Dataset Viewer
data_source
stringclasses 11
values | prompt
listlengths 1
1
| ability
stringclasses 1
value | reward_model
dict | extra_info
dict | correct_answer
float64 -20,240,000
3.56B
|
|---|---|---|---|---|---|
train-math-numinamath1.5_olympiads | [
{
"content": "33. How many six-digit numbers are there in which all digits are odd?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"15625\"]",
"style": "rule"
} | {
"index": 7,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 1
}
} | 15,624 |
train-math-deepscaler | [
{
"content": "What is the value of the least positive base ten number which requires six digits for its binary representation?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"32\"]",
"style": "rule"
} | {
"index": 8,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 32 |
train-math-numinamath1.5_olympiads | [
{
"content": "7.109. $5^{2 x-1}+2^{2 x}-5^{2 x}+2^{2 x+2}=0$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"1\"]",
"style": "rule"
} | {
"index": 24,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 1 |
train-math-deepscaler | [
{
"content": "There is only one set of five prime numbers that form an arithmetic sequence with a common difference of 6. What is the sum of those five prime numbers?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"85\"]",
"style": "rule"
} | {
"index": 15,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 85 |
train-math-deepscaler | [
{
"content": "What is the positive difference between $\\frac{8^2 - 8^2}{8}$ and $\\frac{8^2 \\times 8^2}{8}$?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"512\"]",
"style": "rule"
} | {
"index": 9,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 512 |
train-math-deepscaler | [
{
"content": "A certain circle's area is $x$ square units, and its circumference is $y$ units. The value of $x + y$ is $80\\pi$. What is the radius of the circle, in units?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"8\"]",
"style": "rule"
} | {
"index": 5,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 8 |
train-math-deepscaler | [
{
"content": "Triangle $ABC$ has side-lengths $AB = 12, BC = 24,$ and $AC = 18.$ The line through the incenter of $\\triangle ABC$ parallel to $\\overline{BC}$ intersects $\\overline{AB}$ at $M$ and $\\overline{AC}$ at $N.$ What is the perimeter of $\\triangle AMN?$\n$\\textbf{(A)}\\ 27 \\qquad \\textbf{(B)}\\ 30 \\qquad \\textbf{(C)}\\ 33 \\qquad \\textbf{(D)}\\ 36 \\qquad \\textbf{(E)}\\ 42$\n",
"role": "user"
}
]
| math | {
"ground_truth": "[\"30\"]",
"style": "rule"
} | {
"index": 57,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 30 |
train-math-numinamath1.5_olympiads | [
{
"content": "663. The grasshopper jumped from the point with coordinate 8 to the point with coordinate 17.5. Then it made another jump of the same length (in the same direction). At the point with what coordinate did it end up?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"27\"]",
"style": "rule"
} | {
"index": 6,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 27 |
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 |
train-math-deepscaler | [
{
"content": "Call a $3$-digit number geometric if it has $3$ distinct digits which, when read from left to right, form a geometric sequence. Find the difference between the largest and smallest geometric numbers.\n",
"role": "user"
}
]
| math | {
"ground_truth": "[\"840\"]",
"style": "rule"
} | {
"index": 60,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 840 |
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 |
train-math-numinamath1.5_olympiads | [
{
"content": "What is the value of $(-1)^{5}-(-1)^{4}$ ?\n(A) -2\n(B) -1\n(C) 0\n(D) 1\n(E) 2",
"role": "user"
}
]
| math | {
"ground_truth": "[\"-2\"]",
"style": "rule"
} | {
"index": 2,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | -2 |
train-math-deepscaler | [
{
"content": "Simplify completely: $$\\sqrt[3]{30^3+40^3+50^3}$$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"60\"]",
"style": "rule"
} | {
"index": 12,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 60 |
train-math-numinamath1.5_olympiads | [
{
"content": "6.032. $\\sqrt{x+\\sqrt{x+11}}+\\sqrt{x-\\sqrt{x+11}}=4$.\n\n6.032. $\\sqrt{x+\\sqrt{x+11}}+\\sqrt{x-\\sqrt{x+11}}=4$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"5\"]",
"style": "rule"
} | {
"index": 13,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 5 |
train-math-numinamath1.5_olympiads | [
{
