data_source
stringclasses 11
values | prompt
listlengths 1
1
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stringclasses 1
value | reward_model
dict | extra_info
dict | ground_truth
stringlengths 1
497
| failed_count
int32 1
15
|
|---|---|---|---|---|---|---|
train-math-numinamath1.5_olympiads | [
{
"content": "Determine the largest possible radius of a circle that is tangent to both the $x$-axis and $y$-axis, and passes through the point $(9,2)$.\n\n(A circle in the $x y$-plane with centre $(a, b)$ and radius $r$ has equation $(x-a)^{2}+(y-b)^{2}=r^{2}$.)",
"role": "user"
}
]
| math | {
"ground_truth": "[\"17\"]",
"style": "rule"
} | {
"index": 23,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 17 | 3 |
train-math-numinamath1.5_olympiads | [
{
"content": "7. (10 points) In each small square of a $4 \\times 4$ grid, a non-zero natural number is filled. The product of the 4 numbers in each row, each column, and each diagonal is the same. The figure provides some of the filled numbers. What is the number in the small square where the star is located? $\\qquad$\n\nWill keep the format and line breaks as requested.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"1\"]",
"style": "rule"
} | {
"index": 42,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 13,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 1 | 15 |
train-math-numinamath1.5_olympiads | [
{
"content": "4. Once, a team of Knights and a team of Liars met in the park and decided to ride the circular carousel, which can accommodate 40 people (the \"Chain\" carousel, where everyone sits one behind the other). When they sat down, each person saw two others, one in front of them and one behind them, and said: \"At least one of the people sitting in front of me or behind me belongs to my team.\" One seat remained empty, and they invited another Liar. This Liar said: \"Together with me, we can arrange ourselves on the carousel so that this rule is satisfied again.\" How many people were in the team of Knights? (A Knight always tells the truth, a Liar always lies.)",
"role": "user"
}
]
| math | {
"ground_truth": "[\"26\"]",
"style": "rule"
} | {
"index": 63,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 12,
"DeepSeek-R1-Distill-Qwen-7B": 13
}
} | 26 | 15 |
train-math-numinamath1.5_olympiads | [
{
"content": "436. The Crossing. Six relatives need to cross a river in a small boat that can only hold two people at a time. Mr. Webster, who was in charge of the crossing, had a falling out with his father-in-law and son. Unfortunately, I must also note that Mrs. Webster is not speaking to her mother and her daughter-in-law. The tension between them is so high that it would be unsafe to allow feuding parties to cross together or to remain on the same bank of the river. Additionally, to prevent further disputes, no man can be left with two women or two men with three women.\n\nHow can this respectable family cross to the opposite bank in the fewest number of trips? No tricks such as using a rope or swimming to another bank are allowed.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"9\"]",
"style": "rule"
} | {
"index": 41,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 13,
"DeepSeek-R1-Distill-Qwen-7B": 13
}
} | 9 | 14 |
train-math-deepscaler | [
{
"content": "Vasya has a stick that is 22 cm long. He wants to break it into three pieces with integer lengths such that the pieces can form a triangle. In how many ways can he do this? (Ways that result in identical triangles are considered the same).",
"role": "user"
}
]
| math | {
"ground_truth": "[\"10\"]",
"style": "rule"
} | {
"index": 51,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 4,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 10 | 10 |
train-math-deepscaler | [
{
"content": "In the diagram, $\\triangle PQR$ is right-angled at $P$ and has $PQ=2$ and $PR=2\\sqrt{3}$. Altitude $PL$ intersects median $RM$ at $F$. What is the length of $PF$? [asy]\ndraw((0,0)--(10,0)--(0,10*sqrt(3))--cycle);\ndraw((0,0)--(7.5,4.33)); draw((0,10*sqrt(3))--(5,0));\ndraw((6.68,3.86)--(7.17,3.01)--(7.99,3.49));\nlabel(\"$P$\",(0,0),SW); label(\"$M$\",(5,0),S); label(\"$Q$\",(10,0),SE);\n\nlabel(\"$L$\",(7.5,4.33),NE); label(\"$R$\",(0,10*sqrt(3)),N); label(\"$F$\",(4.29,2.47),NW);\n[/asy]",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{4\\\\sqrt{3}}{7}\"]",
"style": "rule"
} | {
"index": 43,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 5,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | \frac{4\sqrt{3}}{7} | 1 |
train-math-deepscaler | [
{
"content": "How many orbitals contain one or more electrons in an isolated ground state iron atom (Z = 26)?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"15\"]",
"style": "rule"
} | {
"index": 52,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 11,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 15 | 11 |
train-math-numinamath1.5_olympiads | [
{
"content": "| |\n\nIn the bag, there are 70 balls that differ only in color: 20 red, 20 blue, 20 yellow, and the rest are black and white.\n\nWhat is the smallest number of balls that need to be drawn from the bag, without seeing them, to ensure that among them there are at least 10 balls of the same color?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"38\"]",
"style": "rule"
} | {
"index": 56,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 10,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 3
}
} | 38 | 4 |
train-math-deepscaler | [
{
"content": "Five people are crowding into a booth against a wall at a noisy restaurant. If at most three can fit on one side, how many seating arrangements accommodate them all?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"240\"]",
"style": "rule"
} | {
"index": 55,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 4
}
} | 240 | 4 |
train-math-deepscaler | [
{
"content": "The real number $x$ satisfies $x^2 - 5x + 6 < 0.$ Find all possible values of $x^2 + 5x + 6.$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"(20,30)\"]",
"style": "rule"
} | {
"index": 21,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | (20,30) | 8 |
train-math-numinamath1.5_olympiads | [
{
"content": "8. In the interval $[0, \\pi]$, the number of solutions to the trigonometric equation $\\cos 7 x=\\cos 5 x$ is $\\qquad$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"7\"]",
"style": "rule"
} | {
"index": 44,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 7 | 1 |
train-math-deepscaler | [
{
"content": "On graph paper, two right triangles are drawn. Find the sum of the angles BCA and \\(\\mathrm{B}_{1} \\mathrm{C}_{1} \\mathrm{~A}_{1}\\).",
"role": "user"
}
]
| math | {
"ground_truth": "[\"90\"]",
"style": "rule"
} | {
"index": 29,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 6,
"DeepSeek-R1-Distill-Qwen-32B": 3,
"DeepSeek-R1-Distill-Qwen-7B": 3
}
} | 90 | 6 |
train-math-numinamath1.5_olympiads | [
{
