data_source stringclasses 1 value | prompt listlengths 2 2 | ability stringclasses 1 value | reward_model dict | extra_info dict | answer stringlengths 1 41 |
|---|---|---|---|---|---|
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(In the preliminaries of optimal method and experimental design) When using the 0.618 method to find the optimal amount to add in an experiment, if the current range of excellenc... | math | {
"ground_truth": "684",
"style": "rule"
} | {
"cluster_id": 0,
"difficulty": 58.59375,
"index": 8826,
"split": "train"
} | 684 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the probability that in a deck of 52 cards, the second card has a different suit than the first, and the third card has a different suit than the first and second.\nPle... | math | {
"ground_truth": "\\frac{169}{425}",
"style": "rule"
} | {
"cluster_id": 0,
"difficulty": 65.625,
"index": 6584,
"split": "train"
} | \frac{169}{425} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Xiao Kang exercises every day by doing several sets of push-ups, 8 per set, and several sets of pull-ups, 5 per set. On the first day, he did a total of 41 reps (combining both e... | math | {
"ground_truth": "106",
"style": "rule"
} | {
"cluster_id": 0,
"difficulty": 13.28125,
"index": 15867,
"split": "train"
} | 106 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the value of the arithmetic series $1-3+5-7+9-11+\\cdots +2021-2023+2025$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
... | math | {
"ground_truth": "1013",
"style": "rule"
} | {
"cluster_id": 0,
"difficulty": 43.75,
"index": 9306,
"split": "train"
} | 1013 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Kiana has two older twin brothers. The product of their three ages is 128. What is the sum of their three ages?\nPlease reason step by step, and put your final answer within \\bo... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"cluster_id": 0,
"difficulty": 67.1875,
"index": 5426,
"split": "train"
} | 18 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A steak initially at a temperature of 5°C is put into an oven. After 15 minutes, its temperature reaches 45°C. After another 15 minutes, its temperature is 77°C. The oven maintai... | math | {
"ground_truth": "205",
"style": "rule"
} | {
"cluster_id": 0,
"difficulty": 88.28125,
"index": 3091,
"split": "train"
} | 205 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 6 locked suitcases and 6 keys for them. However, it is unknown which key opens which suitcase. What is the minimum number of attempts needed to ensure that all suitcase... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"cluster_id": 0,
"difficulty": 64.84375,
"index": 6651,
"split": "train"
} | 45 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Serezha and Misha, while walking in the park, came across a meadow surrounded by linden trees. Serezha walked around the meadow, counting the trees. Misha did the same but starte... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"cluster_id": 0,
"difficulty": 37.5,
"index": 11071,
"split": "train"
} | 100 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Xiao Hua plays a certain game where each round can be played several times freely. Each score in a round is one of the numbers $8$, $a$ (a natural number), or $0$. The total scor... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"cluster_id": 0,
"difficulty": 32.8125,
"index": 12010,
"split": "train"
} | 13 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the minimum number of children required in a school to be sure that at least 3 of them have their birthday on the same day? (Keep in mind that some people are born on Feb... | math | {
"ground_truth": "733",
"style": "rule"
} | {
"cluster_id": 0,
"difficulty": 81.25,
"index": 2897,
"split": "train"
} | 733 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(1) Given that $0 < x < \\dfrac{4}{3}$, find the maximum value of $x(4-3x)$.\n\n(2) Point $(x,y)$ moves along the line $x+2y=3$. Find the minimum value of $2^{x}+4^{y}$.\nPlease ... | math | {
"ground_truth": "4 \\sqrt{2}",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 37.5,
"index": 11953,
"split": "train"
