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 |
|---|---|---|---|---|---|---|---|---|
[
"P(x) = 1"
] | [
"skywork"
] | b053460f3025132c6d91bec802657bb56a85efd1f695bc86405735ca03a835f6 | [
{
"content": "Find all monic polynomials $P(x)$ such that the polynomial $P(x)^2-1$ is divisible by the polynomial $P(x+1)$.",
"role": "user"
}
] | Find all monic polynomials $P(x)$ such that the polynomial $P(x)^2-1$ is divisible by the polynomial $P(x+1)$. | "[\" P(x) = 1 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107361, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117325"}] | {
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[
"11232_4"
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"skywork"
] | 2464e5481723425ea4e80fd0459251d23777d1ede1d5bc83e72cf54fe63ed36a | [
{
"content": "What is the base 4 representation of the base 2 number $101101110_2$?",
"role": "user"
}
] | What is the base 4 representation of the base 2 number $101101110_2$? | "[\"11232_4\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 107379, "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:117326"}] | {
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[
"1 : 3"
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"skywork"
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{
"content": "A quadrilateral pyramid \\( S A B C D \\) is given, with the base being the parallelogram \\( A B C D \\). A plane is drawn through the midpoint of edge \\( A B \\) that is parallel to the lines \\( A C \\) and \\( S D \\). In what ratio does this plane divide edge \\( S B \\)?",
"role": "user... | A quadrilateral pyramid \( S A B C D \) is given, with the base being the parallelogram \( A B C D \). A plane is drawn through the midpoint of edge \( A B \) that is parallel to the lines \( A C \) and \( S D \). In what ratio does this plane divide edge \( S B \)? | "[\"1 : 3\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107353, "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:117327"}] | {
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[
"27"
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"skywork"
] | 776ff2ab4c80ae86c22de0cef6cec80994e36135f02cfa93932adf8a67d4c487 | [
{
"content": "Problem 4. Let $n$ be a non-zero natural number. We will say that a set $A$ of natural numbers is complete of size $n$ if its elements are non-zero, and the set of all remainders obtained by dividing an element of $A$ by an element of $A$ is $\\{0,1,2, \\ldots, n\\}$. For example, the set $\\{3,4,... | Problem 4. Let $n$ be a non-zero natural number. We will say that a set $A$ of natural numbers is complete of size $n$ if its elements are non-zero, and the set of all remainders obtained by dividing an element of $A$ by an element of $A$ is $\{0,1,2, \ldots, n\}$. For example, the set $\{3,4,5\}$ is a complete set of ... | "[\"27\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107372, "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:117328"}] | {
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[
"\\left(\\frac{\\pi}{4}, \\frac{5 \\pi}{4}\\right)"
] | [
"skywork"
] | 88cc77323b7f01dab9ac077e9e229f7820bc1ad68f8bf524da0045541bbc2806 | [
{
"content": "Example 2 If $\\cos ^{5} \\theta-\\sin ^{5} \\theta<7\\left(\\sin ^{3} \\theta-\\cos ^{3} \\theta\\right)$, where $\\theta \\in[0,2 \\pi)$, then the range of values for $\\theta$ is $\\qquad$ [2]\n(2011, National High School Mathematics Joint Competition)",
"role": "user"
}
] | Example 2 If $\cos ^{5} \theta-\sin ^{5} \theta<7\left(\sin ^{3} \theta-\cos ^{3} \theta\right)$, where $\theta \in[0,2 \pi)$, then the range of values for $\theta$ is $\qquad$ [2]
(2011, National High School Mathematics Joint Competition) | "[\"\\\\left(\\\\frac{\\\\pi}{4}, \\\\frac{5 \\\\pi}{4}\\\\right)\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107368, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:117329"}] | {
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[
"11"
] | [
"skywork"
] | 06c5fe9ec8121273f44f06376b39432e9cb159742cd730f183f63fa361f33614 | [
{
"content": "4. In rectangle $A B C D$, it is known that $A B=5, B C=9$, points $E, F, G, H$ are on sides $A B, B C, C D, D A$ respectively, such that $A E=C G=3, B F=D H=4, P$ is a point inside the rectangle. If the area of quadrilateral $A E P H$ is 15, then the area of quadrilateral $P F C G$ is $\\qquad$",... | 4. In rectangle $A B C D$, it is known that $A B=5, B C=9$, points $E, F, G, H$ are on sides $A B, B C, C D, D A$ respectively, such that $A E=C G=3, B F=D H=4, P$ is a point inside the rectangle. If the area of quadrilateral $A E P H$ is 15, then the area of quadrilateral $P F C G$ is $\qquad$ | "[\"11\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107362, "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:117330"}] | {
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[
"193"
] | [
"skywork"
] | 9a6ce250d96c326d573e48f7e400c1df420e60d828f35c9d5eac6ba8979e5d7f | [
{
"content": "16. (2005 Belarusian Mathematical Olympiad) Let $a, b$ be positive integers such that $79 \\mid(a+77 b)$, and $77 \\mid(a+79 b)$, find the smallest possible value of the sum $a+b$.",
"role": "user"
}
] | 16. (2005 Belarusian Mathematical Olympiad) Let $a, b$ be positive integers such that $79 \mid(a+77 b)$, and $77 \mid(a+79 b)$, find the smallest possible value of the sum $a+b$. | "[\"193\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107382, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117331"}] | {
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[
"\\frac{4\\sin\\alpha(1-\\sin\\alpha)}{(1+\\sin\\alpha)^{2}}"
] | [
"skywork"
] | 65fdc724a03746781857684590f02f7b3ba56235d8f28f97f18cf6774b0a1a8a | [
{
"content": "Given a right circular cone with a semi-aperture angle $\\alpha$. What fraction of the cone's volume is the volume of the sphere inscribed in the cone?",
"role": "user"
}
] | Given a right circular cone with a semi-aperture angle $\alpha$. What fraction of the cone's volume is the volume of the sphere inscribed in the cone? | "[\"\\\\frac{4\\\\sin\\\\alpha(1-\\\\sin\\\\alpha)}{(1+\\\\sin\\\\alpha)^{2}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107373, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117332"}] | {
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[
"57"
] | [
"skywork"
] | 7d712c83642cc65000d95509d14eb185af4e71340378c26d45f81ee21416fa2d | [
{
"content": "For natural numbers $m$ greater than or equal to 2, the decomposition of their cube powers can be represented as follows: $2^3 = 3 + 5$, $3^3 = 7 + 9 + 11$, $4^3 = 13 + 15 + 17 + 19$. Then, \n(1) The smallest number in the decomposition of $8^3$ is; \n(2) Following the above pattern, the $n$-th ... | For natural numbers $m$ greater than or equal to 2, the decomposition of their cube powers can be represented as follows: $2^3 = 3 + 5$, $3^3 = 7 + 9 + 11$, $4^3 = 13 + 15 + 17 + 19$. Then,
(1) The smallest number in the decomposition of $8^3$ is;
(2) Following the above pattern, the $n$-th equation can be represen... | "[\"57\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107347, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:117333"}] | {
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[
"-19"
] | [
"skywork"
] | 173a8192563efe49843457d1db7a721b5d94d00f4e37b91f41833632f53ab20e | [
{
"content": "Problem 7. For what least value of the parameter $a$ will the coefficient of $x^{4}$ in the expansion of the polynomial $\\left(1-2 x+a x^{2}\\right)^{8}$ be equal to $-1540?$",
"role": "user"
}
] | Problem 7. For what least value of the parameter $a$ will the coefficient of $x^{4}$ in the expansion of the polynomial $\left(1-2 x+a x^{2}\right)^{8}$ be equal to $-1540?$ | "[\"-19\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107383, "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:117334"}] | {
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} |
[
"\\frac{1}{2}"
] | [
"skywork"
] | fc0868629587fc97caa25df802fd6e54e16e164764595d00a300500aaeae509b | [
{
"content": "Given an arithmetic sequence $\\{a_n\\}$, if $d < 0$, $T_n$ is the sum of the first $n$ terms of $\\{a_n\\}$, and $T_3=15$, also $a_1+1, a_2+3, a_3+9$ form a geometric sequence with common ratio $q$, calculate the value of $q$.",
"role": "user"
}
] | Given an arithmetic sequence $\{a_n\}$, if $d < 0$, $T_n$ is the sum of the first $n$ terms of $\{a_n\}$, and $T_3=15$, also $a_1+1, a_2+3, a_3+9$ form a geometric sequence with common ratio $q$, calculate the value of $q$. | "[\"\\\\frac{1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107369, "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:117336"}] | {
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} |
[
"\\frac{\\sqrt{3} - \\sqrt{2}}{2}"
] | [
"skywork"
] | a08c48131a9f673da104d7cb2200f6e0119b0141a1da6b3b094624d17412ec58 | [
{
"content": "Calculate the value of \\(\\sin \\left(-\\frac{5 \\pi}{3}\\right) + \\cos \\left(-\\frac{5 \\pi}{4}\\right) + \\tan \\left(-\\frac{11 \\pi}{6}\\right) + \\cot \\left(-\\frac{4 \\pi}{3}\\right)\\).",
"role": "user"
}
] | Calculate the value of \(\sin \left(-\frac{5 \pi}{3}\right) + \cos \left(-\frac{5 \pi}{4}\right) + \tan \left(-\frac{11 \pi}{6}\right) + \cot \left(-\frac{4 \pi}{3}\right)\). | "[\"\\\\frac{\\\\sqrt{3} - \\\\sqrt{2}}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107377, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117337"}] | {
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} |
[
"670"
