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 |
|---|---|---|---|---|---|---|---|---|
[
"2"
] | [
"skywork"
] | 6625940e7125c809cf8f5fea38567c2dc9de8b193fde89bf74f1c6f980b5d826 | [
{
"content": "2. If $n \\in \\mathbf{N}, n \\geqslant 2, a_{i} \\in\\{0,1, \\cdots, 9\\}$\n$$\n\\begin{array}{l}\n(i=1,2, \\cdots, n), a_{1} a_{2} \\neq 0 \\text {, and } \\\\\n\\sqrt{a_{1} a_{2} \\cdots a_{n}}-\\sqrt{a_{2} a_{3} \\cdots a_{n}}=a_{1}, \\\\\n\\end{array}\n$$\n\nthen $n=$ $\\qquad$, where $\\over... | 2. If $n \in \mathbf{N}, n \geqslant 2, a_{i} \in\{0,1, \cdots, 9\}$
$$
\begin{array}{l}
(i=1,2, \cdots, n), a_{1} a_{2} \neq 0 \text {, and } \\
\sqrt{a_{1} a_{2} \cdots a_{n}}-\sqrt{a_{2} a_{3} \cdots a_{n}}=a_{1}, \\
\end{array}
$$
then $n=$ $\qquad$, where $\overline{a_{1} a_{2} \cdots a_{n}}$ is the $n$-digit num... | "[\"2\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2146, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "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:16119"}] | {
"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
} |
[
"72"
] | [
"skywork"
] | 879e0c73b10dc709a4af7ec5e44d9db0844bd270efe691143780c9b29bb77a33 | [
{
"content": "Let $f(x)$ be a third-degree polynomial with real coefficients satisfying\n\\[|f(1)|=|f(2)|=|f(3)|=|f(5)|=|f(6)|=|f(7)|=12.\\] Find $|f(0)|$.",
"role": "user"
}
] | Let $f(x)$ be a third-degree polynomial with real coefficients satisfying
\[|f(1)|=|f(2)|=|f(3)|=|f(5)|=|f(6)|=|f(7)|=12.\] Find $|f(0)|$. | "[\"72\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 2160, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16120"}, {"dataset": "skywork", "extra_in... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3\\sqrt{5} - 5}{5}"
] | [
"skywork"
] | 5012e0168938a933d97b2336747c5cc51d2d1c4fe4c4999bf02c77989172fb3c | [
{
"content": "Kelvin the Frog is hopping on a number line (extending to infinity in both directions). Kelvin starts at $0$. Every minute, he has a $\\frac{1}{3}$ chance of moving $1$ unit left, a $\\frac{1}{3}$ chance of moving $1$ unit right, and $\\frac{1}{3}$ chance of getting eaten. Find the expected number... | Kelvin the Frog is hopping on a number line (extending to infinity in both directions). Kelvin starts at $0$. Every minute, he has a $\frac{1}{3}$ chance of moving $1$ unit left, a $\frac{1}{3}$ chance of moving $1$ unit right, and $\frac{1}{3}$ chance of getting eaten. Find the expected number of times Kelvin returns ... | "[\"\\\\frac{3\\\\sqrt{5} - 5}{5}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2151, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16121"}] | {
"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
} |
[
"125"
] | [
"skywork"
] | a0c94abef3e61c570e04dd31336ba9249a9f8561d43a559cf1c2af691e93558e | [
{
"content": "35.2. Two motorcyclists set out simultaneously from points $A$ and $B$ towards each other and met 50 km from $B$. Upon arriving at points $A$ and $B$, the motorcyclists immediately turned around and met again 25 km from $A$. How many kilometers is it from $A$ to $B$?",
"role": "user"
}
] | 35.2. Two motorcyclists set out simultaneously from points $A$ and $B$ towards each other and met 50 km from $B$. Upon arriving at points $A$ and $B$, the motorcyclists immediately turned around and met again 25 km from $A$. How many kilometers is it from $A$ to $B$? | "[\"125\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2149, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:16122"}] | {
"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"
] | 74988bd901b9b1de753727eb6704c90c0272c7f97eb83c03171e668528fa516f | [
{
"content": "Example 3 Given $x, y \\in\\left[-\\frac{\\pi}{4}, \\frac{\\pi}{4}\\right], a \\in \\mathbf{R}$, and\n$$\n\\left\\{\\begin{array}{l}\nx^{3}+\\sin x-2 a=0, \\\\\n4 y^{3}+\\sin y \\cdot \\cos y+a=0 .\n\\end{array}\\right.\n$$\n\nThen $\\cos (x+2 y)=$ $\\qquad$\n(1994, National High School Mathematic... | Example 3 Given $x, y \in\left[-\frac{\pi}{4}, \frac{\pi}{4}\right], a \in \mathbf{R}$, and
$$
\left\{\begin{array}{l}
x^{3}+\sin x-2 a=0, \\
4 y^{3}+\sin y \cdot \cos y+a=0 .
\end{array}\right.
$$
Then $\cos (x+2 y)=$ $\qquad$
(1994, National High School Mathematics Joint Competition) | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2148, "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:16123"}] | {
"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{2\\sqrt{59}}{15}"
] | [
"skywork"
] | 253f383cf8151d1f01964f57a942f2fde2a97ac555143815cc1801d2b4edb532 | [
{
"content": "10. A sphere touches all the edges of the pyramid $S A B C$, and the lateral edges $S A, S B$, and $S C$ at points $A^{\\prime}, B^{\\prime}$, and $C^{\\prime}$. Find the volume of the pyramid $S A^{\\prime} B^{\\prime} C^{\\prime}$, if $A B=B C=S B=5$ and $A C=4$.",
"role": "user"
}
] | 10. A sphere touches all the edges of the pyramid $S A B C$, and the lateral edges $S A, S B$, and $S C$ at points $A^{\prime}, B^{\prime}$, and $C^{\prime}$. Find the volume of the pyramid $S A^{\prime} B^{\prime} C^{\prime}$, if $A B=B C=S B=5$ and $A C=4$. | "[\"\\\\frac{2\\\\sqrt{59}}{15}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2129, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16124"}] | {
"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
} |
[
"102"
] | [
"skywork"
] | 403f7987828282340997076791414eeac02f977c1a8ffe50a4ad0e7486678a1b | [
{
"content": "1. If four consecutive natural numbers are all composite, then the minimum value of the sum of these four numbers is ( ).\n(A) 100\n( B ) 101\n( C ) 102\n(D) 103",
"role": "user"
}
] | 1. If four consecutive natural numbers are all composite, then the minimum value of the sum of these four numbers is ( ).
(A) 100
( B ) 101
( C ) 102
(D) 103 | "[\"102\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2157, "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:16125"}] | {
"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
} |
[
"170"
] | [
"skywork"
] | f17d02b75578ca5fd3ac5f3c4c51612b08c8787f707d85fa26b2492597c2f58a | [
{
"content": "35. The least common multiple of natural numbers $a$ and $b$ is 165, and their greatest common divisor is $5, a+b$ has the maximum value of",
"role": "user"
}
] | 35. The least common multiple of natural numbers $a$ and $b$ is 165, and their greatest common divisor is $5, a+b$ has the maximum value of | "[\"170\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2141, "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:16126"}] | {
"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
} |
[
"15"
] | [
"skywork"
] | 54c5ee62784064792abbbe481f22b82189653f5dd90731e92ded46e4ef390bb6 | [
{
"content": "9. Arrange the $n$ positive integers from $1 \\sim n (n>1)$ in a row so that the sum of any two adjacent numbers is a perfect square. What is the minimum value of $n$?",
"role": "user"
}
] | 9. Arrange the $n$ positive integers from $1 \sim n (n>1)$ in a row so that the sum of any two adjacent numbers is a perfect square. What is the minimum value of $n$? | "[\"15\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2165, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16127"}] | {
"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
} |
[
"29"
] | [
"skywork"
] | 4f9868be2ae26bbeabf18515b77b9ee6b95e9dcf37303c5d3e916da4a257f315 | [
{
"content": "Let \\(a \\star b = ab - 2\\). Compute the remainder when \\((((579 \\star 569) \\star 559) \\star \\cdots \\star 19) \\star 9\\) is divided by 100.",
"role": "user"
}
] | Let \(a \star b = ab - 2\). Compute the remainder when \((((579 \star 569) \star 559) \star \cdots \star 19) \star 9\) is divided by 100. | "[\"29\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2163, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 11, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16128"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"n+1"
] | [
"skywork"
] | 6d3effcff11297749830b3a1f9c22ea71ff2cad24f5c872ea9ec79b8f9bc1ef6 | [
{
"content": "Let $n\\ge 3$ be an integer. Annalena has infinitely many cowbells in each of $n$ different colours. Given an integer $m \\ge n + 1$ and a group of $m$ cows standing in a circle, she is tasked with tying one cowbell around the neck of every cow so that every group of $n + 1$ consecutive cows have ... | Let $n\ge 3$ be an integer. Annalena has infinitely many cowbells in each of $n$ different colours. Given an integer $m \ge n + 1$ and a group of $m$ cows standing in a circle, she is tasked with tying one cowbell around the neck of every cow so that every group of $n + 1$ consecutive cows have cowbells of all the poss... | "[\" n+1 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2152, "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:16129"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{720}"
] | [
"skywork"
] | 02b441be56d45087c6666ddb29908829f5cf9607f8d841b421be41d7c8c8a1c3 | [
{
"content": "5. Cards (from 7th grade, 2 points). When Vitya was in the first grade, he had a set of digits with 12 cards: two cards with the digit 1, two cards with the digit 2, and so on up to the digit 6. Vitya laid them out in a row on the table in a random order from left to right, and then removed the fi... | 5. Cards (from 7th grade, 2 points). When Vitya was in the first grade, he had a set of digits with 12 cards: two cards with the digit 1, two cards with the digit 2, and so on up to the digit 6. Vitya laid them out in a row on the table in a random order from left to right, and then removed the first one, the first two... | "[\"\\\\frac{1}{720}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2154, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:16130"}] | {
"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
} |
[
"88"
] | [
"skywork"
] | 8530e93dee1344906a38402269b807376667418c488e7825cc80b2d3c1dd7d4a | [
{
"content": "Shapovalov A.V.\n\nThe cells of a chessboard are numbered from 1 to 64 in such a way that adjacent numbers are in adjacent (by side) cells.\n\nWhat is the smallest possible sum of the numbers on the diagonal?\n\n#",
"role": "user"
}
] | Shapovalov A.V.