"content": "14. Calculate:\n$$\n\\frac{\\frac{1}{1 \\times 2}+\\frac{1}{2 \\times 3}+\\frac{1}{3 \\times 4}+\\frac{1}{4 \\times 5}+\\ldots+\\frac{1}{2021 \\times 2022}}{\\left(1-\\frac{1}{2}\\right)\\left(1-\\frac{1}{3}\\right)\\left(1-\\frac{1}{4}\\right)\\left(1-\\frac{1}{5}\\right) \\ldots\\left(1-\\frac{1}{2022}\\right)}=\n$$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"2021\"]",
"style": "rule"
} | {
"index": 11,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 2,021 |
train-math-numinamath1.5_aops_forum | [
{
"content": "Find the area of the region in the coordinate plane satisfying the three conditions\n\n$\\star$ $x \\le\u0014 2y$\n$\\star$ $y \u0014\\le 2x$\n$\\star$ $x + y \\le\u0014 60.$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"600\"]",
"style": "rule"
} | {
"index": 39,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 600 |
train-math-numinamath1.5_olympiads | [
{
"content": "If $(x+y)^{2}-(x-y)^{2}=20$, then $x y$ is equal to:\n(a) 0 ;\n(b) 1 ;\n(c) 2 ;\n(d) 5 ;\n(e) 10 .",
"role": "user"
}
]
| math | {
"ground_truth": "[\"5\"]",
"style": "rule"
} | {
"index": 4,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 12,
"DeepSeek-R1-Distill-Qwen-32B": 7,
"DeepSeek-R1-Distill-Qwen-7B": 2
}
} | 5 |
train-math-numinamath1.5_olympiads | [
{
"content": "The graphs of the functions $y=k x+b$ and $y=b x+k$ intersect. Find the abscissa of the point of intersection.\n\n#",
"role": "user"
}
]
| math | {
"ground_truth": "[\"1\"]",
"style": "rule"
} | {
"index": 10,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 1 |
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 |
train-math-still3 | [
{
"content": "A $4$-foot by $16$-foot rectangular piece of plywood will be cut into $8$ congruent rectangles with no wood left over and no wood lost due to the cuts. What is the positive difference, in feet, between the greatest possible perimeter of a single piece and the least possible perimeter of a single piece?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"21\"]",
"style": "rule"
} | {
"index": 45,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 7,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 3
}
} | 21 |
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 |
train-math-numinamath1.5_aops_forum | [
{
"content": "Determine the smallest positive integer, $n$, which satisfies the equation $n^3+2n^2 = b$, where $b$ is the square of an odd integer.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"7\"]",
"style": "rule"
} | {
"index": 30,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 7 |
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 |
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 |
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 |
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 |
train-math-deepscaler | [
{
"content": "One half of the water is poured out of a full container. Then one third of the remainder is poured out. Continue the process: one fourth of the remainder for the third pouring, one fifth of the remainder for the fourth pouring, etc. After how many pourings does exactly one tenth of the original water remain?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"9\"]",
"style": "rule"
} | {
"index": 18,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 9 |
train-math-numinamath1.5_olympiads | [
{
"content": "Question 230, Let $S$ be the set of ordered 7-tuples $\\left(a_{1}, a_{2}, \\ldots, a_{7}\\right)$, where $a_{i}=1$ or 0. For any two elements $a=\\left(a_{1}, a_{2}, \\ldots, a_{7}\\right)$ and $b=\\left(b_{1}, b_{2}, \\ldots, b_{7}\\right)$ in $S$, define the distance between $a$ and $b$ as $\\sum_{i=1}^{7}\\left|a_{i}-b_{i}\\right|$. The set $T$ is a subset of $S$, where the distance between any two elements is at least 3. Find the maximum value of $|T|$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"16\"]",
"style": "rule"
} | {
"index": 61,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 16 |
train-math-numinamath1.5_cn_contest | [
{
"content": "4. Given the function $y=x^{3}$, the tangent line at $x=a_{k}$ intersects the $x$-axis at point $a_{k+1}$. If $a_{1}=1, S_{n}=\\sum_{i=1}^{n} a_{i}$, then $\\lim _{n \\rightarrow \\infty} S_{n}$ $=$ . $\\qquad$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"3\"]",
"style": "rule"
} | {
"index": 35,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 3 |
train-math-deepscaler | [
{
"content": "Determine the number of ways to arrange the letters of the word PROOF.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"60\"]",
"style": "rule"
} | {
