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 |
|---|---|---|---|---|---|---|---|---|
[
"18"
] | [
"skywork"
] | 14e50cb63ce8d95a3c7263ed672531633b70ea2840c76ee3cf651a6d67231f93 | [
{
"content": "Tim has a working analog 12-hour clock with two hands that run continuously (instead of, say, jumping on the minute). He also has a clock that runs really slow—at half the correct rate, to be exact. At noon one day, both clocks happen to show the exact time. At any given instant, the hands on each... | Tim has a working analog 12-hour clock with two hands that run continuously (instead of, say, jumping on the minute). He also has a clock that runs really slow—at half the correct rate, to be exact. At noon one day, both clocks happen to show the exact time. At any given instant, the hands on each clock form an angle b... | "[\"18\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107132, "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:117102"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"k=3"
] | [
"skywork"
] | 6241d27e45fc5ac8426480e64b6948392c2a09e5a231471459054147798009fc | [
{
"content": "Find the least $k$ for which the number $2010$ can be expressed as the sum of the squares of $k$ integers.",
"role": "user"
}
] | Find the least $k$ for which the number $2010$ can be expressed as the sum of the squares of $k$ integers. | "[\"k=3\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107150, "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:117103"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"21"
] | [
"skywork"
] | 01b2a257566274fc6e96bd68e55053f2aa725b877f045d5f0bb5fc384e10885f | [
{
"content": "The sum of two numbers $x$ and $y$ is 399, and the value of the fraction $\\frac{x}{y}$ is 0.9. What is the value of $y - x$?",
"role": "user"
}
] | The sum of two numbers $x$ and $y$ is 399, and the value of the fraction $\frac{x}{y}$ is 0.9. What is the value of $y - x$? | "[\"21\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107152, "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:117104"}] | {
"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{6}}{2}"
] | [
"skywork"
] | 27cca344d1009288c41430fc6e3e6b6108ea7c2125e78d828bc0e92359082bbb | [
{
"content": "16 In a cube $A B C D-A_{1} B_{1} C_{1} D_{1}$ with edge length 1, $E$ and $F$ are points on $A A_{1}$ and $C C_{1}$ respectively, and $A E=C_{1} F$. The minimum value of the area of quadrilateral $E B F D_{1}$ is $\\qquad$.",
"role": "user"
}
] | 16 In a cube $A B C D-A_{1} B_{1} C_{1} D_{1}$ with edge length 1, $E$ and $F$ are points on $A A_{1}$ and $C C_{1}$ respectively, and $A E=C_{1} F$. The minimum value of the area of quadrilateral $E B F D_{1}$ is $\qquad$. | "[\"\\\\frac{\\\\sqrt{6}}{2}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107106, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117105"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"n=7 \\text{ and } n=23"
] | [
"skywork"
] | 95b261fd553e5f6901bdc8abb022b3006ce5625d6284c1af68e695f977d105ad | [
{
"content": "Find all natural numbers $n$ greater than 3 such that $1+C_{n}^{1}+C_{n}^{2}+C_{3}^{3}$ divides $2^{2000}$.\n\nTranslate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.",
"role": "user"
}
] | Find all natural numbers $n$ greater than 3 such that $1+C_{n}^{1}+C_{n}^{2}+C_{3}^{3}$ divides $2^{2000}$.
Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly. | "[\"n=7 \\\\text{ and } n=23\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107139, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 13, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117106"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 5431e33f1c9e8b8b74ff96c51718debce75a1463004833b460293a83e8dd67ac | [
{
"content": "How many integers $n$ with $0\\leq n < 840$ are there such that $840$ divides $n^8-n^4+n-1$?\n\n$ \\textbf{(A)}\\ 1\n\\qquad\\textbf{(B)}\\ 2\n\\qquad\\textbf{(C)}\\ 3\n\\qquad\\textbf{(D)}\\ 6\n\\qquad\\textbf{(E)}\\ 8\n$",
"role": "user"
}
] | How many integers $n$ with $0\leq n < 840$ are there such that $840$ divides $n^8-n^4+n-1$?
$ \textbf{(A)}\ 1
\qquad\textbf{(B)}\ 2
\qquad\textbf{(C)}\ 3
\qquad\textbf{(D)}\ 6
\qquad\textbf{(E)}\ 8
$ | "[\"2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107141, "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:117107"}] | {
"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"
] | a841214b6a02dbc3b875989ddc917c638a17b75bb6faf9b82831d5f8bbe90cd1 | [
{
"content": "Дубанов И.С.\n\nIn five pots standing in a row, Rabbit poured three kilograms of honey (not necessarily into each and not necessarily equally). Winnie-the-Pooh can take any two adjacent pots. What is the maximum amount of honey that Winnie-the-Pooh can guarantee to eat?\n\n#",
"role": "user"
... | Дубанов И.С.
In five pots standing in a row, Rabbit poured three kilograms of honey (not necessarily into each and not necessarily equally). Winnie-the-Pooh can take any two adjacent pots. What is the maximum amount of honey that Winnie-the-Pooh can guarantee to eat?
# | "[\"1\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107137, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117109"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 861b04487a2f031ea917d0ff994970454f192680ebfc929009d8a72084306c72 | [
{
"content": "Problem 4. One mole of an ideal gas undergoes a closed cycle, in which:\n\n$1-2$ - isobaric process, during which the volume increases by 4 times;\n\n$2-3$ - isothermal process, during which the pressure increases;\n\n$3-1$ - a process in which the gas is compressed according to the law $T=\\gamma... | Problem 4. One mole of an ideal gas undergoes a closed cycle, in which:
$1-2$ - isobaric process, during which the volume increases by 4 times;
$2-3$ - isothermal process, during which the pressure increases;
$3-1$ - a process in which the gas is compressed according to the law $T=\gamma V^{2}$.
Find how many times... | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107140, "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:117110"}] | {
"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
} |
[
"18"
] | [
"skywork"
] | 38b19be932516b8edcf447ff6eb898dfb2525d14fd865ddabe947e5eeea250ac | [
{
"content": "If $x=3, y=2 x$ and $z=3 y$, the value of $z$ is\n(A) 8\n(B) 9\n(C) 6\n(D) 18\n(E) 15",
"role": "user"
}
] | If $x=3, y=2 x$ and $z=3 y$, the value of $z$ is
(A) 8
(B) 9
(C) 6
(D) 18
(E) 15 | "[\"18\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107147, "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:117111"}] | {
"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
} |
[
"14751"
] | [
"skywork"
] | 975a108571e521df578a0ce6ea5fb4f3faf02af9642c30b6e04a3b5e8b45788c | [
{
"content": "Bogdanov I.I.\n\nGiven a $100 \\times 100$ grid, the cells of which are colored black and white. In all columns, there are an equal number of black cells, while in all rows, there are different numbers of black cells. What is the maximum possible number of pairs of adjacent (by side) cells of diff... | Bogdanov I.I.
