data_source stringclasses 1 value | prompt listlengths 1 1 | ability stringclasses 1 value | reward_model dict | extra_info dict | ground_truth stringlengths 1 159 |
|---|---|---|---|---|---|
deepscaler | [
{
"content": "There are 6 class officers, among which there are 3 boys and 3 girls.\n\n(1) Now, 3 people are randomly selected to participate in the school's voluntary labor. Calculate the probability that at least 2 of the selected people are girls.\n\n(2) If these 6 people stand in a row for a photo, where bo... | math | {
"ground_truth": "96",
"style": "rule"
} | {
"difficulty": 28.90625,
"index": 12832,
"split": "train"
} | 96 |
deepscaler | [
{
"content": "(1) Use the Euclidean algorithm to find the greatest common divisor (GCD) of 117 and 182, and verify it using the method of successive subtraction. \n(2) Use the Horner's method to calculate the value of the polynomial \\\\(f(x)=1-9x+8x^{2}-4x^{4}+5x^{5}+3x^{6}\\\\) at \\\\(x=-1\\\\). Let's think... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"difficulty": 32.8125,
"index": 12353,
"split": "train"
} | 12 |
deepscaler | [
{
"content": "Compute $\\left\\lceil\\displaystyle\\sum_{k=2018}^{\\infty}\\frac{2019!-2018!}{k!}\\right\\rceil$ . (The notation $\\left\\lceil x\\right\\rceil$ denotes the least integer $n$ such that $n\\geq x$ .)\n\n*Proposed by Tristan Shin* Let's think step by step and output the final answer within \... | math | {
"ground_truth": "2019",
"style": "rule"
} | {
"difficulty": 48.4375,
"index": 9403,
"split": "train"
} | 2019 |
deepscaler | [
{
"content": "Find \\(AX\\) in the diagram where \\(AC = 27\\) units, \\(BC = 36\\) units, and \\(BX = 30\\) units. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "22.5",
"style": "rule"
} | {
"difficulty": 92.1875,
"index": 1653,
"split": "train"
} | 22.5 |
deepscaler | [
{
"content": "If $x, y, z \\in \\mathbb{R}$ are solutions to the system of equations $$ \\begin{cases}\nx - y + z - 1 = 0\nxy + 2z^2 - 6z + 1 = 0\n\\end{cases} $$ what is the greatest value of $(x - 1)^2 + (y + 1)^2$ ? Let's think step by step and output the final answer within \\boxed{}.",
"role": "us... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"difficulty": 93.75,
"index": 1719,
"split": "train"
} | 11 |
deepscaler | [
{
"content": "The positive integer divisors of 294, except 1, are arranged around a circle so that every pair of adjacent integers has a common factor greater than 1. What is the sum of the two integers adjacent to 21? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
... | math | {
"ground_truth": "49",
"style": "rule"
} | {
"difficulty": 96.09375,
"index": 1198,
"split": "train"
} | 49 |
deepscaler | [
{
"content": "Select 4 individuals from a group of 6 to visit Paris, London, Sydney, and Moscow, with the requirement that each city is visited by one person, each individual visits only one city, and among these 6 individuals, individuals A and B shall not visit Paris. The total number of different selection s... | math | {
"ground_truth": "240",
"style": "rule"
} | {
"difficulty": 42.96875,
"index": 10257,
"split": "train"
} | 240 |
deepscaler | [
{
"content": "For any two positive integers m and n, define an operation \"※\" as follows: when m and n are both positive even numbers or positive odd numbers, m※n=m+n; when one of m and n is a positive even number and the other is a positive odd number, m※n=mn. Determine the number of elements in the set M={(a... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"difficulty": 67.96875,
"index": 6180,
"split": "train"
} | 15 |
deepscaler | [
{
"content": "Find the smallest possible value of \\(x\\) in the simplified form \\(x=\\frac{a+b\\sqrt{c}}{d}\\) if \\(\\frac{7x}{8}-1=\\frac{4}{x}\\), where \\(a, b, c,\\) and \\(d\\) are integers. What is \\(\\frac{acd}{b}\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role"... | math | {
"ground_truth": "-105",
"style": "rule"
} | {
"difficulty": 17.96875,
"index": 15379,
"split": "train"
} | -105 |
deepscaler | [
{
"content": "Alec must purchase 14 identical shirts and only has $\\$130$. There is a flat $\\$2$ entrance fee for shopping at the warehouse store where he plans to buy the shirts. The price of each shirt is the same whole-dollar amount. Assuming a $5\\%$ sales tax is added to the price of each shirt, what ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"difficulty": 17.1875,
"index": 15423,
"split": "train"