The cells of a chessboard are numbered from 1 to 64 in such a way that adjacent numbers are in adjacent (by side) cells.
What is the smallest possible sum of the numbers on the diagonal?
# | "[\"88\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2162, "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:16131"}] | {
"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{40}{81}"
] | [
"skywork"
] | 3dfc1452f6f6a8e3bcffb807a3c015fbe043f68fbd07ee5fd3e45d172b4781d7 | [
{
"content": "You have a whole cake in your pantry. On your first trip to the pantry, you eat one-third of the cake. On each successive trip, you eat one-third of the remaining cake. After four trips to the pantry, what fractional part of the cake have you eaten?",
"role": "user"
}
] | You have a whole cake in your pantry. On your first trip to the pantry, you eat one-third of the cake. On each successive trip, you eat one-third of the remaining cake. After four trips to the pantry, what fractional part of the cake have you eaten? | "[\"\\\\frac{40}{81}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2174, "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:16132"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 186b0c36a1037cabd190290435c87288678d4204b886d57603a99a4d3c7b81d5 | [
{
"content": "17. In a certain country, an aviation network has already been established, where any city is connected to no more than three other cities, and from any city to another city, it takes no more than one transfer. How many cities can this country have at most?",
"role": "user"
}
] | 17. In a certain country, an aviation network has already been established, where any city is connected to no more than three other cities, and from any city to another city, it takes no more than one transfer. How many cities can this country have at most? | "[\"10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2159, "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:16133"}] | {
"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
} |
[
"-19"
] | [
"skywork"
] | 959d16db76895554b67d1a068a7b9c5756ddec9d248a9f271cfa1212cc15191c | [
{
"content": "Given the lengths of the three sides of $\\triangle ABC$ are $AB=7$, $BC=5$, and $CA=6$, the value of $\\overrightarrow {AB}\\cdot \\overrightarrow {BC}$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | Given the lengths of the three sides of $\triangle ABC$ are $AB=7$, $BC=5$, and $CA=6$, the value of $\overrightarrow {AB}\cdot \overrightarrow {BC}$ is \_\_\_\_\_\_. | "[\"-19\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2166, "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:16134"}] | {
"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
} |
[
"x\\in(-3;-2)\\cup(-1;0)"
] | [
"skywork"
] | 6c7be22cf9f3faffcb44d341edb2f69350f8eb451a0b57198e2ab84e02048599 | [
{
"content": "9.163. $\\frac{\\lg 7-\\lg \\left(-8 x-x^{2}\\right)}{\\lg (x+3)}>0$.\n\n9.163. $\\frac{\\log 7-\\log \\left(-8 x-x^{2}\\right)}{\\log (x+3)}>0$.",
"role": "user"
}
] | 9.163. $\frac{\lg 7-\lg \left(-8 x-x^{2}\right)}{\lg (x+3)}>0$.
9.163. $\frac{\log 7-\log \left(-8 x-x^{2}\right)}{\log (x+3)}>0$. | "[\"x\\\\in(-3;-2)\\\\cup(-1;0)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2161, "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:16135"}] | {
"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
} |
[
"18"
] | [
"skywork"
] | 49b8fdafc53a6bd7e37ae1370b583663c3542ace43ffb71ad9a6e171c8c75140 | [
{
"content": "1. The equation $x^{2}+2 a x+2 a^{2}+4 a+3=0$ has real solutions. For which value of the real parameter $a$, is the sum of the squares of its solutions the largest?",
"role": "user"
}
] | 1. The equation $x^{2}+2 a x+2 a^{2}+4 a+3=0$ has real solutions. For which value of the real parameter $a$, is the sum of the squares of its solutions the largest? | "[\"18\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2167, "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:16137"}] | {
"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
} |
[
"C"
] | [
"skywork"
] | 51d325b2513986bd4b7996f87eb1cdaa56b681ffa69f000c40f771cef6d4efb3 | [
{
"content": "2. Let $f(x)$ be a function defined on the set of real numbers with a period of 2, and it is an even function. It is known that when $x \\in[2,3]$, $f(x)=x$, then when $x \\in[-2,0]$, the analytical expression of $f(x)$ is\nA. $f(x)=x+4$\nB. $f(x)=2-x$\nC. $f(x)=3-|x+1|$\nD. $f(x)=2+|x+1|$",
"... | 2. Let $f(x)$ be a function defined on the set of real numbers with a period of 2, and it is an even function. It is known that when $x \in[2,3]$, $f(x)=x$, then when $x \in[-2,0]$, the analytical expression of $f(x)$ is
A. $f(x)=x+4$
B. $f(x)=2-x$
C. $f(x)=3-|x+1|$
D. $f(x)=2+|x+1|$ | "[\"C\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2145, "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:16138"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | 25eaa48a772c8611e9f4fba04176332b67bf0d085bcfaabe65322313113e32c6 | [
{
"content": "Let $B(n)$ be the number of ones in the base two expression for the positive integer $n.$ Determine whether\n$$\\exp \\left( \\sum_{n=1}^{\\infty} \\frac{ B(n)}{n(n+1)} \\right)$$\nis a rational number.",
"role": "user"
}
] | Let $B(n)$ be the number of ones in the base two expression for the positive integer $n.$ Determine whether
$$\exp \left( \sum_{n=1}^{\infty} \frac{ B(n)}{n(n+1)} \right)$$
is a rational number. | "[\" 4 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2183, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16139"}] | {
"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{9}{10}"
] | [
"skywork"
] | 35ca027346facf13c870f01e962098a8fab3f4a3cc6b4db65707bd61e76b125d | [
{
"content": "Suppose that $ABC$ is an isosceles triangle with $AB=AC$. Let $P$ be the point on side $AC$ so that $AP=2CP$. Given that $BP=1$, determine the maximum possible area of $ABC$.",
"role": "user"
}
] | Suppose that $ABC$ is an isosceles triangle with $AB=AC$. Let $P$ be the point on side $AC$ so that $AP=2CP$. Given that $BP=1$, determine the maximum possible area of $ABC$. | "[\"\\\\frac{9}{10}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2170, "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:16140"}] | {
"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
} |
[
"34"
] | [
"skywork"
] | e071807583c46bcc1a8afbe947bcba3c806c4c4ceba2181f05e6a3df68f2285c | [
{
"content": "Select 4 students from 7 students, including 4 boys and 3 girls, to participate in an environmental knowledge contest, ensuring both boys and girls are among the selected students. Calculate the number of different selection methods.",
"role": "user"
}
] | Select 4 students from 7 students, including 4 boys and 3 girls, to participate in an environmental knowledge contest, ensuring both boys and girls are among the selected students. Calculate the number of different selection methods. | "[\"34\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2180, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16141"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 3765c9ca652180feec86a018fddad3ecf2109949e930b6cdc02aad5912b1950e | [
{
"content": "There are three identical red balls, three identical yellow balls, and three identical green balls. In how many different ways can they be split into three groups of three balls each?",
"role": "user"
}
] | There are three identical red balls, three identical yellow balls, and three identical green balls. In how many different ways can they be split into three groups of three balls each? | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2168, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16142"}] | {
"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
} |
[
"137"
] | [
"skywork"
] | a7ba376627e6506bb3c99d06c8ab8b6d8f0946f4d6fb8a2226795253fc24287e | [
{
"content": "One base of a trapezoid is $50$ units longer than the other base. The segment that joins the midpoints of the legs divides the trapezoid into two regions whose areas are in the ratio $1: 2$. Let $x$ be the length of the segment joining the legs of the trapezoid that is parallel to the bases and th... | One base of a trapezoid is $50$ units longer than the other base. The segment that joins the midpoints of the legs divides the trapezoid into two regions whose areas are in the ratio $1: 2$. Let $x$ be the length of the segment joining the legs of the trapezoid that is parallel to the bases and that divides the trapezo... | "[\"137\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2158, "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:16143"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"n"
] | [
"skywork"
] | b2bf0f33535ba7b5f546aa76121a704ed98e7a2473f609a2a783d7c543a7107d | [
{
"content": "Find all numbers $n \\geq 4$ such that there exists a convex polyhedron with exactly $n$ faces, whose all faces are right-angled triangles.\n(Note that the angle between any pair of adjacent faces in a convex polyhedron is less than $180^\\circ$.)\n\n[i]Proposed by Hesam Rajabzadeh[/i]",
"role... | Find all numbers $n \geq 4$ such that there exists a convex polyhedron with exactly $n$ faces, whose all faces are right-angled triangles.