Given a $100 \times 100$ grid, the cells of which are colored black and white. In all columns, there are an equal number of black cells, while in all rows, there are different numbers of black cells. What is the maximum possible number of pairs of adjacent (by side) cells of different colors? | "[\"14751\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107138, "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:117112"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"-4"
] | [
"skywork"
] | 4efc451854f77878c2f37dd7c6a0927d4dcbf86ebe86dcfc3020d3a5028b93ef | [
{
"content": "What is the greatest integer value of $x$ for which $5-4x>17$?",
"role": "user"
}
] | What is the greatest integer value of $x$ for which $5-4x>17$? | "[\"-4\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107161, "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:117113"}] | {
"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{28800}{7}"
] | [
"skywork"
] | cbd54e07208ea804873633597ba9dc550e8d79f479c31ff503e879e6a01dd331 | [
{
"content": "When studying the traffic situation in a certain city, road density refers to the number of vehicles passing through a certain section of road divided by time, and vehicle density is the number of vehicles passing through a certain section of road divided by the length of that section. The traffic... | When studying the traffic situation in a certain city, road density refers to the number of vehicles passing through a certain section of road divided by time, and vehicle density is the number of vehicles passing through a certain section of road divided by the length of that section. The traffic flow is defined as $v... | "[\"\\\\frac{28800}{7}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107104, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117115"}] | {
"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{\\sqrt{3}}{3}"
] | [
"skywork"
] | f61051c97f766ccdce485b27e32b9097151b86dc91707bbe9986881ed66cbee7 | [
{
"content": "2.231. $\\frac{1+z}{1+\\sqrt{1+z}}-\\frac{1-z}{1-\\sqrt{1-z}} ; z=\\frac{\\sqrt{3}}{2}$.",
"role": "user"
}
] | 2.231. $\frac{1+z}{1+\sqrt{1+z}}-\frac{1-z}{1-\sqrt{1-z}} ; z=\frac{\sqrt{3}}{2}$. | "[\"\\\\frac{\\\\sqrt{3}}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107159, "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:117116"}] | {
"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
} |
[
"50"
] | [
"skywork"
] | 950338cc055b6c660318bcff14f1907ac92e789e0a7f30183bc41329ede6c425 | [
{
"content": "Given the arithmetic sequence $\\left\\{ a_n \\right\\}$ where each term is positive, the sum of the first $n$ terms is $S_n$. When $n \\in N^*, n \\geqslant 2$, it holds that $S_n = \\frac{n}{n-1}\\left( a_n^2 - a_1^2 \\right)$. Find the value of $S_{20} - 2S_{10}$.",
"role": "user"
}
] | Given the arithmetic sequence $\left\{ a_n \right\}$ where each term is positive, the sum of the first $n$ terms is $S_n$. When $n \in N^*, n \geqslant 2$, it holds that $S_n = \frac{n}{n-1}\left( a_n^2 - a_1^2 \right)$. Find the value of $S_{20} - 2S_{10}$. | "[\"50\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107134, "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:117117"}] | {
"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
} |
[
"80200"
] | [
"skywork"
] | bbcae246e4031488a902eee3745d82b4c29de96c063e7199e3fd792cbc2ff523 | [
{
"content": "For $p=1, 2, \\cdots, 10$ let $S_p$ be the sum of the first $40$ terms of the arithmetic progression whose first term is $p$ and whose common difference is $2p-1$; then $S_1+S_2+\\cdots+S_{10}$ is",
"role": "user"
}
] | For $p=1, 2, \cdots, 10$ let $S_p$ be the sum of the first $40$ terms of the arithmetic progression whose first term is $p$ and whose common difference is $2p-1$; then $S_1+S_2+\cdots+S_{10}$ is | "[\"80200\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107151, "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:117118"}] | {
"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{21}{32}"
] | [
"skywork"
] | ea3fddd57aa639ae7d40502e5460797cd2a3d46577c07b4ae66bef17ff001164 | [
{
"content": "You found a whole pizza in your refrigerator. On your first trip, you eat one third of the pizza. On each successive trip, you eat half of what remains from the previous trip. After six trips in total to the refrigerator, what fractional part of the pizza have you eaten?",
"role": "user"
}
] | You found a whole pizza in your refrigerator. On your first trip, you eat one third of the pizza. On each successive trip, you eat half of what remains from the previous trip. After six trips in total to the refrigerator, what fractional part of the pizza have you eaten? | "[\"\\\\frac{21}{32}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 107155, "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:117119"}] | {
"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
} |
[
"11, 72, 62"
] | [
"skywork"
] | 59af3560476dd2d90be89f39f1b22bb3810674031f5c674374e8ee9d8e9a12b0 | [
{
"content": "The paper is written on consecutive integers $1$ through $n$. Then are deleted all numbers ending in $4$ and $9$ and the rest alternating between $-$ and $+$. Finally, an opening parenthesis is added after each character and at the end of the expression the corresponding number of parentheses: $1 ... | The paper is written on consecutive integers $1$ through $n$. Then are deleted all numbers ending in $4$ and $9$ and the rest alternating between $-$ and $+$. Finally, an opening parenthesis is added after each character and at the end of the expression the corresponding number of parentheses: $1 - (2 + 3 - (5 + 6 - (7... | "[\"11, 72, 62\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107146, "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:117120"}] | {
"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}{2}"
] | [
"skywork"
] | e65bc186d9f67e010683a572dd054ac8ff9c9205fe62f2ca9215eb7f312eee3a | [
{
"content": "Let $E$ be the midpoint of side $[AB]$ of square $ABCD$. Let the circle through $B$ with center $A$ and segment $[EC]$ meet at $F$. What is $|EF|/|FC|$? \n\n$ \n\\textbf{(A)}\\ 2\n\\qquad\\textbf{(B)}\\ \\dfrac{3}{2}\n\\qquad\\textbf{(C)}\\ \\sqrt{5}-1\n\\qquad\\textbf{(D)}\\ 3\n\\qquad\\textbf{(E... | Let $E$ be the midpoint of side $[AB]$ of square $ABCD$. Let the circle through $B$ with center $A$ and segment $[EC]$ meet at $F$. What is $|EF|/|FC|$?
$
\textbf{(A)}\ 2
\qquad\textbf{(B)}\ \dfrac{3}{2}
\qquad\textbf{(C)}\ \sqrt{5}-1
\qquad\textbf{(D)}\ 3
\qquad\textbf{(E)}\ \sqrt{3}
$ | "[\"\\\\frac{3}{2}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107153, "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:117122"}] | {
"all_reference_components_parse": true,
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[
"1"
] | [
"skywork"
] | 9d0dd6803813a3fb6b747f8fbeae74c2b8a4e4e83199d2fc1876160bb4c1a0c0 | [
{
"content": "The sequence $(x_n)$ is defined as follows:\n$$x_1=2,\\, x_{n+1}=\\sqrt{x_n+8}-\\sqrt{x_n+3}$$\nfor all $n\\geq 1$.\na. Prove that $(x_n)$ has a finite limit and find that limit.\nb. For every $n\\geq 1$, prove that\n$$n\\leq x_1+x_2+\\dots +x_n\\leq n+1.$$",
"role": "user"
}
] | The sequence $(x_n)$ is defined as follows:
$$x_1=2,\, x_{n+1}=\sqrt{x_n+8}-\sqrt{x_n+3}$$
for all $n\geq 1$.
a. Prove that $(x_n)$ has a finite limit and find that limit.
b. For every $n\geq 1$, prove that
$$n\leq x_1+x_2+\dots +x_n\leq n+1.$$ | "[\" 1 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107156, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117123"}] | {
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[
"5:6:7"
] | [
"skywork"
] | c447c4cc761deb79929e2272fe5338811f56d7cd40afcf8337780158e56a30be | [
{
"content": "[ Sum of angles in a triangle. Theorem about the exterior angle.]\n\nThe angles of a triangle are in the ratio $2: 3: 4$. Find the ratio of the exterior angles of the triangle.",
"role": "user"
}
] | [ Sum of angles in a triangle. Theorem about the exterior angle.]
The angles of a triangle are in the ratio $2: 3: 4$. Find the ratio of the exterior angles of the triangle. | "[\"5:6:7\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107164, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 16, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117124"}] | {
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[
"5"
] | [
"skywork"
] | 887b501bbc0f32ff06e5731b16990f8618db9addb0ee1a553c3bca0448dd07e9 | [
{
"content": "Example 3 Given that $\\alpha, \\beta$ are the roots of the equation $x^{2}-x-1=0$. Then the value of $\\alpha^{4}+3 \\beta$ is $\\qquad$\n(2003, National Junior High School Mathematics Competition, Tianjin Preliminary Contest)",
"role": "user"
}
] | Example 3 Given that $\alpha, \beta$ are the roots of the equation $x^{2}-x-1=0$. Then the value of $\alpha^{4}+3 \beta$ is $\qquad$
(2003, National Junior High School Mathematics Competition, Tianjin Preliminary Contest) | "[\"5\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107163, "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:117125"}] | {
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[
"10"
] | [
"skywork"
] | 51d6e19bc12e579e23b14c36728ec77128bd5c8a80d7c415963c9ece04b063eb | [
{
"content": "13. Let $m$ be a real number not less than -1, such that the equation $x^{2}+2(m-2) x+m^{2}-3 m+3=0$ has two distinct real roots $x_{1}$ and $x_{2}$.\n(1) If $x_{1}^{2}+x_{2}^{2}=6$. Find the value of $m$;\n(2) Find the maximum value of $\\frac{m x_{1}^{2}}{1-x_{1}}+\\frac{m x_{2}^{2}}{1-x_{2}}$."... | 13. Let $m$ be a real number not less than -1, such that the equation $x^{2}+2(m-2) x+m^{2}-3 m+3=0$ has two distinct real roots $x_{1}$ and $x_{2}$.
(1) If $x_{1}^{2}+x_{2}^{2}=6$. Find the value of $m$;
(2) Find the maximum value of $\frac{m x_{1}^{2}}{1-x_{1}}+\frac{m x_{2}^{2}}{1-x_{2}}$. | "[\"10\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107145, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:117126"}] | {
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} |
[
"2^{101}-4"
] | [
"skywork"
] | 137092b463bcdecd23f58cff33fed8f96630b9fbd731a0e123f75ecca8f34efb | [
{
"content": "1. In a certain country, the alphabet consists of three letters: \"M\", \"G\", and \"U\". A word is any finite sequence of these letters, in which two consonants cannot stand next to each other and two vowels cannot stand next to each other. How many 200-letter words are there in this country that... | 1. In a certain country, the alphabet consists of three letters: "M", "G", and "U". A word is any finite sequence of these letters, in which two consonants cannot stand next to each other and two vowels cannot stand next to each other. How many 200-letter words are there in this country that contain each of the three l... | "[\"2^{101}-4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107160, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 9}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117127"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"84"
] | [
"skywork"
] | 769056833c90db7939b9b671bef066740d6b821273bae685fe590eddb10fcb87 | [
{
"content": "E csudaszép emlék födi szent porait Diophantosnak $S$ éveinek számát hirdeti a fölirat.\n\nThis beautiful monument covers the sacred ashes of Diophantus, the inscription on the monument proclaims the number of his years $S$.\n\nÉltének hatodát boldog gyermekkorda kapta, tizenkettede szőtt álmokat ... | E csudaszép emlék födi szent porait Diophantosnak $S$ éveinek számát hirdeti a fölirat.
This beautiful monument covers the sacred ashes of Diophantus, the inscription on the monument proclaims the number of his years $S$.
Éltének hatodát boldog gyermekkorda kapta, tizenkettede szőtt álmokat ifjúkorán.