} | 8 |
deepscaler | [
{
"content": "The Maplewood Youth Soccer Team consists of 25 players, including four who are goalies. During a special drill, each goalie takes a turn in the net while the other 24 players (including the remaining goalies) attempt penalty kicks. \nCalculate the total number of penalty kicks that must be taken s... | math | {
"ground_truth": "96",
"style": "rule"
} | {
"difficulty": 45.3125,
"index": 9024,
"split": "train"
} | 96 |
deepscaler | [
{
"content": "There are 99 positive integers, and their sum is 101101. Find the greatest possible value of the greatest common divisor of these 99 positive integers. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "101",
"style": "rule"
} | {
"difficulty": 57.8125,
"index": 7427,
"split": "train"
} | 101 |
deepscaler | [
{
"content": "Given a circle with center $C$ and equation $x^{2}+y^{2}+2x-4y+m=0$, which intersects with the line $2x+y-3=0$ at points $A$ and $B$:\n\n$(1)$ If $\\triangle ABC$ is an equilateral triangle, find the value of $m$; \n$(2)$ Is there a constant $m$ such that the circle with diameter $AB$ passes thro... | math | {
"ground_truth": "-\\frac{18}{5}",
"style": "rule"
} | {
"difficulty": 70.3125,
"index": 4109,
"split": "train"
} | -\frac{18}{5} |
deepscaler | [
{
"content": "A club has 10 members, 5 boys and 5 girls. Two of the members are chosen at random. What is the probability that they are both girls? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{2}{9}",
"style": "rule"
} | {
"difficulty": 10.9375,
"index": 15960,
"split": "train"
} | \dfrac{2}{9} |
deepscaler | [
{
"content": "How many ways are there to place $3$ indistinguishable red chips, $3$ indistinguishable blue chips, and $3$ indistinguishable green chips in the squares of a $3 \\times 3$ grid so that no two chips of the same color are directly adjacent to each other, either vertically or horizontally? Let's thin... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"difficulty": 4.6875,
"index": 17477,
"split": "train"
} | 36 |
deepscaler | [
{
"content": "Let $ABCD$ and $BCFG$ be two faces of a cube with $AB=10$. A beam of light is emitted from vertex $A$ and reflects off face $BCFG$ at point $P$, which is 3 units from $\\overline{BG}$ and 4 units from $\\overline{BC}$. The beam continues its path, reflecting off the faces of the cube. The length o... | math | {
"ground_truth": "55",
"style": "rule"
} | {
"difficulty": 92.96875,
"index": 1323,
"split": "train"
} | 55 |
deepscaler | [
{
"content": "Samantha leaves her house at 7:15 a.m. to catch the school bus, starts her classes at 8:00 a.m., and has 8 classes that last 45 minutes each, a 40-minute lunch break, and spends an additional 90 minutes in extracurricular activities. If she takes the bus home and arrives back at 5:15 p.m., calcula... | math | {
"ground_truth": "110",
"style": "rule"
} | {
"difficulty": 52.34375,
"index": 7489,
"split": "train"
} | 110 |
deepscaler | [
{
"content": "Find the area of triangle $DEF$ below, where $DF = 8$ and $\\angle D = 45^\\circ$.\n\n[asy]\nunitsize(1inch);\npair D,E,F;\nD = (0,0);\nE= (sqrt(2),0);\nF = (0,sqrt(2));\ndraw (D--E--F--D,linewidth(0.9));\ndraw(rightanglemark(E,D,F,3));\nlabel(\"$D$\",D,S);\nlabel(\"$E$\",E,S);\nlabel(\"$F$\",F,N)... | math | {
"ground_truth": "32",
"style": "rule"
} | {
"difficulty": 49.21875,
"index": 10321,
"split": "train"
} | 32 |
deepscaler | [
{
"content": "Each of the three cutlets needs to be fried on a pan on both sides for five minutes each side. The pan can hold only two cutlets at a time. Is it possible to fry all three cutlets in less than 20 minutes (ignoring the time for flipping and transferring the cutlets)? Let's think step by step and ou... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"difficulty": 80.46875,
"index": 2612,
"split": "train"
} | 15 |
deepscaler | [
{
"content": "The positive integers from 1 to 576 are written in a 24 by 24 grid so that the first row contains the numbers 1 to 24, the second row contains the numbers 25 to 48, and so on. An 8 by 8 square is drawn around 64 of these numbers. The sum of the numbers in the four corners of the 8 by 8 square is 1... | math | {
"ground_truth": "499",
"style": "rule"
} | {
"difficulty": 85.15625,
"index": 2201,
"split": "train"
} | 499 |
deepscaler | [
{
"content": "The quadratic equation $ax^2+8x+c=0$ has exactly one solution. If $a+c=10$, and $a<c$ find the ordered pair $(a,c)$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "(2,8)",