(Note that the angle between any pair of adjacent faces in a convex polyhedron is less than $180^\circ$.)
[i]Proposed by Hesam Rajabzadeh[/i] | "[\" n \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2176, "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:16144"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 99206324ace9481f537ffbe5bf073514c75a85a810de3e3c91524d5979dd0914 | [
{
"content": "Trapezoids Auxiliary similar triangles $]$\n\nPoint $M$ is located on the lateral side $A B$ of trapezoid $A B C D$, such that $A M: B M=2: 1$. A line passing through point $M$ parallel to the bases $A D$ and $B C$ intersects the lateral side $C D$ at point $N$. Find $M N$, if $A D=18, B C=6$.",
... | Trapezoids Auxiliary similar triangles $]$
Point $M$ is located on the lateral side $A B$ of trapezoid $A B C D$, such that $A M: B M=2: 1$. A line passing through point $M$ parallel to the bases $A D$ and $B C$ intersects the lateral side $C D$ at point $N$. Find $M N$, if $A D=18, B C=6$. | "[\"10\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2178, "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:16145"}] | {
"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{2n^2}{5}"
] | [
"skywork"
] | ee37fb49d065865d183b70e78859e1ac1c0b61e618cbf7058fb42ce00b723474 | [
{
"content": "Let $ n\\geq 2$ be a positive integer. Find the [u]maximum[/u] number of segments with lenghts greater than $ 1,$ determined by $ n$ points which lie on a closed disc with radius $ 1.$",
"role": "user"
}
] | Let $ n\geq 2$ be a positive integer. Find the [u]maximum[/u] number of segments with lenghts greater than $ 1,$ determined by $ n$ points which lie on a closed disc with radius $ 1.$ | "[\"\\\\frac{2n^2}{5}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2181, "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:16146"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"(-2;7)"
] | [
"skywork"
] | 88d6d8f73d95ab5e46e9c9e1b48a21f9c9afb3fbf193f6006e11e82b7b8eb3e6 | [
{
"content": "7.269. $\\left\\{\\begin{array}{l}3^{-x} \\cdot 2^{y}=1152 \\\\ \\log _{\\sqrt{5}}(x+y)=2 .\\end{array}\\right.$",
"role": "user"
}
] | 7.269. $\left\{\begin{array}{l}3^{-x} \cdot 2^{y}=1152 \\ \log _{\sqrt{5}}(x+y)=2 .\end{array}\right.$ | "[\"(-2;7)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2184, "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:16147"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"8"
] | [
"skywork"
] | bccc4edd0d4e2830bea32f10eb7be9eb5fec52c4132fd09f3c15731f71f19b4d | [
{
"content": "Let $n \\ge 2$ be a positive integer, and write in a digit form \\[\\frac{1}{n}=0.a_1a_2\\dots.\\] Suppose that $n = a_1 + a_2 + \\cdots$. Determine all possible values of $n$.",
"role": "user"
}
] | Let $n \ge 2$ be a positive integer, and write in a digit form \[\frac{1}{n}=0.a_1a_2\dots.\] Suppose that $n = a_1 + a_2 + \cdots$. Determine all possible values of $n$. | "[\"8\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2186, "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:16148"}] | {
"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{125}{12}"
] | [
"skywork"
] | 02c21afc66ad7e1a617ab4b07fa40f0497aa8645efb96e348017ffb8f406ad7f | [
{
"content": "Rectangle $ABCD$ has $AB=4$ and $BC=3$. Segment $EF$ is constructed through $B$ so that $EF$ is perpendicular to $DB$, and $A$ and $C$ lie on $DE$ and $DF$, respectively. What is $EF$?\n$\\mathrm{(A)}\\ 9 \\qquad \\mathrm{(B)}\\ 10 \\qquad \\mathrm{(C)}\\ \\frac {125}{12} \\qquad \\mathrm{(D)}\\ \... | Rectangle $ABCD$ has $AB=4$ and $BC=3$. Segment $EF$ is constructed through $B$ so that $EF$ is perpendicular to $DB$, and $A$ and $C$ lie on $DE$ and $DF$, respectively. What is $EF$?
$\mathrm{(A)}\ 9 \qquad \mathrm{(B)}\ 10 \qquad \mathrm{(C)}\ \frac {125}{12} \qquad \mathrm{(D)}\ \frac {103}{9} \qquad \mathrm{(E)}\ ... | "[\"\\\\frac{125}{12}\"]" | train-math-numinamath1.5_amc_aime | [{"dataset": "skywork", "extra_info": {"index": 2190, "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:16149"}] | {
"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
} |
[
"179101"
] | [
"skywork"
] | d3fe854d3e90ab1c37541d8df55b9af24225d6bf41f97edd39a6f4791112c0b7 | [
{
"content": "6 Let $a_{n}=\\frac{n(n+1)}{2}$, from the sequence $\\left\\{a_{n}\\right\\}$, remove all numbers that can be divided by 3, and the remaining terms are arranged in ascending order to form the sequence $\\left\\{b_{n}\\right\\}$, then $b_{200}=(\\quad$.\n(A) 200808\n(B) 179101\n(C) 153201\n(D) 1168... | 6 Let $a_{n}=\frac{n(n+1)}{2}$, from the sequence $\left\{a_{n}\right\}$, remove all numbers that can be divided by 3, and the remaining terms are arranged in ascending order to form the sequence $\left\{b_{n}\right\}$, then $b_{200}=(\quad$.
(A) 200808
(B) 179101
(C) 153201
(D) 116808 | "[\"179101\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2172, "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:16150"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"28"
] | [
"skywork"
] | 32141923cdbc7fc1c3aa90c259dd5317574dbbe845231b893551e51c593ab35f | [
{
"content": "9. (12 points) The teacher draws 9 cards from 13 cards labeled $1 \\sim 13$, and sticks them on the foreheads of 9 students. Everyone can see the numbers of the other 8 people but not their own. (All 9 students are honest and smart, and the cards $6, 9$ cannot be inverted.) The teacher asks: \"Now... | 9. (12 points) The teacher draws 9 cards from 13 cards labeled $1 \sim 13$, and sticks them on the foreheads of 9 students. Everyone can see the numbers of the other 8 people but not their own. (All 9 students are honest and smart, and the cards $6, 9$ cannot be inverted.) The teacher asks: "Now, those who know the num... | "[\"28\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2164, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16151"}] | {
"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{R_{2}}{R_{1}}=\\frac{4}{3},R_{1}=\\frac{\\sqrt{3}}{4},R_{2}=\\frac{1}{\\sqrt{3}}"
] | [
"skywork"
] | dcb221556f5871b3016052be99a3159fcf64c4eeffe7453e11bb1b1b87ec7311 | [
{
"content": "6. [5 points] a) Two parallel lines $\\ell_{1}$ and $\\ell_{2}$ touch the circle $\\omega_{1}$ with center $O_{1}$ at points $A$ and $B$ respectively. The circle $\\omega_{2}$ with center $O_{2}$ touches the line $\\ell_{1}$ at point $D$, intersects the line $\\ell_{2}$ at points $B$ and $E$, and ... | 6. [5 points] a) Two parallel lines $\ell_{1}$ and $\ell_{2}$ touch the circle $\omega_{1}$ with center $O_{1}$ at points $A$ and $B$ respectively. The circle $\omega_{2}$ with center $O_{2}$ touches the line $\ell_{1}$ at point $D$, intersects the line $\ell_{2}$ at points $B$ and $E$, and intersects the circle $\omeg... | "[\"\\\\frac{R_{2}}{R_{1}}=\\\\frac{4}{3},R_{1}=\\\\frac{\\\\sqrt{3}}{4},R_{2}=\\\\frac{1}{\\\\sqrt{3}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2175, "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:16152"}] | {
"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
} |
[
"16"
] | [
"skywork"
] | 9189b9feaa24d59b8a051c0ece0532d6e768495c2a7c4ead2f3e3a07da7bd21f | [
{
"content": "8. $\\sum_{0 \\leqslant i<j \\leqslant 50} \\mathrm{C}_{50}^{i} \\mathrm{C}_{50}^{j}$ modulo 31 is",
"role": "user"
}
] | 8. $\sum_{0 \leqslant i<j \leqslant 50} \mathrm{C}_{50}^{i} \mathrm{C}_{50}^{j}$ modulo 31 is | "[\"16\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2192, "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:16153"}] | {
"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
} |
[
"1000"
] | [
"skywork"
] | 72d8d85fd1b41f72b74f8516ef68f2ea39f4d4f35522bd38d18cdec524b3d84c | [
{
"content": "For his birthday, Bert gets a box that holds $125$ jellybeans when filled to capacity. A few weeks later, Carrie gets a larger box full of jellybeans. Her box is twice as high, twice as wide and twice as long as Bert's. Approximately, how many jellybeans did Carrie get?",
"role": "user"
}
] | For his birthday, Bert gets a box that holds $125$ jellybeans when filled to capacity. A few weeks later, Carrie gets a larger box full of jellybeans. Her box is twice as high, twice as wide and twice as long as Bert's. Approximately, how many jellybeans did Carrie get? | "[\"1000\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2173, "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:16154"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | f3d74db23532f8208afb9e9d1b33a18f40ad4cffc5833c8b6c4053fea23bb20a | [
{
"content": "10. Alberto, Barbara, and Carlo are playing cards. In each hand, the winner gains 2 points, while the other two players each lose 1 point. Initially, everyone has 0 points. What is the probability that, after 10 hands, they are all back to zero points?\n(A) 0\n(B) $\\frac{1}{5}$\n(C) $\\frac{1}{3}... | 10. Alberto, Barbara, and Carlo are playing cards. In each hand, the winner gains 2 points, while the other two players each lose 1 point. Initially, everyone has 0 points. What is the probability that, after 10 hands, they are all back to zero points?
