}16 & -2 \\\\\\\\ 0 & 4 \\\\end{pmatrix}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2287, "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:16238"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"40"
] | [
"skywork"
] | 24c7085a1acbf4c6cfb15d71d76ff52a7f329a9ca208f0731df0c0a34b08692f | [
{
"content": "8. The mean of five numbers is 25 . Abbie adds 5 to the first number, 10 to the second number, 15 to the third number, 20 to the fourth number and 25 to the fifth number to obtain a new set of five numbers. What is the mean of the numbers in the new set?\nA 100\nB 50\nC 40\nD 30\nE 25",
"role"... | 8. The mean of five numbers is 25 . Abbie adds 5 to the first number, 10 to the second number, 15 to the third number, 20 to the fourth number and 25 to the fifth number to obtain a new set of five numbers. What is the mean of the numbers in the new set?
A 100
B 50
C 40
D 30
E 25 | "[\"40\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2270, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16239"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"873"
] | [
"skywork"
] | ab4acab0587578c5829b4a61ca6c8824062a0c2fc7060c3ffa6eba3f4bc62fe4 | [
{
"content": "Problem 12. (6 points)\n\nVictor received a large sum of money as a birthday gift in the amount of 45 thousand rubles. The young man decided to save this part of his savings in dollars on a currency deposit. The term of the deposit agreement was 2 years, with an interest rate of 4.7% per annum, co... | Problem 12. (6 points)
Victor received a large sum of money as a birthday gift in the amount of 45 thousand rubles. The young man decided to save this part of his savings in dollars on a currency deposit. The term of the deposit agreement was 2 years, with an interest rate of 4.7% per annum, compounded quarterly. On t... | "[\"873\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2266, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16240"}] | {
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[
"13"
] | [
"skywork"
] | 53ecf05dc2a46f423257db74fe3344f32aa5dfe4a5055029b2553ca470469c79 | [
{
"content": "The average (mean) of $3,5,6,8$, and $x$ is 7 . What is the value of $x$ ?",
"role": "user"
}
] | The average (mean) of $3,5,6,8$, and $x$ is 7 . What is the value of $x$ ? | "[\"13\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2295, "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:16241"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"298"
] | [
"skywork"
] | bd6bbcc0a5b1b7792ccde3ba1a52615094da24a87fa3f8320e8d75099fa75195 | [
{
"content": "Each of the 2001 students at a high school studies either Spanish or French, and some study both. The number who study Spanish is between 80 percent and 85 percent of the school population, and the number who study French is between 30 percent and 40 percent. Let $m$ be the smallest number of stud... | Each of the 2001 students at a high school studies either Spanish or French, and some study both. The number who study Spanish is between 80 percent and 85 percent of the school population, and the number who study French is between 30 percent and 40 percent. Let $m$ be the smallest number of students who could study b... | "[\"298\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2272, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:16242"}, {"dataset": "skywork", "extra_inf... | {
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} |
[
"1"
] | [
"skywork"
] | e7bf5f591a559502ee51dab8522cc6ef2ae377487312aff897efd2181198672a | [
{
"content": "6.136. $\\frac{x^{2}+1}{x+1}+\\frac{x^{2}+2}{x-2}=-2$.\n\n6.136. $\\frac{x^{2}+1}{x+1}+\\frac{x^{2}+2}{x-2}=-2$. \n\n(Note: The equation is the same in both languages, so the translation is identical to the original text.)",
"role": "user"
}
] | 6.136. $\frac{x^{2}+1}{x+1}+\frac{x^{2}+2}{x-2}=-2$.
6.136. $\frac{x^{2}+1}{x+1}+\frac{x^{2}+2}{x-2}=-2$.
(Note: The equation is the same in both languages, so the translation is identical to the original text.) | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2284, "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:16243"}] | {
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[
"1609"
] | [
"skywork"
] | 4648d72a517933dbb0ae5b292b65beb3e3f4861948f953bd53d40b09a72538e5 | [
{
"content": "A natural number is written on the board. If its last digit (in the units place) is erased, the remaining non-zero number is divisible by 20. If the first digit is erased, the remaining number is divisible by 21. What is the smallest number that could be on the board if its second digit is not 0?"... | A natural number is written on the board. If its last digit (in the units place) is erased, the remaining non-zero number is divisible by 20. If the first digit is erased, the remaining number is divisible by 21. What is the smallest number that could be on the board if its second digit is not 0? | "[\"1609\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2283, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:16244"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"15"
] | [
"skywork"
] | 73b8a5bb7196e537c60f3b8ba034afef093a48cf83e55904baba90ca3ba9a797 | [
{
"content": "Given that point $M(x\\_0, y\\_0)$ moves on the circle $x^{2}+y^{2}=4$, $N(4,0)$, and point $P(x,y)$ is the midpoint of segment $MN$.\n\n(1) Find the trajectory equation of point $P(x,y)$;\n\n(2) Find the maximum and minimum distances from point $P(x,y)$ to the line $3x+4y-86=0$.",
"role": "us... | Given that point $M(x\_0, y\_0)$ moves on the circle $x^{2}+y^{2}=4$, $N(4,0)$, and point $P(x,y)$ is the midpoint of segment $MN$.
(1) Find the trajectory equation of point $P(x,y)$;
(2) Find the maximum and minimum distances from point $P(x,y)$ to the line $3x+4y-86=0$. | "[\"15\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2242, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16245"}] | {
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"90"
] | [
"skywork"
] | 00a28e6139eec17b2a14d6c32f11d23615f46bd67996e0343a0d13f7e6f11cd8 | [
{
"content": "5. The maximum number of consecutive integers whose sum is 45 is ( ).\n(A) 9\n(B) 25\n(C) 45\n(D) 90\n(E) 120",
"role": "user"
}
] | 5. The maximum number of consecutive integers whose sum is 45 is ( ).