"content": "32. As shown in the figure, rays $a$ and $d$ with a common endpoint $A$ are perpendicular to each other, the angle between $a$ and $c$ is $60^{\\circ}$, and the angle between $b$ and $d$ is $45^{\\circ}$. Find the measure of the angle between $b$ and $c$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"15\"]",
"style": "rule"
} | {
"index": 58,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 3,
"DeepSeek-R1-Distill-Qwen-32B": 3,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | 15 | 1 |
train-math-numinamath1.5_olympiads | [
{
"content": "37. Given a segment and a line parallel to it. Using only a ruler, divide the segment in half.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"M\"]",
"style": "rule"
} | {
"index": 47,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 8,
"DeepSeek-R1-Distill-Qwen-32B": 4,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | M | 12 |
train-math-deepscaler | [
{
"content": "How many integers from 1 through 9999, inclusive, do not contain any of the digits 2, 3, 4 or 5?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"1295\"]",
"style": "rule"
} | {
"index": 69,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | 1295 | 1 |
train-math-numinamath1.5_olympiads | [
{
"content": "$\\begin{aligned} & \\text { [Combinations and Permutations]} \\\\ & {[\\text { Problems with Constraints }]}\\end{aligned}$\n\nThere are 12 books on a shelf. In how many ways can five books be chosen from them such that no two of them are next to each other?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"56\"]",
"style": "rule"
} | {
"index": 67,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 56 | 2 |
train-math-deepscaler | [
{
"content": "Let \\(z=\\frac{1+i}{\\sqrt{2}}.\\)What is \\(\\left(z^{1^2}+z^{2^2}+z^{3^2}+\\dots+z^{{12}^2}\\right) \\cdot \\left(\\frac{1}{z^{1^2}}+\\frac{1}{z^{2^2}}+\\frac{1}{z^{3^2}}+\\dots+\\frac{1}{z^{{12}^2}}\\right)?\\)",
"role": "user"
}
]
| math | {
"ground_truth": "[\"36\"]",
"style": "rule"
} | {
"index": 64,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 10,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | 36 | 13 |
train-math-deepscaler | [
{
"content": "Eleven positive integers from a list of fifteen positive integers are $3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23$. What is the largest possible value of the median of this list of fifteen positive integers?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"17\"]",
"style": "rule"
} | {
"index": 79,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 3,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | 17 | 2 |
train-math-deepscaler | [
{
"content": "On one particular Wednesday, Jack worked \\( t-2 \\) hours and earned \\( 3t-2 \\) dollars per hour. His coworker Bob worked 1.5 times more hours than Jack but earned \\( 2t-7 \\) dollars per hour less than Jack. After paying a fixed tax of $10 each, they both netted the same amount of earnings. Determine the value of \\( t \\).",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{19}{3}\"]",
"style": "rule"
} | {
"index": 50,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | \frac{19}{3} | 3 |
train-math-deepscaler | [
{
"content": "In the numbers from 100 to 999, how many numbers have digits in strictly increasing or strictly decreasing order?\n\n(From the 41st American High School Mathematics Exam, 1990)",
"role": "user"
}
]
| math | {
"ground_truth": "[\"204\"]",
"style": "rule"
} | {
"index": 95,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 204 | 12 |
train-math-deepscaler | [
{
"content": "Find the volume of the region in space defined by\n\\[|x + y + 2z| + |x + y - 2z| \\le 12\\]\nand $x, y, z \\ge 0$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"54\"]",
"style": "rule"
} | {
"index": 84,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | 54 | 3 |
train-math-deepscaler | [
{
"content": "The mean (average), the median, and the mode of the five numbers \\( 12, 9, 11, 16, x \\) are all equal. What is the value of \\( x \\)?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"12\"]",
"style": "rule"
} | {
"index": 86,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | 12 | 1 |
train-math-numinamath1.5_olympiads | [
{
"content": "An open organ pipe has its first overtone $N_{1}=512$, if it is blown with air (the speed of sound in air is $V=340 \\frac{\\mathrm{m}}{\\mathrm{sec}}$). How high will the fundamental frequency of this pipe be if it is blown with hydrogen, in which the speed of sound is $V^{\\prime}=1200 \\overline{\\mathrm{m}} \\sec$?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"904\"]",
"style": "rule"
} | {
"index": 83,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 7,
"DeepSeek-R1-Distill-Qwen-32B": 7,
"DeepSeek-R1-Distill-Qwen-7B": 7
}
} | 904 | 15 |
train-math-deepscaler | [
{
"content": "A certain department store sells suits and ties, with each suit priced at $1000$ yuan and each tie priced at $200 yuan. During the \"National Day\" period, the store decided to launch a promotion offering two discount options to customers.<br/>Option 1: Buy one suit and get one tie for free;<br/>Option 2: Pay 90% of the original price for both the suit and the tie.<br/>Now, a customer wants to buy 20 suits and $x$ ties $\\left(x > 20\\right)$.<br/>$(1)$ If the customer chooses Option 1, the payment will be ______ yuan (expressed as an algebraic expression in terms of $x$). If the customer chooses Option 2, the payment will be ______ yuan (expressed as an algebraic expression in terms of $x$).<br/>$(2)$ If $x=30$, calculate and determine which option is more cost-effective at this point.<br/>$(3)$ When $x=30$, can you come up with a more cost-effective purchasing plan? Please describe your purchasing method.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"21800\"]",
"style": "rule"
} | {
"index": 68,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 14,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 5
}
} | 21800 | 10 |
train-math-numinamath1.5_olympiads | [
{
"content": "Task 1. Boys and girls formed a circle in such a way that the number of children whose right neighbor is of the same gender is equal to the number of children whose right neighbor is of a different gender. What could be the total number of children in the circle?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"4\"]",
"style": "rule"
} | {
"index": 78,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 3,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | 4 | 2 |
train-math-deepscaler | [
{
"content": "What is the repeating sequence? Determine what is the repeating sequence in the decimal expansion of the fraction \\(\\frac{1}{49}\\).",
"role": "user"
}
]
| math | {
"ground_truth": "[\"020408163265306122448979591836734693877551\"]",
"style": "rule"
} | {
"index": 109,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 10,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 4
}
} | 020408163265306122448979591836734693877551 | 7 |