"index": 37,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 5,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 60 |
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 |
train-math-numinamath1.5_olympiads | [
{
"content": "Problem 3. Find the most probable number of hits in the ring in five throws, if the probability of hitting the ring with the ball in one throw is $p=0.6$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"3\"]",
"style": "rule"
} | {
"index": 20,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 3 |
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 |
train-math-numinamath1.5_olympiads | [
{
"content": "## Task 2 - 030512\n\nAfter the Circle Olympics for Young Mathematicians, a Pioneer was asked how many points he had scored. Jokingly, he said:\n\n\"If you add 10 to the number of my points and double the sum, I am still 10 points short of 100.\"\n\na) How many points did the Thälmann Pioneer score?\n\nb) How did you find the result?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"35\"]",
"style": "rule"
} | {
"index": 17,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 35 |
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 |
train-math-numinamath1.5_olympiads | [
{
"content": "## Task 3 - 060833\n\nGiven are $3000 \\mathrm{~g}$ of a 7.2 percent sodium chloride solution in water (i.e., in every $100 \\mathrm{~g}$ of the solution, exactly 7.2 g of sodium chloride is contained). By boiling this solution, so much water evaporates that exactly $2400 \\mathrm{~g}$ of the concentrated solution remains.\n\nWhat is the percentage of the resulting solution?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"9\"]",
"style": "rule"
} | {
"index": 22,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 11,
"DeepSeek-R1-Distill-Qwen-7B": 12
}
} | 9 |
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
}
} | 1,295 |
train-math-deepscaler | [
{
"content": "Given that $\\log_{10}\\sin x + \\log_{10}\\cos x= -2$ and that $\\log_{10}(\\sin x+\\cos x)=\\frac{1}{2}(\\log_{10}m-2)$, find $m$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"102\"]",
"style": "rule"
} | {
"index": 38,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 102 |
train-math-still3 | [
{
"content": "Given Odell and Kershaw run for $30$ minutes on a circular track, Odell runs clockwise at $250 m/min$ and uses the inner lane with a radius of $50$ meters, while Kershaw runs counterclockwise at $300 m/min$ and uses the outer lane with a radius of $60$ meters, starting on the same radial line as Odell. How many times do Odell and Kershaw pass each other?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"47\"]",
"style": "rule"
} | {
"index": 40,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 47 |
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 |
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 |
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 |
train-math-numinamath1.5_olympiads | [
{
"content": "1. The number of proper subsets of the set $A=\\left\\{x \\in \\mathbf{Z} \\mid \\log _{2} x \\leqslant 2\\right\\}$ is ( ).\n(A) 7\n(B) 8\n(C) 15\n(D) 16",
"role": "user"
}
]
| math | {
"ground_truth": "[\"15\"]",
"style": "rule"
} | {
"index": 16,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 15 |
train-math-deepscaler | [
{
"content": "When $1 + 3 + 3^2 + \\cdots + 3^{1004}$ is divided by $500$, what is the remainder?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"121\"]",
"style": "rule"
} | {
"index": 91,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 3
}
} | 121 |
train-math-deepscaler | [
{
"content": "Let $M$ be the greatest five-digit number whose digits have a product of $180$. Find the sum of the digits of $M$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"20\"]",
"style": "rule"
} | {
"index": 90,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 2
}
} | 20 |
train-math-numinamath1.5_olympiads | [
{
"content": "2. Marta has invented a new arithmetic operation called \"smile\" for which she will use the symbol :). The smile is defined using the known operations of addition and multiplication by the expression\n\n$$\na \\odot b=a \\cdot b+3 \\cdot a+b\n$$\n\nWhat is $x$ if $(x \\odot 5) \\cdot 6=72123$?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"1001\"]",
"style": "rule"
} | {
"index": 85,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 1,001 |
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 |
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 |
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 |
train-math-numinamath1.5_olympiads | [