(A) 9
(B) 25
(C) 45
(D) 90
(E) 120 | "[\"90\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2279, "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:16246"}] | {
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"label_correctness_independently_verified": false,
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{7}{6}"
] | [
"skywork"
] | 5eba93b7f54ff920bb95a96673a8e51e88a5dc9a3b15588ec4703c17e6dd1a41 | [
{
"content": "Points $P, Q, R, S, T, U, V,$ and $W$ lie, in that order, on line $\\overline{PW}$, dividing it into seven equal segments, each of length 1. Point $X$ is not on line $PW$. Points $Y$ and $Z$ lie on line segments $\\overline{XR}$ and $\\overline{XW}$ respectively. The line segments $\\overline{YQ},... | Points $P, Q, R, S, T, U, V,$ and $W$ lie, in that order, on line $\overline{PW}$, dividing it into seven equal segments, each of length 1. Point $X$ is not on line $PW$. Points $Y$ and $Z$ lie on line segments $\overline{XR}$ and $\overline{XW}$ respectively. The line segments $\overline{YQ}, \overline{ZT},$ and $\ove... | "[\"\\\\frac{7}{6}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2258, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:16248"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{5}{11}"
] | [
"skywork"
] | e59c67fd2a00af64df9d881309e4846fe0efcdd28a9923b8e73b870259af76a3 | [
{
"content": "A deck consists of four red cards, four green cards, and four blue cards. Each color has cards labeled $A$, $B$, $C$, $D$. A winning pair is defined as two cards of the same color or two cards with the same label. Determine the probability of drawing a winning pair.",
"role": "user"
}
] | A deck consists of four red cards, four green cards, and four blue cards. Each color has cards labeled $A$, $B$, $C$, $D$. A winning pair is defined as two cards of the same color or two cards with the same label. Determine the probability of drawing a winning pair. | "[\"\\\\frac{5}{11}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2281, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:16249"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2\\sin26"
] | [
"skywork"
] | 495530055da540a3c8ebf98dcc15b26575452f615a47e879d8be5730cf4a2604 | [
{
"content": "403. Simplify the expression\n\n$$\n\\frac{\\sin 11^{\\circ} \\cos 15^{\\circ}+\\sin 15^{\\circ} \\cos 11^{\\circ}}{\\sin 18^{\\circ} \\cos 12^{\\circ}+\\sin 12^{\\circ} \\cos 18^{\\circ}}\n$$",
"role": "user"
}
] | 403. Simplify the expression
$$
\frac{\sin 11^{\circ} \cos 15^{\circ}+\sin 15^{\circ} \cos 11^{\circ}}{\sin 18^{\circ} \cos 12^{\circ}+\sin 12^{\circ} \cos 18^{\circ}}
$$ | "[\"2\\\\sin26\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2298, "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:16250"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"f(n) = cn"
] | [
"skywork"
] | 4c2da9a3bec87a6e1ca02b5e9680aa50fbd4f11aba0137ef666a0ebdf131fcea | [
{
"content": "Let $\\alpha$ be given positive real number, find all the functions $f: N^{+} \\rightarrow R$ such that $f(k + m) = f(k) + f(m)$ holds for any positive integers $k$, $m$ satisfying $\\alpha m \\leq k \\leq (\\alpha + 1)m$.",
"role": "user"
}
] | Let $\alpha$ be given positive real number, find all the functions $f: N^{+} \rightarrow R$ such that $f(k + m) = f(k) + f(m)$ holds for any positive integers $k$, $m$ satisfying $\alpha m \leq k \leq (\alpha + 1)m$. | "[\"f(n) = cn\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 2276, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "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:16251"}] | {
"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
} |
[
"17"
] | [
"skywork"
] | b3ffe18cd3be0723bc5cae455eef3b9e4e1ce4086e124cb2809960728dd50442 | [
{
"content": "(5) Find the smallest positive integer $n$ with the following property: If each vertex of a regular $n$-gon is arbitrarily colored with one of three colors (red, yellow, blue), then among these $n$ vertices, there must exist four vertices of the same color that form the vertices of an isosceles tr... | (5) Find the smallest positive integer $n$ with the following property: If each vertex of a regular $n$-gon is arbitrarily colored with one of three colors (red, yellow, blue), then among these $n$ vertices, there must exist four vertices of the same color that form the vertices of an isosceles trapezoid (a convex quad... | "[\"17\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2274, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16252"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"18900"
] | [
"skywork"
] | 2e8b172a82b8af74214e9ceeff3f48ee9ae7ae2008efde1b2126df5a26dada22 | [
{
"content": "Consider a wardrobe that consists of $6$ red shirts, $7$ green shirts, $8$ blue shirts, $9$ pairs of pants, $10$ green hats, $10$ red hats, and $10$ blue hats. Additionally, you have $5$ ties in each color: green, red, and blue. Every item is distinct. How many outfits can you make consisting of o... | Consider a wardrobe that consists of $6$ red shirts, $7$ green shirts, $8$ blue shirts, $9$ pairs of pants, $10$ green hats, $10$ red hats, and $10$ blue hats. Additionally, you have $5$ ties in each color: green, red, and blue. Every item is distinct. How many outfits can you make consisting of one shirt, one pair of ... | "[\"18900\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2278, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:16253"}] | {
"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
} |
[
"36"
] | [
"skywork"
] | cce051f23cf1fbcb62cb9a80f14062ca28eb1ed425fffe6e39be672b0dc62c5f | [
{
"content": "In rectangle $ABCD$, $AB = 12$ and $BC = 10$. Points $E$ and $F$ lie inside rectangle $ABCD$ so that $BE = 9$, $DF = 8$, $\\overline{BE} \\parallel \\overline{DF}$, $\\overline{EF} \\parallel \\overline{AB}$, and line $BE$ intersects segment $\\overline{AD}$. The length $EF$ can be expressed in th... | In rectangle $ABCD$, $AB = 12$ and $BC = 10$. Points $E$ and $F$ lie inside rectangle $ABCD$ so that $BE = 9$, $DF = 8$, $\overline{BE} \parallel \overline{DF}$, $\overline{EF} \parallel \overline{AB}$, and line $BE$ intersects segment $\overline{AD}$. The length $EF$ can be expressed in the form $m \sqrt{n} - p$, wher... | "[\"36\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2271, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16254"}, {"dataset": "skywork", "extra_in... | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\dfrac{1}{1024}"
] | [
"skywork"
] | 4567d03dcd37a835b71a20cb4fc0d112e79d8d858601139e0a6b3ef3bc4e9681 | [
{
"content": "We flip a fair coin 12 times. What is the probability that we get exactly 9 heads and all heads occur consecutively?",
"role": "user"
}
] | We flip a fair coin 12 times. What is the probability that we get exactly 9 heads and all heads occur consecutively? | "[\"\\\\dfrac{1}{1024}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2302, "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:16255"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 913be0729c87499b8501b5261b75a73d2312dbcd88c9d6ad35ce32b5255f12c8 | [
{
"content": "How many positive integers $A$ are there such that if we append $3$ digits to the rightmost of decimal representation of $A$, we will get a number equal to $1+2+\\cdots + A$?\n\n$ \n\\textbf{a)}\\ 0\n\\qquad\\textbf{b)}\\ 1\n\\qquad\\textbf{c)}\\ 2\n\\qquad\\textbf{d)}\\ 2002\n\\qquad\\textbf{e)}\... | How many positive integers $A$ are there such that if we append $3$ digits to the rightmost of decimal representation of $A$, we will get a number equal to $1+2+\cdots + A$?
$
\textbf{a)}\ 0
\qquad\textbf{b)}\ 1
\qquad\textbf{c)}\ 2
\qquad\textbf{d)}\ 2002
\qquad\textbf{e)}\ \text{None of above}
$ | "[\"1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2269, "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:16256"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"\\frac{n-1}{2n}"
] | [
"skywork"
] | 075c2c1de9063d911acde35839d9735f9c370016e07643a51b854f16b6330974 | [
{
"content": "For each positive integer $n$, find the largest real number $C_n$ with the following property. Given any $n$ real-valued functions $f_1(x), f_2(x), \\cdots, f_n(x)$ defined on the closed interval $0 \\le x \\le 1$, one can find numbers $x_1, x_2, \\cdots x_n$, such that $0 \\le x_i \\le 1$ satisfy... | For each positive integer $n$, find the largest real number $C_n$ with the following property. Given any $n$ real-valued functions $f_1(x), f_2(x), \cdots, f_n(x)$ defined on the closed interval $0 \le x \le 1$, one can find numbers $x_1, x_2, \cdots x_n$, such that $0 \le x_i \le 1$ satisfying
\[|f_1(x_1)+f_2(x_2)+\c... | "[\"\\\\frac{n-1}{2n}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2280, "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:16257"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{27}{5005}"
] | [
"skywork"
] | cd11fe7a0bfcbf407538a1c595fae8414d048c6b4662b9efc550af503819c031 | [
{