] | [
"skywork"
] | c41512870a40eed5667a226d996f42caa35c06f19d7ac32dde071dc7700c85a5 | [
{
"content": "Consider all four-digit numbers (including leading zeros) from $0000$ to $9999$. A number is considered balanced if the sum of its two leftmost digits equals the sum of its two rightmost digits. Calculate the total number of such balanced four-digit numbers.",
"role": "user"
}
] | Consider all four-digit numbers (including leading zeros) from $0000$ to $9999$. A number is considered balanced if the sum of its two leftmost digits equals the sum of its two rightmost digits. Calculate the total number of such balanced four-digit numbers. | "[\"670\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107378, "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:117339"}] | {
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} |
[
"\\frac{\\pi^{2}}{6}"
] | [
"skywork"
] | 69f57b5fabe729788b03873835848f2ee877b5eebc6afbec5809b348ad770e5c | [
{
"content": "8. The planar region $S=\\left\\{(x, y) \\mid x, y \\in\\left[0, \\frac{\\pi}{2}\\right], \\sin ^{2} x-\\sin x \\sin y+\\sin ^{2} y \\leqslant \\frac{3}{4}\\right\\}$ has an area equal to",
"role": "user"
}
] | 8. The planar region $S=\left\{(x, y) \mid x, y \in\left[0, \frac{\pi}{2}\right], \sin ^{2} x-\sin x \sin y+\sin ^{2} y \leqslant \frac{3}{4}\right\}$ has an area equal to | "[\"\\\\frac{\\\\pi^{2}}{6}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107375, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117340"}] | {
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} |
[
"\\frac{4}{\\pi}"
] | [
"skywork"
] | e77e4bd64f01e0a3884c3b26c79226c12005c08cc328f6b41d1a0fe9711a9c04 | [
{
"content": "A square and a circle intersect such that each side of the square contains a chord of the circle, and the length of each chord is the diameter of the circle. What is the ratio of the area of the square to the area of the circle?",
"role": "user"
}
] | A square and a circle intersect such that each side of the square contains a chord of the circle, and the length of each chord is the diameter of the circle. What is the ratio of the area of the square to the area of the circle? | "[\"\\\\frac{4}{\\\\pi}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 107393, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117341"}] | {
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[
"\\sqrt{41}"
] | [
"skywork"
] | 3692c8f7565024f428b91db1b3c7d75377fc756c550d0c233995980c781cfc53 | [
{
"content": "Given an ellipse $\\frac{x^2}{25}+\\frac{y^2}{m^2}=1\\left(m \\gt 0\\right)$ with one focus at $F\\left(0,4\\right)$, find $m$.",
"role": "user"
}
] | Given an ellipse $\frac{x^2}{25}+\frac{y^2}{m^2}=1\left(m \gt 0\right)$ with one focus at $F\left(0,4\right)$, find $m$. | "[\"\\\\sqrt{41}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107386, "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:117342"}] | {
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[
"19"
] | [
"skywork"
] | 02a39d65a703f63c8dffd64fb12e3d92d0cfa8b7d3bf535ba261695a9901a499 | [
{
"content": "Among the 95 numbers $1^2, 2^2, 3^2, \\ldots, 95^2$, how many of them have an odd digit in the tens place?",
"role": "user"
}
] | Among the 95 numbers $1^2, 2^2, 3^2, \ldots, 95^2$, how many of them have an odd digit in the tens place? | "[\"19\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107396, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "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:117343"}] | {
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[
"21.333\\%"
] | [
"skywork"
] | ced24de29b12b6a08b8fbdc88fbdd72369b71f2246094322c57fdc2b0c443dcb | [
{
"content": "A solid box is 20 cm by 12 cm by 10 cm. A new solid is formed by removing a cube 4 cm on a side from each corner of this box. What percent of the original volume is removed?",
"role": "user"
}
] | A solid box is 20 cm by 12 cm by 10 cm. A new solid is formed by removing a cube 4 cm on a side from each corner of this box. What percent of the original volume is removed? | "[\"21.333\\\\%\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 107406, "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:117345"}] | {
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} |
[
"194"
] | [
"skywork"
] | fe59f00830c4995f2f43f0a48e21fecbc9cbc0edb398eea5654f7c84e34f2299 | [
{
"content": "17. As shown in Figure 2, in trapezoid $A B C D$, $A B$ $/ / C D, B C=C D=$ $43, A D \\perp B D, A C$ intersects $B D$ at point $O, P$ is the midpoint of $B D, O P=11$. If $A D=m \\sqrt{n}(m, n \\in$ $\\mathbf{Z}_{+}, \\sqrt{n}$ is in simplest radical form), then the value of $m+n$ is ( ).\n(A) 65... | 17. As shown in Figure 2, in trapezoid $A B C D$, $A B$ $/ / C D, B C=C D=$ $43, A D \perp B D, A C$ intersects $B D$ at point $O, P$ is the midpoint of $B D, O P=11$. If $A D=m \sqrt{n}(m, n \in$ $\mathbf{Z}_{+}, \sqrt{n}$ is in simplest radical form), then the value of $m+n$ is ( ).
(A) 65
(B) 132
(C) 157
(D) 194
(E)... | "[\"194\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107367, "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:117346"}] | {
"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
} |
[
"450"
] | [
"skywork"
] | 9083526c5a9ddef64daf221b99b1867cd03e627f1269ee2ce592fe352e370410 | [
{
"content": "4. On the shores of a circular island (viewed from above), there are cities $A, B, C$, and $D$. A straight asphalt road $A C$ divides the island into two equal halves. A straight asphalt road $B D$ is shorter than road $A C$ and intersects it. The speed of a cyclist on any asphalt road is 15 km/h.... | 4. On the shores of a circular island (viewed from above), there are cities $A, B, C$, and $D$. A straight asphalt road $A C$ divides the island into two equal halves. A straight asphalt road $B D$ is shorter than road $A C$ and intersects it. The speed of a cyclist on any asphalt road is 15 km/h. The island also has s... | "[\"450\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107363, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117347"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{2}"
] | [
"skywork"
] | 72072c28ec8c09701aa15c872541d14bb5702b82ebada058505bad2349d10512 | [
{
"content": "Given the hyperbola $$\\frac {x^{2}}{a^{2}} - \\frac {y^{2}}{b^{2}} = 1$$ (a > 0, b > 0), a circle with center at point (b, 0) and radius a is drawn. The circle intersects with one of the asymptotes of the hyperbola at points M and N, and ∠MPN = 90°. Calculate the eccentricity of the hyperbola.",
... | Given the hyperbola $$\frac {x^{2}}{a^{2}} - \frac {y^{2}}{b^{2}} = 1$$ (a > 0, b > 0), a circle with center at point (b, 0) and radius a is drawn. The circle intersects with one of the asymptotes of the hyperbola at points M and N, and ∠MPN = 90°. Calculate the eccentricity of the hyperbola. | "[\"\\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107364, "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:117349"}] | {
"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
} |
[
"80"
] | [
"skywork"
] | fe2860aec77e17c9750f5a4832857dab292ba3697356e79f2a245ed3aedb138d | [
{
"content": "The average cost of a long-distance call in the USA in $1985$ was\n$41$ cents per minute, and the average cost of a long-distance\ncall in the USA in $2005$ was $7$ cents per minute. Find the\napproximate percent decrease in the cost per minute of a long-\ndistance call.",
"role": "user"
}
] | The average cost of a long-distance call in the USA in $1985$ was
$41$ cents per minute, and the average cost of a long-distance
call in the USA in $2005$ was $7$ cents per minute. Find the
approximate percent decrease in the cost per minute of a long-
distance call. | "[\"80\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107415, "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:117350"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"(3)"
] | [
"skywork"
] | 14187785f0aa591a9e6d7e3b7fd0f88e04aa19dfab816f5025be724a4c11477f | [
{
"content": "Given the following four propositions: \n(1) Two lines parallel to the same plane are parallel to each other. \n(2) Two lines perpendicular to the same line are parallel to each other. \n(3) Through a point outside a known plane, there exists exactly one plane parallel to the given plane. \n(4... | Given the following four propositions:
(1) Two lines parallel to the same plane are parallel to each other.
(2) Two lines perpendicular to the same line are parallel to each other.
(3) Through a point outside a known plane, there exists exactly one plane parallel to the given plane.
(4) Through a line outside a... | "[\"(3)\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107389, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117351"}] | {
"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
} |
[
"1011"
] | [
"skywork"
] | f4365630e24a910a0b20dc8f75f3c3e91af28195150eb98f177f054a8ad6a45f | [
{
"content": "Find the largest $k$ for which there exists a permutation $(a_1, a_2, \\ldots, a_{2022})$ of integers from $1$ to $2022$ such that for at least $k$ distinct $i$ with $1 \\le i \\le 2022$ the number $\\frac{a_1 + a_2 + \\ldots + a_i}{1 + 2 + \\ldots + i}$ is an integer larger than $1$.\n\n[i](Propo... | Find the largest $k$ for which there exists a permutation $(a_1, a_2, \ldots, a_{2022})$ of integers from $1$ to $2022$ such that for at least $k$ distinct $i$ with $1 \le i \le 2022$ the number $\frac{a_1 + a_2 + \ldots + a_i}{1 + 2 + \ldots + i}$ is an integer larger than $1$.