He spent one-s... | "[\"84\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107143, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117128"}] | {
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} |
[
"3^{671} \\cdot 4"
] | [
"skywork"
] | 00a2148c79ba2505c2c5a48b6dc7751c73db199b0a4f1bbc2cf467a0ed70667e | [
{
"content": "Zlatan has 2017 socks of various colours. He wants to proudly display one sock of each of the colours, and he counts that there are $N$ ways to select socks from his collection for display. Given this information, what is the maximum value of $N$?",
"role": "user"
}
] | Zlatan has 2017 socks of various colours. He wants to proudly display one sock of each of the colours, and he counts that there are $N$ ways to select socks from his collection for display. Given this information, what is the maximum value of $N$? | "[\"3^{671} \\\\cdot 4\"]" | train-math-omnimath | [{"dataset": "skywork", "extra_info": {"index": 107148, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117129"}] | {
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[
"2"
] | [
"skywork"
] | a37403249338a779bc49f2d31a4efe44539b812ab61e1b228a2688e013ca2007 | [
{
"content": "1. Solve the equation $9^{x-1}+3^{x+2}=90$.",
"role": "user"
}
] | 1. Solve the equation $9^{x-1}+3^{x+2}=90$. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107180, "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:117130"}] | {
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} |
[
"497"
] | [
"skywork"
] | 88440cbfa68c22fadeb2abe4bfe6dcb28dcf0bf7e13e7e64ec0a251f9ceba201 | [
{
"content": "Triangle $ABC$ is so that $AB = 15$, $BC = 22$, and $AC = 20$. Let $D, E, F$ lie on $BC$, $AC$, and $AB$, respectively, so $AD$, $BE$, $CF$ all contain a point $K$. Let $L$ be the second intersection of the circumcircles of $BFK$ and $CEK$. Suppose that $\\frac{AK}{KD} = \\frac{11}{7}$ , and $BD =... | Triangle $ABC$ is so that $AB = 15$, $BC = 22$, and $AC = 20$. Let $D, E, F$ lie on $BC$, $AC$, and $AB$, respectively, so $AD$, $BE$, $CF$ all contain a point $K$. Let $L$ be the second intersection of the circumcircles of $BFK$ and $CEK$. Suppose that $\frac{AK}{KD} = \frac{11}{7}$ , and $BD = 6$. If $KL^2 =\frac{a}{... | "[\"497\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107158, "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:117131"}] | {
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} |
[
"(1, 1, 1, 1), (1, 2, 3, 2), (1, 2, 4, 3)"
] | [
"skywork"
] | e6f40bf2e1a7e97136a90f5cc652321fb28e18220afbfde51ef1e2a4bef7d3b9 | [
{
"content": "Find all $4$-tuples $(a,b,c,d)$ of natural numbers with $a \\le b \\le c$ and $a!+b!+c!=3^d$",
"role": "user"
}
] | Find all $4$-tuples $(a,b,c,d)$ of natural numbers with $a \le b \le c$ and $a!+b!+c!=3^d$ | "[\"(1, 1, 1, 1), (1, 2, 3, 2), (1, 2, 4, 3)\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107170, "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:117132"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2\\sqrt{10}"
] | [
"skywork"
] | 185924879eb690b029dde323b1569f1ba6e7d0d13fd467b96dff49795bf6d880 | [
{
"content": "Suppose $z$ is a complex number such that $z^2 = 24-32i$. Find $|z|$.",
"role": "user"
}
] | Suppose $z$ is a complex number such that $z^2 = 24-32i$. Find $|z|$. | "[\"2\\\\sqrt{10}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107192, "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:117133"}] | {
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"reference_components": 1,
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} |
[
"\\frac {1}{2}"
] | [
"skywork"
] | 5fb9ff021426c4584f372ab5ad19b4bcaca45e83dd00e762c3b772ad4eba6b91 | [
{
"content": "Given the geometric sequence $\\{a_n\\}$, $a_5a_7=2$, $a_2+a_{10}=3$, determine the value of $\\frac{a_{12}}{a_4}$.",
"role": "user"
}
] | Given the geometric sequence $\{a_n\}$, $a_5a_7=2$, $a_2+a_{10}=3$, determine the value of $\frac{a_{12}}{a_4}$. | "[\"\\\\frac {1}{2}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107168, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117134"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"42"
] | [
"skywork"
] | 8f9492893a788e2fd16d318f6a5904f3e894d8a41b9db8e709aee4ac66f40e17 | [
{
"content": "Given a geometric sequence {a_n} satisfies a_1 = 3, and a_1 + a_3 + a_5 = 21, find the value of a_3 + a_5 + a_7.",
"role": "user"
}
] | Given a geometric sequence {a_n} satisfies a_1 = 3, and a_1 + a_3 + a_5 = 21, find the value of a_3 + a_5 + a_7. | "[\"42\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107149, "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:117135"}] | {
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} |
[
"\\left[\\sum_{k=1}^{n}(\\sqrt{k}-\\sqrt{k-1})^{2}\\right]^{\\frac{1}{2}}"
] | [
"skywork"
] | 9fb4746b8631b6b2068c7b9938133bffa363b925a4f65b019c27dd91765d5b8d | [
{
"content": "$\\square$ Example 17 Let $x_{i} \\geqslant 0(i=1,2, \\cdots, n)$ and $\\sum_{i=1}^{n} x_{i}^{2}+2 \\sum_{1 \\leqslant i<j \\leqslant n} \\sqrt{\\frac{i}{j}} x_{i} x_{j}$ $=1$, find the maximum and minimum values of $\\sum_{i=1}^{n} x_{i}$. (2001 National High School Mathematics League Additional ... | $\square$ Example 17 Let $x_{i} \geqslant 0(i=1,2, \cdots, n)$ and $\sum_{i=1}^{n} x_{i}^{2}+2 \sum_{1 \leqslant i<j \leqslant n} \sqrt{\frac{i}{j}} x_{i} x_{j}$ $=1$, find the maximum and minimum values of $\sum_{i=1}^{n} x_{i}$. (2001 National High School Mathematics League Additional Question) | "[\"\\\\left[\\\\sum_{k=1}^{n}(\\\\sqrt{k}-\\\\sqrt{k-1})^{2}\\\\right]^{\\\\frac{1}{2}}\"]" | train-math-numinamath1.5_inequalities | [{"dataset": "skywork", "extra_info": {"index": 107172, "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:117136"}] | {
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} |
[
"2x-2"
] | [
"skywork"
] | f1cd919d61f6dc860a7e274b371e3d0d4c8f3e83f485d5985b8a558f2e1877e6 | [
{
"content": "When the polynomial $x^3-2$ is divided by the polynomial $x^2-2$, the remainder is",
"role": "user"
}
] | When the polynomial $x^3-2$ is divided by the polynomial $x^2-2$, the remainder is | "[\"2x-2\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107183, "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:117138"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"8001"
] | [
"skywork"
] | 15aefd409a5555251b4e1b299cb7253fdf3d417ff5dd80492eee16d07cc4fc42 | [
{
"content": "For nonnegative integers $n$, let $f(n)$ be the number of digits of $n$ that are at least $5$. Let $g(n)=3^{f(n)}$. Compute\n\\[\\sum_{i=1}^{1000} g(i).\\]\n\n[i]Proposed by Nathan Ramesh",
"role": "user"
}
] | For nonnegative integers $n$, let $f(n)$ be the number of digits of $n$ that are at least $5$. Let $g(n)=3^{f(n)}$. Compute
\[\sum_{i=1}^{1000} g(i).\]
[i]Proposed by Nathan Ramesh | "[\"8001\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107167, "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:117139"}] | {
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"reference_components": 1,
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} |
[
"\\frac{1011}{2}\\cdot\\cot\\frac{\\pi}{4044}"
] | [
"skywork"
] | f0e8b2fa4537923b9a491664e5bdbc89b86d1a64ea2256eafca968a12bd2f4c0 | [
{
"content": "Let $P$ be a 2023 -sided polygon. All but one side has length 1 . What is the maximum possible area of $P$ ?",
"role": "user"
}
] | Let $P$ be a 2023 -sided polygon. All but one side has length 1 . What is the maximum possible area of $P$ ? | "[\"\\\\frac{1011}{2}\\\\cdot\\\\cot\\\\frac{\\\\pi}{4044}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107185, "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:117140"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2012"
] | [
"skywork"
] | 39bcd865d21d373b925b97310eaf348fea37986c05d63939a90ebc25f040c55d | [
{
"content": "In Anchuria, a standardized state exam is conducted. The probability of guessing the correct answer to each exam question is 0.25. In 2011, in order to obtain a certificate, it was necessary to answer correctly three out of 20 questions. In 2012, the School Management of Anchuria decided that thre... | In Anchuria, a standardized state exam is conducted. The probability of guessing the correct answer to each exam question is 0.25. In 2011, in order to obtain a certificate, it was necessary to answer correctly three out of 20 questions. In 2012, the School Management of Anchuria decided that three questions were too f... | "[\"2012\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107175, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117141"}] | {
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"reference_components": 1,
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[
"20"
] | [
"skywork"
] | 1d70eba63fbdeb557c6d36d848729def59868788dd7d283f7a6725b08004877d | [
{
"content": "All of the triangles in the diagram below are similar to isosceles triangle $ABC$, in which $AB=AC$. Each of the $7$ smallest triangles has area $1,$ and $\\triangle ABC$ has area $40$. What is the area of trapezoid $DBCE$?",
"role": "user"
}
] | All of the triangles in the diagram below are similar to isosceles triangle $ABC$, in which $AB=AC$. Each of the $7$ smallest triangles has area $1,$ and $\triangle ABC$ has area $40$. What is the area of trapezoid $DBCE$? | "[\"20\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107188, "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:117142"}] | {
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"reference_components": 1,
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} |
[
"502"
] | [
"skywork"
] | fb5e3ca86ae9c64b7664a5c860357220302e4398081573e0c3112aabf14f545b | [
{
"content": "Given the set \\( A = \\{1, 2, 3, \\ldots, 1002\\} \\), Petya and Vasya play a game. Petya names a number \\( n \\), and Vasya then selects a subset of \\( A \\) consisting of \\( n \\) elements. Vasya wins if there are no two coprime numbers in the subset he selects; otherwise, Petya wins. What i... | Given the set \( A = \{1, 2, 3, \ldots, 1002\} \), Petya and Vasya play a game. Petya names a number \( n \), and Vasya then selects a subset of \( A \) consisting of \( n \) elements. Vasya wins if there are no two coprime numbers in the subset he selects; otherwise, Petya wins. What is the minimum \( n \) that Petya ... | "[\"502\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107166, "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:117143"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"\\frac{3 \\pi}{4}"
] | [
"skywork"
] | 1deeb9e4d2dd82651c5511c0efc837f4bdcd77ced25c9b0b42d0d2a37707dbd4 | [
{
"content": "1. Given $\\alpha, \\beta$ are acute angles, $\\cos \\alpha=\\frac{\\sqrt{5}}{5}, \\cos \\beta=$ $\\frac{\\sqrt{10}}{10}$. Then $\\alpha+\\beta=$ $\\qquad$ .",
"role": "user"
}
] | 1. Given $\alpha, \beta$ are acute angles, $\cos \alpha=\frac{\sqrt{5}}{5}, \cos \beta=$ $\frac{\sqrt{10}}{10}$. Then $\alpha+\beta=$ $\qquad$ . | "[\"\\\\frac{3 \\\\pi}{4}\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107186, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 11, "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:117144"}] | {
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"reference_components": 1,
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} |
[
"78"
] | [
"skywork"
] | 74937520bee148a4e834d376d4e046dc89fd80296415473679e85df5eb2417e9 | [
{
"content": "On the board, there are three two-digit numbers. One starts with 5, another starts with 6, and the third one starts with 7. The teacher asked three students to each choose any two of these numbers and add them together. The first student got 147, and the results of the second and third students we... | On the board, there are three two-digit numbers. One starts with 5, another starts with 6, and the third one starts with 7. The teacher asked three students to each choose any two of these numbers and add them together. The first student got 147, and the results of the second and third students were different three-dig... | "[\"78\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107173, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117145"}] | {
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} |
[
"1080"
] | [
"skywork"
] | 22f37f2cdb31611f51b74269c2022f59aebf6b2c60be1468c136ed5f0ef3a009 | [
{
"content": "A club has 12 members, and wishes to pick a president, a vice-president, a secretary, and a treasurer. However, the president and vice-president must have been members of the club for at least 3 years. If 4 of the existing members meet this criterion, in how many ways can these positions be filled... | A club has 12 members, and wishes to pick a president, a vice-president, a secretary, and a treasurer. However, the president and vice-president must have been members of the club for at least 3 years. If 4 of the existing members meet this criterion, in how many ways can these positions be filled, given that each memb... | "[\"1080\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107171, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117146"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"skywork"
] | 8c2a2738b776e5150e6c658f25307aa22f1a1be8b5fc4cd95f225f4bd18bfd17 | [
{
"content": "There are 29 students in a class: some are honor students who always tell the truth, and some are troublemakers who always lie.\n\nAll the students in this class sat at a round table.\n\n- Several students said: \"There is exactly one troublemaker next to me.\"\n- All other students said: \"There ... | There are 29 students in a class: some are honor students who always tell the truth, and some are troublemakers who always lie.