"content": "7. The rules of a single-player card game are as follows: Place seven pairs of different cards into a backpack. The player randomly draws and returns cards each time, but when a pair is drawn, the paired cards are set aside. Each time, the player draws three cards (if there are fewer than three ca... | 7. The rules of a single-player card game are as follows: Place seven pairs of different cards into a backpack. The player randomly draws and returns cards each time, but when a pair is drawn, the paired cards are set aside. Each time, the player draws three cards (if there are fewer than three cards left, all remainin... | "[\"\\\\frac{27}{5005}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2273, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16258"}] | {
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[
"\\frac{2\\sqrt{3}}{3}"
] | [
"skywork"
] | 2b59efacd97e27b58a99bee545a0366d0194f8cc6f441db86563eca3b18a5eb1 | [
{
"content": "Let $C$ and $D$ be points on the semicircle with center $O$ and diameter $AB$ such that $ABCD$ is a convex quadrilateral. Let $Q$ be the intersection of the diagonals $[AC]$ and $[BD]$, and $P$ be the intersection of the lines tangent to the semicircle at $C$ and $D$. If $m(\\widehat{AQB})=2m(\\wi... | Let $C$ and $D$ be points on the semicircle with center $O$ and diameter $AB$ such that $ABCD$ is a convex quadrilateral. Let $Q$ be the intersection of the diagonals $[AC]$ and $[BD]$, and $P$ be the intersection of the lines tangent to the semicircle at $C$ and $D$. If $m(\widehat{AQB})=2m(\widehat{COD})$ and $|AB|=2... | "[\"\\\\frac{2\\\\sqrt{3}}{3}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2291, "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:16259"}] | {
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[
"831"
] | [
"skywork"
] | 912437d9e84c5d04d706535f5d06bb4379711dd345911d4ea4a52b303af3c089 | [
{
"content": "1. A three-digit number has its middle digit three times smaller than the sum of the other two, and the sum of the last two digits is half of the first digit. If the digits in the tens and units places are swapped, the resulting number is 18 less than the given number. What is that number?",
"... | 1. A three-digit number has its middle digit three times smaller than the sum of the other two, and the sum of the last two digits is half of the first digit. If the digits in the tens and units places are swapped, the resulting number is 18 less than the given number. What is that number? | "[\"831\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2297, "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:16260"}] | {
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} |
[
"n = 1, 3"
] | [
"skywork"
] | 4b4939b2dbed37fa4e6321715d98dfc7add7ccc9dbb6b69adc3eed419dbfc203 | [
{
"content": "Find all positive integer $n$ such that the equation $x^3+y^3+z^3=n \\cdot x^2 \\cdot y^2 \\cdot z^2$ has positive integer solutions.",
"role": "user"
}
] | Find all positive integer $n$ such that the equation $x^3+y^3+z^3=n \cdot x^2 \cdot y^2 \cdot z^2$ has positive integer solutions. | "[\"n = 1, 3\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2292, "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:16261"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{8}{3}"
] | [
"skywork"
] | 74edecafc1e7d81f0ba8f324fe23746b8da90ec73c6aea42e4310001b1e073de | [
{
"content": "2. Let $f(x)=\\min (4 x+1, x+2,-2 x+4)$, the maximum value of $f(x)$ is $\\qquad$ .",
"role": "user"
}
] | 2. Let $f(x)=\min (4 x+1, x+2,-2 x+4)$, the maximum value of $f(x)$ is $\qquad$ . | "[\"\\\\frac{8}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2286, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "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:16263"}] | {
"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
} |
[
"17"
] | [
"skywork"
] | d9d4a649a84ad20db3548f630268fe0f1d7e192054656e6bc214267f27725367 | [
{
"content": "Let $ S$ be a set of $ 100$ points in the plane. The distance between every pair of points in $ S$ is different, with the largest distance being $ 30$. Let $ A$ be one of the points in $ S$, let $ B$ be the point in $ S$ farthest from $ A$, and let $ C$ be the point in $ S$ farthest from $ B$. ... | Let $ S$ be a set of $ 100$ points in the plane. The distance between every pair of points in $ S$ is different, with the largest distance being $ 30$. Let $ A$ be one of the points in $ S$, let $ B$ be the point in $ S$ farthest from $ A$, and let $ C$ be the point in $ S$ farthest from $ B$. Let $ d$ be the distan... | "[\"17\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2288, "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:16264"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"25"
] | [
"skywork"
] | 2a08087ccad51cda4d4ed879944914bcb3e68bfe54330e3e40e5d0da10448718 | [
{
"content": "A line passing through vertex $A$ of triangle $ABC$ intersects side $BC$ at point $M$. In this case, $BM = AB$, $\\angle BAM = 35^\\circ$, and $\\angle CAM = 15^\\circ$.\n\nFind the angles of triangle $ABC$.",
"role": "user"
}
] | A line passing through vertex $A$ of triangle $ABC$ intersects side $BC$ at point $M$. In this case, $BM = AB$, $\angle BAM = 35^\circ$, and $\angle CAM = 15^\circ$.
Find the angles of triangle $ABC$. | "[\"25\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2289, "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:16265"}] | {
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"plain_numeric_reference": true,
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} |
[
"2.4"
] | [
"skywork"
] | 474c03df73f95fdc1452879f430a187176de21768a42d4afca751e54d45cbd46 | [
{
"content": "Given the random variables $\\xi + \\eta = 8$, if $\\xi \\sim B(10, 0.6)$, then calculate $E\\eta$ and $D\\eta$.",
"role": "user"
}
] | Given the random variables $\xi + \eta = 8$, if $\xi \sim B(10, 0.6)$, then calculate $E\eta$ and $D\eta$. | "[\"2.4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2294, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16266"}] | {
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} |
[
"6"
] | [
"skywork"
] | 5116c7da3573b6d4c03c86d32d385f7e2ba4512233042b1f22f1a95ce0bbc63d | [
{
"content": "4. (7 points) When copying a problem, Lin Lin mistakenly wrote a repeating decimal as 0.123456. If the digits are correct but the dots indicating the repeating section were omitted, there are $\\qquad$ possible original decimals.",
"role": "user"
}
] | 4. (7 points) When copying a problem, Lin Lin mistakenly wrote a repeating decimal as 0.123456. If the digits are correct but the dots indicating the repeating section were omitted, there are $\qquad$ possible original decimals. | "[\"6\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2293, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16267"}] | {
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} |
[
"(-3,\\frac{1-\\sqrt{5}}{2})\\cup(\\frac{-1+\\sqrt{5}}{2},3)"
] | [
"skywork"
] | 83a1e7167cbed149f14b083250f6d81b32ef207d5a85989aa633762fc6817e05 | [
{
"content": "7. The solution set of the inequality $|x|^{3}-2 x^{2}-4|x|+3<0$ is",
"role": "user"
}
] | 7. The solution set of the inequality $|x|^{3}-2 x^{2}-4|x|+3<0$ is | "[\"(-3,\\\\frac{1-\\\\sqrt{5}}{2})\\\\cup(\\\\frac{-1+\\\\sqrt{5}}{2},3)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2312, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16268"}] | {
"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
} |
[
"\\textbf{(A)}\\frac{4}{9}"
] | [
"skywork"
] | 27b70bfee206d60cd27a9964f53d37f3bcf2212d17cc41ade380230452bfa2b4 | [
{
"content": "In $\\triangle ABC,$ a point $E$ is on $\\overline{AB}$ with $AE=1$ and $EB=2.$ Point $D$ is on $\\overline{AC}$ so that $\\overline{DE} \\parallel \\overline{BC}$ and point $F$ is on $\\overline{BC}$ so that $\\overline{EF} \\parallel \\overline{AC}.$ What is the ratio of the area of $CDEF$ to th... | In $\triangle ABC,$ a point $E$ is on $\overline{AB}$ with $AE=1$ and $EB=2.$ Point $D$ is on $\overline{AC}$ so that $\overline{DE} \parallel \overline{BC}$ and point $F$ is on $\overline{BC}$ so that $\overline{EF} \parallel \overline{AC}.$ What is the ratio of the area of $CDEF$ to the area of $\triangle ABC?$
$\te... | "[\"\\\\textbf{(A)}\\\\frac{4}{9}\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 2313, "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:16269"}] | {
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"reference_components": 1,
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} |
[
"-1"
] | [
"skywork"
] | eb07fca3ba5c9b0cdfca07cc3e6c4b9efc3b72ebc577cc3b28c975e62e3a232c | [
{
"content": "2. Given the quadratic equation in $x$: $a(1+\\mathrm{i}) x^{2}+\\left(1+a^{2} \\mathrm{i}\\right) x+a^{2}+\\mathrm{i}=0$ has real roots, find the value of the real number $a$.\n\n untranslated text:\n已知关于 $x$ 的二次方程 $a(1+\\mathrm{i}) x^{2}+\\left(1+a^{2} \\mathrm{i}\\right) x+a^{2}+\\mathrm{i}=0$ ... | 2. Given the quadratic equation in $x$: $a(1+\mathrm{i}) x^{2}+\left(1+a^{2} \mathrm{i}\right) x+a^{2}+\mathrm{i}=0$ has real roots, find the value of the real number $a$.