[i](Proposed by Oleksii Masalitin)[/i] | "[\"1011\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107392, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:117352"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"21"
] | [
"skywork"
] | 0a228ada296ffdc6e858f643837be30c7984f3b0fb1f6bc67041ab694ba2179a | [
{
"content": "For a nonnegative integer $n$, let $r_9(n)$ be the remainder when $n$ is divided by $9$. Consider all nonnegative integers $n$ for which $r_9(7n) \\leq 5$. Find the $15^{\\text{th}}$ entry in an ordered list of all such $n$.",
"role": "user"
}
] | For a nonnegative integer $n$, let $r_9(n)$ be the remainder when $n$ is divided by $9$. Consider all nonnegative integers $n$ for which $r_9(7n) \leq 5$. Find the $15^{\text{th}}$ entry in an ordered list of all such $n$. | "[\"21\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107390, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:117353"}] | {
"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
} |
[
"60"
] | [
"skywork"
] | 75dbdcef63f0b1aa70d765dcee380bf9c1caa5d1615341ac70fc0409e67430e5 | [
{
"content": "For every dollar Ben spent on pastries, David spent $50$ cents less. Ben paid $20$ more than David. Calculate the amount Ben and David spent together in the pastry shop.",
"role": "user"
}
] | For every dollar Ben spent on pastries, David spent $50$ cents less. Ben paid $20$ more than David. Calculate the amount Ben and David spent together in the pastry shop. | "[\"60\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107391, "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:117354"}] | {
"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{56}{65}"
] | [
"skywork"
] | a7124844a44ec0cf9e2d6791b260b55a6b51addd070eaf5bd5d3a58be773d01a | [
{
"content": "Given that $cos({\\frac{π}{4}-α})=\\frac{3}{5}$, $sin({\\frac{{5π}}{4}+β})=-\\frac{{12}}{{13}}$, $α∈({\\frac{π}{4},\\frac{{3π}}{4}})$, $β∈({0,\\frac{π}{4}})$, calculate the value of $\\sin \\left(\\alpha +\\beta \\right)$.",
"role": "user"
}
] | Given that $cos({\frac{π}{4}-α})=\frac{3}{5}$, $sin({\frac{{5π}}{4}+β})=-\frac{{12}}{{13}}$, $α∈({\frac{π}{4},\frac{{3π}}{4}})$, $β∈({0,\frac{π}{4}})$, calculate the value of $\sin \left(\alpha +\beta \right)$. | "[\"\\\\frac{56}{65}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107385, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117355"}] | {
"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
} |
[
"126.5"
] | [
"skywork"
] | 5ab62e9c38529ee9c0fb47d1c7678fb9b9530e3b15444cc8e81d85adc5143d43 | [
{
"content": "## Task 23/86\n\nAt a New Year's Eve party, there are a total of 23 people present. After midnight, one guest claims that each of the attendees has toasted with exactly eleven people. Verify this claim!",
"role": "user"
}
] | ## Task 23/86
At a New Year's Eve party, there are a total of 23 people present. After midnight, one guest claims that each of the attendees has toasted with exactly eleven people. Verify this claim! | "[\"126.5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107388, "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:117356"}] | {
"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"
] | f3b3f9fe0f3fafe284c1e1f4e4ac56b17070e0eed3166ee3f5710ef9023444d7 | [
{
"content": "Determine the positive integers expressible in the form $\\frac{x^2+y}{xy+1}$, for at least $2$ pairs $(x,y)$ of positive integers",
"role": "user"
}
] | Determine the positive integers expressible in the form $\frac{x^2+y}{xy+1}$, for at least $2$ pairs $(x,y)$ of positive integers | "[\"1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107398, "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:117357"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3\\sqrt{5}"
] | [
"skywork"
] | 8d7bef9789aae06a9351e916e898352909e1ee5b381297de1ec66416e2ee34f4 | [
{
"content": "The height $BL$ of the rhombus $ABCD$, dropped perpendicular to the side $AD$, intersects the diagonal $AC$ at point $E$. Find $AE$ if $BL = 8$ and $AL:LD = 3:2$.",
"role": "user"
}
] | The height $BL$ of the rhombus $ABCD$, dropped perpendicular to the side $AD$, intersects the diagonal $AC$ at point $E$. Find $AE$ if $BL = 8$ and $AL:LD = 3:2$. | "[\"3\\\\sqrt{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107412, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:117358"}] | {
"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
} |
[
"60^{\\circ}"
] | [
"skywork"
] | 25f40c9370f53dd9895a1fc3803480799779f08f94f835db807aba2057ab0a97 | [
{
"content": "4. In $\\triangle A B C$, $A D$ is the median on side $B C$, $A B=\\sqrt{2}$, $A D=\\sqrt{6}$, $A C=\\sqrt{26}$. Then $\\angle A B C=$ $\\qquad$",
"role": "user"
}
] | 4. In $\triangle A B C$, $A D$ is the median on side $B C$, $A B=\sqrt{2}$, $A D=\sqrt{6}$, $A C=\sqrt{26}$. Then $\angle A B C=$ $\qquad$ | "[\"60^{\\\\circ}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107414, "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:117359"}] | {
"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
} |
[
"905"
] | [
"skywork"
] | 7098b7c8edaa1f17fd5fc8b9e97ec67541b6af7ab94d9550da5db1c428db3553 | [
{
"content": "54. There are four different natural numbers, the sum of which is 1991. If it is required that the greatest common divisor of these four numbers is as large as possible, then the largest number among these four numbers is $\\qquad$ .",
"role": "user"
}
] | 54. There are four different natural numbers, the sum of which is 1991. If it is required that the greatest common divisor of these four numbers is as large as possible, then the largest number among these four numbers is $\qquad$ . | "[\"905\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107402, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117360"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | dc8f9863489969a6dc7aef40fb38f6e65683487073f63f6b118ad8099324ba31 | [
{
"content": "1. Given the inequality\n$$\n3 x+4 \\sqrt{x y} \\leqslant a(x+y)\n$$\n\nholds for all positive numbers $x$ and $y$. Then the minimum value of the real number $a$ is . $\\qquad$",
"role": "user"
}
] | 1. Given the inequality
$$
3 x+4 \sqrt{x y} \leqslant a(x+y)
$$
holds for all positive numbers $x$ and $y$. Then the minimum value of the real number $a$ is . $\qquad$ | "[\"4\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107401, "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:117361"}] | {
"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
} |
[
"184320"
] | [
"skywork"
] | 2abeb00f95e223249496caae5829a10ad42315bf4bfcde231611d6e02bed6dbf | [
{
"content": "2. For any natural number $n$, we denote by $p(n)$ the product of the digits of this natural number, written in decimal. Calculate the sum\n\n$$\np(1)+p(2)+\\cdots+p(2001)\n$$",
"role": "user"
}
] | 2. For any natural number $n$, we denote by $p(n)$ the product of the digits of this natural number, written in decimal. Calculate the sum
$$
p(1)+p(2)+\cdots+p(2001)
$$ | "[\"184320\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107400, "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:117362"}] | {
"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
} |
[
"146"
] | [
"skywork"
] | 2d62d68bef83bab225319f7dad5699adeb57980d4982c0024bf39b15db91ba09 | [
{
"content": "Problem 10.8. Two bandits stole 300 gold coins. They decided to divide them as follows: the first bandit puts some coins (possibly all) into a bag, and the second bandit chooses who gets this bag; then this action is repeated several times. The division ends when\n\n- either all the money is gone,... | Problem 10.8. Two bandits stole 300 gold coins. They decided to divide them as follows: the first bandit puts some coins (possibly all) into a bag, and the second bandit chooses who gets this bag; then this action is repeated several times. The division ends when
- either all the money is gone,
- or someone gets 11 ba... | "[\"146\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107395, "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:117363"}] | {
"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
} |
[
"32"
] | [
"skywork"
] | f6c3088b9292a3b9fda587a932d0a7a6ae49506fa5459d8442b91d9f15ff288f | [
{
"content": "Let $f(x)=|2\\{x\\}-1|$ where $\\{x\\}$ denotes the fractional part of $x$. The number $n$ is the smallest positive integer such that the equation \\[nf(xf(x))=x\\] has at least $2012$ real solutions. What is $n$? Note: the fractional part of $x$ is a real number $y=\\{x\\}$ such that $0\\le y<... | Let $f(x)=|2\{x\}-1|$ where $\{x\}$ denotes the fractional part of $x$. The number $n$ is the smallest positive integer such that the equation \[nf(xf(x))=x\] has at least $2012$ real solutions. What is $n$? Note: the fractional part of $x$ is a real number $y=\{x\}$ such that $0\le y<1$ and $x-y$ is an integer.