"style": "rule"
} | {
"difficulty": 18.75,
"index": 15440,
"split": "train"
} | (2,8) |
deepscaler | [
{
"content": "Elective 4-4: Coordinate System and Parametric Equations\n\nIn the Cartesian coordinate system $xOy$, with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. If the polar equation of curve $C$ is $\\rho\\cos^2\\theta-4\\sin\\th... | math | {
"ground_truth": "\\frac{\\sqrt{6}}{6}",
"style": "rule"
} | {
"difficulty": 78.90625,
"index": 4829,
"split": "train"
} | \frac{\sqrt{6}}{6} |
deepscaler | [
{
"content": "A two-digit positive integer $x$ has the property that when 109 is divided by $x$, the remainder is 4. What is the sum of all such two-digit positive integers $x$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "71",
"style": "rule"
} | {
"difficulty": 28.125,
"index": 13946,
"split": "train"
} | 71 |
deepscaler | [
{
"content": "Semicircles of diameter 2'' are lined up as shown. What is the area, in square inches, of the shaded region in a 1-foot length of this pattern? Express your answer in terms of $\\pi$.\n\n[asy]import graph;\nsize(101);\n\npath tophalf = Arc((0,0),1,180,0) -- Arc((2,0),1,180,0) -- Arc((4,0),1,180,0)... | math | {
"ground_truth": "6\\pi",
"style": "rule"
} | {
"difficulty": 69.53125,
"index": 5395,
"split": "train"
} | 6\pi |
deepscaler | [
{
"content": "Triangle $ABC$ has vertices $A(0, 8)$, $B(2, 0)$, $C(8, 0)$. A line through $B$ cuts the area of $\\triangle ABC$ in half; find the sum of the slope and $y$-intercept of this line. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"difficulty": 77.34375,
"index": 5181,
"split": "train"
} | -2 |
deepscaler | [
{
"content": "Express $7.\\overline{123}$ as a common fraction in lowest terms. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2372}{333}",
"style": "rule"
} | {
"difficulty": 25,
"index": 13409,
"split": "train"
} | \frac{2372}{333} |
deepscaler | [
{
"content": "Taylor is tiling his 12 feet by 16 feet living room floor. He plans to place 1 foot by 1 foot tiles along the edges to form a border, and then use 2 feet by 2 feet tiles to fill the remaining floor area. How many tiles will he use in total? Let's think step by step and output the final answer with... | math | {
"ground_truth": "87",
"style": "rule"
} | {
"difficulty": 32.8125,
"index": 11032,
"split": "train"
} | 87 |
deepscaler | [
{
"content": "The sphere with radius 1 and center $(0,0,1)$ rests on the $xy$-plane. A light source is at $P = (0,-1,2).$ Then the boundary of the shadow of the sphere can be expressed in the form $y = f(x),$ for some function $f(x).$ Find the function $f(x).$ Let's think step by step and output the final an... | math | {
"ground_truth": "\\frac{x^2}{4} - 1",
"style": "rule"
} | {
"difficulty": 98.4375,
"index": 1028,
"split": "train"
} | \frac{x^2}{4} - 1 |
deepscaler | [
{
"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 $a$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2}{e}",
"style": "rule"
} | {
"difficulty": 30.46875,
"index": 10931,
"split": "train"
} | \frac{2}{e} |
deepscaler | [
{
"content": "Al, Bill, and Cal will each randomly be assigned a whole number from $1$ to $10$, inclusive, with no two of them getting the same number. What is the probability that Al's number will be a whole number multiple of Bill's and Bill's number will be a whole number multiple of Cal's? Let's think step ... | math | {
"ground_truth": "\\frac{1}{80}",
"style": "rule"
} | {
"difficulty": 70.3125,
"index": 4069,
"split": "train"
} | \frac{1}{80} |
deepscaler | [
{
"content": "A solid right prism $PQRSTU$ has a height of 20, as shown. Its bases are equilateral triangles with side length 15. Points $M$, $N$, and $O$ are the midpoints of edges $PQ$, $QR$, and $RS$, respectively. Determine the perimeter of triangle $MNO$. Let's think step by step and output the final answe... | math | {
"ground_truth": "32.5",
"style": "rule"
} | {
"difficulty": 88.28125,
"index": 1880,
"split": "train"
} | 32.5 |
deepscaler | [
{
"content": "On graph paper, large and small triangles are drawn (all cells are square and of the same size). How many small triangles can be cut out from the large triangle? Triangles cannot be rotated or flipped (the large triangle has a right angle in the bottom left corner, the small triangle has a right a... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"difficulty": 96.875,