train-math-numinamath1.5_cn_contest | [
{
"content": "Seven, the 25 knights of King Arthur sat at their round table, and three knights (any of whom were chosen with equal probability) were selected to slay the dragon. Let $\\mathrm{p}$ be the probability that at least two of the three selected knights are seated next to each other. If $\\mathrm{p}$ is written as a reduced fraction, find the sum of the numerator and the denominator.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"57\"]",
"style": "rule"
} | {
"index": 94,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 14,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 9
}
} | 57 | 14 |
train-math-numinamath1.5_aops_forum | [
{
"content": "find all pairs of relatively prime natural numbers $ (m,n) $ in such a way that there exists non constant polynomial f satisfying \\[ gcd(a+b+1, mf(a)+nf(b) > 1 \\]\nfor every natural numbers $ a $ and $ b $",
"role": "user"
}
]
| math | {
"ground_truth": "[\" (m, n) = (1, 1) \"]",
"style": "rule"
} | {
"index": 92,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | (m, n) = (1, 1) | 14 |
train-math-deepscaler | [
{
"content": "A normal line (a line that passes through a point of tangency and is perpendicular to the tangent line) is drawn to the parabola \\( y = x^2 \\) at point \\( A \\). The normal line intersects the parabola at another point \\( B \\). Let \\( O \\) be the origin of coordinates. When the area of triangle \\( \\triangle OAB \\) is minimized, what is the y-coordinate of point \\( A \\)?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{-3+\\\\sqrt{33}}{24}\"]",
"style": "rule"
} | {
"index": 96,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 3
}
} | \frac{-3+\sqrt{33}}{24} | 10 |
train-math-deepscaler | [
{
"content": "Let $A$ be a point on the parabola $y = x^2 - 4x + 4,$ and let $B$ be a point on the line $y = 2x - 3.$ Find shortest possible distance $AB.$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{2\\\\sqrt{5}}{5}\"]",
"style": "rule"
} | {
"index": 111,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 15
}
} | \frac{2\sqrt{5}}{5} | 4 |
train-math-numinamath1.5_aops_forum | [
{
"content": "Let $n>1$ be an integer and $S_n$ the set of all permutations $\\pi : \\{1,2,\\cdots,n \\} \\to \\{1,2,\\cdots,n \\}$ where $\\pi$ is bijective function. For every permutation $\\pi \\in S_n$ we define:\n\n\\[ F(\\pi)= \\sum_{k=1}^n |k-\\pi(k)| \\ \\ \\text{and} \\ \\ M_{n}=\\frac{1}{n!}\\sum_{\\pi \\in S_n} F(\\pi) \\]\nwhere $M_n$ is taken with all permutations $\\pi \\in S_n$. Calculate the sum $M_n$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{n^2 - 1}{3}\"]",
"style": "rule"
} | {
"index": 108,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | \frac{n^2 - 1}{3} | 10 |
train-math-numinamath1.5_olympiads | [
{
"content": "Example 22. Solve the inequality\n\n$$\n\\left(\\sqrt{x^{2}-4 x+3}+1\\right) \\log _{2} \\frac{x}{5}+\\frac{1}{x}\\left(\\sqrt{8 x-2 x^{2}-6}+1\\right) \\leqslant 0\n$$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"1\"]",
"style": "rule"
} | {
"index": 124,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 1 | 14 |
train-math-deepscaler | [
{
"content": "Complex numbers $p,$ $q,$ $r$ form an equilateral triangle with side length 24 in the complex plane. If $|p + q + r| = 48,$ find $|pq + pr + qr|.$ These complex numbers have been translated by the same complex number $z$ compared to their original positions on the origin.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"768\"]",
"style": "rule"
} | {
"index": 122,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 12,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 6
}
} | 768 | 12 |
train-math-numinamath1.5_olympiads | [
{
"content": "10. (20 points) Find the smallest value of the parameter $c$ such that the system of equations has a unique solution\n\n$$\n\\left\\{\\begin{array}{l}\n2(x+7)^{2}+(y-4)^{2}=c \\\\\n(x+4)^{2}+2(y-7)^{2}=c\n\\end{array}\\right.\n$$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"6\"]",
"style": "rule"
} | {
"index": 127,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 10,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 3
}
} | 6 | 15 |
train-math-deepscaler | [
{
"content": "Given the total number of stations is 6 and 3 of them are selected for getting off, calculate the probability that person A and person B get off at different stations.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{2}{3}\"]",
"style": "rule"
} | {
"index": 129,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 8,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | \frac{2}{3} | 7 |
train-math-deepscaler | [
{
"content": "All the complex roots of $(z + 2)^6 = 64z^6$, when plotted in the complex plane, lie on a circle. Find the radius of this circle.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{2}{\\\\sqrt{3}}\"]",
"style": "rule"
} | {
"index": 154,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | \frac{2}{\sqrt{3}} | 14 |
train-math-numinamath1.5_cn_contest | [
{
"content": "Example 1 Let $\\alpha=\\frac{\\sqrt{5}+1}{2}$. Then $\\left[\\alpha^{16}\\right]=$ $\\qquad$ .\n(2008, \"Five Sheep Cup\" Mathematics Competition (Junior High School))\n[Analysis] Note that $\\alpha=\\frac{\\sqrt{5}+1}{2}$ and $\\beta=\\frac{\\sqrt{5}-1}{2}$ $(0<\\beta<1)$ can make $\\alpha+\\beta=\\sqrt{5}$ and $\\alpha \\beta=1$. Therefore, the value of $\\alpha^{16}+\\beta^{16}$ can be calculated to make a judgment.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"2206\"]",
"style": "rule"
} | {
"index": 125,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 10,
"DeepSeek-R1-Distill-Qwen-32B": 6,
"DeepSeek-R1-Distill-Qwen-7B": 7
}
} | 2206 | 9 |
train-math-deepscaler | [
{
"content": "Given the function $f(x)=\\sin x+\\cos x$, where $x\\in \\mathbb{R}$.\n- (I) Find the value of $f\\left( \\frac{\\pi}{2}\\right)$;\n- (II) Find the smallest positive period of the function $f(x)$;\n- (III) Find the minimum value of the function $g(x)=f\\left(x+ \\frac{\\pi}{4}\\right)+f\\left(x+ \\frac{3\\pi}{4}\\right)$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"-2\"]",
"style": "rule"
} | {
"index": 141,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | -2 | 1 |
train-math-deepscaler | [
{
"content": "Given that $\\frac{a}{25-a}+\\frac{b}{65-b}+\\frac{c}{60-c}=7$, evaluate $\\frac{5}{25-a}+\\frac{13}{65-b}+\\frac{12}{60-c}$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"2\"]",
"style": "rule"
} | {
"index": 148,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | 2 | 1 |
train-math-numinamath1.5_olympiads | [
{
"content": "18.55 $ABCD$ is a rectangle (as shown in the figure), $P$ is any point on $AB$, $PS \\perp BD$, $PR \\perp AC$, $AF \\perp BD$, $PQ \\perp AF$, then $PR + PS$ equals\n(A) $PQ$.\n(B) $AE$.\n(C) $PT + AT$.\n(D) $AF$.\n(E) $EF$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"D\"]",
"style": "rule"
} | {