$\t... | "[\"32\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 107407, "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:117364"}] | {
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[
"1602"
] | [
"skywork"
] | 32204b4a32e162907b3996a94c276fc1f16d3d324782057950afedb8fc94408f | [
{
"content": "Name the smallest four-digit number in which all digits are different and the second digit is 6.",
"role": "user"
}
] | Name the smallest four-digit number in which all digits are different and the second digit is 6. | "[\"1602\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107431, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117365"}] | {
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[
"674"
] | [
"skywork"
] | 19266c01982b7958f8438403e896c6789e60f5415c47f40d84a3a5b534a471ea | [
{
"content": "A tournament among 2021 ranked teams is played over 2020 rounds. In each round, two teams are selected uniformly at random among all remaining teams to play against each other. The better ranked team always wins, and the worse ranked team is eliminated. Let $p$ be the probability that the second b... | A tournament among 2021 ranked teams is played over 2020 rounds. In each round, two teams are selected uniformly at random among all remaining teams to play against each other. The better ranked team always wins, and the worse ranked team is eliminated. Let $p$ be the probability that the second best ranked team is eli... | "[\"674\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107411, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117367"}] | {
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[
"1 : 2"
] | [
"skywork"
] | dabed3ec79b525829191d91302ecb10efa0619294d2bd4d03b89eae4f456627a | [
{
"content": "Let \\(ABC\\) be a triangle such that \\(\\frac{|BC|}{|AB| - |BC|} = \\frac{|AB| + |BC|}{|AC|}\\). Determine the ratio \\(\\angle A : \\angle C\\).",
"role": "user"
}
] | Let \(ABC\) be a triangle such that \(\frac{|BC|}{|AB| - |BC|} = \frac{|AB| + |BC|}{|AC|}\). Determine the ratio \(\angle A : \angle C\). | "[\"1 : 2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107399, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "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:117368"}] | {
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[
"125000"
] | [
"skywork"
] | 7482c5d5651997983d23c99c0f64e882786a84df55b8de444f9aa6b7d8656f5d | [
{
"content": "What is the value of $49^3 + 3(49^2) + 3(49) + 1$?",
"role": "user"
}
] | What is the value of $49^3 + 3(49^2) + 3(49) + 1$? | "[\"125000\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107424, "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:117369"}] | {
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[
"10"
] | [
"skywork"
] | a12238e1d8a95adc01ca0d87f735fa35e440f68487a935baa79f55c1a6ab1f8a | [
{
"content": "8. As shown in Figure $11, \\angle A O B=$ $30^{\\circ}, \\angle A O B$ contains a fixed point $P$, and $O P=10, O A$ has a point $Q, O B$ has a fixed point $R$. If the perimeter of $\\triangle P Q R$ is minimized, find its minimum value.",
"role": "user"
}
] | 8. As shown in Figure $11, \angle A O B=$ $30^{\circ}, \angle A O B$ contains a fixed point $P$, and $O P=10, O A$ has a point $Q, O B$ has a fixed point $R$. If the perimeter of $\triangle P Q R$ is minimized, find its minimum value. | "[\"10\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107405, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117370"}] | {
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[
"14"
] | [
"skywork"
] | bc1687253d5eff292f05f92885b98c33a830231474f86fa7736cb42091ba58c9 | [
{
"content": "7.24 Find the smallest natural number $n$ with the following property: when any 5 vertices of a regular $n$-gon $S$ are painted red, there is always a line of symmetry $l$ of $S$ such that the reflection of each red point across $l$ is not a red point.",
"role": "user"
}
] | 7.24 Find the smallest natural number $n$ with the following property: when any 5 vertices of a regular $n$-gon $S$ are painted red, there is always a line of symmetry $l$ of $S$ such that the reflection of each red point across $l$ is not a red point. | "[\"14\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107409, "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:117371"}] | {
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[
"23,65,34,86"
] | [
"skywork"
] | 9784bdc4b09506b3f89929aa6d7eb91a85683dbde40d2da8bb7cd66b2b7efdec | [
{
"content": "II. (25 points) Given a two-digit number, whose tens and units digits are $p$ and $q$ respectively, the quadratic function $y=x^{2}+q x+p$ intersects the $x$-axis at two distinct points $A$ and $B$, with the vertex at $C$, and $S_{\\triangle A B C} \\leqslant 1$.\n(1) Find the range of $q^{2}-4 p$... | II. (25 points) Given a two-digit number, whose tens and units digits are $p$ and $q$ respectively, the quadratic function $y=x^{2}+q x+p$ intersects the $x$-axis at two distinct points $A$ and $B$, with the vertex at $C$, and $S_{\triangle A B C} \leqslant 1$.
(1) Find the range of $q^{2}-4 p$;
(2) Find all such two-d... | "[\"23,65,34,86\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107384, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117372"}] | {
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[
"2015"
] | [
"skywork"
] | c9b1ea9a4a9639e6fa6d4eb3b736b0f9ac4695bf138efd933b520bc59a9cb115 | [
{
"content": "Example $10 f(x)$ is a continuous function defined on the interval $[0,2015]$, and $f(0)=f(2015)$. Find the minimum number of real number pairs $(x, y)$ that satisfy the following conditions.\n(1) $f(x)=f(y)$;\n(2) $x-y \\in \\mathbf{Z}_{+}$.",
"role": "user"
}
] | Example $10 f(x)$ is a continuous function defined on the interval $[0,2015]$, and $f(0)=f(2015)$. Find the minimum number of real number pairs $(x, y)$ that satisfy the following conditions.
(1) $f(x)=f(y)$;
(2) $x-y \in \mathbf{Z}_{+}$. | "[\"2015\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107413, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117373"}] | {
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[
"1"
] | [
"skywork"
] | 7fced91fd55d0743df3a4786a955748525c495900224632a262c17c05425e35a | [
{
"content": "What is the smallest value of $k$ for which the inequality\n\\begin{align*}\nad-bc+yz&-xt+(a+c)(y+t)-(b+d)(x+z)\\leq \\\\\n&\\leq k\\left(\\sqrt{a^2+b^2}+\\sqrt{c^2+d^2}+\\sqrt{x^2+y^2}+\\sqrt{z^2+t^2}\\right)^2\n\\end{align*}\nholds for any $8$ real numbers $a,b,c,d,x,y,z,t$?\n\nEdit: Fixed a mis... | What is the smallest value of $k$ for which the inequality
\begin{align*}
ad-bc+yz&-xt+(a+c)(y+t)-(b+d)(x+z)\leq \\
&\leq k\left(\sqrt{a^2+b^2}+\sqrt{c^2+d^2}+\sqrt{x^2+y^2}+\sqrt{z^2+t^2}\right)^2
\end{align*}
holds for any $8$ real numbers $a,b,c,d,x,y,z,t$?
Edit: Fixed a mistake! Thanks @below. | "[\"1\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107410, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117374"}] | {
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[
"\\frac{\\sqrt{2}}{2}"
] | [
"skywork"
] | 2133bf3170e86adc4deabed0de447068b1b8067518559672021b00b26265ce71 | [
{
"content": "8. Given real numbers $x, y, z$ satisfy $x^{2}+y^{2}+z^{2}=1$. Then the maximum value of $x y+y z$ is $\\qquad$ .",
"role": "user"
}
] | 8. Given real numbers $x, y, z$ satisfy $x^{2}+y^{2}+z^{2}=1$. Then the maximum value of $x y+y z$ is $\qquad$ . | "[\"\\\\frac{\\\\sqrt{2}}{2}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107425, "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:117375"}] | {
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} |
[
"14"
] | [
"skywork"
] | 9e96062ea0a06c25a89bf71fc2ee037b9d5c640ad8fb6aadba26e650082f7848 | [
{
"content": "14. A census taker stands in front of Aunt Wang's house and asks Aunt Wang: “Your age is 40, what are the ages of the three orphans you adopted?” Aunt Wang says: “The product of their ages equals my age, and the sum of their ages equals our house number.” The census taker looks at the house number... | 14. A census taker stands in front of Aunt Wang's house and asks Aunt Wang: “Your age is 40, what are the ages of the three orphans you adopted?” Aunt Wang says: “The product of their ages equals my age, and the sum of their ages equals our house number.” The census taker looks at the house number and says: “I still ca... | "[\"14\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107403, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117376"}] | {
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[
"2 + \\sqrt{2}"
] | [
"skywork"
] | ee5598ba7adcf63d45bbeaa762031968632c8570f3428b42c5a068b511a1f25a | [
{
"content": "Find the positive root of\n\\[x^3 - 3x^2 - x - \\sqrt{2} = 0.\\]",
"role": "user"
}
] | Find the positive root of
\[x^3 - 3x^2 - x - \sqrt{2} = 0.\] | "[\"2 + \\\\sqrt{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107436, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117377"}] | {
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} |
[
"2"
] | [
"skywork"
] | d5c4055734ded1df0b6d2d16baa57378760c3f51b3f82854cc9bad938e3fd6c9 | [
{