untranslated text:
已知关于 $x$ 的二次方程 $a(1+\mathrm{i}) x^{2}+\left(1+a^{2} \mathrm{i}\right) x+a^{2}+\mathrm{i}=0$ 有实根, 求实数 $a$ 的值.
translated text:... | "[\"-1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2309, "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:16270"}] | {
"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
} |
[
"135"
] | [
"skywork"
] | 9f9fea1204c5983eaa13ad1cbe5b34994646677d3766eda394b0a9d8cc624ec5 | [
{
"content": "7. For any positive integer $n$, define\n$$\nS(n)=\\left[\\frac{n}{10^{[\\lg n]}}\\right]+10\\left(n-10^{[\\lg n]}\\left[\\frac{n}{10^{[\\lg n]}}\\right]\\right) \\text {. }\n$$\n\nThen among the positive integers $1,2, \\cdots, 5000$, the number of positive integers $n$ that satisfy $S(S(n))=n$ i... | 7. For any positive integer $n$, define
$$
S(n)=\left[\frac{n}{10^{[\lg n]}}\right]+10\left(n-10^{[\lg n]}\left[\frac{n}{10^{[\lg n]}}\right]\right) \text {. }
$$
Then among the positive integers $1,2, \cdots, 5000$, the number of positive integers $n$ that satisfy $S(S(n))=n$ is $\qquad$ . | "[\"135\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2303, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16271"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"115"
] | [
"skywork"
] | 565ad2ad3db6f5592ea65b1aa5bb11d33ba533ae113d70fbb1895ce785a80abc | [
{
"content": "1. Calculate: $1+\\frac{1}{2}(1+2)+\\frac{1}{3}(1+2+3)+$ $\\cdots+\\frac{1}{20}(1+2+\\cdots+20)$.",
"role": "user"
}
] | 1. Calculate: $1+\frac{1}{2}(1+2)+\frac{1}{3}(1+2+3)+$ $\cdots+\frac{1}{20}(1+2+\cdots+20)$. | "[\"115\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2316, "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:16272"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"8"
] | [
"skywork"
] | ab6aa03bf04af08ead766604704210d9406f1d3c27a420be599f7446a271c16b | [
{
"content": "For every $3^\\circ$ rise in temperature, the volume of a certain gas expands by $4$ cubic centimeters. If the volume of the gas is $24$ cubic centimeters when the temperature is $32^\\circ$, what was the volume of the gas in cubic centimeters when the temperature was $20^\\circ$?",
"role": "... | For every $3^\circ$ rise in temperature, the volume of a certain gas expands by $4$ cubic centimeters. If the volume of the gas is $24$ cubic centimeters when the temperature is $32^\circ$, what was the volume of the gas in cubic centimeters when the temperature was $20^\circ$? | "[\"8\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2323, "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:16273"}] | {
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"reference_components": 1,
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} |
[
"2,-10"
] | [
"skywork"
] | 977fbdb4b4dc0551ba9d2d5a9295ae0e1bcc880e74f1837d6f8692bb7456b805 | [
{
"content": "Find all integers $n$ such that $n^{2}+8 n+44$ is a perfect square.",
"role": "user"
}
] | Find all integers $n$ such that $n^{2}+8 n+44$ is a perfect square. | "[\"2,-10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2320, "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:16274"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{9}{343}"
] | [
"skywork"
] | d77a3ebf39f50542854a7c68b5ee63991ffbec00a4a03d0f5583cc36532c7abe | [
{
"content": "Let $a,$ $b,$ and $c$ be three positive real numbers whose sum is 1. If no one of these numbers is more than three times any other, find the minimum value of the product $abc.$",
"role": "user"
}
] | Let $a,$ $b,$ and $c$ be three positive real numbers whose sum is 1. If no one of these numbers is more than three times any other, find the minimum value of the product $abc.$ | "[\"\\\\frac{9}{343}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2307, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:16275"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"180/71"
] | [
"skywork"
] | e62a254f3827f66b46c8ad12b7b6b092d69c7f4ef93c6178307e2fe9c9db886d | [
{
"content": "Suppose $\\mathcal{T}=A_0A_1A_2A_3$ is a tetrahedron with $\\angle A_1A_0A_3 = \\angle A_2A_0A_1 = \\angle A_3A_0A_2 = 90^\\circ$ , $A_0A_1=5, A_0A_2=12$ and $A_0A_3=9$ . A cube $A_0B_0C_0D_0E_0F_0G_0H_0$ with side length $s$ is inscribed inside $\\mathcal{T}$ with $B_0\\in \\overlin... | Suppose $\mathcal{T}=A_0A_1A_2A_3$ is a tetrahedron with $\angle A_1A_0A_3 = \angle A_2A_0A_1 = \angle A_3A_0A_2 = 90^\circ$ , $A_0A_1=5, A_0A_2=12$ and $A_0A_3=9$ . A cube $A_0B_0C_0D_0E_0F_0G_0H_0$ with side length $s$ is inscribed inside $\mathcal{T}$ with $B_0\in \overline{A_0A_1}, D_0 \in \overline{A... | "[\"180/71\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2317, "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:16276"}, {"dataset": "skywork", "extra_inf... | {
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[
"2.60"
] | [
"skywork"
] | 0a190f2b147f182e35df7258ec461f10257b75baeeef5187af67d4422124370f | [
{
"content": "A factory implements a time-based wage system, where each worker is paid 6 yuan for every hour worked, for a total of 8 hours per day. However, the clock used for timing is inaccurate: it takes 69 minutes for the minute hand to coincide with the hour hand once. Calculate the amount of wages underp... | A factory implements a time-based wage system, where each worker is paid 6 yuan for every hour worked, for a total of 8 hours per day. However, the clock used for timing is inaccurate: it takes 69 minutes for the minute hand to coincide with the hour hand once. Calculate the amount of wages underpaid to each worker per... | "[\"2.60\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2296, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16277"}] | {
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[
"542"
] | [
"skywork"
] | 9c72f2d507fd2ad8c47d277c566583c6fad8ecf5ff591df1014d39a493082513 | [
{
"content": "The sum of the first $2011$ terms of a geometric sequence is $200$ . The sum of the first $4022$ terms is $380$ . Find the sum of the first $6033$ terms.",
"role": "user"
}
] | The sum of the first $2011$ terms of a geometric sequence is $200$ . The sum of the first $4022$ terms is $380$ . Find the sum of the first $6033$ terms. | "[\"542\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 2314, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16278"}, {"dataset": "skywork", "extra_inf... | {
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[
"2^n"
] | [
"skywork"
] | 9074e03d30e43f1107b936fa72926d7b8410d727b22b82a6cf402bb2b8b5af37 | [
{
"content": "Given a finite string $S$ of symbols $X$ and $O$, we write $@(S)$ for the number of $X$'s in $S$ minus the number of $O$'s. (For example, $@(XOOXOOX) =-1$.) We call a string $S$ [b]balanced[/b] if every substring $T$ of (consecutive symbols) $S$ has the property $-2 \\leq @(T) \\leq 2$. (Thus $XOO... | Given a finite string $S$ of symbols $X$ and $O$, we write $@(S)$ for the number of $X$'s in $S$ minus the number of $O$'s. (For example, $@(XOOXOOX) =-1$.) We call a string $S$ [b]balanced[/b] if every substring $T$ of (consecutive symbols) $S$ has the property $-2 \leq @(T) \leq 2$. (Thus $XOOXOOX$ is not balanced si... | "[\" 2^n \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2282, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:16279"}] | {
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[
"975"
] | [
"skywork"
] | 9be91786ea44998b93183dbf208fee387b2571942510e4594232453410fb70e7 | [
{
"content": "For a positive integer $p$, define the positive integer $n$ to be $p$-safe if $n$ differs in absolute value by at least $3$ from all multiples of $p$. Considering the prime numbers $5$, $7$, and $11$, find the number of positive integers less than or equal to $15,000$ which are simultaneously $5$-... | For a positive integer $p$, define the positive integer $n$ to be $p$-safe if $n$ differs in absolute value by at least $3$ from all multiples of $p$. Considering the prime numbers $5$, $7$, and $11$, find the number of positive integers less than or equal to $15,000$ which are simultaneously $5$-safe, $7$-safe, and $1... | "[\"975\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2325, "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:16280"}] | {
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} |
[
"1727\\mathrm{~}"
] | [
"skywork"
] | b07b840af02b315a557422c0365b822348096aaeb87f6f366df24a0c1297b0c0 | [
{
"content": "From the geographical latitudes of two places $\\left(A: 47^{\\circ} 6^{\\prime}, B: 59^{\\circ} 56^{\\prime} 30^{\\prime \\prime}\\right)$ and their time difference ( $\\left.59^{\\prime} 29^{\\prime \\prime}\\right)$, determine their distance from each other, $(r=6378,3 \\mathrm{~km})$.",