"index": 281,
"split": "train"
} | 12 |
deepscaler | [
{
"content": "Let \\[\\begin{aligned} a &= \\sqrt{2}+\\sqrt{3}+\\sqrt{6}, \\\\ b &= -\\sqrt{2}+\\sqrt{3}+\\sqrt{6}, \\\\ c&= \\sqrt{2}-\\sqrt{3}+\\sqrt{6}, \\\\ d&=-\\sqrt{2}-\\sqrt{3}+\\sqrt{6}. \\end{aligned}\\]Evaluate $\\left(\\frac1a + \\frac1b + \\frac1c + \\frac1d\\right)^2.$ Let's think step by step and... | math | {
"ground_truth": "\\frac{96}{529}",
"style": "rule"
} | {
"difficulty": 59.375,
"index": 8518,
"split": "train"
} | \frac{96}{529} |
deepscaler | [
{
"content": "An auditorium with $20$ rows of seats has $10$ seats in the first row. Each successive row has one more seat than the previous row. If students taking an exam are permitted to sit in any row, but not next to another student in that row, then the maximum number of students that can be seated for ... | math | {
"ground_truth": "200",
"style": "rule"
} | {
"difficulty": 14.84375,
"index": 14546,
"split": "train"
} | 200 |
deepscaler | [
{
"content": "What percent of the five-by-five square is shaded?\n\n[asy]\nsize(5cm,5cm);\nfill((0,0)--(10,0)--(10,10)--(0,10)--cycle,gray(0.7));\nfill((0,20)--(10,20)--(10,30)--(0,30)--cycle,gray(0.7));\nfill((0,40)--(10,40)--(10,50)--(0,50)--cycle,gray(0.7));\nfill((10,10)--(20,10)--(20,20)--(10,20)--cycle,gr... | math | {
"ground_truth": "52\\%",
"style": "rule"
} | {
"difficulty": 54.6875,
"index": 7743,
"split": "train"
} | 52\% |
deepscaler | [
{
"content": "Given that α is an acute angle, cos(α+π/6) = 2/3, find the value of sinα. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{\\sqrt{15} - 2}{6}",
"style": "rule"
} | {
"difficulty": 90.625,
"index": 411,
"split": "train"
} | \dfrac{\sqrt{15} - 2}{6} |
deepscaler | [
{
"content": "The sum of the first $n$ terms of an arithmetic sequence $\\{a_n\\}$ is $S_n$. Given that $S_{10}=0$ and $S_{15}=25$, find the minimum value of $nS_n$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-49",
"style": "rule"
} | {
"difficulty": 21.875,
"index": 13880,
"split": "train"
} | -49 |
deepscaler | [
{
"content": "In a group of 10 basketball teams which includes 2 strong teams, the teams are randomly split into two equal groups for a competition. What is the probability that the 2 strong teams do not end up in the same group? Let's think step by step and output the final answer within \\boxed{}.",
"role... | math | {
"ground_truth": "\\frac{5}{9}",
"style": "rule"
} | {
"difficulty": 41.40625,
"index": 9998,
"split": "train"
} | \frac{5}{9} |
deepscaler | [
{
"content": "Natural numbers \\( a, b, c \\) are such that \\( 1 \\leqslant a < b < c \\leqslant 3000 \\). Find the largest possible value of the quantity\n\n$$\n\\gcd(a, b) + \\gcd(b, c) + \\gcd(c, a)\n$$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "3000",
"style": "rule"
} | {
"difficulty": 40.625,
"index": 10395,
"split": "train"
} | 3000 |
deepscaler | [
{
"content": "A truck travels due west at $\\frac{3}{4}$ mile per minute on a straight road. At the same time, a circular storm, whose radius is $60$ miles, moves southwest at $\\frac{1}{2}\\sqrt{2}$ mile per minute. At time $t=0$, the center of the storm is $130$ miles due north of the truck. Determine the ave... | math | {
"ground_truth": "208",
"style": "rule"
} | {
"difficulty": 33.59375,
"index": 11315,
"split": "train"
} | 208 |
deepscaler | [
{
"content": "Given the parametric equation of line $l$ as $ \\begin{cases} x=m+ \\frac { \\sqrt {2}}{2}t \\\\ y= \\frac { \\sqrt {2}}{2}t \\end{cases} (t\\text{ is the parameter})$, establish a polar coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axi... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"difficulty": 28.90625,
"index": 14354,
"split": "train"
} | 16 |
deepscaler | [
{
"content": "A certain shopping mall's sales volume (unit: ten thousand pieces) for five consecutive years is as shown in the table below:\n\n| $x$(year) | 1 | 2 | 3 | 4 | 5 |\n|-----------|---|---|---|---|---|\n| $y$(sales volume) | 5 | 5 | 6 | 7 | 7 |\n\n$(1)$ Find the linear regression equation $\\hat{y}=\\... | math | {
"ground_truth": "\\frac{2}{5}",
"style": "rule"
} | {
"difficulty": 25.78125,
"index": 14192,
"split": "train"
} | \frac{2}{5} |
deepscaler | [
{
"content": "How many functions $f:\\{0,1\\}^{3} \\rightarrow\\{0,1\\}$ satisfy the property that, for all ordered triples \\left(a_{1}, a_{2}, a_{3}\\right) and \\left(b_{1}, b_{2}, b_{3}\\right) such that $a_{i} \\geq b_{i}$ for all $i, f\\left(a_{1}, a_{2}, a_{3}\\right) \\geq f\\left(b_{1}, b_{2}, b_{3}\\r... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"difficulty": 77.34375,