"index": 144,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 6,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | D | 5 |
train-math-deepscaler | [
{
"content": "In triangle $ABC,$ the side lengths $a,$ $b,$ and $c$ satisfy $a + 2b + 2c = a^2$ and $a + 2b - 2c = -3.$ Find the largest angle of the triangle, in degrees.\n\nNote: $a$ is the side length opposite $\\angle A,$ etc.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"120^\\\\circ\"]",
"style": "rule"
} | {
"index": 143,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 120^\circ | 2 |
train-math-numinamath1.5_olympiads | [
{
"content": "13. The number 144 is very special in that it enjoys the mirror property: not only is it true that $144=12^{2}$ (i.e., it is a perfect square), but it is also true that $441=21^{2}$, meaning that reversing the order of its digits results in precisely the square of the number obtained by reversing the digits of its square root. The number 100 also has the mirror property, as does the number 1, while the number 49 does not. How many positive integers with at most 3 digits enjoy the mirror property?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"12\"]",
"style": "rule"
} | {
"index": 151,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 14,
"DeepSeek-R1-Distill-Qwen-32B": 3,
"DeepSeek-R1-Distill-Qwen-7B": 2
}
} | 12 | 15 |
train-math-numinamath1.5_olympiads | [
{
"content": "56. As shown in the figure, the side length of square $\\mathrm{ABCD}$ is $10, \\mathrm{AG}=\\mathrm{CH}=8, \\mathrm{BG}=\\mathrm{DH}=6$, connect $\\mathrm{GH}$, then the length of line segment $\\mathrm{GH}$ is",
"role": "user"
}
]
| math | {
"ground_truth": "[\"2\\\\sqrt{2}\"]",
"style": "rule"
} | {
"index": 155,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 5,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 2\sqrt{2} | 7 |
train-math-deepscaler | [
{
"content": "How many different triangles can be formed having a perimeter of 7 units if each side must have integral length?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"2\"]",
"style": "rule"
} | {
"index": 157,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 2 | 1 |
train-math-deepscaler | [
{
"content": "Consider a 9x9 chessboard where the squares are labelled from a starting square at the bottom left (1,1) increasing incrementally across each row to the top right (9,9). Each square at position $(i,j)$ is labelled with $\\frac{1}{i+j-1}$. Nine squares are chosen such that there is exactly one chosen square in each row and each column. Find the minimum product of the labels of the nine chosen squares.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{1}{362880}\"]",
"style": "rule"
} | {
"index": 160,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 14,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | \frac{1}{362880} | 15 |
train-math-deepscaler | [
{
"content": "Find the least positive integer $n$ such that $$\\frac 1{\\sin 30^\\circ\\sin 31^\\circ}+\\frac 1{\\sin 32^\\circ\\sin 33^\\circ}+\\cdots+\\frac 1{\\sin 88^\\circ\\sin 89^\\circ}+\\cos 89^\\circ=\\frac 1{\\sin n^\\circ}.$$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"n = 1\"]",
"style": "rule"
} | {
"index": 164,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 14,
"DeepSeek-R1-Distill-Qwen-32B": 7,
"DeepSeek-R1-Distill-Qwen-7B": 11
}
} | n = 1 | 9 |
train-math-numinamath1.5_olympiads | [
{
"content": "21. [12] Let $A B C D$ be a quadrilateral inscribed in a circle with center $O$. Let $P$ denote the intersection of $A C$ and $B D$. Let $M$ and $N$ denote the midpoints of $A D$ and $B C$. If $A P=1, B P=3, D P=\\sqrt{3}$, and $A C$ is perpendicular to $B D$, find the area of triangle $M O N$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{3}{4}\"]",
"style": "rule"
} | {
"index": 156,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 9,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | \frac{3}{4} | 14 |
train-math-deepscaler | [
{
"content": "Given positive numbers $a$ and $b$ satisfying $a+b=1$, $c\\in R$, find the minimum value of $\\frac{3a}{b{c}^{2}+b}+\\frac{1}{ab{c}^{2}+ab}+3c^{2}$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"6\\\\sqrt{2} - 3\"]",
"style": "rule"
} | {
"index": 163,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 12,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 6
}
} | 6\sqrt{2} - 3 | 12 |
train-math-deepscaler | [
{
"content": "Scenario: In a math activity class, the teacher presented a set of questions and asked the students to explore the pattern by reading the following solution process:\n\n$\\sqrt{1+\\frac{5}{4}}=\\sqrt{\\frac{9}{4}}=\\sqrt{{(\\frac{3}{2})}^{2}}=\\frac{3}{2}$;\n$\\sqrt{1+\\frac{7}{9}}=\\sqrt{\\frac{16}{9}}=\\sqrt{{(\\frac{4}{3})}^{2}}=\\frac{4}{3}$;\n$\\sqrt{1+\\frac{9}{16}}=\\sqrt{\\frac{25}{16}}=\\sqrt{{(\\frac{5}{4})}^{2}}=\\frac{5}{4}$;\n$\\ldots$\n\nPractice and exploration:\n$(1)$ According to this pattern, calculate: $\\sqrt{1+\\frac{17}{64}}=$______;\n$(2)$ Calculate: $\\sqrt{1+\\frac{5}{4}}×\\sqrt{1+\\frac{7}{9}}×\\sqrt{1+\\frac{9}{16}}×⋅⋅⋅×\\sqrt{1+\\frac{21}{100}}$;\nTransfer and application:\n$(3)$ If $\\sqrt{1+\\frac{2023}{{n}^{2}}}=x$ follows the above pattern, please directly write down the value of $x$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{1012}{1011}\"]",
"style": "rule"
} | {
"index": 133,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 8,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 5
}
} | \frac{1012}{1011} | 3 |
train-math-numinamath1.5_olympiads | [
{
"content": "7. Let $S=\\{1,2,3, \\ldots, 9,10\\}$. A non-empty subset of $S$ is considered \"Good\" if the number of even integers in the subset is more than or equal to the number of odd integers in the same subset. For example, the subsets $\\{4,8\\},\\{3,4,7,8\\}$ and $\\{1,3,6,8,10\\}$ are \"Good\". How many subsets of $S$ are \"Good\"?\n(A) 482\n(B) 507\n(C) 575\n(D) 637\n(E) 667",
"role": "user"
}
]
| math | {
"ground_truth": "[\"637\"]",
"style": "rule"
} | {
"index": 161,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 637 | 6 |
train-math-deepscaler | [
{
"content": "In the plane rectangular coordinate system $xOy$, the equation of the hyperbola $C$ is $x^{2}-y^{2}=1$. Find all real numbers $a$ greater than 1 that satisfy the following requirement: Through the point $(a, 0)$, draw any two mutually perpendicular lines $l_{1}$ and $l_{2}$. If $l_{1}$ intersects the hyperbola $C$ at points $P$ and $Q$, and $l_{2}$ intersects $C$ at points $R$ and $S$, then $|PQ| = |RS|$ always holds.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\sqrt{2}\"]",
"style": "rule"
} | {
"index": 158,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 7,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | \sqrt{2} | 8 |
train-math-numinamath1.5_cn_contest | [
{
"content": "2. Let $a<-1$, and the variable $x$ satisfies $x^{2}+a x \\leqslant-x$, and the minimum value of $x^{2}+a x$ is $-\\frac{1}{2}$. Then $a=$ $\\qquad$ .",
"role": "user"
}
]
| math | {