} | 4 \sqrt{2} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the asymptote equation of the hyperbola $y^{2}+\\frac{x^2}{m}=1$ is $y=\\pm \\frac{\\sqrt{3}}{3}x$, find the value of $m$.\nPlease reason step by step, and put your fi... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 40.625,
"index": 9152,
"split": "train"
} | -3 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given points $A(-2,0)$ and $B(2,0)$, the slope of line $PA$ is $k_1$, and the slope of line $PB$ is $k_2$, with the product $k_1k_2=-\\frac{3}{4}$.\n$(1)$ Find the equation of th... | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 98.4375,
"index": 1230,
"split": "train"
} | \frac{3}{2} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=x^{3}+3ax^{2}+bx+a^{2}$ has an extreme value of $0$ at $x=-1$, find the value of $a-b$.\nPlease reason step by step, and put your final answer within \\b... | math | {
"ground_truth": "-7",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 51.5625,
"index": 8597,
"split": "train"
} | -7 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the circle $x^{2}-2x+y^{2}-2y+1=0$, find the cosine value of the angle between the two tangents drawn from the point $P(3,2)$.\nPlease reason step by step, and put your fin... | math | {
"ground_truth": "\\frac{3}{5}",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 53.90625,
"index": 8476,
"split": "train"
} | \frac{3}{5} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the minimum value of the discriminant of a quadratic trinomial whose graph does not intersect the regions below the x-axis and above the graph of the function \\( y = \\frac... | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 78.90625,
"index": 4778,
"split": "train"
} | -4 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the line \\(x=\\frac{\\pi}{4}\\) intersects the curve \\(C: (x-\\arcsin a)(x-\\arccos a) + (y-\\arcsin a)(y+\\arccos a)=0\\), determine the minimum value of the chord length a... | math | {
"ground_truth": "\\frac{\\pi}{2}",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 60.9375,
"index": 7086,
"split": "train"
} | \frac{\pi}{2} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f\\left(x\\right)=ax^{2}-1$ and $g\\left(x\\right)=\\ln \\left(ax\\right)$ have an \"$S$ point\", then find the value of $a$.\nPlease reason step by step, and put your final... | math | {
"ground_truth": "\\frac{2}{e}",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 30.46875,
"index": 10931,
"split": "train"
} | \frac{2}{e} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function \\( f(x)=\\sqrt{3} \\sin 2x + 2 \\cos^2 x + a \\), if the minimum value of \\( f(x) \\) on the interval \\(\\left[ 0, \\frac{\\pi}{2} \\right] \\) is \\(-1\\),... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 46.09375,
"index": 10260,
"split": "train"
} | -1 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the coordinate plane, let $A = (-8, 0)$ , $B = (8, 0)$ , and $C = (t, 6)$ . What is the maximum value of $\\sin m\\angle CAB \\cdot \\sin m\\angle CBA$ , over all real nu... | math | {
"ground_truth": "3/8",
"style": "rule"
} | {
"cluster_id": 1,
"difficulty": 75.78125,
"index": 3752,
"split": "train"
} | 3/8 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"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:\nPlease reason step by step, and put your final ans... | math | {
"ground_truth": "48",
"style": "rule"
} | {
"cluster_id": 2,
"difficulty": 35.15625,
"index": 12264,
"split": "train"
} | 48 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Pat Peano has plenty of 0's, 1's, 3's, 4's, 5's, 6's, 7's, 8's and 9's, but he has only twenty-two 2's. How far can he number the pages of his scrapbook with these digits?\nPlea... | math | {
"ground_truth": "119",
"style": "rule"
} | {
"cluster_id": 2,
"difficulty": 47.65625,
"index": 10562,
"split": "train"
} | 119 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What are the first three digits to the right of the decimal point in the decimal representation of $\\left(10^{1001}+1\\right)^{3/2}$?\nPlease reason step by step, and put your f... | math | {
"ground_truth": "743",
"style": "rule"
} | {
"cluster_id": 2,