"content": "3. Find the numerical value of the expression\n\n$$\n\\frac{1}{a^{2}+1}+\\frac{1}{b^{2}+1}+\\frac{2}{a b+1}\n$$\n\nif it is known that $a$ is not equal to $b$ and the sum of the first two terms is equal to the third.",
"role": "user"
}
] | 3. Find the numerical value of the expression
$$
\frac{1}{a^{2}+1}+\frac{1}{b^{2}+1}+\frac{2}{a b+1}
$$
if it is known that $a$ is not equal to $b$ and the sum of the first two terms is equal to the third. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107408, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117378"}] | {
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[
"8.45"
] | [
"skywork"
] | 14f3fdfc6d9b7b0a6fac3ad083505a4a6f923cbe6b3efa954460aa6abbea96ff | [
{
"content": "A triangular region is enclosed by the lines with equations $y = \\frac{1}{2} x + 3$, $y = -2x + 6$ and $y = 1$. What is the area of the triangular region? Express your answer as a decimal to the nearest hundredth.",
"role": "user"
}
] | A triangular region is enclosed by the lines with equations $y = \frac{1}{2} x + 3$, $y = -2x + 6$ and $y = 1$. What is the area of the triangular region? Express your answer as a decimal to the nearest hundredth. | "[\"8.45\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107433, "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:117379"}] | {
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} |
[
"f^{-1}(x)=\\frac{5}{2}-\\sqrt{x+\\frac{1}{4}}(x>-\\frac{1}{4})"
] | [
"skywork"
] | cbab46d83171f608b4c880ec558b6ac625f2c24530a61bde8b9cb1898cc977fc | [
{
"content": "(1) Given $f(x+1)=x^{2}-3 x+2, x \\in\\left(-\\infty, \\frac{3}{2}\\right)$, find $f^{-1}(x)$.",
"role": "user"
}
] | (1) Given $f(x+1)=x^{2}-3 x+2, x \in\left(-\infty, \frac{3}{2}\right)$, find $f^{-1}(x)$. | "[\"f^{-1}(x)=\\\\frac{5}{2}-\\\\sqrt{x+\\\\frac{1}{4}}(x>-\\\\frac{1}{4})\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107419, "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:117380"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"13"
] | [
"skywork"
] | 54777e9c3ac9e6858857b6405daec7669ce1b338f03a155792a589bb4da3fea9 | [
{
"content": "A sequence of squares is made of identical square tiles. The edge of each square is one tile length longer than the edge of the previous square. The first three squares are shown. How many more tiles does the seventh square require than the sixth?",
"role": "user"
}
] | A sequence of squares is made of identical square tiles. The edge of each square is one tile length longer than the edge of the previous square. The first three squares are shown. How many more tiles does the seventh square require than the sixth? | "[\"13\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107417, "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:117381"}] | {
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} |
[
"2, 3, \\frac{1}{2}, \\frac{1}{3}"
] | [
"skywork"
] | 6353a27fca8f15718753e31de474aebdc2515c595a5f53451756663b8a45c473 | [
{
"content": "Find the roots of\n\\[6x^4 - 35x^3 + 62x^2 - 35x + 6 = 0.\\]Enter the roots, separated by commas.",
"role": "user"
}
] | Find the roots of
\[6x^4 - 35x^3 + 62x^2 - 35x + 6 = 0.\]Enter the roots, separated by commas. | "[\"2, 3, \\\\frac{1}{2}, \\\\frac{1}{3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107443, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:117382"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | 730b3c254d28af0a34f419c7fe8677db51a4322c7e73de79115f2ef07e008976 | [
{
"content": "One, (40 points) Find the smallest real number $\\lambda$, such that there exists a sequence $\\left\\{a_{n}\\right\\}$ with all terms greater than 1, for which for any positive integer $n$ we have $\\prod_{i=1}^{n+1} a_{i}<a_{n}^{\\lambda}$.",
"role": "user"
}
] | One, (40 points) Find the smallest real number $\lambda$, such that there exists a sequence $\left\{a_{n}\right\}$ with all terms greater than 1, for which for any positive integer $n$ we have $\prod_{i=1}^{n+1} a_{i}<a_{n}^{\lambda}$. | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107421, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:117383"}] | {
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[
"14"
] | [
"skywork"
] | 61821b621cfd1e86e81ebe0484507c694d22de23cc7157b09dd56285990b5254 | [
{
"content": "An amusement park has a series of miniature buildings and landscape models from various places in the United States, scaled at $1: 20$. If the height of the United States Capitol Building is 289 feet, what is the nearest integer height of its model in feet?",
"role": "user"
}
] | An amusement park has a series of miniature buildings and landscape models from various places in the United States, scaled at $1: 20$. If the height of the United States Capitol Building is 289 feet, what is the nearest integer height of its model in feet? | "[\"14\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107444, "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:117384"}] | {
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[
"\\frac{36}{5}"
] | [
"skywork"
] | a141c8f9f9f493a974b3cba2dd7ae79f700b4ad2d38d4a6d0b525d599ac003f5 | [
{
"content": "As shown in the figure, the side length of square $A B C D$ is 4, and the side length of square $C E F G$ is 12. Points $D$, $C$, and $E$ are collinear. Connect $D F$, and draw $G I / / D F$ intersecting the extension of $D A$ at point $I$. Draw $I H \\perp D F$ intersecting $D F$ at point $H$. Th... | As shown in the figure, the side length of square $A B C D$ is 4, and the side length of square $C E F G$ is 12. Points $D$, $C$, and $E$ are collinear. Connect $D F$, and draw $G I / / D F$ intersecting the extension of $D A$ at point $I$. Draw $I H \perp D F$ intersecting $D F$ at point $H$. Then the length of $I H$ ... | "[\"\\\\frac{36}{5}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107418, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117386"}] | {
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[
"210"
] | [
"skywork"
] | 8051b2798507955ef8a97e1896907c9ff82a1c4e750daf00735530561fcf4fa6 | [
{
"content": "David drives from his home to the airport to catch a flight. He drives $35$ miles in the first hour, but realizes that he will be $1$ hour late if he continues at this speed. He increases his speed by $15$ miles per hour for the rest of the way to the airport and arrives $30$ minutes early. How ma... | David drives from his home to the airport to catch a flight. He drives $35$ miles in the first hour, but realizes that he will be $1$ hour late if he continues at this speed. He increases his speed by $15$ miles per hour for the rest of the way to the airport and arrives $30$ minutes early. How many miles is the airpor... | "[\"210\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107430, "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:117387"}] | {
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} |
[
"400\\mathrm{~}^{2}"
] | [
"skywork"
] | 4046db948a663e57bdc7836e100c3b4505381750e1308008cc1165dfe6270b90 | [
{
"content": "17. The square $A B C D$ consists of four congruent rectangles arranged around a central square. The perimeter of each of the rectangles is $40 \\mathrm{~cm}$. What is the area of the square $A B C D$ ?\nA $400 \\mathrm{~cm}^{2}$ B $200 \\mathrm{~cm}^{2} \\mathrm{C} 160 \\mathrm{~cm}^{2} \\mathrm{... | 17. The square $A B C D$ consists of four congruent rectangles arranged around a central square. The perimeter of each of the rectangles is $40 \mathrm{~cm}$. What is the area of the square $A B C D$ ?
A $400 \mathrm{~cm}^{2}$ B $200 \mathrm{~cm}^{2} \mathrm{C} 160 \mathrm{~cm}^{2} \mathrm{D} 120 \mathrm{~cm}^{2} \math... | "[\"400\\\\mathrm{~}^{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107435, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117390"}] | {
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[
"10"
] | [
"skywork"
] | ad5f3ea49429bc426ac518571d01dd9c5b054934330267727f6e30ea45bca430 | [
{
"content": "8. Given that $f(x)$ is an increasing function on $\\mathbf{R}$, and for any $x \\in$ $\\mathbf{R}$, we have\n$$\nf\\left(f(x)-3^{x}\\right)=4 .\n$$\n\nThen $f(2)=$",
"role": "user"
}
] | 8. Given that $f(x)$ is an increasing function on $\mathbf{R}$, and for any $x \in$ $\mathbf{R}$, we have
$$
f\left(f(x)-3^{x}\right)=4 .
$$
Then $f(2)=$ | "[\"10\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107427, "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:117391"}] | {
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[
"2"
] | [
"skywork"
] | 12494b1f74dca80064e9a234f80f29aa25965393a22a543164fb962ab051ba3c | [
{
"content": "Let $f\\left(x\\right)=x^2-14x+52$ and $g\\left(x\\right)=ax+b$, where $a$ and $b$ are positive. Find $a$, given that $f\\left(g\\left(-5\\right)\\right)=3$ and $f\\left(g\\left(0\\right)\\right)=103$.\n\n$\\text{(A) }2\\qquad\\text{(B) }5\\qquad\\text{(C) }7\\qquad\\text{(D) }10\\qquad\\text{(E) ... | Let $f\left(x\right)=x^2-14x+52$ and $g\left(x\right)=ax+b$, where $a$ and $b$ are positive. Find $a$, given that $f\left(g\left(-5\right)\right)=3$ and $f\left(g\left(0\right)\right)=103$.