All the students in this class sat at a round table.
- Several students said: "There is exactly one troublemaker next to me."
- All other students said: "There are exactly two troublemakers ... | "[\"10\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107182, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 9, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117147"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"90"
] | [
"skywork"
] | 8a10fff2dc7befa85334ef41dee6d463460d3d39caafc541971a2761dd8d3142 | [
{
"content": "For a triangle with angles $\\alpha, \\beta, \\gamma$,\n\n$$\n\\sin \\alpha+\\sin \\beta=(\\cos \\alpha+\\cos \\beta) \\sin \\gamma\n$$\n\nis satisfied. What is the measure of angle $\\gamma$?",
"role": "user"
}
] | For a triangle with angles $\alpha, \beta, \gamma$,
$$
\sin \alpha+\sin \beta=(\cos \alpha+\cos \beta) \sin \gamma
$$
is satisfied. What is the measure of angle $\gamma$? | "[\"90\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107178, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "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:117148"}] | {
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"reference_present": true
} |
[
"63"
] | [
"skywork"
] | 95f750429e0708c74f5490568c1359fca7b1df75b3e9a6c83806c6e4485dac49 | [
{
"content": "Let $\\triangle ABC$ be a triangle with circumcircle $\\Omega$ and let $N$ be the midpoint of the major arc $\\widehat{BC}$. The incircle $\\omega$ of $\\triangle ABC$ is tangent to $AC$ and $AB$ at points $E$ and $F$ respectively. Suppose point $X$ is placed on the same side of $EF$ as $A$ such... | Let $\triangle ABC$ be a triangle with circumcircle $\Omega$ and let $N$ be the midpoint of the major arc $\widehat{BC}$. The incircle $\omega$ of $\triangle ABC$ is tangent to $AC$ and $AB$ at points $E$ and $F$ respectively. Suppose point $X$ is placed on the same side of $EF$ as $A$ such that $\triangle XEF\sim\tr... | "[\"63\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107165, "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:117149"}] | {
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} |
[
"\\{1, 2, 3, 6, 7, 15\\}"
] | [
"skywork"
] | ec38ff29e13b22d7bff8e69fb4482f2032cfc1e31d9ff6e9c273102a97311fad | [
{
"content": "Find all natural numbers that can be expressed in a unique way as a sum of five or less perfect squares.",
"role": "user"
}
] | Find all natural numbers that can be expressed in a unique way as a sum of five or less perfect squares. | "[\" \\\\{1, 2, 3, 6, 7, 15\\\\} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107187, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117150"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"30"
] | [
"skywork"
] | 1e42a7b6f69c7554d1f229e5d612e2ad9053fb0355134c05e6e9f0676f598d8e | [
{
"content": "A courier set out on a moped from city $A$ to city $B$, which are 120 km apart. One hour later, a second courier on a motorcycle left from $A$. The second courier caught up to the first, delivered a message, and immediately returned to $A$ at the same speed, arriving back in $A$ at the same time t... | A courier set out on a moped from city $A$ to city $B$, which are 120 km apart. One hour later, a second courier on a motorcycle left from $A$. The second courier caught up to the first, delivered a message, and immediately returned to $A$ at the same speed, arriving back in $A$ at the same time the first courier reach... | "[\"30\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107190, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 1, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117151"}] | {
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} |
[
"AD=13,BK=\\frac{120}{13},P_{EBM}=\\frac{340}{13}"
] | [
"skywork"
] | 4bcf0546c3660235df3e9173e7109d1cd6eb3cbde645181dc541cfc4a64b4f71 | [
{
"content": "5. Given a parallelogram $A B C D$. A circle $\\Omega$ with a diameter of 13 is circumscribed around triangle $A B M$, where $M$ is the point of intersection of the diagonals of the given parallelogram. $\\Omega$ intersects the ray $C B$ and the segment $A D$ again at points $E$ and $K$ respective... | 5. Given a parallelogram $A B C D$. A circle $\Omega$ with a diameter of 13 is circumscribed around triangle $A B M$, where $M$ is the point of intersection of the diagonals of the given parallelogram. $\Omega$ intersects the ray $C B$ and the segment $A D$ again at points $E$ and $K$ respectively. The length of arc $A... | "[\"AD=13,BK=\\\\frac{120}{13},P_{EBM}=\\\\frac{340}{13}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107174, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117152"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
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"reference_components": 1,
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} |
[
"n = 3^s p_1 p_2 \\ldots p_{1999}"
] | [
"skywork"
] | eef27597c6f69171e5f4d01e2247581965e3c12bbc9e7880879212bc1f8cfc5a | [
{
"content": "Determine if there exists a positive integer $n$ such that $n$ has exactly $2000$ prime divisors and $2^{n}+1$ is divisible by $n$.",
"role": "user"
}
] | Determine if there exists a positive integer $n$ such that $n$ has exactly $2000$ prime divisors and $2^{n}+1$ is divisible by $n$. | "[\" n = 3^s p_1 p_2 \\\\ldots p_{1999} \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107196, "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:117153"}] | {
"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
} |
[
"64"
] | [
"skywork"
] | d527a8266989d744cc60603b5f4726787e91e7ed6ba122b447dc8a8d2f8390a2 | [
{
"content": "Suppose $S_n$ is the set of positive divisors of $n$, and denote $|X|$ as the number of elements in a set $X$. Let $\\xi$ be the set of positive integers $n$ where $|S_n| = 2m$ is even, and $S_n$ can be partitioned evenly into pairs $\\{a_i, b_i\\}$ for integers $1 \\le i \\le m$ such that the fol... | Suppose $S_n$ is the set of positive divisors of $n$, and denote $|X|$ as the number of elements in a set $X$. Let $\xi$ be the set of positive integers $n$ where $|S_n| = 2m$ is even, and $S_n$ can be partitioned evenly into pairs $\{a_i, b_i\}$ for integers $1 \le i \le m$ such that the following conditions hold:
$\b... | "[\"64\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107176, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117154"}] | {
"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
} |
[
"324"
] | [
"skywork"
] | 80df2cf52e542df72b58108971d24bc0ea8a1f2a292971b6649775d4ac9e5c29 | [
{
"content": "Find the number of pairs of integers \\((x ; y)\\) that satisfy the equation \\(y^{2} - xy = 700000000\\).",
"role": "user"
}
] | Find the number of pairs of integers \((x ; y)\) that satisfy the equation \(y^{2} - xy = 700000000\). | "[\"324\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107197, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 6}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117155"}] | {
"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
} |
[
"1103_6"
] | [
"skywork"
] | faa0769fd651c2f320df54a3f986c81e7defb25ff268f4841001965e97a5b5cf | [
{
"content": "Find the sum of $555_6$, $55_6$ and $5_6$ in base $6$.",
"role": "user"
}
] | Find the sum of $555_6$, $55_6$ and $5_6$ in base $6$. | "[\"1103_6\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107216, "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:117156"}] | {
"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{25}{8}"
] | [
"skywork"
] | 500398d0340177da2eb34768d518b16f866a4b4267ee307e1d8c579ceeb4b182 | [
{
"content": "7. If $x, y>0$, and $x+2 y=1$, then the minimum value of $u=\\left(x+\\frac{1}{x}\\right)\\left(y+\\frac{1}{4 y}\\right)$ is\n\n保留源文本的换行和格式，翻译结果如下：\n\n7. If $x, y>0$, and $x+2 y=1$, then the minimum value of $u=\\left(x+\\frac{1}{x}\\right)\\left(y+\\frac{1}{4 y}\\right)$ is",
"role": "user"
... | 7. If $x, y>0$, and $x+2 y=1$, then the minimum value of $u=\left(x+\frac{1}{x}\right)\left(y+\frac{1}{4 y}\right)$ is
保留源文本的换行和格式，翻译结果如下：
7. If $x, y>0$, and $x+2 y=1$, then the minimum value of $u=\left(x+\frac{1}{x}\right)\left(y+\frac{1}{4 y}\right)$ is | "[\"\\\\frac{25}{8}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107209, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "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:117157"}] | {
"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
} |
[
"382"
] | [
"skywork"
] | 2f089ca5c17056d3af3ecc3e9c1e688feeeec8859240e1d299b697ee1e455b90 | [
{
"content": "We glue together $990$ one inch cubes into a $9$ by $10$ by $11$ inch rectangular solid. Then we paint the outside of the solid. How many of the original $990$ cubes have just one of their sides painted?",
"role": "user"
}
] | We glue together $990$ one inch cubes into a $9$ by $10$ by $11$ inch rectangular solid. Then we paint the outside of the solid. How many of the original $990$ cubes have just one of their sides painted? | "[\"382\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107200, "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:117158"}] | {