"ground_truth": "[\"-\\\\frac{3}{2}\"]",
"style": "rule"
} | {
"index": 185,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 9,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 3
}
} | -\frac{3}{2} | 7 |
train-math-deepscaler | [
{
"content": "Randomly split 2.5 into the sum of two non-negative numbers, and round each number to its nearest integer. What is the probability that the sum of the two resulting integers is 3?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{2}{5}\"]",
"style": "rule"
} | {
"index": 181,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 7,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | \frac{2}{5} | 6 |
train-math-numinamath1.5_aops_forum | [
{
"content": "Find all functions $f: \\mathbb{R}^{+} \\rightarrow \\mathbb{R}$ and $g: \\mathbb{R}^{+} \\rightarrow \\mathbb{R}$ such that\n$$f(x^2 + y^2) = g(xy)$$\nholds for all $x, y \\in \\mathbb{R}^{+}$.\n",
"role": "user"
}
]
| math | {
"ground_truth": "[\" f(x) = c \"]",
"style": "rule"
} | {
"index": 168,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | f(x) = c | 7 |
train-math-numinamath1.5_aops_forum | [
{
"content": "[b]Problem Section #1\na) A set contains four numbers. The six pairwise sums of distinct elements of the set, in no particular order, are $189, 320, 287, 264, x$, and y. Find the greatest possible value of: $x + y$.\n\n[color=red]NOTE: There is a high chance that this problems was copied.[/color]",
"role": "user"
}
]
| math | {
"ground_truth": "[\"761\"]",
"style": "rule"
} | {
"index": 180,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 12,
"DeepSeek-R1-Distill-Qwen-32B": 3,
"DeepSeek-R1-Distill-Qwen-7B": 2
}
} | 761 | 6 |
train-math-deepscaler | [
{
"content": "Find the minimum positive integer $k$ such that there exists a function $f$ from the set $\\Bbb{Z}$ of all integers to $\\{1, 2, \\ldots k\\}$ with the property that $f(x) \\neq f(y)$ whenever $|x-y| \\in \\{5, 7, 12\\}$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"4\"]",
"style": "rule"
} | {
"index": 179,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 12,
"DeepSeek-R1-Distill-Qwen-32B": 7,
"DeepSeek-R1-Distill-Qwen-7B": 4
}
} | 4 | 3 |
train-math-still3 | [
{
"content": "Define an ordered triple $(A, B, C)$ of sets to be minimally intersecting if $|A \\cap B| = |B \\cap C| = |C \\cap A| = 1$ and $A \\cap B \\cap C = \\emptyset$. Let $N$ be the number of minimally intersecting ordered triples of sets for which each set is a subset of $\\{1,2,3,4,5,6,7,8\\}$. Find the remainder when $N$ is divided by 1000.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"64\"]",
"style": "rule"
} | {
"index": 194,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 11,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 4
}
} | 64 | 14 |
train-math-deepscaler | [
{
"content": "If the six-digit number $\\overline{201 a b 7}$ is divisible by 11 and 13, then the two-digit number $\\overline{a b}$ equals:",
"role": "user"
}
]
| math | {
"ground_truth": "[\"48\"]",
"style": "rule"
} | {
"index": 190,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 8,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 48 | 5 |
train-math-deepscaler | [
{
"content": "The numbers $1, 2, 3, 4, 5$ are to be arranged in a circle. An arrangement is $\\textit{bad}$ if it is not true that for every $n$ from $1$ to $15$ one can find a subset of the numbers that appear consecutively on the circle that sum to $n$. Arrangements that differ only by a rotation or a reflection are considered the same. How many different bad arrangements are there?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"2\"]",
"style": "rule"
} | {
"index": 198,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 13,
"DeepSeek-R1-Distill-Qwen-32B": 7,
"DeepSeek-R1-Distill-Qwen-7B": 8
}
} | 2 | 3 |
train-math-numinamath1.5_olympiads | [
{
"content": "3. Given an infinitely decreasing geometric progression. The sum of all its terms with odd indices is 10 more than the sum of all terms with even indices. And the difference between the sum of the squares of all terms at odd positions and the sum of the squares of all terms at even positions is 20. Find the first term and the common ratio of the progression.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"b_{1}=5,q=-\\\\frac{1}{2}\"]",
"style": "rule"
} | {
"index": 193,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 14,
"DeepSeek-R1-Distill-Qwen-7B": 14
}
} | b_{1}=5,q=-\frac{1}{2} | 5 |
train-math-deepscaler | [
{
"content": "Points $M$ , $N$ , $P$ are selected on sides $\\overline{AB}$ , $\\overline{AC}$ , $\\overline{BC}$ , respectively, of triangle $ABC$ . Find the area of triangle $MNP$ given that $AM=MB=BP=15$ and $AN=NC=CP=25$ .\n\n*Proposed by Evan Chen*",
"role": "user"
}
]
| math | {
"ground_truth": "[\"150\"]",
"style": "rule"
} | {
"index": 199,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 4,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 150 | 15 |
train-math-deepscaler | [
{
"content": "On a particular street in Waterloo, there are exactly 14 houses, each numbered with an integer between 500 and 599, inclusive. The 14 house numbers form an arithmetic sequence in which 7 terms are even and 7 terms are odd. One of the houses is numbered 555 and none of the remaining 13 numbers has two equal digits. What is the smallest of the 14 house numbers?\n\n(An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, 3, 5, 7, 9 is an arithmetic sequence with four terms.)",
"role": "user"
}
]
| math | {
"ground_truth": "[\"506\"]",
"style": "rule"
} | {
"index": 174,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 506 | 15 |
train-math-numinamath1.5_olympiads | [
{
"content": "7. Definition: $u(n)$ represents the unit digit of the natural number $n$, for example $u(13)=3$. Let $a_{n}=u(7 n)-u(n)$, then $a_{1}+a_{2}+a_{3}+\\cdots+a_{2020}=$ $\\qquad$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"0\"]",
"style": "rule"
} | {
"index": 205,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 6,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 0 | 1 |
train-math-numinamath1.5_olympiads | [
{
"content": "3. 3.1. Find the number of four-digit numbers composed of the digits $1,2,3,4,5,6,7$ (each digit is used no more than once) that are divisible by 15.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"36\"]",
"style": "rule"
} | {
"index": 196,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 12,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | 36 | 10 |
train-math-deepscaler | [
{
"content": "Given the ellipse $G$: $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 (a > b > 0)$ with an eccentricity of $\\frac{\\sqrt{6}}{3}$, and its right focus at $(2\\sqrt{2}, 0)$. A line $l$ with a slope of $1$ intersects the ellipse $G$ at points $A$ and $B$. An isosceles triangle is formed with $AB$ as the base and $P$ $(-3, 2)$ as the apex.\n\n(1) Find the equation of the ellipse $G$;\n\n(2) Calculate the area of $\\triangle PAB$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{9}{2}\"]",