$\text{(A) }2\qquad\text{(B) }5\qquad\text{(C) }7\qquad\text{(D) }10\qquad\text{(E) }17$ | "[\"2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107423, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117392"}] | {
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[
"2021"
] | [
"skywork"
] | da721d8ad0c8720cba2e411501d56ad72ddc5598bb4affaa2b99e12f2388093f | [
{
"content": "1. Calculate: $\\frac{202120212019 \\cdot 202120212021 \\cdot 202120212023}{100010001 \\cdot\\left(202120212021^{2}-4\\right)}$.",
"role": "user"
}
] | 1. Calculate: $\frac{202120212019 \cdot 202120212021 \cdot 202120212023}{100010001 \cdot\left(202120212021^{2}-4\right)}$. | "[\"2021\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107442, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "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:117393"}] | {
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} |
[
"3"
] | [
"skywork"
] | 417a7d27057d289d7874634ca4c45070e03dd941dbdcf9f492ca44d7bf312161 | [
{
"content": "(1) If the circumcenter of $\\triangle A B O$ lies on the ellipse, find the value of the real number $p$;\n(2) If the circumcircle of $\\triangle A B O$ passes through the point $N\\left(0, \\frac{13}{2}\\right)$, find the value of the real number $p$.\n11. (20 points) As shown in Figure 4, the el... | (1) If the circumcenter of $\triangle A B O$ lies on the ellipse, find the value of the real number $p$;
(2) If the circumcircle of $\triangle A B O$ passes through the point $N\left(0, \frac{13}{2}\right)$, find the value of the real number $p$.
11. (20 points) As shown in Figure 4, the ellipse $C_{1}: \frac{x^{2}}{4}... | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107397, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117394"}] | {
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[
"31"
] | [
"skywork"
] | 05c9fc37f0942c4576445022cfcb61f72cdc3f6b38a0f1f133315530b6655ada | [
{
"content": "Consider a terminal with fifteen gates arranged in a straight line with exactly $90$ feet between adjacent gates. A passenger's departure gate is assigned at random. Later, the gate is changed to another randomly chosen gate. Calculate the probability that the passenger walks $360$ feet or less to... | Consider a terminal with fifteen gates arranged in a straight line with exactly $90$ feet between adjacent gates. A passenger's departure gate is assigned at random. Later, the gate is changed to another randomly chosen gate. Calculate the probability that the passenger walks $360$ feet or less to the new gate. Express... | "[\"31\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107437, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117395"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"150"
] | [
"skywork"
] | dc8524296e7e1f21b84e477f567fd4575b62260b58d7f76e305c19870e5eb4ab | [
{
"content": "The distances between the points are given as $A B = 30$, $B C = 80$, $C D = 236$, $D E = 86$, $E A = 40$. What is the distance $E C$?",
"role": "user"
}
] | The distances between the points are given as $A B = 30$, $B C = 80$, $C D = 236$, $D E = 86$, $E A = 40$. What is the distance $E C$? | "[\"150\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107428, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117396"}] | {
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} |
[
"\\frac{1}{650}"
] | [
"skywork"
] | 195865421a15bce08f522c739c68635f73d3855bf30822e68bae672cd7dde94d | [
{
"content": "Three cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is an Ace, the second card is a diamond, and the third card is a Jack?",
"role": "user"
}
] | Three cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is an Ace, the second card is a diamond, and the third card is a Jack? | "[\"\\\\frac{1}{650}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107438, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117397"}] | {
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"reference_components": 1,
"reference_present": true
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[
"4756"
] | [
"skywork"
] | e5de47c282275ec32fbd79e78e6d60c10c4366f5f4d16f7571df5978ff436885 | [
{
"content": "Work base 3. (so each digit is 0,1,2)\r\n\r\nA good number of size $n$ is a number in which there are no consecutive $1$'s and no consecutive $2$'s. How many good 10-digit numbers are there?",
"role": "user"
}
] | Work base 3. (so each digit is 0,1,2)
A good number of size $n$ is a number in which there are no consecutive $1$'s and no consecutive $2$'s. How many good 10-digit numbers are there? | "[\"4756\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107439, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117398"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 702e12bf9ba2dd07c919c33ae8493238a1f5a86383706be85250c00c1b966e56 | [
{
"content": "40. The angle $A$ at the vertex of the isosceles triangle $A B C$ is $100^{\\circ}$. On the ray $A B$, a segment $A M$ is laid off, equal to the base $B C$. Find the measure of angle $B C M$.",
"role": "user"
}
] | 40. The angle $A$ at the vertex of the isosceles triangle $A B C$ is $100^{\circ}$. On the ray $A B$, a segment $A M$ is laid off, equal to the base $B C$. Find the measure of angle $B C M$. | "[\"10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107448, "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:117400"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2.1:3.8:1"
] | [
"skywork"
] | 9f985fd095f1d5aecf33a05d9ea7bd692039f8d1333cc43a7bb7214abb9f742b | [
{
"content": "## Task 2 - V10722\n\nThe route from Berlin to Karl-Marx-Stadt is served by Deutsche Lufthansa with aircraft of the AN 2 type. The aircraft takes off from Berlin at 09:45 and lands after 220 flight kilometers at 11:00 in Karl-Marx-Stadt.\n\nAn aircraft of the IL 14 P type takes off from Leipzig at... | ## Task 2 - V10722
The route from Berlin to Karl-Marx-Stadt is served by Deutsche Lufthansa with aircraft of the AN 2 type. The aircraft takes off from Berlin at 09:45 and lands after 220 flight kilometers at 11:00 in Karl-Marx-Stadt.
An aircraft of the IL 14 P type takes off from Leipzig at 12:30 and lands in Barth ... | "[\"2.1:3.8:1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107440, "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:117402"}] | {
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} |
[
"1755"
] | [
"skywork"
] | 2047842d66174291d821167c7544694041484a8a131771b8e2f229aad67c19f4 | [
{
"content": "To actively create a \"demonstration school for the prevention and control of myopia in children and adolescents in the city\" and cultivate students' good eye habits, a certain school conducted a competition on correct eye knowledge this semester. $20$ student answer sheets were randomly selected... | To actively create a "demonstration school for the prevention and control of myopia in children and adolescents in the city" and cultivate students' good eye habits, a certain school conducted a competition on correct eye knowledge this semester. $20$ student answer sheets were randomly selected and their scores (denot... | "[\"1755\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107420, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:117403"}] | {
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} |
[
"24068"
] | [
"skywork"
] | 8df81a225303c93e50c2f0ee8d9d958fd060d28f7744438eeaabee628c58a205 | [
{
"content": "22. Given ten 0's and ten 1's, how many 0-1 binary sequences can be formed such that no three or more than three 0's are together? For example, 01001001010011101011 is such a sequence, but the sequence 01001000101001110111 does not satisfy this condition.",
"role": "user"
}
] | 22. Given ten 0's and ten 1's, how many 0-1 binary sequences can be formed such that no three or more than three 0's are together? For example, 01001001010011101011 is such a sequence, but the sequence 01001000101001110111 does not satisfy this condition. | "[\"24068\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107456, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117404"}] | {
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[
"-\\frac{15}{4}"
] | [
"skywork"
] | d06405986f076f39ef82caef770c867dce5e7091c296ec8563102271f0f71b6f | [
{
"content": "2. Given two linear functions $f(x)$ and $g(x)$ such that the graphs $y=f(x)$ and $y=g(x)$ are parallel lines, not parallel to the coordinate axes. Find the minimum value of the function $2(g(x))^{2}-$ $f(x)$, if the minimum value of the function $2(f(x))^{2}-g(x)$ is $\\frac{7}{2}$.",
"role":... | 2. Given two linear functions $f(x)$ and $g(x)$ such that the graphs $y=f(x)$ and $y=g(x)$ are parallel lines, not parallel to the coordinate axes. Find the minimum value of the function $2(g(x))^{2}-$ $f(x)$, if the minimum value of the function $2(f(x))^{2}-g(x)$ is $\frac{7}{2}$. | "[\"-\\\\frac{15}{4}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107416, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117405"}] | {