"r... | From the geographical latitudes of two places $\left(A: 47^{\circ} 6^{\prime}, B: 59^{\circ} 56^{\prime} 30^{\prime \prime}\right)$ and their time difference ( $\left.59^{\prime} 29^{\prime \prime}\right)$, determine their distance from each other, $(r=6378,3 \mathrm{~km})$. | "[\"1727\\\\mathrm{~}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2308, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16281"}] | {
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[
"8\\sqrt{2}"
] | [
"skywork"
] | 1b455ba1b8c0dca71a5841d8115d53c232a41fbe1000859122c0bf1206c8658e | [
{
"content": "In a diagram, $\\triangle ABC$ and $\\triangle BDC$ are right-angled, with $\\angle ABC = \\angle BDC = 45^\\circ$, and $AB = 16$. Determine the length of $BC$.",
"role": "user"
}
] | In a diagram, $\triangle ABC$ and $\triangle BDC$ are right-angled, with $\angle ABC = \angle BDC = 45^\circ$, and $AB = 16$. Determine the length of $BC$. | "[\"8\\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2299, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16282"}] | {
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[
"P(x)=a(x^2-x)"
] | [
"skywork"
] | 15180e81e3934969933f0c86e6471113489c49fdf7356ea5c9e3a95b50e05ae8 | [
{
"content": "5・138 Find all polynomials $P(x)$ that satisfy\n$$x P(x-1) \\equiv (x-2) P(x), x \\in R$$",
"role": "user"
}
] | 5・138 Find all polynomials $P(x)$ that satisfy
$$x P(x-1) \equiv (x-2) P(x), x \in R$$ | "[\"P(x)=a(x^2-x)\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 2306, "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:16283"}] | {
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} |
[
"\\frac{10}{17}"
] | [
"skywork"
] | 39db8eaac7d9d06927d88e66ea50b74d7c0cf56c1c50fecae2c167c92cfcc43a | [
{
"content": "Let $S_{n}$ and $T_{n}$ represent the sum of the first $n$ terms of the arithmetic sequences ${a_{n}}$ and ${b_{n}}$, respectively. Given that $\\frac{S_{n}}{T_{n}} = \\frac{n+1}{2n-1}$, where $n \\in \\mathbb{N}^*$, find the value of $\\frac{a_{3} + a_{7}}{b_{1} + b_{9}}$.",
"role": "user"
... | Let $S_{n}$ and $T_{n}$ represent the sum of the first $n$ terms of the arithmetic sequences ${a_{n}}$ and ${b_{n}}$, respectively. Given that $\frac{S_{n}}{T_{n}} = \frac{n+1}{2n-1}$, where $n \in \mathbb{N}^*$, find the value of $\frac{a_{3} + a_{7}}{b_{1} + b_{9}}$. | "[\"\\\\frac{10}{17}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2304, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16284"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"358"
] | [
"skywork"
] | ea7e0e302c947107cbf2682605484115023f4a6374a3a925d82ec6c877956cf6 | [
{
"content": "In a parlor game, the magician asks one of the participants to think of a three digit number $(abc)$ where $a$, $b$, and $c$ represent digits in base $10$ in the order indicated. The magician then asks this person to form the numbers $(acb)$, $(bca)$, $(bac)$, $(cab)$, and $(cba)$, to add these fi... | In a parlor game, the magician asks one of the participants to think of a three digit number $(abc)$ where $a$, $b$, and $c$ represent digits in base $10$ in the order indicated. The magician then asks this person to form the numbers $(acb)$, $(bca)$, $(bac)$, $(cab)$, and $(cba)$, to add these five numbers, and to rev... | "[\"358\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2311, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:16285"}, {"dataset": "skywork", "extra_in... | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.9544"
] | [
"skywork"
] | 57eb0be4ffdc1110a2934cb06515ffa9b03aa0bfd94ac1eb423d56bedb6ae0fd | [
{
"content": "Example 20. The diameter of a part manufactured in the workshop is a random variable distributed according to the normal law with parameters $a=4.5$ cm and $\\sigma=0.05$ cm. Find the probability that the diameter size of a randomly taken part differs from the mathematical expectation by no more t... | Example 20. The diameter of a part manufactured in the workshop is a random variable distributed according to the normal law with parameters $a=4.5$ cm and $\sigma=0.05$ cm. Find the probability that the diameter size of a randomly taken part differs from the mathematical expectation by no more than $1$ mm. | "[\"0.9544\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2326, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "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:16286"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | 9b734ef59899406a835be96e42a89a2c5312dc77a8264406f4793c79268bf3b1 | [
{
"content": "121. Find all values of the digit $a$, if the number $\\overline{875 a}$ is divisible by 6.",
"role": "user"
}
] | 121. Find all values of the digit $a$, if the number $\overline{875 a}$ is divisible by 6. | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2333, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16287"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"50"
] | [
"skywork"
] | 7f194aefe3f7d392586fb1d33b426f9a0fcc552660c1810389f925463d2ed775 | [
{
"content": "Given that $O$ is the circumcenter of $\\triangle A B C$, $X$ and $Y$ are points on $A C$ and $A B$ respectively, such that $B X$ and $C Y$ intersect at $O$, and $\\angle B A C = \\angle A Y X = \\angle X Y C$. Find the measure of $\\angle B A C$.",
"role": "user"
}
] | Given that $O$ is the circumcenter of $\triangle A B C$, $X$ and $Y$ are points on $A C$ and $A B$ respectively, such that $B X$ and $C Y$ intersect at $O$, and $\angle B A C = \angle A Y X = \angle X Y C$. Find the measure of $\angle B A C$. | "[\"50\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2319, "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:16288"}] | {
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} |
[
"\\frac{\\pi}{2}"
] | [
"skywork"
] | 980be75af728426333397edd385026f7425cb21ac7fb04f595c5458cf6248fad | [
{
"content": "If the line \\(x=\\frac{\\pi}{4}\\) intersects the curve \\(C: (x-\\arcsin a)(x-\\arccos a) + (y-\\arcsin a)(y+\\arccos a)=0\\), determine the minimum value of the chord length as \\(a\\) varies.",
"role": "user"
}
] | If the line \(x=\frac{\pi}{4}\) intersects the curve \(C: (x-\arcsin a)(x-\arccos a) + (y-\arcsin a)(y+\arccos a)=0\), determine the minimum value of the chord length as \(a\) varies. | "[\"\\\\frac{\\\\pi}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2310, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16289"}] | {
"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{5}{11}"
] | [
"skywork"
] | e2bc3d237c4fd39dbcf8a2754ab2aa58c19bd0942abdd1745485df2b811565e2 | [
{
"content": "5. Nathaniel and Obediah play a game in which they take turns rolling a fair six-sided die and keep a running tally of the sum of the results of all rolls made. A player wins if, after he rolls, the number on the running tally is a multiple of 7 . Play continues until either player wins, or else i... | 5. Nathaniel and Obediah play a game in which they take turns rolling a fair six-sided die and keep a running tally of the sum of the results of all rolls made. A player wins if, after he rolls, the number on the running tally is a multiple of 7 . Play continues until either player wins, or else indefinitely. If Nathan... | "[\"\\\\frac{5}{11}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2328, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16290"}, {"dataset": "skywork", "extra_in... | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 36c0c40515f963999d467cf886ed5b1b5a2f05cc99715546314c500bc73fa142 | [
{
"content": "In triangle $ABC,$ if median $\\overline{AD}$ makes an angle of $45^\\circ$ with side $\\overline{BC},$ then find the value of $|\\cot B - \\cot C|.$",
"role": "user"
}
] | In triangle $ABC,$ if median $\overline{AD}$ makes an angle of $45^\circ$ with side $\overline{BC},$ then find the value of $|\cot B - \cot C|.$ | "[\"2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2343, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16291"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{k}{1-k}for0<k<1"
] | [
"skywork"
] | 6907c33a92a096e24ed9e9b843c9e9cf02e693b19f5411ae09a58956ad5d2668 | [
{
"content": "## Task 6B - 241246B\n\nDetermine all positive real numbers $k$ for which the sequence $\\left(x_{n}\\right)$ defined by\n\n$$\nx_{1}=1, \\quad x_{n+1}=\\sqrt{k\\left(x_{n}^{2}+x_{n}\\right)} \\quad(n=1,2,3, \\ldots)\n$$\n\nis convergent.\n\nFor each such number $k$, determine the limit of the seq... | ## Task 6B - 241246B
Determine all positive real numbers $k$ for which the sequence $\left(x_{n}\right)$ defined by
$$
x_{1}=1, \quad x_{n+1}=\sqrt{k\left(x_{n}^{2}+x_{n}\right)} \quad(n=1,2,3, \ldots)
$$
is convergent.