{
"content": "34. For a large cube with integer edge length, several faces are fully painted, and then it is divided into small cubes with edge length 1. At this point, the ratio of the number of small cubes with at least one face painted to the number of small cubes with no faces painted is $1: 3$. What is the minimum edge length of the original large cube? $\\qquad$ .",
"role": "user"
}
]
| math | {
"ground_truth": "[\"4\"]",
"style": "rule"
} | {
"index": 81,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 14,
"DeepSeek-R1-Distill-Qwen-32B": 12,
"DeepSeek-R1-Distill-Qwen-7B": 2
}
} | 4 |
train-math-deepscaler | [
{
"content": "A strip of size $1 \\times 10$ is divided into unit squares. The numbers $1, 2, \\ldots, 10$ are written in these squares. First, the number 1 is written in one of the squares, then the number 2 is written in one of the neighboring squares, then the number 3 is written in one of the squares neighboring those already occupied, and so on (the choice of the first square and the choice of neighbor at each step are arbitrary). In how many ways can this be done?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"512\"]",
"style": "rule"
} | {
"index": 72,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 4,
"DeepSeek-R1-Distill-Qwen-32B": 4,
"DeepSeek-R1-Distill-Qwen-7B": 3
}
} | 512 |
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 |
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
}
} | 21,792 |
train-math-numinamath1.5_olympiads | [
{
"content": "4. Let $V$ be a set of 2019 points in space, no four of which are coplanar. Some of these points are connected by line segments, and let $E$ be the set of these line segments. Find the smallest positive integer $n$ such that if $E$ has at least $n$ elements, then $E$ must contain 908 pairwise disjoint subsets, each consisting of two line segments that share a common endpoint.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"2795\"]",
"style": "rule"
} | {
"index": 76,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 2,796 |
train-math-deepscaler | [
{
"content": "If the three lines $3y-2x=1$, $x+2y=2$ and $4x-6y=5$ are drawn in the plane, how many points will lie at the intersection of at least two of the three lines?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"2\"]",
"style": "rule"
} | {
"index": 104,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 2 |
train-math-deepscaler | [
{
"content": "What is $100(100-3)-(100 \\cdot 100-3)$?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"-297\"]",
"style": "rule"
} | {
"index": 110,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | -297 |
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 |
train-math-numinamath1.5_amc_aime | [
{
"content": "A cylindrical barrel with radius $4$ feet and height $10$ feet is full of water. A solid cube with side length $8$ feet is set into the barrel so that the diagonal of the cube is vertical. The volume of water thus displaced is $v$ cubic feet. Find $v^2$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"384\"]",
"style": "rule"
} | {
"index": 74,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 384 |
train-math-numinamath1.5_olympiads | [
{
"content": "Let $\\Gamma$.\n\nThe teacher is going to give the children a problem of the following type. He will inform them that he has thought of a polynomial $P(x)$\n\nof degree 2017 with integer coefficients, the leading coefficient of which is 1. Then he will inform them of $k$ integers $n_{1}, n_{2}, \\ldots, n_{k}$ and separately inform them of the value of the expression $P\\left(n_{1}\\right) P\\left(n_{2}\\right) \\ldots P\\left(n_{k}\\right)$. From this data, the children are supposed to find the polynomial that the teacher could have thought of. For what smallest $k$ can the teacher formulate a problem of this type so that the polynomial found by the children necessarily coincides with the one thought of?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"2017\"]",
"style": "rule"
} | {
"index": 70,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 14,
"DeepSeek-R1-Distill-Qwen-32B": 15,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 2,017 |
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 |
train-math-deepscaler | [
{
"content": "For a natural number \\( N \\), if at least eight out of the nine natural numbers from 1 to 9 can divide \\( N \\), then \\( N \\) is called a \"Ba Xian number\". What is the smallest \"Ba Xian number\" greater than 2000?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"2016\"]",