(A) 0
(B) $\frac{1}{5}$
(C) $\frac{1}{3}$
(D) $\frac{\left(\begin{a... | "[\"0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2179, "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:16155"}] | {
"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{\\sqrt{3}- 1}{2}"
] | [
"skywork"
] | 7516800e8ad8ff0e457ed23ac3a35d673c569de709e6baab59046f48c24930c7 | [
{
"content": "Point $D$ lies on side $AC$ of equilateral triangle $ABC$ such that the measure of angle $DBC$ is $45$ degrees. What is the ratio of the area of triangle $ADB$ to the area of triangle $CDB$? Express your answer as a common fraction in simplest radical form.",
"role": "user"
}
] | Point $D$ lies on side $AC$ of equilateral triangle $ABC$ such that the measure of angle $DBC$ is $45$ degrees. What is the ratio of the area of triangle $ADB$ to the area of triangle $CDB$? Express your answer as a common fraction in simplest radical form. | "[\"\\\\frac{\\\\sqrt{3}- 1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2200, "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:16156"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-10"
] | [
"skywork"
] | 8697586d80e408bcbbb986bb25717424759b8fdee7af40ca9d13beeac6a9c4c1 | [
{
"content": "If the polynomial $x^{3}+x^{10}=a_{0}+a_{1}(x+1)+...+a_{9}(x+1)^{9}+a_{10}(x+1)^{10}$, then $a_{9}=$ \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | If the polynomial $x^{3}+x^{10}=a_{0}+a_{1}(x+1)+...+a_{9}(x+1)^{9}+a_{10}(x+1)^{10}$, then $a_{9}=$ \_\_\_\_\_\_. | "[\"-10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2193, "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:16157"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"36"
] | [
"skywork"
] | 50fada4e3473b0cc4b558dfa8715dfd9c3b0143428cc0299408dc6efe44d0c35 | [
{
"content": "A hyperbola with its center shifted to $(1,1)$ passes through point $(4, 2)$. The hyperbola opens horizontally, with one of its vertices at $(3, 1)$. Determine $t^2$ if the hyperbola also passes through point $(t, 4)$.",
"role": "user"
}
] | A hyperbola with its center shifted to $(1,1)$ passes through point $(4, 2)$. The hyperbola opens horizontally, with one of its vertices at $(3, 1)$. Determine $t^2$ if the hyperbola also passes through point $(t, 4)$. | "[\"36\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2177, "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:16158"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{5}"
] | [
"skywork"
] | db0bece6a6cbbefd610aab38d502cc2e941896e1ef110ff527d1cc56284e79d4 | [
{
"content": "Xiao Ming throws a die with uniform density three times and observes the number of points on the upper face each time. It is known that the numbers of points in the three throws are all different. Calculate the probability that the sum of the three numbers of points does not exceed $8$.",
"rol... | Xiao Ming throws a die with uniform density three times and observes the number of points on the upper face each time. It is known that the numbers of points in the three throws are all different. Calculate the probability that the sum of the three numbers of points does not exceed $8$. | "[\"\\\\frac{1}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2169, "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:16159"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2\\sqrt{5.4}"
] | [
"skywork"
] | e40ceb584730f0f3e43fef33d21c2266ccce476e819239bada19d4469cc31be4 | [
{
"content": "Find the distance between the foci of the ellipse\n\\[\\frac{x^2}{36} + \\frac{y^2}{9} = 5.\\]",
"role": "user"
}
] | Find the distance between the foci of the ellipse
\[\frac{x^2}{36} + \frac{y^2}{9} = 5.\] | "[\"2\\\\sqrt{5.4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2187, "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:16160"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"skywork"
] | 34e8f4b96cac83019e5aa4fa1e8e8fbb34ac80ba969a5f1e5e3c4671db893315 | [
{
"content": "The Planar National Park is a undirected 3-regular planar graph (i.e. all vertices have degree 3). A visitor walks through the park as follows: she begins at a vertex and starts walking along an edge. When she reaches the other endpoint, she turns left. On the next vertex she turns right, and so o... | The Planar National Park is a undirected 3-regular planar graph (i.e. all vertices have degree 3). A visitor walks through the park as follows: she begins at a vertex and starts walking along an edge. When she reaches the other endpoint, she turns left. On the next vertex she turns right, and so on, alternating left an... | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2188, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16161"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"$\\frac{3}{2}\\sqrt{2}-\\frac{3}{2}$"
] | [
"skywork"
] | 499546ce85013f1db4c31e65bb8e2677ee2a659b5f61ece84ec9a4ab7feeda71 | [
{
"content": "The solutions to the equation $(z+6)^8=81$ are connected in the complex plane to form a convex regular polygon, three of whose vertices are labeled $A,B,$ and $C$ . What is the least possible area of $\\triangle ABC?$",
"role": "user"
}
] | The solutions to the equation $(z+6)^8=81$ are connected in the complex plane to form a convex regular polygon, three of whose vertices are labeled $A,B,$ and $C$ . What is the least possible area of $\triangle ABC?$ | "[\"$\\\\frac{3}{2}\\\\sqrt{2}-\\\\frac{3}{2}$\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 2194, "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:16162"}] | {
"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
} |
[
"800000"
] | [
"skywork"
] | 294bafa66563d299c57176cf89d1d810b5ea08f462e4337b835cf553c20c32a2 | [
{
"content": "The sequence starts with 800,000; each subsequent term is obtained by dividing the previous term by 3. What is the last integer in this sequence?",
"role": "user"
}
] | The sequence starts with 800,000; each subsequent term is obtained by dividing the previous term by 3. What is the last integer in this sequence? | "[\"800000\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2201, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16163"}] | {
"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
} |
[
"g(2010)"
] | [
"skywork"
] | 633a54f69f3f714b836d0dda74fa6381e60f6c46ddce0301d34067af1bc43f4f | [
{
"content": "Let $g(n)$ be the number of all $n$-digit natural numbers each consisting only of digits $0,1,2,3$ (but not nessesarily all of them) such that the sum of no two neighbouring digits equals $2$. Determine whether $g(2010)$ and $g(2011)$ are divisible by $11$.\n\nI.Kozlov",
"role": "user"
}
] | Let $g(n)$ be the number of all $n$-digit natural numbers each consisting only of digits $0,1,2,3$ (but not nessesarily all of them) such that the sum of no two neighbouring digits equals $2$. Determine whether $g(2010)$ and $g(2011)$ are divisible by $11$.
I.Kozlov | "[\" g(2010) \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2191, "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:16164"}] | {
"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
} |
[
"27"
] | [
"skywork"
] | d7c212d44adae93a282c645e8a91e8f92ede949b42e17702df5266c77374c623 | [
{
"content": "Out of three hundred eleventh-grade students, 77% received excellent and good grades on the first exam, 71% on the second exam, and 61% on the third exam. What is the minimum number of participants who received excellent and good grades on all three exams?",
"role": "user"
}
] | Out of three hundred eleventh-grade students, 77% received excellent and good grades on the first exam, 71% on the second exam, and 61% on the third exam. What is the minimum number of participants who received excellent and good grades on all three exams? | "[\"27\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2185, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16165"}] | {
"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
} |
[
"4.5"
] | [
"skywork"
] | 9a1169cc1e883d743b2752e2d0b4650fcd6442efa00da2bbaba3157e04bf194a | [
{
"content": "Shari walks at a constant rate of 3 miles per hour. After 1.5 hours, how many miles did she walk? Express your answer as a decimal to the nearest tenth.",
"role": "user"
}
] | Shari walks at a constant rate of 3 miles per hour. After 1.5 hours, how many miles did she walk? Express your answer as a decimal to the nearest tenth. | "[\"4.5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2218, "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:16166"}] | {
"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\\pi \\times 250^{2/3}"
] | [
"skywork"
] | 5f681b31fb4cf634d4354fea01483ed5c3f1b247d3e31747270efcd72aaff64a | [
{
"content": "The volume of a hemisphere is $\\frac{500}{3}\\pi$. What is the total surface area of the hemisphere including its base? Express your answer in terms of $\\pi$.",
"role": "user"
}
] | The volume of a hemisphere is $\frac{500}{3}\pi$. What is the total surface area of the hemisphere including its base? Express your answer in terms of $\pi$. | "[\"3\\\\pi \\\\times 250^{2/3}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2210, "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:16167"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{7}{2}"
] | [
"skywork"
] | 746c693ad3df3a167708ba1e3d7bceb6b2037f7820a8a11940d46bb99d18c0bd | [
{
"content": "If $\\frac{1}{x}=2$ and $\\frac{1}{x}+\\frac{3}{y}=3$, then the value of $x+y$ is\n(A) 3\n(B) $\\frac{5}{6}$\n(C) $\\frac{7}{3}$\n(D) $\\frac{7}{2}$\n(E) $\\frac{4}{3}$",
"role": "user"
}
] | If $\frac{1}{x}=2$ and $\frac{1}{x}+\frac{3}{y}=3$, then the value of $x+y$ is
(A) 3
(B) $\frac{5}{6}$
(C) $\frac{7}{3}$
(D) $\frac{7}{2}$
(E) $\frac{4}{3}$ | "[\"\\\\frac{7}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2196, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16168"}] | {