"style": "rule"
} | {
"index": 203,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 4,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | \frac{9}{2} | 1 |
train-math-numinamath1.5_olympiads | [
{
"content": "# 1. Task 1.1 \n\nTimur and Alexander are counting the trees growing around their house. Both are moving in the same direction but start counting from different trees. What is the total number of trees growing around the house if the tree that Timur called the 12th, Alexander counted as $33-\\mathrm{m}$, and the tree that Timur called $105-\\mathrm{m}$, Alexander counted as the 8th?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"118\"]",
"style": "rule"
} | {
"index": 207,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 8,
"DeepSeek-R1-Distill-Qwen-7B": 15
}
} | 118 | 14 |
train-math-numinamath1.5_amc_aime | [
{
"content": "Suppose that\n\\[\\frac{2x}{3}-\\frac{x}{6}\\]\nis an integer. Which of the following statements must be true about $x$?\n$\\mathrm{(A)}\\ \\text{It is negative.}\\\\\\mathrm{(B)}\\ \\text{It is even, but not necessarily a multiple of 3.}\\\\\\mathrm{(C)}\\ \\text{It is a multiple of 3, but not necessarily even.}\\\\\\mathrm{(D)}\\ \\text{It is a multiple of 6, but not necessarily a multiple of 12.}\\\\\\mathrm{(E)}\\ \\text{It is a multiple of 12.}$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"B\"]",
"style": "rule"
} | {
"index": 219,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | B | 3 |
train-math-numinamath1.5_olympiads | [
{
"content": "3 [\n\nFrom one point, two tangents are drawn to a circle. The length of each tangent is 12, and the distance between the points of tangency is 14.4. Find the radius of the circle.\n\n#",
"role": "user"
}
]
| math | {
"ground_truth": "[\"9\"]",
"style": "rule"
} | {
"index": 240,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 4,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 2
}
} | 9 | 14 |
train-math-numinamath1.5_olympiads | [
{
"content": "$2 \\cdot 110$ To make $p=x^{4}+6 x^{3}+11 x^{2}+3 x+31$ a perfect square of an integer, the number of integer values of $x$ is\n(A) 4.\n(B) 3.\n(C) 2.\n(D) 1.\n(E) 0.\n(16th American High School Mathematics Examination, 1965)",
"role": "user"
}
]
| math | {
"ground_truth": "[\"D\"]",
"style": "rule"
} | {
"index": 237,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 9,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 5
}
} | D | 11 |
train-math-numinamath1.5_inequalities | [
{
"content": "$2 \\cdot 62$ Given 1990 piles of stones, each consisting of $1, 2, \\cdots, 1990$ stones, in each round, you are allowed to pick any number of piles and remove the same number of stones from these piles. How many rounds are needed at minimum to remove all the stones?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"11\"]",
"style": "rule"
} | {
"index": 232,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 6,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 11 | 1 |
train-math-deepscaler | [
{
"content": "A food factory regularly purchases flour. It is known that the factory needs 6 tons of flour per day, the price of each ton of flour is 1800 yuan, and the storage and other costs for flour are an average of 3 yuan per ton per day. Each time flour is purchased, a shipping fee of 900 yuan is required. How often should the factory purchase flour to minimize the average daily total cost?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"10\"]",
"style": "rule"
} | {
"index": 245,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 12,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 10 | 4 |
train-math-deepscaler | [
{
"content": "There are two circles: one with center at point \\( A \\) and radius 6, and the other with center at point \\( B \\) and radius 3. Their common internal tangent touches the circles respectively at points \\( C \\) and \\( D \\). The lines \\( AB \\) and \\( CD \\) intersect at point \\( E \\). Find the length of \\( CD \\), given that \\( AE = 10 \\).",
"role": "user"
}
]
| math | {
"ground_truth": "[\"12\"]",
"style": "rule"
} | {
"index": 231,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 12 | 3 |
train-math-numinamath1.5_aops_forum | [
{
"content": "It is given set $A=\\{1,2,3,...,2n-1\\}$. From set $A$, at least $n-1$ numbers are expelled such that:\n$a)$ if number $a \\in A$ is expelled, and if $2a \\in A$ then $2a$ must be expelled\n$b)$ if $a,b \\in A$ are expelled, and $a+b \\in A$ then $a+b$ must be also expelled\nWhich numbers must be expelled such that sum of numbers remaining in set stays minimal",
"role": "user"
}
]
| math | {
"ground_truth": "[\" \\\\{2, 3, \\\\ldots, 2n-1\\\\} \"]",
"style": "rule"
} | {
"index": 236,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 13,
"DeepSeek-R1-Distill-Qwen-32B": 8,
"DeepSeek-R1-Distill-Qwen-7B": 10
}
} | \{2, 3, \ldots, 2n-1\} | 2 |
train-math-still3 | [
{
"content": "Let $S$ be the set of complex numbers of the form $x + yi,$ where $x$ and $y$ are real numbers, such that\n\\[\\frac{1}{2} \\le x \\le \\frac{\\sqrt{2}}{2}.\\]Find the smallest positive integer $m$ such that for all positive integers $n \\ge m,$ there exists a complex number $z \\in S$ such that $z^n = 1.$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"13\"]",
"style": "rule"
} | {
"index": 227,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 14,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 13 | 15 |
train-math-numinamath1.5_amc_aime | [
{
"content": "The increasing sequence of positive integers $a_1,a_2,a_3,\\cdots$ has the property that\n\\[a_{n+2}=a_n+a_{n+1} \\text{ for all } n\\ge 1.\\]\nIf $a_7=120$, then $a_8$ is\n$\\text{(A) } 128\\quad \\text{(B) } 168\\quad \\text{(C) } 193\\quad \\text{(D) } 194\\quad \\text{(E) } 210$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"194\"]",
"style": "rule"
} | {
"index": 244,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 194 | 5 |
train-math-deepscaler | [
{
"content": "Three children need to cover a distance of 84 kilometers using two bicycles. Walking, they cover 5 kilometers per hour, while bicycling they cover 20 kilometers per hour. How long will it take for all three to reach the destination if only one child can ride a bicycle at a time?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"8.4\"]",
"style": "rule"
} | {
"index": 242,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 13,
"DeepSeek-R1-Distill-Qwen-7B": 14
}
} | 8.4 | 14 |
train-math-numinamath1.5_aops_forum | [
{
"content": "Let $f(x)$ be the function defined for $x\\geq 0$ which satisfies the following conditions.\r\n(a) $f(x)=\\begin{cases}x \\ \\ \\ \\ \\ \\ \\ \\ ( 0\\leq x<1) \\\\ 2-x \\ \\ \\ (1\\leq x <2) \\end{cases}$ \r\n\r\n(b) $f(x+2n)=f(x) \\ (n=1,2,\\cdots)$\r\n\r\nFind $\\lim_{n\\to\\infty}\\int_{0}^{2n}f(x)e^{-x}\\ dx.$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"1\"]",