"difficulty": 82.03125,
"index": 3453,
"split": "train"
} | 743 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the units digit of the sum of the nine terms of the sequence $1! + 1, \\, 2! + 2, \\, 3! + 3, \\, ..., \\, 8! + 8, \\, 9! + 9$?\nPlease reason step by step, and put your ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"cluster_id": 2,
"difficulty": 17.96875,
"index": 15087,
"split": "train"
} | 8 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The seven digits in Sam's phone number and the four digits in his house number have the same sum. The four digits in his house number are distinct, and his phone number is 271-3... | math | {
"ground_truth": "9871",
"style": "rule"
} | {
"cluster_id": 2,
"difficulty": 17.1875,
"index": 15439,
"split": "train"
} | 9871 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A mineralogist is hosting a competition to guess the age of an ancient mineral sample. The age is provided by the digits 2, 2, 3, 3, 5, and 9, with the condition that the age mus... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"cluster_id": 2,
"difficulty": 57.8125,
"index": 7919,
"split": "train"
} | 120 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many ways are there to insert +'s between the digits of 111111111111111 (fifteen 1's) so that the result will be a multiple of 30?\nPlease reason step by step, and put your f... | math | {
"ground_truth": "2002",
"style": "rule"
} | {
"cluster_id": 2,
"difficulty": 99.21875,
"index": 1071,
"split": "train"
} | 2002 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "\\( n \\) is a positive integer that is not greater than 100 and not less than 10, and \\( n \\) is a multiple of the sum of its digits. How many such \\( n \\) are there?\nPleas... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"cluster_id": 2,
"difficulty": 8.59375,
"index": 16906,
"split": "train"
} | 24 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Maria ordered a certain number of televisions at $R$ \\$ 1994.00 each. She noticed that in the total amount to be paid, there are no digits 0, 7, 8, or 9. What was the smallest n... | math | {
"ground_truth": "56",
"style": "rule"
} | {
"cluster_id": 2,
"difficulty": 30.46875,
"index": 10975,
"split": "train"
} | 56 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The letters $A$, $B$, $C$ and $D$ represent digits. If $\\begin{array}{ccc}&A&B\\\\ +&C&A\\\\ \\hline &D&A\\end{array}$and $\\begin{array}{ccc}&A&B\\\\ -&C&A\\\\ \\hline &&A\\en... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"cluster_id": 2,
"difficulty": 59.375,
"index": 7754,
"split": "train"
} | 9 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that $\\frac{2}{3}$ of $10$ bananas are worth as much as $8$ oranges. How many oranges are worth as much as $\\frac{1}{2}$ of $5$ bananas?\nPlease reason step by step, an... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"cluster_id": 3,
"difficulty": 23.4375,
"index": 13156,
"split": "train"
} | 3 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A store owner bought $1500$ pencils at $\\$ 0.10$ each. If he sells them for $\\$ 0.25$ each, how many of them must he sell to make a profit of exactly $\\$ 100.00$?\nPlease rea... | math | {
"ground_truth": "1000",
"style": "rule"
} | {
"cluster_id": 3,
"difficulty": 74.21875,
"index": 4793,
"split": "train"
} | 1000 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that socks cost $4 per pair and a T-shirt costs $5 more than a pair of socks, and each member needs one pair of socks and a shirt for home games and another pair of socks a... | math | {
"ground_truth": "91",
"style": "rule"
} | {
"cluster_id": 3,
"difficulty": 10.9375,
"index": 15728,
"split": "train"
} | 91 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A team of fishermen planned to catch 1800 centners of fish within a certain timeframe. During one-third of this period, there was a storm, causing them to fall short of their dai... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"cluster_id": 3,
"difficulty": 79.6875,
"index": 3934,
"split": "train"