"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
} |
[
"(1, 4)"
] | [
"skywork"
] | 4256072a77598936b131c2e4335b2fb1b691d1469ef606bdd9d085ce89f14eb8 | [
{
"content": "Four. (20 points) Given the function\n$$\nf(x)=4 \\sin x \\cdot \\sin ^{2}\\left(\\frac{\\pi}{4}+\\frac{x}{2}\\right)+\\cos 2 x \\text {. }\n$$\n(1) Let the constant $\\omega>0$, if $y=f(\\omega x)$ is an increasing function on the interval $\\left[-\\frac{\\pi}{2}, \\frac{2 \\pi}{3}\\right]$, fin... | Four. (20 points) Given the function
$$
f(x)=4 \sin x \cdot \sin ^{2}\left(\frac{\pi}{4}+\frac{x}{2}\right)+\cos 2 x \text {. }
$$
(1) Let the constant $\omega>0$, if $y=f(\omega x)$ is an increasing function on the interval $\left[-\frac{\pi}{2}, \frac{2 \pi}{3}\right]$, find the range of $\omega$;
(2) Let the set $A=... | "[\"(1, 4)\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2189, "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:16170"}] | {
"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
} |
[
"5"
] | [
"skywork"
] | cead370381099b5fbe5d588a028887640ff192c77a004556df435d5c39c147a7 | [
{
"content": "Find the number of solutions to the equation: \n\n$6\\{x\\}^3 + \\{x\\}^2 + \\{x\\} + 2x = 2018. $\n\nWith {x} we denote the fractional part of the number x.",
"role": "user"
}
] | Find the number of solutions to the equation:
$6\{x\}^3 + \{x\}^2 + \{x\} + 2x = 2018. $
With {x} we denote the fractional part of the number x. | "[\"5\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2198, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16171"}] | {
"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
} |
[
"59"
] | [
"skywork"
] | 8f35582ef060add68f30f4c8a660dc43a89b1e6fc39873573aa3e70a7c312ba3 | [
{
"content": "How many non-similar triangles have angles whose degree measures are distinct positive integers in arithmetic progression?",
"role": "user"
}
] | How many non-similar triangles have angles whose degree measures are distinct positive integers in arithmetic progression? | "[\"59\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2209, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16172"}] | {
"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
} |
[
"50"
] | [
"skywork"
] | 45584f743ed63b07d1ffe17d4f4da59bcf142e6d429456057b672810da3132cb | [
{
"content": "Task 3. Vlad wants to write one number on each side of several cubes so that he can get any 30-digit number by arranging some of the cubes side by side. What is the minimum number of cubes he needs?",
"role": "user"
}
] | Task 3. Vlad wants to write one number on each side of several cubes so that he can get any 30-digit number by arranging some of the cubes side by side. What is the minimum number of cubes he needs? | "[\"50\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2207, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16173"}] | {
"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
} |
[
"$\\frac{10}{7}$"
] | [
"skywork"
] | 060456d1ff544ab7bee06a042a0a6c43da1fda459a93386068510ea21d29bc9d | [
{
"content": "Given the approximate values $\\lg 2 = 0.301$ and $\\lg 3 = 0.477$, find the best approximation for $\\log_{5} 10$.",
"role": "user"
}
] | Given the approximate values $\lg 2 = 0.301$ and $\lg 3 = 0.477$, find the best approximation for $\log_{5} 10$. | "[\"$\\\\frac{10}{7}$\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2204, "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:16174"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"skywork"
] | 28544ead90d08bedc2370e292145fe55373245f1f8ce33a3bed941e4003ff891 | [
{
"content": "1. (2 points) In a row without spaces, all natural numbers are written in ascending order: $1234567891011 . .$. What digit stands at the 2017th place in the resulting long number?",
"role": "user"
}
] | 1. (2 points) In a row without spaces, all natural numbers are written in ascending order: $1234567891011 . .$. What digit stands at the 2017th place in the resulting long number? | "[\"7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2211, "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:16175"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9:2"
] | [
"skywork"
] | a422ddbc6db94f04132117cb57da221059536918b98d8c79cd59fe8145a19c04 | [
{
"content": "A wooden rectangular prism has dimensions 4 by 5 by 6 . This solid is painted green and then cut into 1 by 1 by 1 cubes. The ratio of the number of cubes with exactly two green faces to the number of cubes with three green faces is\n(A) $9: 2$\n(B) $9: 4$\n(C) $6: 1$\n(D) 3:1\n(E) $5: 2$",
"ro... | A wooden rectangular prism has dimensions 4 by 5 by 6 . This solid is painted green and then cut into 1 by 1 by 1 cubes. The ratio of the number of cubes with exactly two green faces to the number of cubes with three green faces is
(A) $9: 2$
(B) $9: 4$
(C) $6: 1$
(D) 3:1
(E) $5: 2$ | "[\"9:2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2206, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:16176"}, {"dataset": "skywork", "extra_... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"n = 2, 3"
] | [
"skywork"
] | e442a428cbc96a780edce55a6929700a8d4d06042869aba1e1e80db570bb4755 | [
{
"content": "We call a number $n$ [i]interesting [/i]if for each permutation $\\sigma$ of $1,2,\\ldots,n$ there exist polynomials $P_1,P_2,\\ldots ,P_n$ and $\\epsilon > 0$ such that:\n$i)$ $P_1(0)=P_2(0)=\\ldots =P_n(0)$\n$ii)$ $P_1(x)>P_2(x)>\\ldots >P_n(x)$ for $-\\epsilon<x<0$\n$iii)$ $P_{\\sigma (1)} (x)>... | We call a number $n$ [i]interesting [/i]if for each permutation $\sigma$ of $1,2,\ldots,n$ there exist polynomials $P_1,P_2,\ldots ,P_n$ and $\epsilon > 0$ such that:
$i)$ $P_1(0)=P_2(0)=\ldots =P_n(0)$
$ii)$ $P_1(x)>P_2(x)>\ldots >P_n(x)$ for $-\epsilon<x<0$
$iii)$ $P_{\sigma (1)} (x)>P_{\sigma (2)}(x)> \ldots >P_{\si... | "[\" n = 2, 3 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2195, "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:16177"}] | {
"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
} |
[
"5"
] | [
"skywork"
] | adbe9ad8ba81e729cdce20f57f3606a877d708c34f47ca9f781e005a38078938 | [
{
"content": "3.3.3 ** Given a monotonically increasing geometric sequence $\\left\\{a_{n}\\right\\}$ that satisfies $a_{2}+a_{3}+a_{4}=28$, and $a_{3}+2$ is the arithmetic mean of $a_{2}$ and $a_{4}$.\n(1) Find the general term formula of the sequence $\\left\\{a_{n}\\right\\}$;\n(2) If $b_{n}=a_{n} \\log _{\\... | 3.3.3 ** Given a monotonically increasing geometric sequence $\left\{a_{n}\right\}$ that satisfies $a_{2}+a_{3}+a_{4}=28$, and $a_{3}+2$ is the arithmetic mean of $a_{2}$ and $a_{4}$.
(1) Find the general term formula of the sequence $\left\{a_{n}\right\}$;
(2) If $b_{n}=a_{n} \log _{\frac{1}{2}} a_{n}, S_{n}=b_{1}+b_{... | "[\"5\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2197, "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:16178"}] | {
"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{2}{9}"
] | [
"skywork"
] | 49a130bcbc4df76b3a3cb7a2443f496dd1e21ed971cf054f9445549465f94035 | [
{
"content": "Suppose that a parabola has vertex $\\left(\\frac{1}{4},-\\frac{9}{8}\\right)$ and equation $y = ax^2 + bx + c$, where $a > 0$ and $a + b + c$ is an integer. Find the smallest possible value of $a.$",
"role": "user"
}
] | Suppose that a parabola has vertex $\left(\frac{1}{4},-\frac{9}{8}\right)$ and equation $y = ax^2 + bx + c$, where $a > 0$ and $a + b + c$ is an integer. Find the smallest possible value of $a.$ | "[\"\\\\frac{2}{9}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2182, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16179"}] | {
"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
} |
[
"2x-8"
] | [
"skywork"
] | 0dd2f2ada12d99d78ac7afbf9169c12a80c1aedfa50d2c06f21b7d21c507fac5 | [
{
"content": "What is the remainder when $x^2+7x-5$ divides $2x^4+11x^3-42x^2-60x+47$?",
"role": "user"
}
] | What is the remainder when $x^2+7x-5$ divides $2x^4+11x^3-42x^2-60x+47$? | "[\"2x-8\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2235, "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:16180"}] | {
"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
} |
[
"5"
] | [
"skywork"
] | 502e92cd8fcf71b10eb27211fcd7cfa1585d4cd5fc4cd867e06b639a663e869b | [
{
"content": "If $y = -x^2 + 5$ and $x$ is a real number, then what is the maximum value possible for $y$?",
"role": "user"
}
] | If $y = -x^2 + 5$ and $x$ is a real number, then what is the maximum value possible for $y$? | "[\"5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2224, "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:16181"}] | {
"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"
] | f1f267263e03f3e912a530ff210be1be1d472d8dab7642e82962ebff4447b673 | [
{
"content": "9. Assemble a square of the smallest area from squares of size $1 \\times 1$, $2 \\times 2$, and $3 \\times 3$, such that the number of squares of each size is the same.",
"role": "user"
}
] | 9. Assemble a square of the smallest area from squares of size $1 \times 1$, $2 \times 2$, and $3 \times 3$, such that the number of squares of each size is the same. | "[\"14\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2205, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16182"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"skywork"
] | 2d4e67fc7eaecf613d0ea4d0fee6bf29c50af9802cbdd7010e1ff3bdd4539de5 | [
{
"content": "12. Given $x, y \\in \\mathbf{R}_{+}, x \\neq 1, y \\neq 1$, satisfying: $\\log _{2} x=\\log _{y} 16, x y=64$. Then $\\left(\\log _{2} \\frac{x}{y}\\right)^{2}$ is $(\\quad$.\n(A) $\\frac{25}{2}$\n(B) 20\n(C) $\\frac{45}{2}$\n(D) 25\n(E) 32",
"role": "user"
}
] | 12. Given $x, y \in \mathbf{R}_{+}, x \neq 1, y \neq 1$, satisfying: $\log _{2} x=\log _{y} 16, x y=64$. Then $\left(\log _{2} \frac{x}{y}\right)^{2}$ is $(\quad$.