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[
"2035"
] | [
"skywork"
] | a75483d65461fd64dbb28c818a55e2aecdc94b44b133f81f13a6247fbbd58620 | [
{
"content": "Given a sequence $\\{a_n\\}$ satisfying $a_1=1$, $a_n=\\log_n(n+1)$ $(n\\geqslant 2,n\\in \\mathbb{N}^*)$, define: $k$ $(k\\in \\mathbb{N}^*)$ that makes the product $a_1\\cdot a_2\\cdot \\cdots \\cdot a_k$ an integer as \"simple number\". Then, the sum of all \"simple numbers\" within the interva... | Given a sequence $\{a_n\}$ satisfying $a_1=1$, $a_n=\log_n(n+1)$ $(n\geqslant 2,n\in \mathbb{N}^*)$, define: $k$ $(k\in \mathbb{N}^*)$ that makes the product $a_1\cdot a_2\cdot \cdots \cdot a_k$ an integer as "simple number". Then, the sum of all "simple numbers" within the interval $[3,2013]$ is. | "[\"2035\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107441, "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:117406"}] | {
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[
"1033"
] | [
"skywork"
] | 9820451c9e61c3cb2649e8979cd26be025f6b26763cfb06b749e5b371c094340 | [
{
"content": "8. Given the function $f:\\{0,1, \\cdots, 2010\\} \\rightarrow \\mathbf{N}$. If for all possible integers $x$, we have\n$$\n\\begin{array}{l}\nf(4 x+2)=f(4 x+1), \\\\\nf(5 x+3)=f(5 x+2), \\\\\nf(7 x+5)=f(7 x+4),\n\\end{array}\n$$\n\nthen $f(x)$ can take at most $\\qquad$ different values.",
"r... | 8. Given the function $f:\{0,1, \cdots, 2010\} \rightarrow \mathbf{N}$. If for all possible integers $x$, we have
$$
\begin{array}{l}
f(4 x+2)=f(4 x+1), \\
f(5 x+3)=f(5 x+2), \\
f(7 x+5)=f(7 x+4),
\end{array}
$$
then $f(x)$ can take at most $\qquad$ different values. | "[\"1033\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107449, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117407"}] | {
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[
"2\\pi-4"
] | [
"skywork"
] | ee5a072d061b350fb22b512eb609c56cbd74097f9002f987f0efc66f113119c4 | [
{
"content": "11.8 Find the area of the figure defined on the coordinate plane by the inequality $x^{2}+y^{2} \\leq 2(|x|-|y|)$.",
"role": "user"
}
] | 11.8 Find the area of the figure defined on the coordinate plane by the inequality $x^{2}+y^{2} \leq 2(|x|-|y|)$. | "[\"2\\\\pi-4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107466, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117409"}] | {
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[
"1,2,3,5"
] | [
"skywork"
] | d730ba92eec5e980710e232b5e336e43a5d0416815dd1acba88b98dabf2412bb | [
{
"content": "8-7. Petya thought of four different digits, not equal to 0. Then he formed all possible four-digit numbers from these digits without repeating any digits. The sum of all these numbers turned out to be 73326. What 4 digits did Petya think of?",
"role": "user"
}
] | 8-7. Petya thought of four different digits, not equal to 0. Then he formed all possible four-digit numbers from these digits without repeating any digits. The sum of all these numbers turned out to be 73326. What 4 digits did Petya think of? | "[\"1,2,3,5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107457, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117410"}] | {
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} |
[
"90"
] | [
"skywork"
] | 882385f21d456ea9188c52ab19f90730bb1af599cb2ba7921ba3781796c3f08e | [
{
"content": "Let $f(n) = \\sum^n_{d=1} \\left\\lfloor \\frac{n}{d} \\right\\rfloor$ and $g(n) = f(n) -f(n - 1)$. For how many $n$ from $1$ to $100$ inclusive is $g(n)$ even?",
"role": "user"
}
] | Let $f(n) = \sum^n_{d=1} \left\lfloor \frac{n}{d} \right\rfloor$ and $g(n) = f(n) -f(n - 1)$. For how many $n$ from $1$ to $100$ inclusive is $g(n)$ even? | "[\"90\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107454, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117411"}] | {
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} |
[
"d_1=-1,d_2=2"
] | [
"skywork"
] | ba444d1636d5197c309900343eb2ea37b98133f059b952961044fb96eb7cbbac | [
{
"content": "## Task $7 / 82$\n\nLet $a ; b ; c ; d$ be four non-zero real numbers for which the equations\n\n$$\n\\frac{a+b}{c}=\\frac{a+c}{b}=\\frac{b+c}{a}=d\n$$\n\nhold. Determine all possible values of $d$.",
"role": "user"
}
] | ## Task $7 / 82$
Let $a ; b ; c ; d$ be four non-zero real numbers for which the equations
$$
\frac{a+b}{c}=\frac{a+c}{b}=\frac{b+c}{a}=d
$$
hold. Determine all possible values of $d$. | "[\"d_1=-1,d_2=2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107445, "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:117412"}] | {
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} |
[
"90^\\circ"
] | [
"skywork"
] | b0b3572ebf6967eecf80f4450204f88d5320195dbe47dc7b374f8c53b975fd29 | [
{
"content": "About pentagon $ABCDE$ is known that angle $A$ and angle $C$ are right and that the sides $| AB | = 4$, $| BC | = 5$, $| CD | = 10$, $| DE | = 6$. Furthermore, the point $C'$ that appears by mirroring $C$ in the line $BD$, lies on the line segment $AE$. Find angle $E$.",
"role": "user"
}
] | About pentagon $ABCDE$ is known that angle $A$ and angle $C$ are right and that the sides $| AB | = 4$, $| BC | = 5$, $| CD | = 10$, $| DE | = 6$. Furthermore, the point $C'$ that appears by mirroring $C$ in the line $BD$, lies on the line segment $AE$. Find angle $E$. | "[\"90^\\\\circ\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107450, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "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:117413"}] | {
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} |
[
"10,017"
] | [
"skywork"
] | 85f0db293c6e15802c2293f4e3d9f4e266b956b8209bf890bb002530b0aff69e | [
{
"content": "What is the least five-digit positive integer which is congruent to 6 (mod 17)?",
"role": "user"
}
] | What is the least five-digit positive integer which is congruent to 6 (mod 17)? | "[\"10,017\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107468, "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:117414"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"500"
] | [
"skywork"
] | ef573f5f404dc8d80885b21915f77397f24944c54eb9124c2513d3419a9cc9cc | [
{
"content": "7. Find the number of consecutive 0 's at the end of the base 10 representation of 2006 !.",
"role": "user"
}
] | 7. Find the number of consecutive 0 's at the end of the base 10 representation of 2006 !. | "[\"500\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107464, "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:117415"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"93"
] | [
"skywork"
] | 64ec33d994df550ac70d584ab4f717e692195047314ac4e83114bfdcf2621c3a | [
{
"content": "Let $S$ be the set of positive integers $N$ with the property that the last four digits of $N$ are $2020,$ and when the last four digits are removed, the result is a divisor of $N.$ For example, $42{,}020$ is in $S$ because $4$ is a divisor of $42{,}020.$ Find the sum of all the digits of all the ... | Let $S$ be the set of positive integers $N$ with the property that the last four digits of $N$ are $2020,$ and when the last four digits are removed, the result is a divisor of $N.$ For example, $42{,}020$ is in $S$ because $4$ is a divisor of $42{,}020.$ Find the sum of all the digits of all the numbers in $S.$ For ex... | "[\"93\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 107458, "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:117416"}] | {
"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
} |
[
"14"
] | [
"skywork"
] | 91abd1e84140d7a1aeacc744894bd0b342dd1173a71b48de0eb28b11b5154017 | [
{
"content": "Anna thinks of an integer that is not a multiple of three, not a perfect square, and the sum of its digits is a prime number. What could the integer be?",
"role": "user"
}
] | Anna thinks of an integer that is not a multiple of three, not a perfect square, and the sum of its digits is a prime number. What could the integer be? | "[\"14\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107459, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117417"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 7b3e140d3b32d454b677da24bba5bef74667d22988bc2226587e32956649e06b | [
{
"content": "Berk tries to guess the two-digit number that Ayca picks. After each guess, Ayca gives a hint indicating the number of digits which match the number picked. If Berk can guarantee to guess Ayca's number in $n$ guesses, what is the smallest possible value of $n$?\n\n$ \n\\textbf{(A)}\\ 9\n\\qquad\\t... | Berk tries to guess the two-digit number that Ayca picks. After each guess, Ayca gives a hint indicating the number of digits which match the number picked. If Berk can guarantee to guess Ayca's number in $n$ guesses, what is the smallest possible value of $n$?