"index": 4192,
"split": "train"
} | 20 |
deepscaler | [
{
"content": "If $\\log 2 = 0.3010$ and $\\log 5 = 0.6990$, calculate the value of $x$ for the equation $2^{x+2} = 200$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "5.64",
"style": "rule"
} | {
"difficulty": 98.4375,
"index": 9,
"split": "train"
} | 5.64 |
deepscaler | [
{
"content": "Calculate the value of\n$$\n\\sqrt{2018 \\times 2021 \\times 2022 \\times 2023 + 2024^{2}} - 2024^{2}\n$$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-12138",
"style": "rule"
} | {
"difficulty": 84.375,
"index": 2450,
"split": "train"
} | -12138 |
deepscaler | [
{
"content": "If a 31-day month is taken at random, find \\( c \\), the probability that there are 5 Sundays in the month. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "3/7",
"style": "rule"
} | {
"difficulty": 75,
"index": 4546,
"split": "train"
} | 3/7 |
deepscaler | [
{
"content": "In right triangle $DEF$, where $DE = 15$, $DF = 9$, and $EF = 12$ units, find the distance from $F$ to the midpoint of segment $DE$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "7.5",
"style": "rule"
} | {
"difficulty": 81.25,
"index": 2619,
"split": "train"
} | 7.5 |
deepscaler | [
{
"content": "In a class, no two boys were born on the same day of the week and no two girls were born in the same month. If another child were to join the class, this would no longer be true. How many children are there in the class? Let's think step by step and output the final answer within \\boxed{}.",
... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"difficulty": 22.65625,
"index": 14159,
"split": "train"
} | 19 |
deepscaler | [
{
"content": "If Greg rolls four fair six-sided dice, what is the probability that he rolls more 1's than 6's? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{421}{1296}",
"style": "rule"
} | {
"difficulty": 44.53125,
"index": 10490,
"split": "train"
} | \dfrac{421}{1296} |
deepscaler | [
{
"content": "Suppose two distinct integers are chosen from between 1 and 29, inclusive. What is the probability that their product is neither a multiple of 2 nor 3? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\dfrac{45}{406}",
"style": "rule"
} | {
"difficulty": 32.8125,
"index": 11988,
"split": "train"
} | \dfrac{45}{406} |
deepscaler | [
{
"content": "Given in a cube ABCD-A1B1C1D1 with edge length 1, P is a moving point inside the cube (including the surface), \nif $x + y + z = s$, and $0 \\leq x \\leq y \\leq z \\leq 1$, then the volume of the geometric body formed by all possible positions of point P is $\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_$. Let'... | math | {
"ground_truth": "\\frac{1}{6}",
"style": "rule"
} | {
"difficulty": 20.3125,
"index": 12758,
"split": "train"
} | \frac{1}{6} |
deepscaler | [
{
"content": "Jamar bought some pencils costing more than a penny each at the school bookstore and paid $1.43$. Sharona bought some of the same pencils and paid $1.87$. How many more pencils did Sharona buy than Jamar? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"difficulty": 32.8125,
"index": 11731,
"split": "train"
} | 4 |
deepscaler | [
{
"content": "How many numbers are in the list $-50, -44, -38, \\ldots, 68, 74$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "22",
"style": "rule"
} | {
"difficulty": 45.3125,
"index": 9580,
"split": "train"
} | 22 |
deepscaler | [
{
"content": "How many rectangles can be formed where each of the four vertices are points on a 4x4 grid with points spaced evenly along the grid lines? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "36",
"style": "rule"
} | {
"difficulty": 86.71875,
"index": 2482,
"split": "train"
} | 36 |
deepscaler | [
{
"content": "Martin is playing a game. His goal is to place tokens on an 8 by 8 chessboard in such a way that there is at most one token per square, and each column and each row contains at most 4 tokens.\n\na) How many tokens can Martin place, at most?\n\nb) If, in addition to the previous constraints, each o... | math | {
"ground_truth": "32",
"style": "rule"
} | {
"difficulty": 44.53125,
"index": 9153,
"split": "train"
} | 32 |
deepscaler | [
{
"content": "What is the coefficient of \\(x^3y^5\\) in the expansion of \\(\\left(\\frac{2}{3}x - \\frac{4}{5}y\\right)^8\\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{458752}{84375}",