(A) $\frac{25}{2}$
(B) 20
(C) $\frac{45}{2}$
(D) 25
(E) 32 | "[\"20\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2203, "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:16183"}] | {
"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
} |
[
"576"
] | [
"skywork"
] | cb6d480e659811a144992cfa05942a4daa3b1c6c8f6b42b3227c5c0f23f3fe62 | [
{
"content": "What is the greatest number of positive integers lesser than or equal to 2016 we can choose such that it doesn't have two of them differing by 1,2, or 6?",
"role": "user"
}
] | What is the greatest number of positive integers lesser than or equal to 2016 we can choose such that it doesn't have two of them differing by 1,2, or 6? | "[\"576\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2219, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16184"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-20"
] | [
"skywork"
] | c771e35978c719943172831f92b5954ce570b5cd8eb9b29fc58baf980a6edba4 | [
{
"content": "Find the coefficient of $x^3$ in the expansion of $(1-x)^5(3+x)$.",
"role": "user"
}
] | Find the coefficient of $x^3$ in the expansion of $(1-x)^5(3+x)$. | "[\"-20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2236, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16185"}] | {
"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
} |
[
"33"
] | [
"skywork"
] | 57fdf4bbbebe2331be233e81c3a3aea58a8589baf4e4c8e55b5bcc964ecd8239 | [
{
"content": "In a physical education class, students line up in four rows to do exercises. One particular class has over 30 students, with three rows having the same number of students and one row having one more student than the other three rows. What is the smallest possible class size for this physical educ... | In a physical education class, students line up in four rows to do exercises. One particular class has over 30 students, with three rows having the same number of students and one row having one more student than the other three rows. What is the smallest possible class size for this physical education class? | "[\"33\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2216, "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:16186"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"16"
] | [
"skywork"
] | d67987ddef27df6f44601a53eb1c6fc5bba2b20749813b36bff3c971df4da9b7 | [
{
"content": "Given the equation $x^{2}+(a-6) x+a=0$ $(a \\neq 0)$ has two integer roots, find the integer value of $a$.\n\n---\n\nThe equation $x^{2}+(a-6) x+a=0$ $(a \\neq 0)$ is known to have two integer roots. Try to find the integer value of $a$.",
"role": "user"
}
] | Given the equation $x^{2}+(a-6) x+a=0$ $(a \neq 0)$ has two integer roots, find the integer value of $a$.
---
The equation $x^{2}+(a-6) x+a=0$ $(a \neq 0)$ is known to have two integer roots. Try to find the integer value of $a$. | "[\"16\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 2213, "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:16187"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"11"
] | [
"skywork"
] | fc2b985ddccdddec2bcdd950d57c21e2706d29c54d71fe9c2bd467665641d05f | [
{
"content": "What is $88 \\div 4 \\div 2$?",
"role": "user"
}
] | What is $88 \div 4 \div 2$? | "[\"11\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2241, "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:16188"}] | {
"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
} |
[
"2005^{1002} / 2004!"
] | [
"skywork"
] | 72a51a043b674dc8566f3226b1d7c3272b13295cf2aa5bc0c5a229e70a7028a4 | [
{
"content": "For a string of $P$ 's and $Q$ 's, the value is defined to be the product of the positions of the $P$ 's. For example, the string $P P Q P Q Q$ has value $1 \\cdot 2 \\cdot 4=8$. Also, a string is called antipalindromic if writing it backwards, then turning all the $P$ 's into $Q$ 's and vice vers... | For a string of $P$ 's and $Q$ 's, the value is defined to be the product of the positions of the $P$ 's. For example, the string $P P Q P Q Q$ has value $1 \cdot 2 \cdot 4=8$. Also, a string is called antipalindromic if writing it backwards, then turning all the $P$ 's into $Q$ 's and vice versa, produces the original... | "[\"2005^{1002} / 2004!\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 2208, "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:16189"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2:1"
] | [
"skywork"
] | 973d37716c86b25140bb7b7475691ad55d0784f3678481fc5402fcf53e39e5e1 | [
{
"content": "The diagram shows a triangle \\(ABC\\) and two lines \\(AD\\) and \\(BE\\), where \\(D\\) is the midpoint of \\(BC\\) and \\(E\\) lies on \\(CA\\). The lines \\(AD\\) and \\(BE\\) meet at \\(Z\\), the midpoint of \\(AD\\). What is the ratio of the length \\(CE\\) to the length \\(EA\\)?",
"rol... | The diagram shows a triangle \(ABC\) and two lines \(AD\) and \(BE\), where \(D\) is the midpoint of \(BC\) and \(E\) lies on \(CA\). The lines \(AD\) and \(BE\) meet at \(Z\), the midpoint of \(AD\). What is the ratio of the length \(CE\) to the length \(EA\)? | "[\"2:1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2214, "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:16190"}] | {
"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
} |
[
"44"
] | [
"skywork"
] | f924d629bea92ea256676c24c026126bdc1b1547a7a2898c11b66dcac9e41545 | [
{
"content": "For how many positive integers $n \\le 500$ is $n!$ divisible by $2^{n-2}$?\n\n[i]Proposed by Eugene Chen[/i]",
"role": "user"
}
] | For how many positive integers $n \le 500$ is $n!$ divisible by $2^{n-2}$?
[i]Proposed by Eugene Chen[/i] | "[\"44\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2238, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16191"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{24-3\\sqrt{3}}"
] | [
"skywork"
] | 64b5b4509979f7e188035fa7ee3479db2a9e33864d959fd164b6947f7cdb5a8a | [
{
"content": "## Task B-3.6.\n\nDuring the New Year's celebration, an irresponsible person fired two fireworks. One of the fireworks lightly injured a passerby. Forensic experts need to discover from which location the two fireworks were fired. They found a mark (black dot) in the wall of a nearby building that... | ## Task B-3.6.
During the New Year's celebration, an irresponsible person fired two fireworks. One of the fireworks lightly injured a passerby. Forensic experts need to discover from which location the two fireworks were fired. They found a mark (black dot) in the wall of a nearby building that had ricocheted and hit ... | "[\"\\\\sqrt{24-3\\\\sqrt{3}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2222, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16192"}] | {
"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
} |
[
"(5,2,0)"
] | [
"skywork"
] | 8080a8cae57aa82ac2d91a9b4fe5c17fc3c34cde3b5d7fedc4aa08b8067a4e96 | [
{
"content": "\\section*{Task 2 - 310932}\n\nIn a collection of curiosities, there was supposed to be a vessel with the following inscription:\n\nFive Stroke Two Zero fits as a measure in me, after the first digit read \"through\" for the stroke! Or turn around, Zero Two Five you will find, after the first digi... | \section*{Task 2 - 310932}
In a collection of curiosities, there was supposed to be a vessel with the following inscription:
Five Stroke Two Zero fits as a measure in me, after the first digit read "through" for the stroke! Or turn around, Zero Two Five you will find, after the first digit add a decimal point!
Indee... | "[\"(5,2,0)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2202, "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:16193"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-7"
] | [
"skywork"
] | 15af5a853cd5c4fabfc8f26c6c10cbe1cd0e9a12ddbca57f3d644537deda7cad | [
{
"content": "1. (1996 28th Canadian Mathematical Olympiad) If $\\alpha, \\beta, \\gamma$ are the roots of the equation $x^{3}-x-1=0$, find the value of $\\frac{1+\\alpha}{1-\\alpha}+\\frac{1+\\beta}{1-\\beta}+\\frac{1+\\gamma}{1-\\gamma}$.",
"role": "user"
}
] | 1. (1996 28th Canadian Mathematical Olympiad) If $\alpha, \beta, \gamma$ are the roots of the equation $x^{3}-x-1=0$, find the value of $\frac{1+\alpha}{1-\alpha}+\frac{1+\beta}{1-\beta}+\frac{1+\gamma}{1-\gamma}$. | "[\"-7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2228, "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:16195"}] | {
"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"
] | bc8d010508b741d6bf9e1158d069496d9a759302f65899e562864c13309ead40 | [
{
"content": "If $1-\\frac{4}{x}+\\frac{4}{x^2}=0$, then $\\frac{2}{x}$ equals",
"role": "user"
}
] | If $1-\frac{4}{x}+\frac{4}{x^2}=0$, then $\frac{2}{x}$ equals | "[\"1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2231, "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:16196"}] | {
"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{\\pi}{2}"
] | [
"skywork"
] | 1930a9c63e4c24d33ed01bd886d73f3da01a5fd0eeb8fb8d482e4bd72fd70b9d | [
{
"content": "18.4 Large Question: Let $A$ be a point on the ellipse $C_{1}: \\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1(a>b>0)$. Its symmetric points with respect to the $y$-axis, the origin, and the $x$-axis are $B$, $C$, and $D$ respectively. $E$ is another point on the ellipse $C_{1}$ such that $A E \\perp ... | 18.4 Large Question: Let $A$ be a point on the ellipse $C_{1}: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)$. Its symmetric points with respect to the $y$-axis, the origin, and the $x$-axis are $B$, $C$, and $D$ respectively. $E$ is another point on the ellipse $C_{1}$ such that $A E \perp A C$.