"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}{3}"
] | [
"skywork"
] | 87999ba5d345ebcbe9726cc0c4003e9f9f07c3a23a4d06df029d3418b08d7dd0 | [
{
"content": "12. In a math exam of a class, the average score of all students who got excellent grades is 95 points, and the average score of students who did not get excellent grades is 80 points. It is known that the average score of the whole class is no less than 90 points. What is the minimum proportion o... | 12. In a math exam of a class, the average score of all students who got excellent grades is 95 points, and the average score of students who did not get excellent grades is 80 points. It is known that the average score of the whole class is no less than 90 points. What is the minimum proportion of students who got exc... | "[\"\\\\frac{2}{3}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107207, "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:117159"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"skywork"
] | 6864a0895cc78cd0dddbd0207650a0f5c652d2fd95cfb17e67fb65d1c888cfd6 | [
{
"content": "5 In a rectangle $A B C D$ with an area of 1 (including the boundary) there are 5 points, no three of which are collinear. Find the minimum number of triangles, formed by these 5 points as vertices, that have an area not greater than $\\frac{1}{4}$.",
"role": "user"
}
] | 5 In a rectangle $A B C D$ with an area of 1 (including the boundary) there are 5 points, no three of which are collinear. Find the minimum number of triangles, formed by these 5 points as vertices, that have an area not greater than $\frac{1}{4}$. | "[\"2\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107195, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117160"}] | {
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[
"31"
] | [
"skywork"
] | 51ec74ecd10f31fe1d231a607a3bdfbb821373b1572656edadc7bd96584f272c | [
{
"content": "For how many ordered pairs of positive integers $(a,b)$ with $a,b<1000$ is it true that $a$ times $b$ is equal to $b^2$ divided by $a$? For example, $3$ times $9$ is equal to $9^2$ divided by $3$.\n\n[i]Ray Li[/i]",
"role": "user"
}
] | For how many ordered pairs of positive integers $(a,b)$ with $a,b<1000$ is it true that $a$ times $b$ is equal to $b^2$ divided by $a$? For example, $3$ times $9$ is equal to $9^2$ divided by $3$.
[i]Ray Li[/i] | "[\"31\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107189, "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:117161"}] | {
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[
"49"
] | [
"skywork"
] | 4db9cf2847e818ba0558fdaf1f87c5c77be5a80d192523ce2d88b03ebea69be9 | [
{
"content": "The square was cut into 25 smaller squares, of which exactly one has a side length different from 1 (each of the others has a side length of 1).\n\nFind the area of the original square.",
"role": "user"
}
] | The square was cut into 25 smaller squares, of which exactly one has a side length different from 1 (each of the others has a side length of 1).
Find the area of the original square. | "[\"49\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107202, "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:117162"}] | {
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[
"36"
] | [
"skywork"
] | e9a38404103cd95554d5b61b8a26de6d15c64da1a4c9880433a6fcc800334bc4 | [
{
"content": "13.419 Two trains, 490 m and 210 m long, are moving towards each other at a constant speed on parallel tracks. The driver of one of them noticed the oncoming train at a distance of $700 \\mathrm{~m}$; after this, the trains met after 28 s. Determine the speed of each train, given that the first tr... | 13.419 Two trains, 490 m and 210 m long, are moving towards each other at a constant speed on parallel tracks. The driver of one of them noticed the oncoming train at a distance of $700 \mathrm{~m}$; after this, the trains met after 28 s. Determine the speed of each train, given that the first train takes 35 s longer t... | "[\"36\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107194, "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:117163"}] | {
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[
"80"
] | [
"skywork"
] | f9f2e3a995b4bd55e7ffa3fcedda2c5b88fe682a7f52e121a1bf2a7de58f38df | [
{
"content": "6. Solve the equation in natural numbers\n\n$$\na b c + a b + b c + a c + a + b + c = 164\n$$\n\nIn your answer, specify the product $a b c$.",
"role": "user"
}
] | 6. Solve the equation in natural numbers
$$
a b c + a b + b c + a c + a + b + c = 164
$$
In your answer, specify the product $a b c$. | "[\"80\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107210, "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:117164"}] | {
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[
"\\frac{11}{72}"
] | [
"skywork"
] | e12131120cca6647a7f0b1cfad5b399f83ddc221652223609614a67d2bed3f8c | [
{
"content": "Alex plans to catch a train today. The train arrives randomly some time between 2:00 and 4:00 PM, waits for 20 minutes, and then leaves. If Alex also arrives randomly between 2:00 and 4:00 PM, what is the probability that the train will be there when Alex arrives?",
"role": "user"
}
] | Alex plans to catch a train today. The train arrives randomly some time between 2:00 and 4:00 PM, waits for 20 minutes, and then leaves. If Alex also arrives randomly between 2:00 and 4:00 PM, what is the probability that the train will be there when Alex arrives? | "[\"\\\\frac{11}{72}\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 107193, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 7, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117165"}] | {
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[
"1302"
] | [
"skywork"
] | bf65583712d749c805b9f55846834263ec8342811857234aa3476b20ca9bdfae | [
{
"content": "2. On a sheet of lined paper, two rectangles are outlined. The first rectangle has a vertical side shorter than the horizontal side, while the second has the opposite. Find the maximum possible area of their common part, if the first rectangle contains 2015 cells, and the second - 2016.",
"rol... | 2. On a sheet of lined paper, two rectangles are outlined. The first rectangle has a vertical side shorter than the horizontal side, while the second has the opposite. Find the maximum possible area of their common part, if the first rectangle contains 2015 cells, and the second - 2016. | "[\"1302\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107177, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 5, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117166"}] | {
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[
"m = n = 6"
] | [
"skywork"
] | 947671fe24e7056388f238725047c0d036146f0c2d326b94478a72ea0223652b | [
{
"content": "On the sides of a non-obtuse triangle $ABC$ a square, a regular $n$-gon and a regular $m$-gon ($m$,$n > 5$) are constructed externally, so that their centers are vertices of a regular triangle. Prove that $m = n = 6$ and find the angles of $\\triangle ABC$.",
"role": "user"
}
] | On the sides of a non-obtuse triangle $ABC$ a square, a regular $n$-gon and a regular $m$-gon ($m$,$n > 5$) are constructed externally, so that their centers are vertices of a regular triangle. Prove that $m = n = 6$ and find the angles of $\triangle ABC$. | "[\" m = n = 6 \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107191, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 8}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117167"}] | {
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[
"120"
] | [
"skywork"
] | f9a99bdcd8a439786110408fa3b78120e01f67644d95724f90ecf045207334f8 | [
{
"content": "9. (3 points) The following is a 3x3 grid, where the characters 【Hua, Luo, Geng, Bei, Shu, Xue, Jing, Ying, Sai】 represent nine different digits from 1 to 9, and these nine numbers meet the following three conditions:\n(1) The sum of the four numbers in each \"square\" is equal.\n(2) Hua $\\times$... | 9. (3 points) The following is a 3x3 grid, where the characters 【Hua, Luo, Geng, Bei, Shu, Xue, Jing, Ying, Sai】 represent nine different digits from 1 to 9, and these nine numbers meet the following three conditions:
(1) The sum of the four numbers in each "square" is equal.
(2) Hua $\times$ Hua $=$ Ying $\times$ Ying... | "[\"120\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107181, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117169"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"162"
] | [
"skywork"
] | ead79fb56947dc654f00514304cd6e478f3d064660f4ba05ab6b3175e962bace | [
{
"content": "5. One of the mascots for the 2012 Olympic Games is called 'Wenlock' because the town of Wenlock in Shropshire first held the Wenlock Olympian Games in 1850. How many years ago was that?\nA 62\nB 152\nC 158\nD 162\nE 172",
"role": "user"
}
] | 5. One of the mascots for the 2012 Olympic Games is called 'Wenlock' because the town of Wenlock in Shropshire first held the Wenlock Olympian Games in 1850. How many years ago was that?