"style": "rule"
} | {
"difficulty": 57.8125,
"index": 8398,
"split": "train"
} | -\frac{458752}{84375} |
deepscaler | [
{
"content": "1. If $A_{10}^{m} =10×9×…×5$, then $m=$ ______.\n2. The number of ways for A, B, C, and D to take turns reading the same book, with A reading first, is ______.\n3. If five boys and two girls are to be arranged in a row for a photo, with boy A required to stand in the middle and the two girls requi... | math | {
"ground_truth": "192",
"style": "rule"
} | {
"difficulty": 95.3125,
"index": 101,
"split": "train"
} | 192 |
deepscaler | [
{
"content": "A point $P$ is chosen at random from the interior of a square $ABCD$. What is the probability that the triangle $ABP$ has a greater area than each of the triangles $BCP$, $CDP$, and $DAP$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"difficulty": 52.34375,
"index": 8544,
"split": "train"
} | \frac{1}{4} |
deepscaler | [
{
"content": "If $\\sin \\left(\\frac{\\pi }{3}+\\alpha \\right)=\\frac{1}{3}$, then find the value of $\\cos \\left(\\frac{\\pi }{3}-2\\alpha \\right)$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{7}{9}",
"style": "rule"
} | {
"difficulty": 55.46875,
"index": 7219,
"split": "train"
} | -\frac{7}{9} |
deepscaler | [
{
"content": "Let $g(x) = 2x^7 - 3x^3 + 4x - 8.$ If $g(6) = 12,$ find $g(-6).$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-28",
"style": "rule"
} | {
"difficulty": 77.34375,
"index": 4951,
"split": "train"
} | -28 |
deepscaler | [
{
"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 will spend exactly $\\$50$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"difficulty": 11.71875,
"index": 15114,
"split": "train"
} | 6 |
deepscaler | [
{
"content": "Convert the following radians to degrees: convert degrees to radians:\n(1) $\\frac{\\pi}{12} =$ \\_\\_\\_\\_\\_\\_ ; (2) $\\frac{13\\pi}{6} =$ \\_\\_\\_\\_\\_\\_ ; (3) $- \\frac{5}{12}\\pi =$ \\_\\_\\_\\_\\_\\_ .\n(4) $36^{\\circ} =$ \\_\\_\\_\\_\\_\\_ $rad$ ; (5) $-105^{\\circ} =$ \\_\\_\\_\\_\\_... | math | {
"ground_truth": "-\\frac{7\\pi}{12}",
"style": "rule"
} | {
"difficulty": 16.40625,
"index": 15618,
"split": "train"
} | -\frac{7\pi}{12} |
deepscaler | [
{
"content": "Given that $α∈\\left( \\frac{π}{2},π\\right) $, and $\\sin \\left(π-α\\right)+\\cos \\left(2π+α\\right)= \\frac{ \\sqrt{2}}{3} $. Find the values of:\n\n$(1)\\sin {α} -\\cos {α} .$\n\n$(2)\\tan {α} $. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "- \\frac{9+4 \\sqrt{2}}{7}",
"style": "rule"
} | {
"difficulty": 18.75,
"index": 15678,
"split": "train"
} | - \frac{9+4 \sqrt{2}}{7} |
deepscaler | [
{
"content": "Seven people stand in a row. (Write out the necessary process, and use numbers for the answers) \n(1) How many ways can person A and person B stand next to each other? \n(2) How many ways can person A and person B stand not next to each other? \n(3) How many ways can person A, person B, and per... | math | {
"ground_truth": "4320",
"style": "rule"
} | {
"difficulty": 71.09375,
"index": 3718,
"split": "train"
} | 4320 |
deepscaler | [
{
"content": "Jo and Blair take turns counting from 1, increasing by 1 each turn. However, if the number is a multiple of 3, they skip it. Jo starts by saying \"1.\" Calculate the 53rd number said. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "80",
"style": "rule"
} | {
"difficulty": 64.84375,
"index": 7136,
"split": "train"
} | 80 |
deepscaler | [
{
"content": "Given the set $M=\\{a, b, -(a+b)\\}$, where $a\\in \\mathbb{R}$ and $b\\in \\mathbb{R}$, and set $P=\\{1, 0, -1\\}$. If there is a mapping $f:x \\to x$ that maps element $x$ in set $M$ to element $x$ in set $P$ (the image of $x$ under $f$ is still $x$), then the set $S$ formed by the points with c... | math | {
"ground_truth": "64",
"style": "rule"
} | {
"difficulty": 48.4375,
"index": 9512,
"split": "train"
} | 64 |
deepscaler | [
{
"content": "Let $[x]$ denote the greatest integer not exceeding $x$, for example, $[3.14] = 3$. Then, find the value of $\\left[\\frac{2017 \\times 3}{11}\\right] + \\left[\\frac{2017 \\times 4}{11}\\right] + \\left[\\frac{2017 \\times 5}{11}\\right] + \\left[\\frac{2017 \\times 6}{11}\\right] + \\left[\\frac... | math | {
"ground_truth": "6048",
"style": "rule"
} | {
"difficulty": 1.5625,
"index": 17955,
"split": "train"
} | 6048 |
deepscaler | [
{