$
\textbf{(A)}\ 9
\qquad\textbf{(B)}\ 10
\qquad\textbf{(... | "[\"10\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107455, "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:117419"}] | {
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} |
[
"1"
] | [
"skywork"
] | 66114af0cd1773ebb48cbaf71252e01343efdf873e8e39758961a9f5414c45da | [
{
"content": "In a certain mathematics competition, there are 6 problems, each worth 7 points (the final score for each problem is an integer, with a minimum of 0 points and a maximum of 7 points). Each contestant's total score is the product of the scores of the 6 problems. If two contestants have the same sco... | In a certain mathematics competition, there are 6 problems, each worth 7 points (the final score for each problem is an integer, with a minimum of 0 points and a maximum of 7 points). Each contestant's total score is the product of the scores of the 6 problems. If two contestants have the same score, the sum of the sco... | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107447, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "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:117420"}] | {
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} |
[
"20"
] | [
"skywork"
] | f7f6375d2df8e1e0d4a0188464b242ea96928cba0ad0e8f6864b28e9863b4dec | [
{
"content": "For how many $n=2,3,4,\\ldots,99,100$ is the base-$n$ number $215216_n$ a multiple of $5$?",
"role": "user"
}
] | For how many $n=2,3,4,\ldots,99,100$ is the base-$n$ number $215216_n$ a multiple of $5$? | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107473, "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:117421"}] | {
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} |
[
"a"
] | [
"skywork"
] | 9868942afe795b6935ebe713f769a5e74ae6ddbdbfabb8882805cbf5cbf18fe3 | [
{
"content": "10.319. The diagonals of an isosceles trapezoid are perpendicular to each other, and its area is $a^{2}$. Determine the height of the trapezoid.",
"role": "user"
}
] | 10.319. The diagonals of an isosceles trapezoid are perpendicular to each other, and its area is $a^{2}$. Determine the height of the trapezoid. | "[\"a\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107460, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 1, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117422"}] | {
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} |
[
"7"
] | [
"skywork"
] | bd81e90458c06fd74a2862142e14e810c26eea31fbd5c7ef57c6264c63ade493 | [
{
"content": "Find all positive integers $n$, such that $n-1$ and $\\frac{n(n+1)}{2}$ are both perfect numbers.",
"role": "user"
}
] | Find all positive integers $n$, such that $n-1$ and $\frac{n(n+1)}{2}$ are both perfect numbers. | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107467, "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:117423"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"skywork"
] | dac1ab6d32a7f6a881cd3c194ede1eb7d0e6707cefb7341c79ec4e46693b63dd | [
{
"content": "For what value of $n$ is the five-digit number $\\underline{7n933}$ divisible by 33? (Note: the underlining is meant to indicate that the number should be interpreted as a five-digit number whose ten thousands digit is 7, whose thousands digit is $n$, and so on).",
"role": "user"
}
] | For what value of $n$ is the five-digit number $\underline{7n933}$ divisible by 33? (Note: the underlining is meant to indicate that the number should be interpreted as a five-digit number whose ten thousands digit is 7, whose thousands digit is $n$, and so on). | "[\"5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107484, "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:117424"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"(-\\infty,-2]"
] | [
"skywork"
] | 2a79cf0c9b65b5462a61868da43365ee29473cf68d21a83b8de533e30e0ccf67 | [
{
"content": "12. The range of negative values of $a$ that make the inequality $\\sin ^{2} x+a \\cos x+a^{2} \\geqslant 1+\\cos x$ hold for all $x \\in \\mathbf{R}$ is $\\qquad$",
"role": "user"
}
] | 12. The range of negative values of $a$ that make the inequality $\sin ^{2} x+a \cos x+a^{2} \geqslant 1+\cos x$ hold for all $x \in \mathbf{R}$ is $\qquad$ | "[\"(-\\\\infty,-2]\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107482, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "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:117425"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | c9ebd94ec6c14eb4cebb3ec8b8814a00e6e615282cd010a4a8a422074f551458 | [
{
"content": "9.2. On a line, there are blue and red points, with no fewer than 5 red points. It is known that on any segment with endpoints at red points, containing a red point inside, there are at least 4 blue points. And on any segment with endpoints at blue points, containing 3 blue points inside, there ar... | 9.2. On a line, there are blue and red points, with no fewer than 5 red points. It is known that on any segment with endpoints at red points, containing a red point inside, there are at least 4 blue points. And on any segment with endpoints at blue points, containing 3 blue points inside, there are at least 2 red point... | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107465, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117426"}] | {
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"reference_components": 1,
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[
"11"
] | [
"skywork"
] | 578652eef05aefacaedf4e8bea6a9189fe1d2e2c295c886734c6a20b6729ac50 | [
{
"content": "Consider a rectangle $ABCD$ containing three squares. Two smaller squares each occupy a part of rectangle $ABCD$, and each smaller square has an area of 1 square inch. A larger square, also inside rectangle $ABCD$ and not overlapping with the smaller squares, has a side length three times that of ... | Consider a rectangle $ABCD$ containing three squares. Two smaller squares each occupy a part of rectangle $ABCD$, and each smaller square has an area of 1 square inch. A larger square, also inside rectangle $ABCD$ and not overlapping with the smaller squares, has a side length three times that of one of the smaller squ... | "[\"11\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107483, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:117427"}] | {
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"plain_numeric_reference": true,
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[
"0 \\le k \\le 2"
] | [
"skywork"
] | 19f05fdb3a489c8f363a4cee7cb96f7f6ed00186ff219977a8df544fa09cb671 | [
{
"content": "a) Find all real numbers $k$ such that there exists a positive constant $c_k$ satisfying $$(x^2 + 1)(y^2 + 1)(z^2 + 1) \\ge c_k(x + y + z)^k$$ for all positive real numbers. \n\nb) Given the numbers $k$ found, determine the largest number $c_k$.",
"role": "user"
}
] | a) Find all real numbers $k$ such that there exists a positive constant $c_k$ satisfying $$(x^2 + 1)(y^2 + 1)(z^2 + 1) \ge c_k(x + y + z)^k$$ for all positive real numbers.
b) Given the numbers $k$ found, determine the largest number $c_k$. | "[\" 0 \\\\le k \\\\le 2 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107470, "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:117428"}] | {
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} |
[
"224"
] | [
"skywork"
] | b261625be55eb003cf0f53fc894ac5ae98f32fce43a2f51f3df27a85227a2fbd | [
{
"content": "## 8. Wooden Numbers\n\nLittle Marko is playing with numbers made of wood. He has two number 1s, seven number 2s, and one number 3. He wants to string them together one by one so that the numbers 1 and 3 are not adjacent. How many different ten-digit numbers can Marko get this way?\n\nResult: $\\q... | ## 8. Wooden Numbers
Little Marko is playing with numbers made of wood. He has two number 1s, seven number 2s, and one number 3. He wants to string them together one by one so that the numbers 1 and 3 are not adjacent. How many different ten-digit numbers can Marko get this way?
Result: $\quad \mathbf{2 2 4}$ | "[\"224\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107475, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117429"}] | {
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"reference_components": 1,
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} |
[
"650"
] | [
"skywork"
] | 906ccef25969a602834aea919c66b6a024ce15677c7031d11d2b75c8c9a450d7 | [
{
"content": "Find the remainder when $1^{2}+3^{2}+5^{2}+\\cdots+99^{2}$ is divided by 1000.",
"role": "user"
}
] | Find the remainder when $1^{2}+3^{2}+5^{2}+\cdots+99^{2}$ is divided by 1000. | "[\"650\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107490, "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:117430"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{9}{8}"
] | [
"skywork"
] | 13cf061ac4119eab302f03b9a22978ad25aceb43a6c7530ca167bd9386a4354f | [
{
"content": "Question 69, The quadratic function $f(x)=x^{2}+m x+n$ has real roots, the inequality $s \\leq(m-1)^{2}+(n-1)^{2}+$ $(m-n)^{2}$ holds for any quadratic function satisfying the above condition, then the maximum value of $s$ is $\\qquad$ _.",
"role": "user"
}
] | Question 69, The quadratic function $f(x)=x^{2}+m x+n$ has real roots, the inequality $s \leq(m-1)^{2}+(n-1)^{2}+$ $(m-n)^{2}$ holds for any quadratic function satisfying the above condition, then the maximum value of $s$ is $\qquad$ _. | "[\"\\\\frac{9}{8}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107451, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:117431"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1994"
] | [
"skywork"
] | 9b17ffc66f6e49b09e4576c2eb803f9ef3e99abe4390c5010ad17b894e7596ad | [
{
"content": "Numbering the pages of an encyclopedia required 6869 digits. How many pages does it contain?",
"role": "user"
}
] | Numbering the pages of an encyclopedia required 6869 digits. How many pages does it contain? | "[\"1994\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107476, "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:117434"}] | {
"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
} |
[
"84"
] | [
"skywork"
] | dca7e0053ea4293d33bdc4114ab099cf1c63321ac95d8fdf2da9b66a5a1020ef | [
{
"content": "A street has 20 houses on each side, for a total of 40 houses. The addresses on the south side of the street form an arithmetic sequence, as do the addresses on the north side of the street. On the south side, the addresses are 4, 10, 16, etc., and on the north side they are 3, 9, 15, etc. A sign ... | A street has 20 houses on each side, for a total of 40 houses. The addresses on the south side of the street form an arithmetic sequence, as do the addresses on the north side of the street. On the south side, the addresses are 4, 10, 16, etc., and on the north side they are 3, 9, 15, etc. A sign painter paints house n... | "[\"84\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107471, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:117435"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"-\\frac{8}{3}"
] | [
"skywork"
] | ee41473a308f787e3c7dc1aada9ae20157d5aa7013ba5897ab0505150921458e | [
{
"content": "6. Given in $\\triangle A B C$, $\\angle B A C=\\frac{2 \\pi}{3}, A B=2, A C=1, D$ is a point on side $B C$, $D C=2 B D$, then $\\overrightarrow{A D} \\cdot \\overrightarrow{B C}=$ $\\qquad$ -",
"role": "user"
}
] | 6. Given in $\triangle A B C$, $\angle B A C=\frac{2 \pi}{3}, A B=2, A C=1, D$ is a point on side $B C$, $D C=2 B D$, then $\overrightarrow{A D} \cdot \overrightarrow{B C}=$ $\qquad$ - | "[\"-\\\\frac{8}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107486, "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:117436"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"(n, m, p) = (\\pm 2, \\pm 3, 2)"
] | [
"skywork"
] | 6130e155be84377c77419b2f06bd154205bc8f8220b12e6f1d45cf2650d10226 | [
{
"content": "Determine all triples $(m , n , p)$ satisfying :\n\\[n^{2p}=m^2+n^2+p+1\\]\nwhere $m$ and $n$ are integers and $p$ is a prime number.",
"role": "user"
}
] | Determine all triples $(m , n , p)$ satisfying :
\[n^{2p}=m^2+n^2+p+1\]
where $m$ and $n$ are integers and $p$ is a prime number. | "[\" (n, m, p) = (\\\\pm 2, \\\\pm 3, 2) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107491, "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:117437"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"(x^2 + 5x + 2)(x^2 + 5x + 9)"
] | [
"skywork"
] | 796869196d2d7d3decccc7075f777a4c41ffe8798ba83e8373127fb15b38a361 | [
{
"content": "Factor $(x^2 + 3x + 2)(x^2 + 7x + 12) + (x^2 + 5x - 6)$ as the product of two non-constant polynomials.",
"role": "user"
}
] | Factor $(x^2 + 3x + 2)(x^2 + 7x + 12) + (x^2 + 5x - 6)$ as the product of two non-constant polynomials. | "[\"(x^2 + 5x + 2)(x^2 + 5x + 9)\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107503, "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:117438"}] | {
"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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