A 62
B 152
C 158
D 162
E 172 | "[\"162\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107212, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 8, "DeepSeek-R1-Distill-Qwen-32B": 10, "DeepSeek-R1-Distill-Qwen-7B": 15}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117170"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"n"
] | [
"skywork"
] | 15f1b6115300e9d13358629fb1c26b8b467923e1ed3ec8c2b284bc4f94761e81 | [
{
"content": "Determine all positive integers $n$ such that for every positive devisor $ d $ of $n$, $d+1$ is devisor of $n+1$.",
"role": "user"
}
] | Determine all positive integers $n$ such that for every positive devisor $ d $ of $n$, $d+1$ is devisor of $n+1$. | "[\" n \"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107205, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 13}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117171"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"8"
] | [
"skywork"
] | 20a36f2d30a306e910310dfa688e3899068bafd1ae54b12257376aa2db847b4c | [
{
"content": "Suppose that all four of the numbers \\[2 - \\sqrt{5}, \\;4+\\sqrt{10}, \\;14 - 2\\sqrt{7}, \\;-\\sqrt{2}\\]are roots of the same nonzero polynomial with rational coefficients. What is the smallest possible degree of the polynomial?",
"role": "user"
}
] | Suppose that all four of the numbers \[2 - \sqrt{5}, \;4+\sqrt{10}, \;14 - 2\sqrt{7}, \;-\sqrt{2}\]are roots of the same nonzero polynomial with rational coefficients. What is the smallest possible degree of the polynomial? | "[\"8\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107208, "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:117172"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"\\angle AMP = \\angle CMQ"
] | [
"skywork"
] | 9b8f80433928840af0e2631284a0544d29db61e4ccd4643455575dd5693d9eff | [
{
"content": "[color=darkred]The sides $AD$ and $CD$ of a tangent quadrilateral $ABCD$ touch the incircle $\\varphi$ at $P$ and $Q,$ respectively. If $M$ is the midpoint of the chord $XY$ determined by $\\varphi$ on the diagonal $BD,$ prove that $\\angle AMP = \\angle CMQ.$[/color]",
"role": "user"
}
] | [color=darkred]The sides $AD$ and $CD$ of a tangent quadrilateral $ABCD$ touch the incircle $\varphi$ at $P$ and $Q,$ respectively. If $M$ is the midpoint of the chord $XY$ determined by $\varphi$ on the diagonal $BD,$ prove that $\angle AMP = \angle CMQ.$[/color] | "[\"\\\\angle AMP = \\\\angle CMQ\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107201, "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:117173"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"skywork"
] | 1681f600f3a022725480c112090aabb60a7155ff5b333233ef70e8a50d9e9e2c | [
{
"content": "SI. 2 Three solutions of the equation $p x+q y+b z=1$ are $(0,3 a, 1),(9 a,-1,2)$ and $(0,3 a, 0)$. Find the value of the coefficient $b$.",
"role": "user"
}
] | SI. 2 Three solutions of the equation $p x+q y+b z=1$ are $(0,3 a, 1),(9 a,-1,2)$ and $(0,3 a, 0)$. Find the value of the coefficient $b$. | "[\"0\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107204, "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:117174"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"36"
] | [
"skywork"
] | 81558c11d7cafb3ce6d16ba30d946f6c7345522b4721d4c467ff7b861555d00f | [
{
"content": "Place four balls numbered 1, 2, 3, and 4 into three boxes labeled A, B, and C. \n(1) If none of the boxes are empty and ball number 3 must be in box B, how many different arrangements are there? \n(2) If ball number 1 cannot be in box A and ball number 2 cannot be in box B, how many different ar... | Place four balls numbered 1, 2, 3, and 4 into three boxes labeled A, B, and C.
(1) If none of the boxes are empty and ball number 3 must be in box B, how many different arrangements are there?
(2) If ball number 1 cannot be in box A and ball number 2 cannot be in box B, how many different arrangements are there? | "[\"36\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107198, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117176"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"skywork"
] | 22b298f8ce9c953d1259dd38a1a4595b4b65903c34268ab5bebffd72412b888c | [
{
"content": "10. (20 points) As shown in Figure 1, in the Cartesian coordinate system $x C y$, the tangent line $l$ of a circle with center at the origin $C$ and radius 1 intersects the $x$-axis at point $N$ and the $y$-axis at point $M$. Point $A(3,4)$, and $\\overrightarrow{A C}=$\n$x \\overrightarrow{A M}+y... | 10. (20 points) As shown in Figure 1, in the Cartesian coordinate system $x C y$, the tangent line $l$ of a circle with center at the origin $C$ and radius 1 intersects the $x$-axis at point $N$ and the $y$-axis at point $M$. Point $A(3,4)$, and $\overrightarrow{A C}=$
$x \overrightarrow{A M}+y \overrightarrow{A N}$. L... | "[\"4\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107199, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117177"}] | {
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"reference_present": true
} |
[
"15"
] | [
"skywork"
] | e68fdf14799dafbca417f2120deb9e951c3369e452040a9c68b8c29b5260155b | [
{
"content": "In how many ways can the number 210 be factored into a product of four natural numbers? The order of the factors does not matter.",
"role": "user"
}
] | In how many ways can the number 210 be factored into a product of four natural numbers? The order of the factors does not matter. | "[\"15\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107223, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 4}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117178"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"f(x)=\\frac{2}{x^{2}}"
] | [
"skywork"
] | 389ea12eebc3d330c2bcd07dc36f5c2dea67b96575195181e00c8f2e79a364d3 | [
{
"content": "22. Given that the function $f(x)$ is defined on $\\mathbf{R}^{+}$, satisfies $f(x)$ is strictly decreasing on $\\mathbf{R}^{+}$, and\n$$\nf(x)>\\frac{1}{x^{2}},\n$$\n\non $\\mathbf{R}^{+}$, it always holds that $f^{2}(x) f\\left(f(x)-\\frac{1}{x^{2}}\\right)=f^{3}(1)$.\n(1) Find the function valu... | 22. Given that the function $f(x)$ is defined on $\mathbf{R}^{+}$, satisfies $f(x)$ is strictly decreasing on $\mathbf{R}^{+}$, and
$$
f(x)>\frac{1}{x^{2}},
$$
on $\mathbf{R}^{+}$, it always holds that $f^{2}(x) f\left(f(x)-\frac{1}{x^{2}}\right)=f^{3}(1)$.
(1) Find the function value $f(1)$;
(2) Provide a function th... | "[\"f(x)=\\\\frac{2}{x^{2}}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107203, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 6, "DeepSeek-R1-Distill-Qwen-32B": 2, "DeepSeek-R1-Distill-Qwen-7B": 5}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117179"}] | {
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} |
[
"81^\\circ"
] | [
"skywork"
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"content": "Let $\\triangle ABC$ have $\\angle ABC=67^{\\circ}$. Point $X$ is chosen such that $AB = XC$, $\\angle{XAC}=32^\\circ$, and $\\angle{XCA}=35^\\circ$. Compute $\\angle{BAC}$ in degrees.\n\n[i]Proposed by Raina Yang[/i]",
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] | Let $\triangle ABC$ have $\angle ABC=67^{\circ}$. Point $X$ is chosen such that $AB = XC$, $\angle{XAC}=32^\circ$, and $\angle{XCA}=35^\circ$. Compute $\angle{BAC}$ in degrees.
[i]Proposed by Raina Yang[/i] | "[\"81^\\\\circ\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107222, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 4, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117180"}] | {
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[
"96"
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"skywork"
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"content": "Four lighthouses are located at points $A$ , $B$ , $C$ , and $D$ . The lighthouse at $A$ is $5$ kilometers from the lighthouse at $B$ , the lighthouse at $B$ is $12$ kilometers from the lighthouse at $C$ , and the lighthouse at $A$ is $13$ kilometers from the lighthouse at $C$ . To an observer at ... | Four lighthouses are located at points $A$ , $B$ , $C$ , and $D$ . The lighthouse at $A$ is $5$ kilometers from the lighthouse at $B$ , the lighthouse at $B$ is $12$ kilometers from the lighthouse at $C$ , and the lighthouse at $A$ is $13$ kilometers from the lighthouse at $C$ . To an observer at $A$ , the angle determ... | "[\"96\"]" | train-math-aime19832023 | [{"dataset": "skywork", "extra_info": {"index": 107214, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 14, "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:117181"}] | {
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[
"(0,1)\\cup[\\mathrm{e}^{\\frac{1}{2e}},+\\infty)"
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"skywork"
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"content": "11. Given $A=\\left\\{x \\mid x^{2}<x\\right\\}, B=\\left\\{x \\mid x^{2}<\\log _{a} x\\right\\}$, and $B \\varsubsetneqq A$, find the range of real number $a$.\n\n untranslated part: \n将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。 \n\nNote: The part \" untranslated part: \" and beyond is a note and not part... | 11. Given $A=\left\{x \mid x^{2}<x\right\}, B=\left\{x \mid x^{2}<\log _{a} x\right\}$, and $B \varsubsetneqq A$, find the range of real number $a$.
untranslated part:
将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。
Note: The part " untranslated part: " and beyond is a note and not part of the translation. It is provided to cl... | "[\"(0,1)\\\\cup[\\\\mathrm{e}^{\\\\frac{1}{2e}},+\\\\infty)\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107219, "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:117182"}] | {
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[
"\\frac{5}{8}"
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] | 68216be7f7ea48032acb45d436cc2cd95fe110abc53a5fff7392db0360aa416e | [
{
"content": "83. Given a parallelogram $A B C D$. Points $M$ and $N$ are the midpoints of sides $B C$ and $C D$ respectively. Find the ratio of the area of quadrilateral AM ND to the area of the parallelogram.",
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] | 83. Given a parallelogram $A B C D$. Points $M$ and $N$ are the midpoints of sides $B C$ and $C D$ respectively. Find the ratio of the area of quadrilateral AM ND to the area of the parallelogram. | "[\"\\\\frac{5}{8}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107217, "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:117183"}] | {
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[
"9"
] | [
"skywork"
] | 0ea61b7780df8c8541191d1dd691a7b47d4fc64bdff8545ab50f50bad9aaa42a | [
{
"content": "Example 3 Find the units digit of $\\left(7^{2004}+36\\right)^{818}$.\n$(2004$, Shanghai Jiao Tong University Independent Recruitment Examination)",
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] | Example 3 Find the units digit of $\left(7^{2004}+36\right)^{818}$.