"style": "rule"
} | {
"index": 239,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 9,
"DeepSeek-R1-Distill-Qwen-7B": 14
}
} | 1 | 5 |
train-math-deepscaler | [
{
"content": "Let $x$ and $y$ be positive real numbers. Find the minimum value of\n\\[\\frac{\\sqrt{(x^2 + y^2)(3x^2 + y^2)}}{xy}.\\]",
"role": "user"
}
]
| math | {
"ground_truth": "[\"1 + \\\\sqrt{3}\"]",
"style": "rule"
} | {
"index": 276,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 1 + \sqrt{3} | 7 |
train-math-numinamath1.5_olympiads | [
{
"content": "Problem 8.5. A field was partially planted with corn, oats, and millet. If the remaining part is completely planted with millet, then millet will occupy half of the entire field. If the remaining part is equally divided between oats and corn, then oats will occupy half of the entire field. By what factor will the amount of corn increase if the remaining part is completely planted with corn?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"3\"]",
"style": "rule"
} | {
"index": 255,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 14,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 3 | 1 |
train-math-still3 | [
{
"content": "A container in the shape of a right circular cone is 12 inches tall and its base has a 5-inch radius. The liquid that is sealed inside is 9 inches deep when the cone is held with its point down and its base horizontal. When the liquid is held with its point up and its base horizontal, the liquid is $m-n\\sqrt[3]{p},$ where $m,$ $n,$ and $p$ are positive integers and $p$ is not divisible by the cube of any prime number. Find $m+n+p.$ ",
"role": "user"
}
]
| math | {
"ground_truth": "[\"52\"]",
"style": "rule"
} | {
"index": 258,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 14,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 3
}
} | 52 | 13 |
train-math-deepscaler | [
{
"content": "How many roots does the equation\n\n$$\n\\overbrace{f(f(\\ldots f}^{10 \\text{ times } f}(x) \\ldots)) + \\frac{1}{2} = 0\n$$\n\nhave, where \\( f(x) = |x| - 1 \\)?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"20\"]",
"style": "rule"
} | {
"index": 261,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 12,
"DeepSeek-R1-Distill-Qwen-32B": 3,
"DeepSeek-R1-Distill-Qwen-7B": 7
}
} | 20 | 13 |
train-math-numinamath1.5_aops_forum | [
{
"content": "Let $ABC$ be a triangle such that $|AB|=7$, $|BC|=8$, $|AC|=6$. Let $D$ be the midpoint of side $[BC]$. If the circle through $A$, $B$ and $D$ cuts $AC$ at $A$ and $E$, what is $|AE|$?\n\n$ \n\\textbf{(A)}\\ \\dfrac 23\n\\qquad\\textbf{(B)}\\ 1\n\\qquad\\textbf{(C)}\\ \\dfrac 32\n\\qquad\\textbf{(D)}\\ 2\n\\qquad\\textbf{(E)}\\ 3\n$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{2}{3}\"]",
"style": "rule"
} | {
"index": 260,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | \frac{2}{3} | 13 |
train-math-deepscaler | [
{
"content": "In a regular octagon, find the ratio of the length of the shortest diagonal to the longest diagonal. Express your answer as a common fraction in simplest radical form.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{\\\\sqrt{2}}{2}\"]",
"style": "rule"
} | {
"index": 289,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 7,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 3
}
} | \frac{\sqrt{2}}{2} | 9 |
train-math-numinamath1.5_olympiads | [
{
"content": "G2.4 Let $d$ and $f$ be positive integers and $a_{1}=0.9$. If $a_{i+1}=a_{i}^{2}$ and $\\prod_{i=1}^{4} a_{i}=\\frac{3^{d}}{f}$, determine the smallest possible value of $d$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"30\"]",
"style": "rule"
} | {
"index": 286,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 30 | 2 |
train-math-numinamath1.5_olympiads | [
{
"content": "KOVSHIN=BOTTLE+GLASS; $\\quad$ TWO KOVSHINS=SEVEN GLASSES; BOTTLE=CUP+TWO GLASSES; $\\quad$ BOTTLE=how many CUPS?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"5\"]",
"style": "rule"
} | {
"index": 293,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 11,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 4
}
} | 5 | 2 |
train-math-numinamath1.5_olympiads | [
{
"content": "15. Given the ellipse $C: \\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1$ passes through the point $M(0,2)$, and the right focus is $F(2,0)$.\n(1) Write the equation of the ellipse $C$;\n(2) A line $l$ passing through point $F$ intersects the ellipse $C$ at points $A, B$, and intersects the $y$-axis at point $P$; if $\\overrightarrow{P A}=m \\overrightarrow{A F}, \\overrightarrow{P B}=n \\overrightarrow{B F}$. Prove that $m+n$ is a constant;\n(3) Under the condition in (2), if point $P$ is not inside the ellipse $C$, and point $Q$ is the point symmetric to $P$ with respect to the origin $O$, find the minimum value of the area of triangle $Q A B$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{16}{3}\"]",
"style": "rule"
} | {
"index": 264,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 14,
"DeepSeek-R1-Distill-Qwen-32B": 4,
"DeepSeek-R1-Distill-Qwen-7B": 7
}
} | \frac{16}{3} | 14 |
train-math-deepscaler | [
{
"content": "In the diagram below, $\\overline{AB}\\parallel \\overline{CD}$ and $\\angle AXE$ is $108^\\circ$ less than 3 times $\\angle CYX$. Find $\\angle BXY$.\n\n[asy]\n\nunitsize(1inch);\n\npair A,B,C,D,X,Y,EE,F;\n\nA = (0,0);\n\nB=(1,0);\n\nC = (0,0.8);\n\nD=(1,0.8);\n\nEE = (0.35,-0.3);\n\nF = (0.8,1.1);\n\ndraw(EE--F);\n\ndraw(A--B);\n\ndraw(C--D);\n\ndot(A);\n\ndot(B);\n\ndot(C);\n\ndot(D);\n\ndot(EE);\n\ndot(F);\n\nlabel(\"$E$\",EE,S);\n\nlabel(\"$F$\",F,N);\n\nX = intersectionpoint(A--B,EE--F);\n\nY = intersectionpoint(C--D,EE--F);\n\nlabel(\"$X$\",X,NNW);\n\nlabel(\"$Y$\",Y,NNW);\n\nlabel(\"$A$\",A,W);\n\nlabel(\"$B$\",B,E);\n\nlabel(\"$C$\",C,W);\n\nlabel(\"$D$\",D,E);\n\ndot(X);\n\ndot(Y);\n\n[/asy]",
"role": "user"
}
]
| math | {
"ground_truth": "[\"54^\\\\circ\"]",
"style": "rule"
} | {
"index": 310,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 13
}
} | 54^\circ | 12 |
train-math-deepscaler | [
{
"content": "In Cologne, there were three brothers who had 9 containers of wine. The first container had a capacity of 1 quart, the second contained 2 quarts, with each subsequent container holding one more quart than the previous one, so the last container held 9 quarts. The task is to divide the wine equally among the three brothers without transferring wine between the containers.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"15\"]",
"style": "rule"
} | {
"index": 301,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 4,
"DeepSeek-R1-Distill-Qwen-7B": 4
}
} | 15 | 2 |
train-math-numinamath1.5_inequalities | [
{
"content": "4. 47. Let $a, b$ be real numbers, and $x^{4}+a x^{3}+b x^{2}+a x+1=0$ has at least one real root. Try to find the minimum value of $a^{2}+b^{2}$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{4}{5}\"]",
"style": "rule"
} | {
"index": 316,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 7,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 2