For each such number $k$, determine the limit of the sequence $\left(x_{n}\right)$. | "[\"\\\\frac{k}{1-k}for0<k<1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2318, "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:16292"}] | {
"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
} |
[
"12"
] | [
"skywork"
] | b3330dc4c83136b5a45f8ab4a139823b1115d6ffcf0688e48122c36e329c6019 | [
{
"content": "We placed 6 different dominoes in a closed chain on the table. The total number of points on the dominoes is $D$. What is the smallest possible value of $D$? (The number of points on each side of the dominoes ranges from 0 to 6, and the number of points must be the same on touching sides of the do... | We placed 6 different dominoes in a closed chain on the table. The total number of points on the dominoes is $D$. What is the smallest possible value of $D$? (The number of points on each side of the dominoes ranges from 0 to 6, and the number of points must be the same on touching sides of the dominoes.) | "[\"12\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2329, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16293"}] | {
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[
"1"
] | [
"skywork"
] | 9f63d54ef0cacdce003bd989bf05f1d3f17892b3134ab55861f3734d81e86f87 | [
{
"content": "11 Find the remainder when $x^{2008}+2008 x+2008$ is divided by $x+1$.",
"role": "user"
}
] | 11 Find the remainder when $x^{2008}+2008 x+2008$ is divided by $x+1$. | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2347, "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:16294"}] | {
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[
"\\text{Penny}"
] | [
"skywork"
] | 2305dd65c24719bb5814aaee0c8e6ed714870cd2d9e2c3bca5859ba0c4d72f64 | [
{
"content": "Joe and Penny play a game. Initially there are $5000$ stones in a pile, and the two players remove stones from the pile by making a sequence of moves. On the $k$-th move, any number of stones between $1$ and $k$ inclusive may be removed. Joe makes the odd-numbered moves and Penny makes the even-nu... | Joe and Penny play a game. Initially there are $5000$ stones in a pile, and the two players remove stones from the pile by making a sequence of moves. On the $k$-th move, any number of stones between $1$ and $k$ inclusive may be removed. Joe makes the odd-numbered moves and Penny makes the even-numbered moves. The play... | "[\"\\\\text{Penny}\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 2322, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16295"}] | {
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[
"1"
] | [
"skywork"
] | 9adcce25e8e1490d362ff52ac07503f63d071bc109e9d9fea8ae449406962148 | [
{
"content": "13. Given constants $a, b$ satisfy $a, b>0, a \\neq 1$, and points $P(a, b), Q(b, a)$ are both on the curve $y=\\cos (x+c)$, where $c$ is a constant. Then $\\log _{a} b=$ $\\qquad$",
"role": "user"
}
] | 13. Given constants $a, b$ satisfy $a, b>0, a \neq 1$, and points $P(a, b), Q(b, a)$ are both on the curve $y=\cos (x+c)$, where $c$ is a constant. Then $\log _{a} b=$ $\qquad$ | "[\"1\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2327, "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:16296"}] | {
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[
"3456"
] | [
"skywork"
] | 087bbf6117c439362163ad4ae5477e108f81b5591f30a6555401e6dd3c88111c | [
{
"content": "The positive integers $x_1$, $x_2$, $\\ldots$, $x_5$, $x_6 = 144$ and $x_7$ are such that $x_{n+3} = x_{n+2}(x_{n+1}+x_n)$ for $n=1,2,3,4$. Determine the value of $x_7$.",
"role": "user"
}
] | The positive integers $x_1$, $x_2$, $\ldots$, $x_5$, $x_6 = 144$ and $x_7$ are such that $x_{n+3} = x_{n+2}(x_{n+1}+x_n)$ for $n=1,2,3,4$. Determine the value of $x_7$. | "[\"3456\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2324, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16297"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"skywork"
] | efe64a14d1d05270a7e7d092e0b8b9a00fd1bd5f062c1a5abfd8f24418941ed6 | [
{
"content": "Let the matrices of order 2 with the real elements $A$ and $B$ so that $AB={{A}^{2}}{{B}^{2}}-{{\\left( AB \\right)}^{2}}$ and $\\det \\left( B \\right)=2$.\na)\tProve that the matrix $A$ is not invertible.\nb)\t Calculate $\\det \\left( A+2B \\right)-\\det \\left( B+2A \\right)$.",
"role": "u... | Let the matrices of order 2 with the real elements $A$ and $B$ so that $AB={{A}^{2}}{{B}^{2}}-{{\left( AB \right)}^{2}}$ and $\det \left( B \right)=2$.
a) Prove that the matrix $A$ is not invertible.
b) Calculate $\det \left( A+2B \right)-\det \left( B+2A \right)$. | "[\"6\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2315, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16298"}] | {
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[
"m = 2 \\text{ and } a_1 \\text{ is a power of two}"
] | [
"skywork"
] | e9883e59d7685e4cc3a0932114134becb63d5b13446e31e94612eb22895e9d2e | [
{
"content": "Let $m$ be a fixed positive integer. The infinite sequence $\\{a_n\\}_{n\\geq 1}$ is defined in the following way: $a_1$ is a positive integer, and for every integer $n\\geq 1$ we have\n$$a_{n+1} = \\begin{cases}a_n^2+2^m & \\text{if } a_n< 2^m \\\\ a_n/2 &\\text{if } a_n\\geq 2^m\\end{cases}$$\nF... | Let $m$ be a fixed positive integer. The infinite sequence $\{a_n\}_{n\geq 1}$ is defined in the following way: $a_1$ is a positive integer, and for every integer $n\geq 1$ we have
$$a_{n+1} = \begin{cases}a_n^2+2^m & \text{if } a_n< 2^m \\ a_n/2 &\text{if } a_n\geq 2^m\end{cases}$$
For each $m$, determine all possible... | "[\"m = 2 \\\\text{ and } a_1 \\\\text{ is a power of two}\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 2301, "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:16299"}] | {
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} |
[
"7"
] | [
"skywork"
] | d3dd5a4afd9145e999e2fef976c0945954e6876322416af140d8870e5fe04198 | [
{
"content": "29. There are 4 cards, each with a different number written on it. The doctor first distributes these 4 cards to four children: Damao, Ermao, Sanmao, and Simaoyi, then collects them back and redistributes them. This process is repeated 3 times. If the sum of the numbers on the cards received by Da... | 29. There are 4 cards, each with a different number written on it. The doctor first distributes these 4 cards to four children: Damao, Ermao, Sanmao, and Simaoyi, then collects them back and redistributes them. This process is repeated 3 times. If the sum of the numbers on the cards received by Damao over the three rou... | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2332, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16300"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"54"
] | [
"skywork"
] | 4c08b6ad61f291be0d0e31866c6b94d4a2006eb792b1090fbc9d16b3aef670de | [
{
"content": "Find the area of a trapezoid with bases 11 and 4 and diagonals 9 and 12.",
"role": "user"
}
] | Find the area of a trapezoid with bases 11 and 4 and diagonals 9 and 12. | "[\"54\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2338, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16301"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"skywork"
] | 12376868273dad922db39f95210b68f9739fda1ad5841fd866dd0f1176d2b3b0 | [
{
"content": "The value of $\\sqrt{3^{3}+3^{3}+3^{3}}$ is\n(A) 3\n(B) 9\n(C) 27\n(D) 81\n(E) 243",
"role": "user"
}
] | The value of $\sqrt{3^{3}+3^{3}+3^{3}}$ is
(A) 3
(B) 9
(C) 27
(D) 81
(E) 243 | "[\"9\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2350, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16302"}] | {
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} |
[
"1"
] | [
"skywork"
] | 05e89d050429b4c88f98e432c7782814095aae79b9f8a4004dddec5e80c09832 | [
{
"content": "153. a) Find all three-digit numbers that are equal to the sum of the factorials of their digits.\n\nb) Find all integers that are equal to the sum of the squares of their digits.",
"role": "user"
}
] | 153. a) Find all three-digit numbers that are equal to the sum of the factorials of their digits.