"style": "rule"
} | {
"index": 113,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 5,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 2,016 |
train-math-numinamath1.5_olympiads | [
{
"content": "2. Xiao Dong lives on the 11th floor of a building. He counted 42 steps from the 3rd floor to the 5th floor. How many steps does he need to walk to get from the ground floor to his floor?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"210\"]",
"style": "rule"
} | {
"index": 102,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 12,
"DeepSeek-R1-Distill-Qwen-32B": 11,
"DeepSeek-R1-Distill-Qwen-7B": 6
}
} | 210 |
train-math-deepscaler | [
{
"content": "If $\\begin{vmatrix} a & b \\\\ c & d \\end{vmatrix} = 5,$ then find\n\\[\\begin{vmatrix} a - c & b - d \\\\ c & d \\end{vmatrix}.\\]",
"role": "user"
}
]
| math | {
"ground_truth": "[\"5\"]",
"style": "rule"
} | {
"index": 123,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 5 |
train-math-numinamath1.5_olympiads | [
{
"content": "Example 1. Using the method of tangents, find the real root of the equation $x^{3}+x-3=0$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"1.213412\"]",
"style": "rule"
} | {
"index": 115,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 1.213412 |
train-math-aime19832023 | [
{
"content": "The number $\\sqrt{104\\sqrt{6}+468\\sqrt{10}+144\\sqrt{15}+2006}$ can be written as $a\\sqrt{2}+b\\sqrt{3}+c\\sqrt{5},$ where $a, b,$ and $c$ are positive integers. Find $abc.$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"936\"]",
"style": "rule"
} | {
"index": 119,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 936 |
train-math-deepscaler | [
{
"content": "The set \\( S \\) is given by \\( S = \\{1, 2, 3, 4, 5, 6\\} \\). A non-empty subset \\( T \\) of \\( S \\) has the property that it contains no pair of integers that share a common factor other than 1. How many distinct possibilities are there for \\( T \\)?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"27\"]",
"style": "rule"
} | {
"index": 118,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 7
}
} | 27 |
train-math-deepscaler | [
{
"content": "Given that $2x + y = 4$ and $x + 2y = 5$, find $5x^2 + 8xy + 5y^2$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"41\"]",
"style": "rule"
} | {
"index": 140,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 41 |
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 |
train-math-deepscaler | [
{
"content": "How many pairs $(x, y)$ of non-negative integers with $0 \\leq x \\leq y$ satisfy the equation $5x^{2}-4xy+2x+y^{2}=624$?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"7\"]",
"style": "rule"
} | {
"index": 138,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 2,
"DeepSeek-R1-Distill-Qwen-7B": 7
}
} | 7 |
train-math-numinamath1.5_olympiads | [
{
"content": "1. A four-digit number, with all digits being distinct, the sum of all digits equals 6, and the number is a multiple of 11, then the number of four-digit numbers that meet this requirement is ( ) .\nA. 6\nB. 7\nC. 8\nD. 9",
"role": "user"
}
]
| math | {
"ground_truth": "[\"6\"]",
"style": "rule"
} | {
"index": 126,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 6 |
train-math-numinamath1.5_olympiads | [
{
"content": "78. The Walking Passenger. The train is moving at a speed of 60 km/h. A passenger is walking from the end of the train to its beginning through the passageways between the cars at a speed of 3 km/h. What is the speed of the passenger relative to the railway track?\n\nWe are not going to engage in sophistry here, like Zeno's paradox of the flying arrow, or Einstein's theory of relativity, but are talking about movement in the ordinary sense of the word relative to the railway track.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"63\"]",
"style": "rule"
} | {
"index": 121,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 8,
"DeepSeek-R1-Distill-Qwen-32B": 8,
"DeepSeek-R1-Distill-Qwen-7B": 7
}
} | 63 |
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 |
train-math-numinamath1.5_olympiads | [
{
"content": "4. The sum of four consecutive integers is 2 . What is the least of these integers?\nA -3\nB -2\n$\\mathrm{C}-1$\nD 0\nE 1",
"role": "user"
}
]
| math | {
"ground_truth": "[\"-1\"]",
"style": "rule"
} | {
"index": 135,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 2,
"DeepSeek-R1-Distill-Qwen-32B": 13,
"DeepSeek-R1-Distill-Qwen-7B": 12
}
} | -1 |
train-math-deepscaler | [
{