"content": "Let $A$ be the set of all numbers which can be represented as the sum of three consecutive positive integers. What is the greatest common divisor of all numbers in $A$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"difficulty": 0,
"index": 17414,
"split": "train"
} | 3 |
deepscaler | [
{
"content": "Given vectors $\\overrightarrow{a}=m \\overrightarrow{i}+5 \\overrightarrow{j}- \\overrightarrow{k}, \\overrightarrow{b}=3 \\overrightarrow{i}+ \\overrightarrow{j}+r \\overrightarrow{k}$, if $\\overrightarrow{a}//\\overrightarrow{b}$, find the values of real numbers $m=$ \\_\\_\\_\\_\\_\\_ and $r=... | math | {
"ground_truth": "-\\frac{1}{5}",
"style": "rule"
} | {
"difficulty": 30.46875,
"index": 11699,
"split": "train"
} | -\frac{1}{5} |
deepscaler | [
{
"content": "In a debate competition with 4 participants, the rules are as follows: each participant must choose one topic from two options, A and B. For topic A, answering correctly earns 100 points, and answering incorrectly results in a loss of 100 points. For topic B, answering correctly earns 90 points, a... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"difficulty": 50.78125,
"index": 7466,
"split": "train"
} | 36 |
deepscaler | [
{
"content": "Suppose a function $f(x)$ is defined on the domain $[-8,4]$. If we define a new function $g(x)$ by $$g(x) = f(-2x),$$ then what is the domain of $g(x)$? Express your answer in interval notation. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "[-2,4]",
"style": "rule"
} | {
"difficulty": 9.375,
"index": 17023,
"split": "train"
} | [-2,4] |
deepscaler | [
{
"content": "Given $6$ cards labeled $1$, $2$, $3$, $4$, $5$, and $6$ are drawn without replacement, calculate the probability that the product of the numbers of the $2$ cards is a multiple of $4$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2}{5}",
"style": "rule"
} | {
"difficulty": 62.5,
"index": 5756,
"split": "train"
} | \frac{2}{5} |
deepscaler | [
{
"content": "Find all real parameters $a$ for which the equation $x^8 +ax^4 +1 = 0$ has four real roots forming an arithmetic progression. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{82}{9}",
"style": "rule"
} | {
"difficulty": 98.4375,
"index": 70,
"split": "train"
} | -\frac{82}{9} |
deepscaler | [
{
"content": "The inverse of \\( f(x) = \\frac{3x-2}{x+4} \\) may be written in the form \\( f^{-1}(x) = \\frac{ax+b}{cx+d} \\), where \\( a, b, c, \\) and \\( d \\) are real numbers. Find \\( \\frac{a}{c} \\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"difficulty": 0,
"index": 17411,
"split": "train"
} | -4 |
deepscaler | [
{
"content": "The fraction \\(\\frac{p}{q}\\) is in its simplest form. If \\(\\frac{7}{10} < \\frac{p}{q} < \\frac{11}{15}\\), where \\(q\\) is the smallest possible positive integer and \\(c = pq\\), find the value of \\(c\\). Let's think step by step and output the final answer within \\boxed{}.",
"role":... | math | {
"ground_truth": "35",
"style": "rule"
} | {
"difficulty": 39.84375,
"index": 12289,
"split": "train"
} | 35 |
deepscaler | [
{
"content": "Alicia had two containers. The first was $\\frac{5}{6}$ full of water and the second was empty. She poured all the water from the first container into the second container, at which point the second container was $\\frac{3}{4}$ full of water. What is the ratio of the volume of the first container ... | math | {
"ground_truth": "\\frac{9}{10}",
"style": "rule"
} | {
"difficulty": 3.90625,
"index": 16472,
"split": "train"
} | \frac{9}{10} |
deepscaler | [
{
"content": "Wendy has 180 feet of fencing. She needs to enclose a rectangular space with an area that is ten times its perimeter. If she uses up all her fencing material, how many feet is the largest side of the enclosure? Let's think step by step and output the final answer within \\boxed{}.",
"role": "u... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"difficulty": 71.875,
"index": 3773,
"split": "train"
} | 60 |
deepscaler | [
{
"content": "What is the smallest positive integer $n$ such that $\\frac{n}{n+150}$ is equal to a terminating decimal? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"difficulty": 61.71875,
"index": 5800,
"split": "train"
} | 10 |
deepscaler | [
{
"content": "What is the smallest positive value of $x$ such that $x + 4321$ results in a palindrome? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule"
} | {
"difficulty": 14.84375,
"index": 14631,
"split": "train"
} | 13 |
deepscaler | [