b) Find all integers that are equal to the sum of the squares of their digits. | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2337, "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:16303"}] | {
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} |
[
"\\frac{15}{4}"
] | [
"skywork"
] | d7612d3773d63fa699ac2329592edf9f46e6e3630b9da769a539252bd30295ea | [
{
"content": "Solve the following equations:\n1. $4x=20$\n2. $x-18=40$\n3. $x\\div7=12$\n4. $8n\\div2=15$",
"role": "user"
}
] | Solve the following equations:
1. $4x=20$
2. $x-18=40$
3. $x\div7=12$
4. $8n\div2=15$ | "[\"\\\\frac{15}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2336, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16304"}] | {
"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
} |
[
"2.4"
] | [
"skywork"
] | 79f1842430e4d1e75ec79619e8b691a7b441f25f5c7d0adb5849e2ec1a0eb8df | [
{
"content": "12.44 In an arithmetic progression, the sixth term is equal to 3, and the difference of the progression is greater than 0.5. For what value of the difference of this progression is the product of the first, fourth, and fifth terms the greatest?",
"role": "user"
}
] | 12.44 In an arithmetic progression, the sixth term is equal to 3, and the difference of the progression is greater than 0.5. For what value of the difference of this progression is the product of the first, fourth, and fifth terms the greatest? | "[\"2.4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2359, "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:16305"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | 5570d1e24fa425e34da9b4906fae84b0d42c89bad18a2df2be53f5a4f9c54836 | [
{
"content": "4. Given the function\n$$\nf(x)=x^{3}-6 x^{2}+17 x-5 \\text {, }\n$$\n\nreal numbers $a, b$ satisfy $f(a)=3, f(b)=23$. Then $a+b=$ $\\qquad$",
"role": "user"
}
] | 4. Given the function
$$
f(x)=x^{3}-6 x^{2}+17 x-5 \text {, }
$$
real numbers $a, b$ satisfy $f(a)=3, f(b)=23$. Then $a+b=$ $\qquad$ | "[\"4\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2334, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16306"}] | {
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} |
[
"1000"
] | [
"skywork"
] | dce1e8877a1c6270c1ef41fecca45009708cae09eea05069efa453fabf0c7748 | [
{
"content": "5. The number of 5-digit natural numbers, divisible by 5 and which have the sum of the first two digits equal to 5, is:\nA. 1000\nB. 3200\nC. 1600\nD. 400\nE. 800",
"role": "user"
}
] | 5. The number of 5-digit natural numbers, divisible by 5 and which have the sum of the first two digits equal to 5, is:
A. 1000
B. 3200
C. 1600
D. 400
E. 800 | "[\"1000\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2353, "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:16307"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"510"
] | [
"skywork"
] | b10095562155265834edc51aced116005467d4f58619c8accfa3a4c8f2915bf3 | [
{
"content": "Mr. Jones teaches algebra. He has a whiteboard with a pre-drawn coordinate grid that runs from $-10$ to $10$ in both the $x$ and $y$ coordinates. Consequently, when he illustrates the graph of a quadratic, he likes to use a quadratic with the following properties:\nI. The quadratic sends intege... | Mr. Jones teaches algebra. He has a whiteboard with a pre-drawn coordinate grid that runs from $-10$ to $10$ in both the $x$ and $y$ coordinates. Consequently, when he illustrates the graph of a quadratic, he likes to use a quadratic with the following properties:
I. The quadratic sends integers to integers.
II. Th... | "[\"510\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2342, "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:16308"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"21"
] | [
"skywork"
] | acff2cbd19f19605eed5d09a07146c53c8d05a6209597258b160c0c1dc4dd93b | [
{
"content": "Each of the integers 226 and 318 have digits whose product is 24 . How many three-digit positive integers have digits whose product is 24 ?\n(A) 4\n(B) 18\n(C) 24\n(D) 12\n(E) 21",
"role": "user"
}
] | Each of the integers 226 and 318 have digits whose product is 24 . How many three-digit positive integers have digits whose product is 24 ?
(A) 4
(B) 18
(C) 24
(D) 12
(E) 21 | "[\"21\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2351, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16309"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"22"
] | [
"skywork"
] | 4918b4711966e722a75b70e2440dcea399810c1c6c086553f628fd0cf90c93a4 | [
{
"content": "What is the value of $6 \\times(5-2)+4$ ?\n(A) 18\n(B) 22\n(C) 24\n(D) 32\n(E) 42",
"role": "user"
}
] | What is the value of $6 \times(5-2)+4$ ?
(A) 18
(B) 22
(C) 24
(D) 32
(E) 42 | "[\"22\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2358, "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:16310"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"-2009"
] | [
"skywork"
] | f54bd401e6265727b3babcc0dc92e1fd862ebad712087b6620f5231ed2954d78 | [
{
"content": "3 If for any $x \\in \\mathbf{R}$, the function $f(x)$ satisfies\n$$\nf(x+2009)=-f(x+2008),\n$$\n\nand $f(2009)=-2009$, then $f(-1)=(\\quad$.\n(A) 1\n(B) -1\n(C) 2009\n(D) -2009",
"role": "user"
}
] | 3 If for any $x \in \mathbf{R}$, the function $f(x)$ satisfies
$$
f(x+2009)=-f(x+2008),
$$
and $f(2009)=-2009$, then $f(-1)=(\quad$.