} | 100 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice buys three burgers and two sodas for $\\$3.20$, and Bill buys two burgers and a soda for $\\$2.00$. How many cents does a burger cost?\nPlease reason step by step, and put ... | math | {
"ground_truth": "80",
"style": "rule"
} | {
"cluster_id": 3,
"difficulty": 18.75,
"index": 15838,
"split": "train"
} | 80 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A tree has 10 pounds of apples at dawn. Every afternoon, a bird comes and eats x pounds of apples. Overnight, the amount of food on the tree increases by 10%. What is the maxi... | math | {
"ground_truth": "10/11",
"style": "rule"
} | {
"cluster_id": 3,
"difficulty": 72.65625,
"index": 4393,
"split": "train"
} | 10/11 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Eleven percent of what number is seventy-seven?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "700",
"style": "rule"
} | {
"cluster_id": 3,
"difficulty": 0,
"index": 17272,
"split": "train"
} | 700 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In order to obtain steel for a specific purpose, the golden section method was used to determine the optimal addition amount of a specific chemical element. After several experim... | math | {
"ground_truth": "2000",
"style": "rule"
} | {
"cluster_id": 3,
"difficulty": 98.4375,
"index": 819,
"split": "train"
} | 2000 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each day Walter gets $3$ dollars for doing his chores or $5$ dollars for doing them exceptionally well. After $10$ days of doing his chores daily, Walter has received a total of ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"cluster_id": 3,
"difficulty": 9.375,
"index": 17140,
"split": "train"
} | 3 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Bill can buy jags, jigs and jogs for $\\$1$, $\\$2$ and $\\$7$ each, respectively. What is the largest number of jogs he can purchase if he must buy at least one of each item and... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"cluster_id": 3,
"difficulty": 11.71875,
"index": 15114,
"split": "train"
} | 6 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Vertex $E$ of equilateral $\\triangle ABE$ is in the interior of square $ABCD$, and $F$ is the point of intersection of diagonal $BD$ and line segment $AE$. If length $AB$ is $\\... | math | {
"ground_truth": "\\frac{\\sqrt{3}}{2}",
"style": "rule"
} | {
"cluster_id": 4,
"difficulty": 62.5,
"index": 6346,
"split": "train"
} | \frac{\sqrt{3}}{2} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The center of the circle inscribed in a trapezoid is at distances of 5 and 12 from the ends of one of the non-parallel sides. Find the length of this side.\nPlease reason step by... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"cluster_id": 4,
"difficulty": 82.03125,
"index": 1925,
"split": "train"
} | 13 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circle is divided into two segments by a chord equal to the side of a regular inscribed triangle. Determine the ratio of the areas of these segments.\nPlease reason step by ste... | math | {
"ground_truth": "\\frac{4\\pi - 3\\sqrt{3}}{8\\pi + 3\\sqrt{3}}",
"style": "rule"
} | {
"cluster_id": 4,
"difficulty": 52.34375,
"index": 8164,
"split": "train"
} | \frac{4\pi - 3\sqrt{3}}{8\pi + 3\sqrt{3}} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a right triangle where $\\measuredangle A = 90^\\circ$ and $M\\in (AB)$ such that $\\frac{AM}{MB}=3\\sqrt{3}-4$ . It is known that the symmetric point of $M$... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"cluster_id": 4,
"difficulty": 28.125,
"index": 13028,
"split": "train"
} | 30 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sides of rhombus \\( EFGH \\) are the hypotenuses of the isosceles right triangles \\( EAF, FDG, GCH, \\) and \\( HBE \\), and all these triangles have common interior points... | math | {
"ground_truth": "2\\sqrt{3}",
"style": "rule"
} | {
"cluster_id": 4,
"difficulty": 79.6875,
"index": 3693,
"split": "train"
} | 2\sqrt{3} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Square $ABCD$ has sides of length 3. Segments $CM$ and $CN$ divide the square's area into three equal parts. How long is segment $CM$?\nPlease reason step by step, and put your f... | math | {