"content": "There exist unique nonnegative integers $A, B$ between 0 and 9, inclusive, such that $(1001 \\cdot A+110 \\cdot B)^{2}=57,108,249$. Find $10 \\cdot A+B$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"75\"]",
"style": "rule"
} | {
"index": 145,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 1,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 75 |
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 |
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
}
} | 2,206 |
train-math-numinamath1.5_olympiads | [
{
"content": "79. A small boat sails upstream from downstream port $A$, and at a point 4 kilometers away from port $A$, it encounters a log drifting with the current. The boat continues its journey to reach upstream port $B$ and immediately turns around, arriving at port $A$ at the same time as the log. Given that the speed of the current is 2 meters/second, and the speed of the boat in still water is 8 meters/second, the distance between ports $A$ and $B$ is $\\qquad$ kilometers.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"8\"]",
"style": "rule"
} | {
"index": 128,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 15
}
} | 8 |
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 |
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 |
train-math-numinamath1.5_olympiads | [
{
"content": "4.48. Find the remainder when the number\n\n$$\n10^{10}+10^{\\left(10^{2}\\right)}+10^{\\left(10^{3}\\right)}+\\ldots+10^{\\left(10^{10}\\right)}\n$$\n\nis divided by 7.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"5\"]",
"style": "rule"
} | {
"index": 152,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 5 |
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 |
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 |
train-math-deepscaler | [
{
"content": "A teacher wrote a sequence of consecutive odd numbers starting from 1 on the blackboard: $1, 3, 5, 7, 9, 11, \\cdots$ After writing, the teacher erased two numbers, dividing the sequence into three segments. If the sums of the first two segments are 961 and 1001 respectively, what is the sum of the two erased odd numbers?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"154\"]",
"style": "rule"
} | {
"index": 139,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 2
}
} | 154 |
train-math-deepscaler | [
{
"content": "The image depicts a top-down view of a three-layered pyramid made of 14 identical cubes. Each cube is assigned a natural number in such a way that the numbers corresponding to the cubes in the bottom layer are all different, and the number on any other cube is the sum of the numbers on the four adjacent cubes from the layer below.\n\nDetermine the smallest number divisible by four that can be assigned to the topmost cube.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"64\"]",
"style": "rule"
} | {
"index": 150,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 1,
"DeepSeek-R1-Distill-Qwen-7B": 8
}
} | 64 |
train-math-numinamath1.5_olympiads | [
{
"content": "Hagrid has 100 animals. Among these animals,\n\n- each is either striped or spotted but not both,\n- each has either wings or horns but not both,\n- there are 28 striped animals with wings,\n- there are 62 spotted animals, and\n- there are 36 animals with horns.\n\nHow many of Hagrid's spotted animals have horns?\n(A) 8\n(B) 10\n(C) 2\n(D) 38\n(E) 26",
"role": "user"
}
]
| math | {
"ground_truth": "[\"26\"]",
"style": "rule"
} | {
"index": 167,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 12,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 26 |
train-math-deepscaler | [
{
"content": "If $x - y = 6$ and $x + y = 12$, what is the value of $y$?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"3\"]",
"style": "rule"
} | {
"index": 182,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 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 |
train-math-numinamath1.5_olympiads | [
{
"content": "4. Person A and Person B agreed to have dinner at a restaurant. Since this restaurant is very popular, after A arrived, they took a waiting number and waited for B. B arrived at the restaurant a while later but didn't see A, so they also took a waiting number. While waiting, B saw A, and both of them showed their waiting numbers. They found that the digits of the two numbers were reverse two-digit numbers, and the sum of the digits (for example, the sum of the digits of the number 23 is $2+3=5$) of both numbers was 8, and B's number was 18 more than A's. What is A's number? $\\qquad$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"35\"]",