(A) 1
(B) -1
(C) 2009
(D) -2009 | "[\"-2009\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2341, "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:16311"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"25"
] | [
"skywork"
] | ac93355b6d39553e7ad770a934ffaf36128b370803aa61091680961a91160820 | [
{
"content": "Find the last three digits of the product of the positive roots of $\\sqrt{1995}x^{\\log_{1995}x}=x^2$.",
"role": "user"
}
] | Find the last three digits of the product of the positive roots of $\sqrt{1995}x^{\log_{1995}x}=x^2$. | "[\"25\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2357, "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:16312"}, {"dataset": "skywork", "extra_inf... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"96"
] | [
"skywork"
] | ada9d5fa4a2e2bca951b2388e07c87fe72abb1524dd0ae522e3bee38616a6453 | [
{
"content": "9.2. Electronic clocks display time from 00.00.00 to 23.59.59. How much time during the day does the number on the display that reads the same from left to right and from right to left light up?",
"role": "user"
}
] | 9.2. Electronic clocks display time from 00.00.00 to 23.59.59. How much time during the day does the number on the display that reads the same from left to right and from right to left light up? | "[\"96\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2340, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16313"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{12}"
] | [
"skywork"
] | 001d26fb143bbb4a9713e8e5de635fa5a22098f6358e3d577bceb1c362f881d6 | [
{
"content": "Given the function $f\\left(x\\right)=\\frac{1}{3}a{x}^{3}-\\frac{1}{2}b{x}^{2}+x$, where $a$ and $b$ are the outcomes of rolling two dice consecutively, find the probability that the function $f'\\left( x \\right)$ takes its extreme value at $x=1$.",
"role": "user"
}
] | Given the function $f\left(x\right)=\frac{1}{3}a{x}^{3}-\frac{1}{2}b{x}^{2}+x$, where $a$ and $b$ are the outcomes of rolling two dice consecutively, find the probability that the function $f'\left( x \right)$ takes its extreme value at $x=1$. | "[\"\\\\frac{1}{12}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2330, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:16314"}] | {
"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, -1]"
] | [
"skywork"
] | 1837347df3ddca12ff5412872bf63c346ef35911797dde594c373b36843d9882 | [
{
"content": "For what values of $x$ is $2x^2+8x\\le-6$? Express your answer in interval notation.",
"role": "user"
}
] | For what values of $x$ is $2x^2+8x\le-6$? Express your answer in interval notation. | "[\"[-3, -1]\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2370, "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:16315"}] | {
"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"
] | 1b3630a39f0e9e4ece8e584870651aecfe104d79d1ace2aa48c0daffedf7b585 | [
{
"content": "Calculate the value of the expression $2 \\times 0 + 2 \\times 4$.",
"role": "user"
}
] | Calculate the value of the expression $2 \times 0 + 2 \times 4$. | "[\"8\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2373, "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:16316"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{13}{18}"
] | [
"skywork"
] | 99d837fd765c5793413f61f9e1d94d18e17e2c79d6c3d527e116da2b8cfa66ef | [
{
"content": "Let \\( a_1, a_2, \\dots \\) be a sequence of positive real numbers such that\n\\[ a_n = 7a_{n-1} - 2n \\] for all \\( n > 1 \\). Find the smallest possible value of \\( a_1 \\).",
"role": "user"
}
] | Let \( a_1, a_2, \dots \) be a sequence of positive real numbers such that
\[ a_n = 7a_{n-1} - 2n \] for all \( n > 1 \). Find the smallest possible value of \( a_1 \). | "[\"\\\\frac{13}{18}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2339, "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:16318"}] | {
"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
} |
[
"17"
] | [
"skywork"
] | c7ececf34db7cd09a69723c5656cccac1dacf35cf10746fec1cdebe7acc4e638 | [
{
"content": "The cube shown is divided into 64 small cubes. Exactly one of the cubes is grey, as shown in the diagram. Two cubes are said to be 'neighbours' if they have a common face.\n\nOn the first day, the white neighbours of the grey cube are changed to grey. On the second day, the white neighbours of all... | The cube shown is divided into 64 small cubes. Exactly one of the cubes is grey, as shown in the diagram. Two cubes are said to be 'neighbours' if they have a common face.
On the first day, the white neighbours of the grey cube are changed to grey. On the second day, the white neighbours of all the grey cubes are chan... | "[\"17\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2335, "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:16319"}] | {
"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
} |
[
"f(x) = x + 1"
] | [
"skywork"
] | 906ae57643cfe067e7ca7e264ef8723b058694a18ba68abb0c4f661924b2338a | [
{
"content": "Find all functions $ f : \\mathbb{R} \\rightarrow \\mathbb{R} $ such that\n\\[ f( xf(x) + 2y) = f(x^2)+f(y)+x+y-1 \\]\nholds for all $ x, y \\in \\mathbb{R}$.",
"role": "user"
}
] | Find all functions $ f : \mathbb{R} \rightarrow \mathbb{R} $ such that
\[ f( xf(x) + 2y) = f(x^2)+f(y)+x+y-1 \]
holds for all $ x, y \in \mathbb{R}$. | "[\"f(x) = x + 1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2349, "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:16320"}] | {
"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
} |
[
"757"
] | [
"skywork"
] | d1ca0510898387ac8eb10cd16f1d58f5bab9846113b02d421fc5c2691d83847f | [
{
"content": "Harold, Tanya, and Ulysses paint a very long picket fence.\nHarold starts with the first picket and paints every $h$ th picket;\nTanya starts with the second picket and paints every $t$ th picket; and\nUlysses starts with the third picket and paints every $u$ th picket.\nCall the positive integer ... | Harold, Tanya, and Ulysses paint a very long picket fence.
Harold starts with the first picket and paints every $h$ th picket;
Tanya starts with the second picket and paints every $t$ th picket; and
Ulysses starts with the third picket and paints every $u$ th picket.
Call the positive integer $100h+10t+u$ paintable whe... | "[\"757\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2331, "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:16321"}, {"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
} |
[
"16"
] | [
"skywork"
] | bbab985930e6be8ba12e8fc392d81b62a1b9a81a94791869d1cf362777a7e562 | [
{
"content": "11. (4 points) The perimeter of a rectangle is 48 cm, and it is known that the length is twice the width. The length of the rectangle is ( )\nA. 8 cm\nB. 16 cm\nC. 24 cm",
"role": "user"
}
] | 11. (4 points) The perimeter of a rectangle is 48 cm, and it is known that the length is twice the width. The length of the rectangle is ( )
A. 8 cm
B. 16 cm
C. 24 cm | "[\"16\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2366, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16322"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"skywork"
] | 2e29da7f9844a2dc329f34d353d4606399d12a94266a768aac4f88034b31b101 | [
{
"content": "(14) From the left focus $F$ of the hyperbola $\\frac{x^{2}}{9}-\\frac{y^{2}}{16}=1$, draw a tangent to the circle $x^{2}+y^{2}=9$, with the point of tangency being $T$. Extend $F T$ to intersect the right branch of the hyperbola at point $P$. If $M$ is the midpoint of segment $F P$, and $O$ is th... | (14) From the left focus $F$ of the hyperbola $\frac{x^{2}}{9}-\frac{y^{2}}{16}=1$, draw a tangent to the circle $x^{2}+y^{2}=9$, with the point of tangency being $T$. Extend $F T$ to intersect the right branch of the hyperbola at point $P$. If $M$ is the midpoint of segment $F P$, and $O$ is the origin, find the value... | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2344, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16323"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"28"
] | [
"skywork"
] | 43227abc88827dde6167e6d3c3a59dcf8f5d8c87f072409198e2cdef5cb13e7f | [
{
"content": "Two 3-digit numbers, $a b c$ and def, have the following property:\n\n| $a b c$ |\n| ---: |\n| $+\\quad d \\quad e f$ |\n| 1000 |\n\nNone of $a, b, c, d, e$, or $f$ is 0 . What is $a+b+c+d+e+f$ ?\n(A) 10\n(B) 19\n(C) 21\n(D) 28\n(E) 30",
"role": "user"
}
] | Two 3-digit numbers, $a b c$ and def, have the following property:
| $a b c$ |
| ---: |
| $+\quad d \quad e f$ |
| 1000 |
None of $a, b, c, d, e$, or $f$ is 0 . What is $a+b+c+d+e+f$ ?
(A) 10
(B) 19
(C) 21
(D) 28
(E) 30 | "[\"28\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2364, "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:16324"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{-3-\\sqrt{41}}{2}<x<\\frac{-3+\\sqrt{41}}{2}"
] | [
"skywork"
] | c14a3643e9be04dc118b33211b9e84dd2a6f97bc47296cac3129a1a391b51771 | [
{
"content": "5. The solution set of the inequality $\\left|x^{2}+3 x-8\\right|>x^{2}+3 x-8$ is",
"role": "user"
}
] | 5. The solution set of the inequality $\left|x^{2}+3 x-8\right|>x^{2}+3 x-8$ is | "[\"\\\\frac{-3-\\\\sqrt{41}}{2}<x<\\\\frac{-3+\\\\sqrt{41}}{2}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2346, "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:16325"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
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