(1) Find the equati... | "[\"\\\\frac{\\\\pi}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2212, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 12}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16197"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3}{4}"
] | [
"skywork"
] | dbd78f4e76ccdb368652813691b89af2016651774ede380aa4529b73c95e63fe | [
{
"content": "In triangle $AHI$, which is equilateral, lines $\\overline{BC}$, $\\overline{DE}$, and $\\overline{FG}$ are all parallel to $\\overline{HI}$. The lengths satisfy $AB = BD = DF = FH$. However, the point $F$ on line segment $AH$ is such that $AF$ is half of $AH$. Determine the ratio of the area of t... | In triangle $AHI$, which is equilateral, lines $\overline{BC}$, $\overline{DE}$, and $\overline{FG}$ are all parallel to $\overline{HI}$. The lengths satisfy $AB = BD = DF = FH$. However, the point $F$ on line segment $AH$ is such that $AF$ is half of $AH$. Determine the ratio of the area of trapezoid $FGIH$ to the are... | "[\"\\\\frac{3}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2217, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 6, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16198"}] | {
"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
} |
[
"98"
] | [
"skywork"
] | 7aa091f76e05822c33e694a1e1c355eaf73190588cd70113ad967c5715f07f5f | [
{
"content": "A point whose coordinates are both integers is called a lattice point. How many lattice points lie on the hyperbola $x^2 - y^2 = 2000^2$ ?",
"role": "user"
}
] | A point whose coordinates are both integers is called a lattice point. How many lattice points lie on the hyperbola $x^2 - y^2 = 2000^2$ ? | "[\"98\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 2239, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16199"}, {"dataset": "skywork", "extra_in... | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"skywork"
] | 00faa7379b2d22099fdb42710e27e33a7975d98ed90d9a3163d8f0639b933652 | [
{
"content": "The points $(2, 9), (12, 14)$, and $(4, m)$, where $m$ is an integer, are vertices of a triangle. What is the sum of the values of $m$ for which the area of the triangle is a minimum?",
"role": "user"
}
] | The points $(2, 9), (12, 14)$, and $(4, m)$, where $m$ is an integer, are vertices of a triangle. What is the sum of the values of $m$ for which the area of the triangle is a minimum? | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2230, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16200"}] | {
"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
} |
[
"169"
] | [
"skywork"
] | 593aec75e180d35563d98d8f57d096a57683289e7ae3f96f06f70e5ca75520f8 | [
{
"content": "Given that $\\alpha$ and $\\beta$ are the roots of $x^2 - 2x - 1 = 0,$ find $5 \\alpha^4 + 12 \\beta^3.$",
"role": "user"
}
] | Given that $\alpha$ and $\beta$ are the roots of $x^2 - 2x - 1 = 0,$ find $5 \alpha^4 + 12 \beta^3.$ | "[\"169\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2244, "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:16201"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.058"
] | [
"skywork"
] | 90abd5d0c0778a7240ff0fc3e4dcf02904b08a0e8e1b6f3e2a79ac8d412049f9 | [
{
"content": "13. Line-up. (From 8th grade, 3 points) Twenty kindergarten children, including 11 girls and 9 boys, stand in a line-up at random. Find the probability that there will be no more than five girls between the first and the last boy.",
"role": "user"
}
] | 13. Line-up. (From 8th grade, 3 points) Twenty kindergarten children, including 11 girls and 9 boys, stand in a line-up at random. Find the probability that there will be no more than five girls between the first and the last boy. | "[\"0.058\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2229, "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:16202"}] | {
"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"
] | 7774eefda3ff3903a586b7a18c3fedb3235af564ec9d454c2bccd148dd192ead | [
{
"content": "16. Let $\\alpha, \\beta$ be real numbers. If for any real numbers $x, y, z$, we have $\\alpha(x y+y z+z x) \\leqslant M \\leqslant \\beta\\left(x^{2}+y^{2}+z^{2}\\right)$ always holds, where $M=\\sqrt{x^{2}+x y+y^{2}} \\cdot \\sqrt{y^{2}+y z+z^{2}}+\\sqrt{y^{2}+y z+z^{2}} \\cdot \\sqrt{z^{2}+z x+... | 16. Let $\alpha, \beta$ be real numbers. If for any real numbers $x, y, z$, we have $\alpha(x y+y z+z x) \leqslant M \leqslant \beta\left(x^{2}+y^{2}+z^{2}\right)$ always holds, where $M=\sqrt{x^{2}+x y+y^{2}} \cdot \sqrt{y^{2}+y z+z^{2}}+\sqrt{y^{2}+y z+z^{2}} \cdot \sqrt{z^{2}+z x+x^{2}}+\sqrt{z^{2}+z x+x^{2}} \cdot ... | "[\"3\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2220, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 10, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16203"}] | {
"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"
] | d24021cd5370eb9e8d7c834b625c7f7769b3bf7b78d625c0e0adc7b3218ee7d4 | [
{
"content": "G2.1 If the sequence $1,6+2 a, 10+5 a, \\ldots$ forms an A.P., find $a$.",
"role": "user"
}
] | G2.1 If the sequence $1,6+2 a, 10+5 a, \ldots$ forms an A.P., find $a$. | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2226, "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:16204"}] | {
"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"
] | d428e4a6a6149b1598d9d380dae0c0ee47639471c56ba35d227a2e7ee4b0fb02 | [
{
"content": "If $10^n = 1000^{20}$, what is the value of $n$?",
"role": "user"
}
] | If $10^n = 1000^{20}$, what is the value of $n$? | "[\"60\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2243, "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:16205"}] | {
"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
} |
[
"259"
] | [
"skywork"
] | 8255794f17277e5dce7205def30754cb03422e8f056abcd2e51a7c8722c3aab9 | [
{
"content": "Rectangle $ABCD$ is given with $AB=63$ and $BC=448.$ Points $E$ and $F$ lie on $AD$ and $BC$ respectively, such that $AE=CF=84.$ The inscribed circle of triangle $BEF$ is tangent to $EF$ at point $P,$ and the inscribed circle of triangle $DEF$ is tangent to $EF$ at point $Q.$ Find $PQ.$",
"rol... | Rectangle $ABCD$ is given with $AB=63$ and $BC=448.$ Points $E$ and $F$ lie on $AD$ and $BC$ respectively, such that $AE=CF=84.$ The inscribed circle of triangle $BEF$ is tangent to $EF$ at point $P,$ and the inscribed circle of triangle $DEF$ is tangent to $EF$ at point $Q.$ Find $PQ.$ | "[\"259\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2215, "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:16206"}] | {
"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
} |
[
"4n^3"
] | [
"skywork"
] | c852f907a0f95000ce872b6381b97bf3930c413c13681e92139e1ebd6fabce1b | [
{
"content": "Let $n$ be a positive integer. A sequence $(a, b, c)$ of $a, b, c \\in \\{1, 2, . . . , 2n\\}$ is called [i]joke [/i] if its shortest term is odd and if only that smallest term, or no term, is repeated. For example, the sequences $(4, 5, 3)$ and $(3, 8, 3)$ are jokes, but $(3, 2, 7)$ and $(3, 8, 8... | Let $n$ be a positive integer. A sequence $(a, b, c)$ of $a, b, c \in \{1, 2, . . . , 2n\}$ is called [i]joke [/i] if its shortest term is odd and if only that smallest term, or no term, is repeated. For example, the sequences $(4, 5, 3)$ and $(3, 8, 3)$ are jokes, but $(3, 2, 7)$ and $(3, 8, 8)$ are not. Determine the... | "[\"4n^3\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2225, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16207"}] | {
"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
} |
[
"96"
] | [
"skywork"
] | 75d71bf9da3a1ad4824fe77f20a0c859c35b06809b761613afa5ea76e8c43229 | [
{
"content": "A1. When paying a deposit, we have to pay a $1.2\\%$ fee. How many dollars will the fee amount to if we have to pay a deposit of 8000 SIT?\n(A) 960\n(B) 115\n(C) 120\n(D) 667\n(E) 96",
"role": "user"
}
] | A1. When paying a deposit, we have to pay a $1.2\%$ fee. How many dollars will the fee amount to if we have to pay a deposit of 8000 SIT?
(A) 960
(B) 115
(C) 120
(D) 667
(E) 96 | "[\"96\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2232, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16208"}] | {
"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
} |
[
"124"
] | [
"skywork"
] | c1ed448569ca98c51d203607cea9a1ab5a42f80e60e42d2e3b67387f98654572 | [
{
"content": "What is $3\\cdot 9+4\\cdot 10+11\\cdot 3+3\\cdot 8$?",
"role": "user"
}
] | What is $3\cdot 9+4\cdot 10+11\cdot 3+3\cdot 8$? | "[\"124\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2267, "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:16209"}] | {
"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
} |
[
"80"
] | [
"skywork"
] | 08171e2a1b082217e598e2178faf1cd60576bc638117d8bae372baf9d3b557bf | [
{
"content": "A two-digit number $A$ is a supernumber if it is possible to find two numbers $B$ and $C$, both also two-digit numbers, such that:\n\n- $A = B + C$;\n- the sum of the digits of $A$ = (sum of the digits of $B$) + (sum of the digits of $C$).\n\nFor example, 35 is a supernumber. Two different ways to... | A two-digit number $A$ is a supernumber if it is possible to find two numbers $B$ and $C$, both also two-digit numbers, such that:
- $A = B + C$;
- the sum of the digits of $A$ = (sum of the digits of $B$) + (sum of the digits of $C$).