$(2004$, Shanghai Jiao Tong University Independent Recruitment Examination) | "[\"9\"]" | train-math-numinamath1.5_cn_contest | [{"dataset": "skywork", "extra_info": {"index": 107230, "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:117184"}] | {
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[
"\\frac{6}{36}"
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"skywork"
] | 2c776fabfcc7305e16f82d5e36c63c20347be35586cfc35f909c0ec522a918b2 | [
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"content": "Example. Two dice are thrown. Find the probability that the number of points on one die is twice the number on the other.",
"role": "user"
}
] | Example. Two dice are thrown. Find the probability that the number of points on one die is twice the number on the other. | "[\"\\\\frac{6}{36}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107228, "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:117185"}] | {
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[
"\\frac{\\sqrt{5}}{5}"
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"skywork"
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"content": "In $\\triangle ABC$, the sides opposite to $\\angle A$, $\\angle B$, and $\\angle C$ are $a$, $b$, and $c$ respectively. If $\\angle B = \\angle C$ and $7a^2 + b^2 + c^2 = 4\\sqrt{3}$, find the maximum value of the area of $\\triangle ABC$.",
"role": "user"
}
] | In $\triangle ABC$, the sides opposite to $\angle A$, $\angle B$, and $\angle C$ are $a$, $b$, and $c$ respectively. If $\angle B = \angle C$ and $7a^2 + b^2 + c^2 = 4\sqrt{3}$, find the maximum value of the area of $\triangle ABC$. | "[\"\\\\frac{\\\\sqrt{5}}{5}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107211, "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:117186"}] | {
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[
"5"
] | [
"skywork"
] | a807857daeb0573f1c9d9ae6f1bc10ece62d4eff9cd4c0d67e5526b1aaa1bf8c | [
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"content": "Bag A has three chips labeled 1, 3, and 5. Bag B has three chips labeled 2, 4, and 6. If one chip is drawn from each bag, how many different values are possible for the sum of the two numbers on the chips?",
"role": "user"
}
] | Bag A has three chips labeled 1, 3, and 5. Bag B has three chips labeled 2, 4, and 6. If one chip is drawn from each bag, how many different values are possible for the sum of the two numbers on the chips? | "[\"5\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107240, "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:117187"}] | {
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[
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"skywork"
] | ef9518b93de01979ce05d0ce744926eda71d4d9c16fdcfc4cac1267dfe73ca5a | [
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"content": "An elephant writes a sequence of numbers on a board starting with 1. Each minute, it doubles the sum of all the numbers on the board so far, and without erasing anything, writes the result on the board. It stops after writing a number greater than one billion. How many distinct prime factors does ... | An elephant writes a sequence of numbers on a board starting with 1. Each minute, it doubles the sum of all the numbers on the board so far, and without erasing anything, writes the result on the board. It stops after writing a number greater than one billion. How many distinct prime factors does the largest number on ... | "[\"2\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107218, "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:117188"}] | {
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[
"54"
] | [
"skywork"
] | 9abd825c4a386c040fc52465a0159dd980d8292f4bbf5e15d3baace4358e178c | [
{
"content": "206. Find all two-digit numbers, each of which is 13 more than the sum of the squares of its digits.",
"role": "user"
}
] | 206. Find all two-digit numbers, each of which is 13 more than the sum of the squares of its digits. | "[\"54\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107235, "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:117189"}] | {
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[
"\\pi-\\arctan(\\frac{4}{3\\sin\\theta})"
] | [
"skywork"
] | be45df0933ab0213c7f7699d56e9d834d3d93c973413dd7aa07a8a666bdf613d | [
{
"content": "13.7.9 Given the parabola $y^{2}=2 p x(p>0), A B$ is a chord passing through the focus $F$. If $A B$ makes an angle $\\theta\\left(0<\\theta \\leqslant \\frac{\\pi}{2}\\right)$ with the $x$-axis, find $\\angle A O B$.\n\n---\n\nThe original text has been translated into English while preserving th... | 13.7.9 Given the parabola $y^{2}=2 p x(p>0), A B$ is a chord passing through the focus $F$. If $A B$ makes an angle $\theta\left(0<\theta \leqslant \frac{\pi}{2}\right)$ with the $x$-axis, find $\angle A O B$.
---
The original text has been translated into English while preserving the original formatting and line bre... | "[\"\\\\pi-\\\\arctan(\\\\frac{4}{3\\\\sin\\\\theta})\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107226, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 16, "DeepSeek-R1-Distill-Qwen-32B": 12, "DeepSeek-R1-Distill-Qwen-7B": 14}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117190"}] | {
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[
"77"
] | [
"skywork"
] | 5c403acf7e6e4a8d82a0db1144e0619413fefe99a449152a2941e02d99de24fe | [
{
"content": "A rectangular table with dimensions $x$ cm $\\times 80$ cm is covered with identical sheets of paper measuring 5 cm $\\times 8$ cm. The first sheet is placed in the bottom-left corner, and each subsequent sheet is placed one centimeter higher and one centimeter to the right of the previous sheet. ... | A rectangular table with dimensions $x$ cm $\times 80$ cm is covered with identical sheets of paper measuring 5 cm $\times 8$ cm. The first sheet is placed in the bottom-left corner, and each subsequent sheet is placed one centimeter higher and one centimeter to the right of the previous sheet. The last sheet is positi... | "[\"77\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107220, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 9, "DeepSeek-R1-Distill-Qwen-32B": 3, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117191"}] | {
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[
"\\frac{\\sqrt{3}}{4}"
] | [
"skywork"
] | 35b9d240bd114d1190ccbb40a6fcff03ea36b0ba68ef4e277107c26109304a15 | [
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"content": "Two adjacent faces of a tetrahedron, which are equilateral triangles with side length 1, form a dihedral angle of 60 degrees. The tetrahedron is rotated around the common edge of these faces. Find the maximum area of the projection of the rotating tetrahedron onto a plane containing the given edge... | Two adjacent faces of a tetrahedron, which are equilateral triangles with side length 1, form a dihedral angle of 60 degrees. The tetrahedron is rotated around the common edge of these faces. Find the maximum area of the projection of the rotating tetrahedron onto a plane containing the given edge. (12 points) | "[\"\\\\frac{\\\\sqrt{3}}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107215, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 15, "DeepSeek-R1-Distill-Qwen-32B": 14, "DeepSeek-R1-Distill-Qwen-7B": 11}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117192"}] | {
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[
"59"
] | [
"skywork"
] | 77d0298cb17cb670c14e261f8e432d30972d35f178c8e376855db75570617860 | [
{
"content": "Humpty Dumpty walks on a straight line, taking either 37 steps to the left or 47 steps to the right per minute.\n\nWhat is the minimum time it will take for him to be one step to the right of the starting point?",
"role": "user"
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] | Humpty Dumpty walks on a straight line, taking either 37 steps to the left or 47 steps to the right per minute.
What is the minimum time it will take for him to be one step to the right of the starting point? | "[\"59\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107227, "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:117194"}] | {
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[
"26"
] | [
"skywork"
] | d4515964a890c4b6dab832098d9b4fb1b54268033f156ae68098240894a6d620 | [
{
"content": "10. [15] Suppose we have an $n$-gon such that each interior angle, measured in degrees, is a positive integer. Suppose further that all angles are less than $180^{\\circ}$, and that all angles are different sizes. What is the maximum possible value of $n$ ? Prove your answer.",
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... | 10. [15] Suppose we have an $n$-gon such that each interior angle, measured in degrees, is a positive integer. Suppose further that all angles are less than $180^{\circ}$, and that all angles are different sizes. What is the maximum possible value of $n$ ? Prove your answer. | "[\"26\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107236, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 4, "DeepSeek-R1-Distill-Qwen-7B": 3}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117195"}] | {
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[
"2309"
] | [
"skywork"
] | b4ca2db3cde72c70d3196cb5fd240cba696f080ffb9e2bf5d8d9d2ec0274ed0d | [
{
"content": "In a $4\\times 4$ grid of unit squares, five squares are chosen at random. The probability that no two chosen squares share a side is $\\tfrac mn$ for positive relatively prime integers $m$ and $n$. Find $m+n$.\n\n[i]Proposed by David Altizio[/i]",
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}
] | In a $4\times 4$ grid of unit squares, five squares are chosen at random. The probability that no two chosen squares share a side is $\tfrac mn$ for positive relatively prime integers $m$ and $n$. Find $m+n$.
[i]Proposed by David Altizio[/i] | "[\"2309\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107238, "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:117196"}] | {
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[
"64"
] | [
"skywork"
] | 388cac6b1a89d9020c87d49e9952383cd364abeec0fdbbc432802e913745135a | [
{
"content": "Find the number of ordered pairs $(a,b)$ of complex numbers such that\n\\[a^4 b^7 = a^8 b^3 = 1.\\]",
"role": "user"
}
] | Find the number of ordered pairs $(a,b)$ of complex numbers such that
\[a^4 b^7 = a^8 b^3 = 1.\] | "[\"64\"]" | train-math-still3 | [{"dataset": "skywork", "extra_info": {"index": 107248, "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:117197"}] | {
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[
"7\\sqrt{63}"
] | [
"skywork"
] | 0c254c444de2f898fed74b6726d7373c4e4ce920123bd913b0a375fc5c6f40b9 | [
{
"content": "Let $H$ be the orthocenter of an acute triangle $ABC$, $AH=2$, $BH=12$, $CH=9$.\nFind the area of the triangle $ABC$.",
"role": "user"
}
] | Let $H$ be the orthocenter of an acute triangle $ABC$, $AH=2$, $BH=12$, $CH=9$.