"ground_truth": "\\sqrt{13}",
"style": "rule"
} | {
"cluster_id": 4,
"difficulty": 53.125,
"index": 8396,
"split": "train"
} | \sqrt{13} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Quadrilateral $ABCD$ has right angles at $B$ and $C$, $\\triangle ABC \\sim \\triangle BCD$, and $AB > BC$. There is a point $E$ in the interior of $ABCD$ such that $\\triangle A... | math | {
"ground_truth": "2+\\sqrt{5}",
"style": "rule"
} | {
"cluster_id": 4,
"difficulty": 82.03125,
"index": 1902,
"split": "train"
} | 2+\sqrt{5} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A triangle has one side of length $13$, and the angle opposite this side is $60^{\\circ}$. The ratio of the other two sides is $4:3$. Calculate the area of this triangle.\nPlease... | math | {
"ground_truth": "39 \\sqrt{3}",
"style": "rule"
} | {
"cluster_id": 4,
"difficulty": 18.75,
"index": 15166,
"split": "train"
} | 39 \sqrt{3} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle XYZ$, the medians $\\overline{XU}$ and $\\overline{YV}$ intersect at right angles. If $XU = 18$ and $YV = 24$, find the area of $\\triangle XYZ$.\nPlease reason st... | math | {
"ground_truth": "288",
"style": "rule"
} | {
"cluster_id": 4,
"difficulty": 39.0625,
"index": 12580,
"split": "train"
} | 288 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a diagram, $\\triangle ABC$ and $\\triangle BDC$ are right-angled, with $\\angle ABC = \\angle BDC = 45^\\circ$, and $AB = 16$. Determine the length of $BC$.\nPlease reason st... | math | {
"ground_truth": "8\\sqrt{2}",
"style": "rule"
} | {
"cluster_id": 4,
"difficulty": 74.21875,
"index": 4837,
"split": "train"
} | 8\sqrt{2} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A factory assigns five newly recruited employees, including A and B, to three different workshops. Each workshop must be assigned at least one employee, and A and B must be assig... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"cluster_id": 5,
"difficulty": 46.09375,
"index": 9903,
"split": "train"
} | 36 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 4 willow trees and 4 poplar trees planted in a row. How many ways can they be planted alternately?\nPlease reason step by step, and put your final answer within \\boxed... | math | {
"ground_truth": "1152",
"style": "rule"
} | {
"cluster_id": 5,
"difficulty": 76.5625,
"index": 5104,
"split": "train"
} | 1152 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Seven frogs are sitting in a row. They come in four colors: two green, two red, two yellow, and one blue. Green frogs refuse to sit next to red frogs, and yellow frogs refuse to ... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"cluster_id": 5,
"difficulty": 98.4375,
"index": 624,
"split": "train"
} | 16 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A paperboy delivers newspapers to 11 houses along Main Street. He may skip delivering to any house, but he must not skip three consecutive houses to avoid losing his job. Determi... | math | {
"ground_truth": "927",
"style": "rule"
} | {
"cluster_id": 5,
"difficulty": 26.5625,
"index": 13738,
"split": "train"
} | 927 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many distinct arrangements of the letters in the word \"balloon\" are there?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}... | math | {
"ground_truth": "1260",
"style": "rule"
} | {
"cluster_id": 5,
"difficulty": 53.125,
"index": 7599,
"split": "train"
} | 1260 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "I have 6 shirts, 6 pairs of pants, and 6 hats. Each item comes in the same 6 colors (so that I have one of each item of each color). I refuse to wear an outfit in which all 3 i... | math | {
"ground_truth": "210",
"style": "rule"
} | {
"cluster_id": 5,
"difficulty": 12.5,
"index": 14387,
"split": "train"
} | 210 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice refuses to sit next to either Bob or Carla. Derek refuses to sit next to Eric. How many ways are there for the five of them to sit in a row of $5$ chairs under these condit... | math | {
"ground_truth": "28",
"style": "rule"
} | {
"cluster_id": 5,
"difficulty": 21.09375,
"index": 13002,
"split": "train"