For example, 35 is a supernumber. Two different ways to show this are $35 = 11 + 2... | "[\"80\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2233, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "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:16210"}] | {
"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
} |
[
"176"
] | [
"skywork"
] | 179179484f80590f8da014c9ff0381e2fee7322fdb0f6c162ea9954b74ca3815 | [
{
"content": "14. (5 points) Two cars, A and B, start from points $A$ and $B$ respectively and travel towards each other. They meet 8 kilometers away from the midpoint between $A$ and $B$. It is known that the speed of car A is 1.2 times that of car B. Find the distance between $A$ and $B$ is $\\qquad$ kilomete... | 14. (5 points) Two cars, A and B, start from points $A$ and $B$ respectively and travel towards each other. They meet 8 kilometers away from the midpoint between $A$ and $B$. It is known that the speed of car A is 1.2 times that of car B. Find the distance between $A$ and $B$ is $\qquad$ kilometers. | "[\"176\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2240, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16211"}] | {
"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
} |
[
"91"
] | [
"skywork"
] | 6780de03a64462bd3203f33ec87fa62f84db6e1e5b3ba2d6a434821c5276edf0 | [
{
"content": "Let $S = {1, 2, \\cdots, 100}.$ $X$ is a subset of $S$ such that no two distinct elements in $X$ multiply to an element in $X.$ Find the maximum number of elements of $X$ . \n\n*2022 CCA Math Bonanza Individual Round #3*",
"role": "user"
}
] | Let $S = {1, 2, \cdots, 100}.$ $X$ is a subset of $S$ such that no two distinct elements in $X$ multiply to an element in $X.$ Find the maximum number of elements of $X$ .
*2022 CCA Math Bonanza Individual Round #3* | "[\"91\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2249, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16212"}] | {
"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"
] | a748567f670c64d771eb9d1e1ef4b22a9dafc035fb6fabdbe49025e0ebf62f73 | [
{
"content": "Find the value of $a$ so that the lines described by\n\\[\\begin{pmatrix} 2 \\\\ -1 \\\\ 0 \\end{pmatrix} + t \\begin{pmatrix} a \\\\ -2 \\\\ 1 \\end{pmatrix}\\]and\n\\[\\begin{pmatrix} 1 \\\\ -3/2 \\\\ -5 \\end{pmatrix} + u \\begin{pmatrix} 1 \\\\ 3/2 \\\\ 2 \\end{pmatrix}\\]are perpendicular.",
... | Find the value of $a$ so that the lines described by
\[\begin{pmatrix} 2 \\ -1 \\ 0 \end{pmatrix} + t \begin{pmatrix} a \\ -2 \\ 1 \end{pmatrix}\]and
\[\begin{pmatrix} 1 \\ -3/2 \\ -5 \end{pmatrix} + u \begin{pmatrix} 1 \\ 3/2 \\ 2 \end{pmatrix}\]are perpendicular. | "[\"1\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2257, "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:16213"}] | {
"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
} |
[
"1.011"
] | [
"skywork"
] | b9f48c155c9957052b4c3e88996119e6fab2a83d3a70e85e823f3168b281ca3d | [
{
"content": "Which of the following numbers is closest to 1: $\frac{11}{10}$, $\frac{111}{100}$, 1.101, $\frac{1111}{1000}$, 1.011?",
"role": "user"
}
] | Which of the following numbers is closest to 1: $ rac{11}{10}$, $ rac{111}{100}$, 1.101, $ rac{1111}{1000}$, 1.011? | "[\"1.011\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2251, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 0, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16214"}] | {
"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{455}{472}"
] | [
"skywork"
] | 98f0f99b00535a9098a9bc9d9817accf51284a1da147942f4c198900ff2bbb0c | [
{
"content": "The Student council has 24 members: 12 boys and 12 girls. A 5-person committee is selected at random. What is the probability that the committee includes at least one boy and at least one girl?",
"role": "user"
}
] | The Student council has 24 members: 12 boys and 12 girls. A 5-person committee is selected at random. What is the probability that the committee includes at least one boy and at least one girl? | "[\"\\\\frac{455}{472}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2260, "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:16215"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{9}{2}"
] | [
"skywork"
] | 1b16bf88d0df01962a6bf078a0ec5c72825ff402b590aaab0ea55b5ffb09be45 | [
{
"content": "There exists a positive number $m$ such that the positive roots of the equation $\\sqrt{3} \\sin x - \\cos x = m$ form an arithmetic sequence in ascending order. If the point $A(1, m)$ lies on the line $ax + by - 2 = 0 (a > 0, b > 0)$, find the minimum value of $\\frac{1}{a} + \\frac{2}{b}$.",
... | There exists a positive number $m$ such that the positive roots of the equation $\sqrt{3} \sin x - \cos x = m$ form an arithmetic sequence in ascending order. If the point $A(1, m)$ lies on the line $ax + by - 2 = 0 (a > 0, b > 0)$, find the minimum value of $\frac{1}{a} + \frac{2}{b}$. | "[\"\\\\frac{9}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2227, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16216"}] | {
"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
} |
[
"35"
] | [
"skywork"
] | 7982f1eb0bc062b5f52a12e4bc3b90355dceb1f1d8211a00989e1e2ae23c87a8 | [
{
"content": "On Monday, Hank drove to work at an average speed of $70 \\mathrm{~km} / \\mathrm{h}$ and arrived 1 minute late. On Tuesday, he left at the same time and took the same route. This time he drove at an average speed of $75 \\mathrm{~km} / \\mathrm{h}$ and arrived 1 minute early. How long is his rout... | On Monday, Hank drove to work at an average speed of $70 \mathrm{~km} / \mathrm{h}$ and arrived 1 minute late. On Tuesday, he left at the same time and took the same route. This time he drove at an average speed of $75 \mathrm{~km} / \mathrm{h}$ and arrived 1 minute early. How long is his route to work?
(A) $30 \mathrm... | "[\"35\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2255, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16217"}] | {
"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
} |
[
"15"
] | [
"skywork"
] | 3c9709869c8dd7655d372b61f53ed378dede0abe19794c604eb7d276a701772f | [
{
"content": "I walk from home to school in 30 minutes, while my brother takes 40 minutes. How many minutes will it take for me to catch up with my brother if he left the house 5 minutes before me?",
"role": "user"
}
] | I walk from home to school in 30 minutes, while my brother takes 40 minutes. How many minutes will it take for me to catch up with my brother if he left the house 5 minutes before me? | "[\"15\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2246, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 2, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16218"}] | {
"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"
] | 3807b21768f3a9064e38a1a842ba502b63c9d5623387b8c18ea264d3086909c8 | [
{
"content": "80. Three students' scores in a math exam are all different, and none of them scored 0 or 100. Each student knows their own score and ranking, but not the scores or rankings of the other two. They then provide information to each other:\n甲 says: “My score is a multiple of 10.”\n乙 says: “My score i... | 80. Three students' scores in a math exam are all different, and none of them scored 0 or 100. Each student knows their own score and ranking, but not the scores or rankings of the other two. They then provide information to each other:
甲 says: “My score is a multiple of 10.”
乙 says: “My score is a multiple of 12.”
丙 s... | "[\"84\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 2237, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 7}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:16219"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{6} + \\sqrt{2}"
] | [
"skywork"
] | a238458d350090d4e3c85e9a7a0720d0df02f3af8e87a8d11f4a84cad431ce25 | [
{
"content": "Let $M$ be a set of points in the Cartesian plane, and let $\\left(S\\right)$ be a set of segments (whose endpoints not necessarily have to belong to $M$) such that one can walk from any point of $M$ to any other point of $M$ by travelling along segments which are in $\\left(S\\right)$. Find the s... | Let $M$ be a set of points in the Cartesian plane, and let $\left(S\right)$ be a set of segments (whose endpoints not necessarily have to belong to $M$) such that one can walk from any point of $M$ to any other point of $M$ by travelling along segments which are in $\left(S\right)$. Find the smallest total length of th... | "[\" \\\\sqrt{6} + \\\\sqrt{2} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 2247, "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:16220"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{4}"
] | [
"skywork"
] | ef416acd584d7b78ae1aa88423d4625aeb6301ff7bede4cb2e9881679e8220e3 | [
{
"content": "Given the parabola $C$: $x^2 = 2py (p > 0)$ and the line $2x-y+2=0$, they intersect at points $A$ and $B$. A vertical line is drawn from the midpoint of the line segment $AB$ to the $x$-axis, intersecting the parabola $C$ at point $Q$. If $\\overrightarrow{QA} \\cdot \\overrightarrow{QB}=0$, calcu... | Given the parabola $C$: $x^2 = 2py (p > 0)$ and the line $2x-y+2=0$, they intersect at points $A$ and $B$. A vertical line is drawn from the midpoint of the line segment $AB$ to the $x$-axis, intersecting the parabola $C$ at point $Q$. If $\overrightarrow{QA} \cdot \overrightarrow{QB}=0$, calculate the value of $p$. | "[\"\\\\frac{1}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 2245, "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:16221"}] | {
"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
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.