}
} | \frac{4}{5} | 1 |
train-math-numinamath1.5_olympiads | [
{
"content": "What is the maximum number of axes of symmetry that the union of $k$ segments on a plane can have?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"2k\"]",
"style": "rule"
} | {
"index": 304,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 11,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 3
}
} | 2k | 11 |
train-math-numinamath1.5_aops_forum | [
{
"content": "Given is a piece at the origin of the coordinate plane. Two persons $A,\\ B$ act as following.\nFirst, $A$ marks on a lattice point, on which the piece cannot be anymore put. Then $B$ moves the piece from the point $(x,\\ y)$ to the point $(x+1,\\ y)$ or $(x,\\ y+1)$, a number of $m$ times $(1\\leq m\\leq k)$. Note that we may not move the piece to a marked point. If $A$ wins when $B$ can't move any pieces, then find all possible integers $k$ such that $A$ will win in a finite number of moves, regardless of how $B$ moves the piece.",
"role": "user"
}
]
| math | {
"ground_truth": "[\" k \"]",
"style": "rule"
} | {
"index": 280,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 14,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | k | 11 |
train-math-deepscaler | [
{
"content": "Evaluate the infinite sum $$\\sum_{n=2}^{\\infty} \\log _{2}\\left(\\frac{1-\\frac{1}{n}}{1-\\frac{1}{n+1}}\\right)$$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"-1\"]",
"style": "rule"
} | {
"index": 326,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | -1 | 3 |
train-math-numinamath1.5_aops_forum | [
{
"content": "Let $P$ be a point inside the equilateral triangle $ABC$ such that $6\\angle PBC = 3\\angle PAC = 2\\angle PCA$. Find the measure of the angle $\\angle PBC$ .",
"role": "user"
}
]
| math | {
"ground_truth": "[\"15^\\\\circ\"]",
"style": "rule"
} | {
"index": 324,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 6,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 2
}
} | 15^\circ | 11 |
train-math-numinamath1.5_olympiads | [
{
"content": "6. (15 points) A metal bar with a temperature of $20^{\\circ} \\mathrm{C}$ was submerged into water taken at a temperature of $100^{\\circ} \\mathrm{C}$. After thermal equilibrium was established, the temperature was found to be $80^{\\circ} \\mathrm{C}$. After this, without removing the first bar from the water, another identical bar with a temperature of $20^{\\circ} \\mathrm{C}$ was submerged into the water. What will the temperature of the water be after thermal equilibrium is established?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"68\\\\mathrm{C}\"]",
"style": "rule"
} | {
"index": 299,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 10
}
} | 68\mathrm{C} | 13 |
train-math-deepscaler | [
{
"content": "If \\(x\\) and \\(y\\) are positive real numbers such that \\(6x^2 + 12xy + 6y^2 = x^3 + 3x^2 y + 3xy^2\\), find the value of \\(x\\).",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{24}{7}\"]",
"style": "rule"
} | {
"index": 311,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 9,
"DeepSeek-R1-Distill-Qwen-32B": 11,
"DeepSeek-R1-Distill-Qwen-7B": 9
}
} | \frac{24}{7} | 2 |
train-math-deepscaler | [
{
"content": "Equilateral triangle $ABC$ has been creased and folded so that vertex $A$ now rests at $A'$ on $\\overline{BC}$ as shown. If $BA' = 1$ and $A'C = 2,$ then find the length of crease $\\overline{PQ}.$\n\n[asy]\nunitsize(1 cm);\n\npair A, Ap, B, C, P, Q;\n\nA = 3*dir(60);\nB = (0,0);\nC = (3,0);\nAp = (1,0);\nP = 8/5*dir(60);\nQ = C + 5/4*dir(120);\n\ndraw(B--C--Q--P--cycle);\ndraw(P--Ap--Q);\ndraw(P--A--Q,dashed);\n\nlabel(\"$A$\", A, N);\nlabel(\"$A'$\", Ap, S);\nlabel(\"$B$\", B, SW);\nlabel(\"$C$\", C, SE);\nlabel(\"$P$\", P, NW);\nlabel(\"$Q$\", Q, NE);\n[/asy]",
"role": "user"
}
]
| math | {
"ground_truth": "[\"\\\\frac{7 \\\\sqrt{21}}{20}\"]",
"style": "rule"
} | {
"index": 315,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 3,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | \frac{7 \sqrt{21}}{20} | 3 |
train-math-numinamath1.5_olympiads | [
{
"content": "2. In front of Vasya lies a stack of 15 red, 15 blue, and 15 yellow cards. Vasya needs to choose 15 out of all 45 cards to earn the maximum number of points. Points are awarded as follows: for each red card, Vasya gets one point. For each blue card, Vasya gets a number of points equal to twice the number of selected red cards, and for each yellow card, Vasya gets a number of points equal to three times the number of selected blue cards. What is the maximum number of points Vasya can earn?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"168\"]",
"style": "rule"
} | {
"index": 320,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 12,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 168 | 9 |
train-math-numinamath1.5_olympiads | [
{
"content": "8. A parallel beam of light falls normally on a thin lens. Behind the lens, at a distance of $80 \\mathrm{~cm}$ from it, there is a screen on which a circular spot of a certain diameter is visible. If the screen is moved 40 cm, a spot of the same diameter will again be visible on the screen. Determine the focal length of the lens.\n\n## (15 points)",
"role": "user"
}
]
| math | {
"ground_truth": "[\"100\"]",
"style": "rule"
} | {
"index": 318,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 11,
"DeepSeek-R1-Distill-Qwen-32B": 14,
"DeepSeek-R1-Distill-Qwen-7B": 9
}
} | 100 | 15 |
train-math-deepscaler | [
{
"content": "Given the universal set $U=\\{1, 2, 3, 4, 5, 6, 7, 8\\}$, a set $A=\\{a_1, a_2, a_3, a_4\\}$ is formed by selecting any four elements from $U$, and the set of the remaining four elements is denoted as $\\complement_U A=\\{b_1, b_2, b_3, b_4\\}$. If $a_1+a_2+a_3+a_4 < b_1+b_2+b_3+b_4$, then the number of ways to form set $A$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"31\"]",
"style": "rule"
} | {
"index": 323,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 13,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 2
}
} | 31 | 12 |
train-math-deepscaler | [
{
"content": "Mattis is hosting a badminton tournament for $40$ players on $20$ courts numbered from $1$ to $20$. The players are distributed with $2$ players on each court. In each round a winner is determined on each court. Afterwards, the player who lost on court $1$, and the player who won on court $20$ stay in place. For the remaining $38$ players, the winner on court $i$ moves to court $i + 1$ and the loser moves to court $i - 1$. The tournament continues until every player has played every other player at least once. What is the minimal number of rounds the tournament can last?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"39\"]",
"style": "rule"
} | {
"index": 322,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 7,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | 39 | 4 |
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