Find the area of the triangle $ABC$. | "[\"7\\\\sqrt{63}\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107255, "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:117198"}] | {
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[
"19"
] | [
"skywork"
] | 2883a10e4633858189f051a8f45fdde55bc4c2afea29f9823e598fd81cb6c955 | [
{
"content": "In writing the integers from 10 through 99 inclusive, how many times is the digit 6 written?",
"role": "user"
}
] | In writing the integers from 10 through 99 inclusive, how many times is the digit 6 written? | "[\"19\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107266, "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:117199"}] | {
"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"
] | 1105d78c0df5e265103114ff72b073589ea32904858024987d191fd3454eea07 | [
{
"content": "The polynomial\n\\[px^4 + qx^3 + rx^2 + sx + t = 0\\]\nhas coefficients that are all integers, and roots $-3$, $4$, $6$, and $\\frac{1}{2}$. If $t$ is a positive integer, find its smallest possible value.",
"role": "user"
}
] | The polynomial
\[px^4 + qx^3 + rx^2 + sx + t = 0\]
has coefficients that are all integers, and roots $-3$, $4$, $6$, and $\frac{1}{2}$. If $t$ is a positive integer, find its smallest possible value. | "[\"72\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107229, "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:117200"}] | {
"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
} |
[
"364"
] | [
"skywork"
] | 3fa4ea09780f437e4a2e1740ddb9ce7c5ddf2ca6811dabad1c6fda639afc4c1c | [
{
"content": "Suggestion: Let $a=\\sqrt{2 n+1}$ and $b=$ $\\sqrt{2 n-1}$.\n\nFacts that Help: Use the identity\n\n$\\left(a^{2}+a b+b^{2}\\right)(a-b)=a^{3}-b^{3}$.\nFor a positive integer $n$ consider the function\n\n$$\nf(n)=\\frac{4 n+\\sqrt{4 n^{2}-1}}{\\sqrt{2 n+1}+\\sqrt{2 n-1}}\n$$\n\nCalculate the value... | Suggestion: Let $a=\sqrt{2 n+1}$ and $b=$ $\sqrt{2 n-1}$.
Facts that Help: Use the identity
$\left(a^{2}+a b+b^{2}\right)(a-b)=a^{3}-b^{3}$.
For a positive integer $n$ consider the function
$$
f(n)=\frac{4 n+\sqrt{4 n^{2}-1}}{\sqrt{2 n+1}+\sqrt{2 n-1}}
$$
Calculate the value of
$$
f(1)+f(2)+f(3)+\cdots+f(40)
$$ | "[\"364\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107231, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 12, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 0}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117201"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"f(x) = x \\text{ or } f(x) = \\frac{1}{x}"
] | [
"skywork"
] | d7011bc24516ddbfe292f0b4769b12faf0a6bf587661d4ec8b555d2c419ea9e4 | [
{
"content": "Find all functions $ f: (0, \\infty) \\mapsto (0, \\infty)$ (so $ f$ is a function from the positive real numbers) such that\n\\[ \\frac {\\left( f(w) \\right)^2 \\plus{} \\left( f(x) \\right)^2}{f(y^2) \\plus{} f(z^2) } \\equal{} \\frac {w^2 \\plus{} x^2}{y^2 \\plus{} z^2}\n\\]\nfor all positive ... | Find all functions $ f: (0, \infty) \mapsto (0, \infty)$ (so $ f$ is a function from the positive real numbers) such that
\[ \frac {\left( f(w) \right)^2 \plus{} \left( f(x) \right)^2}{f(y^2) \plus{} f(z^2) } \equal{} \frac {w^2 \plus{} x^2}{y^2 \plus{} z^2}
\]
for all positive real numbers $ w,x,y,z,$ satisfying $ wx ... | "[\"f(x) = x \\\\text{ or } f(x) = \\\\frac{1}{x}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107225, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 8, "DeepSeek-R1-Distill-Qwen-7B": 10}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117202"}] | {
"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{1006}{12}"
] | [
"skywork"
] | e17f345eb93c5ef8284696949b46f9c7c6219a74bb91c2cdba885f5794a1f786 | [
{
"content": "Given that the mean score of the students in the first section is 92 and the mean score of the students in the second section is 78, and the ratio of the number of students in the first section to the number of students in the second section is 5:7, calculate the combined mean score of all the stu... | Given that the mean score of the students in the first section is 92 and the mean score of the students in the second section is 78, and the ratio of the number of students in the first section to the number of students in the second section is 5:7, calculate the combined mean score of all the students in both sections... | "[\"\\\\frac{1006}{12}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107261, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 13, "DeepSeek-R1-Distill-Qwen-32B": 15, "DeepSeek-R1-Distill-Qwen-7B": 16}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117204"}] | {
"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 {\\pi}{4}"
] | [
"skywork"
] | 572f0839161e4c408ab90d4f0e2e0f2364a2e151c0555f62fe6db09f4b8624d6 | [
{
"content": "Given that $| \\overrightarrow{a}|=1$, $| \\overrightarrow{b}|= \\sqrt {2}$, and $\\overrightarrow{a} \\perp ( \\overrightarrow{a}- \\overrightarrow{b})$, find the angle between vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$.",
"role": "user"
}
] | Given that $| \overrightarrow{a}|=1$, $| \overrightarrow{b}|= \sqrt {2}$, and $\overrightarrow{a} \perp ( \overrightarrow{a}- \overrightarrow{b})$, find the angle between vectors $\overrightarrow{a}$ and $\overrightarrow{b}$. | "[\"\\\\frac {\\\\pi}{4}\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107256, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 5, "DeepSeek-R1-Distill-Qwen-32B": 7, "DeepSeek-R1-Distill-Qwen-7B": 2}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117205"}] | {
"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
} |
[
"45"
] | [
"skywork"
] | 15d674580b9b1f4237f06c176f4b773c2bbfcc677f2855f98ee866a08d94ade2 | [
{
"content": "21. Observant Yura noticed that if in a two-digit number expressing the distance in kilometers they traveled today, a zero is inserted between the tens and units digits, the resulting number is 9 times greater than the original. What distance did they travel?",
"role": "user"
}
] | 21. Observant Yura noticed that if in a two-digit number expressing the distance in kilometers they traveled today, a zero is inserted between the tens and units digits, the resulting number is 9 times greater than the original. What distance did they travel? | "[\"45\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107257, "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:117206"}] | {
"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
} |
[
"50199"
] | [
"skywork"
] | 5c7f0aebf8d9bd41946c164616616f3d7c042b06455cd8590bd6ec2e494c047b | [
{
"content": "Suppose \\( a_{n} \\) denotes the last two digits of \\( 7^{n} \\). For example, \\( a_{2} = 49 \\), \\( a_{3} = 43 \\). Find the value of \\( a_{1} + a_{2} + a_{3} + \\cdots + a_{2007} \\).",
"role": "user"
}
] | Suppose \( a_{n} \) denotes the last two digits of \( 7^{n} \). For example, \( a_{2} = 49 \), \( a_{3} = 43 \). Find the value of \( a_{1} + a_{2} + a_{3} + \cdots + a_{2007} \). | "[\"50199\"]" | train-math-deepscaler | [{"dataset": "skywork", "extra_info": {"index": 107242, "model_difficulty": {"DeepSeek-R1-Distill-Qwen-1.5B": 3, "DeepSeek-R1-Distill-Qwen-32B": 0, "DeepSeek-R1-Distill-Qwen-7B": 1}}, "file": "data/math-00000-of-00001.parquet", "row_id": "skywork:data/math-00000-of-00001.parquet:117207"}] | {
"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
} |
[
"\\arccos\\frac{11}{16}"
] | [
"skywork"
] | a95665c6749acee7e436e653b87a5ce217707388d23e2462ef0d285636d6e61c | [
{
"content": "4. In $\\triangle A B C$, $\\sin A: \\sin B: \\sin C=2: 3: 4$, then $\\angle A B C=$ $\\qquad$ (result expressed in terms of inverse trigonometric function values).",
"role": "user"
}
] | 4. In $\triangle A B C$, $\sin A: \sin B: \sin C=2: 3: 4$, then $\angle A B C=$ $\qquad$ (result expressed in terms of inverse trigonometric function values). | "[\"\\\\arccos\\\\frac{11}{16}\"]" | train-math-numinamath1.5_olympiads | [{"dataset": "skywork", "extra_info": {"index": 107253, "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:117208"}] | {
"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
} |
[
"167"
] | [
"skywork"
] | db5970406771d9db6608375ac8aa45ebd027f1acdf0dc9d2b35fc8f71b4b72be | [
{
"content": "Let $f : R \\to R$ be a function satisfying the equation $f(x^2 + x + 3) + 2f(x^2 - 3x + 5) =6x^2 - 10x + 17$ for all real numbers $x$. What is the value of $f(85)$?",
"role": "user"
}
] | Let $f : R \to R$ be a function satisfying the equation $f(x^2 + x + 3) + 2f(x^2 - 3x + 5) =6x^2 - 10x + 17$ for all real numbers $x$. What is the value of $f(85)$? | "[\"167\"]" | train-math-numinamath1.5_aops_forum | [{"dataset": "skywork", "extra_info": {"index": 107234, "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:117209"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
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