} | 28 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a certain product requires $6$ processing steps, where $2$ of these steps must be consecutive and another $2$ steps cannot be consecutive, calculate the number of poss... | math | {
"ground_truth": "144",
"style": "rule"
} | {
"cluster_id": 5,
"difficulty": 52.34375,
"index": 7659,
"split": "train"
} | 144 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Joe has written 5 questions of different difficulties for a test with problems numbered 1 though 5. He wants to make sure that problem $i$ is harder than problem $j$ whenever $i-... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"cluster_id": 5,
"difficulty": 64.0625,
"index": 6588,
"split": "train"
} | 25 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many ways are there to put 7 balls in 2 boxes if the balls are distinguishable but the boxes are not?\nPlease reason step by step, and put your final answer within \\boxed{}.... | math | {
"ground_truth": "64",
"style": "rule"
} | {
"cluster_id": 5,
"difficulty": 26.5625,
"index": 13214,
"split": "train"
} | 64 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\sqrt{5 + x} + \\sqrt{20 - x} = 7$, what is the value of $(5 + x)(20 - x)$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}... | math | {
"ground_truth": "144",
"style": "rule"
} | {
"cluster_id": 6,
"difficulty": 13.28125,
"index": 15177,
"split": "train"
} | 144 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate: $\\frac{{\\cos190°(1+\\sqrt{3}\\tan10°)}}{{\\sin290°\\sqrt{1-\\cos40°}}}=\\_\\_\\_\\_\\_\\_$.\nPlease reason step by step, and put your final answer within \\boxed{}."... | math | {
"ground_truth": "2\\sqrt{2}",
"style": "rule"
} | {
"cluster_id": 6,
"difficulty": 63.28125,
"index": 6398,
"split": "train"
} | 2\sqrt{2} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( a + x^2 = 2015 \\), \\( b + x^2 = 2016 \\), \\( c + x^2 = 2017 \\), and \\( abc = 24 \\), find the value of \\( \\frac{a}{bc} + \\frac{b}{ac} + \\frac{c}{ab} - \\frac{1}{a... | math | {
"ground_truth": "1/8",
"style": "rule"
} | {
"cluster_id": 6,
"difficulty": 88.28125,
"index": 2062,
"split": "train"
} | 1/8 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $g(x) = 2x^7 - 3x^3 + 4x - 8.$ If $g(6) = 12,$ find $g(-6).$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-28",
"style": "rule"
} | {
"cluster_id": 6,
"difficulty": 77.34375,
"index": 4951,
"split": "train"
} | -28 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $3(-2) = \\nabla +2$, then what does $\\nabla$ equal?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-8",
"style": "rule"
} | {
"cluster_id": 6,
"difficulty": 6.25,
"index": 16346,
"split": "train"
} | -8 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x + \\frac{1}{x} = \\sqrt{3}$, then find $x^{18}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"cluster_id": 6,
"difficulty": 58.59375,
"index": 7767,
"split": "train"
} | -1 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute $16\\left (\\frac{125}{2}+\\frac{25}{4}+\\frac{9}{16}+1\\right)$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "1125",
"style": "rule"
} | {
"cluster_id": 6,
"difficulty": 2.34375,
"index": 16625,
"split": "train"
} | 1125 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x+y=10$ and $xy=12$, what is the value of $x^3-y^3$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "176\\sqrt{13}",
"style": "rule"
} | {
"cluster_id": 6,
"difficulty": 61.71875,
"index": 6469,
"split": "train"
} | 176\sqrt{13} |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate $(-1)^{53} + 3^{(2^3 + 5^2 - 4!)}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "19682",
"style": "rule"
} | {
"cluster_id": 6,
"difficulty": 46.09375,
"index": 9816,
"split": "train"
} | 19682 |
deepscaler | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a \\star b = \\frac{\\sqrt{a^2+b}}{\\sqrt{a^2 - b}}$. If $y \\star 15 = 5$, find $y$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": ... | math | {
"ground_truth": "\\frac{\\sqrt{65}}{2}",
"style": "rule"
} | {
"cluster_id": 6,
"difficulty": 41.40625,
"index": 9595,
"split": "train"
} | \frac{\sqrt{65}}{2} |
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