"style": "rule"
} | {
"index": 166,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 4,
"DeepSeek-R1-Distill-Qwen-32B": 9,
"DeepSeek-R1-Distill-Qwen-7B": 2
}
} | 35 |
train-math-deepscaler | [
{
"content": "Let $x_{1}, x_{2}, \\ldots, x_{2022}$ be nonzero real numbers. Suppose that $x_{k}+\\frac{1}{x_{k+1}}<0$ for each $1 \\leq k \\leq 2022$, where $x_{2023}=x_{1}$. Compute the maximum possible number of integers $1 \\leq n \\leq 2022$ such that $x_{n}>0$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"1010\"]",
"style": "rule"
} | {
"index": 171,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 13,
"DeepSeek-R1-Distill-Qwen-7B": 15
}
} | 1,010 |
train-math-numinamath1.5_olympiads | [
{
"content": "G2.4 There are $d$ different ways for arranging 5 girls in a row. Find $d$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"120\"]",
"style": "rule"
} | {
"index": 177,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 120 |
train-math-numinamath1.5_olympiads | [
{
"content": "Task 1. We have 1000 balls in 40 different colors, with exactly 25 balls of each color. Determine the smallest value of $n$ with the following property: if you randomly arrange the 1000 balls in a circle, there will always be $n$ balls next to each other where at least 20 different colors occur.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"452\"]",
"style": "rule"
} | {
"index": 175,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 16,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 452 |
train-math-deepscaler | [
{
"content": "The store owner bought 2000 pens at $0.15 each and plans to sell them at $0.30 each, calculate the number of pens he needs to sell to make a profit of exactly $150.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"1000\"]",
"style": "rule"
} | {
"index": 192,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 13,
"DeepSeek-R1-Distill-Qwen-32B": 11,
"DeepSeek-R1-Distill-Qwen-7B": 10
}
} | 1,000 |
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 |
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 |
train-math-deepscaler | [
{
"content": "Simplify: $$\\sqrt[3]{2744000}$$",
"role": "user"
}
]
| math | {
"ground_truth": "[\"140\"]",
"style": "rule"
} | {
"index": 204,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 140 |
train-math-numinamath1.5_olympiads | [
{
"content": "2. How many roots does the equation\n\n$\\sqrt[3]{|x|}+10[x]=10 x$ ? ( $[x]$ - the integer part of the number $x$, i.e., $[x] \\in Z,[x] \\leq x<[x]+1$).\n\n(5 points)",
"role": "user"
}
]
| math | {
"ground_truth": "[\"2000\"]",
"style": "rule"
} | {
"index": 184,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 16,
"DeepSeek-R1-Distill-Qwen-32B": 9,
"DeepSeek-R1-Distill-Qwen-7B": 16
}
} | 2,000 |
train-math-aime19832023 | [
{
"content": "How many of the first $1000$ positive integers can be expressed in the form $\\lfloor 2x \\rfloor + \\lfloor 4x \\rfloor + \\lfloor 6x \\rfloor + \\lfloor 8x \\rfloor$ , where $x$ is a real number, and $\\lfloor z \\rfloor$ denotes the greatest integer less than or equal to $z$ ?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"600\"]",
"style": "rule"
} | {
"index": 183,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 15,
"DeepSeek-R1-Distill-Qwen-32B": 5,
"DeepSeek-R1-Distill-Qwen-7B": 9
}
} | 600 |
train-math-numinamath1.5_olympiads | [
{
"content": "7.1. In a hotel, rooms are arranged in a row in order from 1 to 10000. Masha and Alina checked into the hotel in two different rooms. The sum of the room numbers they are staying in is 2022, and the sum of the room numbers of all the rooms between them is 3033. In which room is Masha staying, if her room has a lower number than Alina's room?",
"role": "user"
}
]
| math | {
"ground_truth": "[\"1009\"]",
"style": "rule"
} | {
"index": 188,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 0,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 1,009 |
train-math-deepscaler | [
{
"content": "Given the function $f(x)=x+ \\frac{1}{x}$, and $g(x)=f^{2}(x)-af(x)+2a$ has four distinct zeros $x\\_1$, $x\\_2$, $x\\_3$, $x\\_4$, determine the value of $[2-f(x\\_1)]\\cdot[2-f(x\\_2)]\\cdot[2-f(x\\_3)]\\cdot[2-f(x\\_4)]$.",
"role": "user"
}
]
| math | {
"ground_truth": "[\"16\"]",
"style": "rule"
} | {
"index": 189,
"model_difficulty": {
"DeepSeek-R1-Distill-Qwen-1.5B": 7,
"DeepSeek-R1-Distill-Qwen-32B": 0,
"DeepSeek-R1-Distill-Qwen-7B": 0
}
} | 16 |
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 |
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