{
"content": "Suppose that $a$ and $b$ are positive integers such that $(a+bi)^2 = 3+4i$. What is $a+bi$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "2 + i",
"style": "rule"
} | {
"difficulty": 4.6875,
"index": 17948,
"split": "train"
} | 2 + i |
deepscaler | [
{
"content": "Find $2 \\cdot 5^{-1} + 8 \\cdot 11^{-1} \\pmod{56}$.\n\nExpress your answer as an integer from $0$ to $55$, inclusive. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "50",
"style": "rule"
} | {
"difficulty": 17.96875,
"index": 15610,
"split": "train"
} | 50 |
deepscaler | [
{
"content": "The quadratic \\( x^2 + 1800x + 1800 \\) can be written in the form \\( (x+b)^2 + c \\), where \\( b \\) and \\( c \\) are constants. What is \\( \\frac{c}{b} \\)? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-898",
"style": "rule"
} | {
"difficulty": 10.15625,
"index": 15188,
"split": "train"
} | -898 |
deepscaler | [
{
"content": "Given the equations $\\left(625\\right)^{0.24}$ and $\\left(625\\right)^{0.06}$, find the value of their product. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "5^{6/5}",
"style": "rule"
} | {
"difficulty": 99.21875,
"index": 1338,
"split": "train"
} | 5^{6/5} |
deepscaler | [
{
"content": "The GDP of a certain city last year was 84,300,000 ten thousand yuan. Represent this number in scientific notation. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "8.43 \\times 10^7",
"style": "rule"
} | {
"difficulty": 88.28125,
"index": 3268,
"split": "train"
} | 8.43 \times 10^7 |
deepscaler | [
{
"content": "Joe had walked half way from home to school when he realized he was late. He ran the rest of the way to school. He ran 3 times as fast as he walked. Joe took 6 minutes to walk half way to school. How many minutes did it take Joe to get from home to school? Let's think step by step and output the f... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"difficulty": 10.15625,
"index": 15627,
"split": "train"
} | 8 |
deepscaler | [
{
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. Given vectors $m=(\\sin \\frac{A}{2},\\cos \\frac{A}{2})$ and $n=(\\cos \\frac{A}{2},-\\cos \\frac{A}{2})$, and $2m\\cdot n+|m|=\\frac{ \\sqrt{2}}{2}$, find $\\angle A=$____. Let's think step by step an... | math | {
"ground_truth": "\\frac{5\\pi }{12}",
"style": "rule"
} | {
"difficulty": 21.875,
"index": 13570,
"split": "train"
} | \frac{5\pi }{12} |
deepscaler | [
{
"content": "Let $a\\oplus b=3a+4b$ for all real numbers $a$ and $b$. Find $3\\oplus 1$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "13",
"style": "rule"
} | {
"difficulty": 2.34375,
"index": 17423,
"split": "train"
} | 13 |
deepscaler | [
{
"content": "Given that the probability of bus No. 3 arriving at the bus stop within 5 minutes is 0.20 and the probability of bus No. 6 arriving within 5 minutes is 0.60, calculate the probability that the passenger can catch the bus he needs within 5 minutes. Let's think step by step and output the final answ... | math | {
"ground_truth": "0.80",
"style": "rule"
} | {
"difficulty": 47.65625,
"index": 10678,
"split": "train"
} | 0.80 |
deepscaler | [
{
"content": "Inside the cube $A B C D A_{1} B_{1} C_{1} D_{1}$ is the center $O$ of a sphere with radius 10. The sphere intersects the face $A A_{1} D_{1} D$ along a circle with radius 1, the face $A_{1} B_{1} C_{1} D_{1}$ along a circle with radius 1, and the face $C D D_{1} C_{1}$ along a circle with radius ... | math | {
"ground_truth": "17",
"style": "rule"
} | {
"difficulty": 73.4375,
"index": 4053,
"split": "train"
} | 17 |
deepscaler | [
{
"content": "For the numbers \\(1000^{2}, 1001^{2}, 1002^{2}, \\ldots\\), the last two digits are discarded. How many of the first terms in the resulting sequence form an arithmetic progression? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"difficulty": 71.09375,
"index": 5285,
"split": "train"
} | 10 |
deepscaler | [
{
"content": "Riders on a Ferris wheel travel in a circle in a vertical plane. A particular wheel has radius $20$ feet and revolves at the constant rate of one revolution per minute. How many seconds does it take a rider to travel from the bottom of the wheel to a point $10$ vertical feet above the bottom? Let'... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"difficulty": 56.25,
"index": 7266,
"split": "train"
} | 10 |
deepscaler | [
{
"content": "A rabbit and a hedgehog participated in a running race on a 550 m long circular track, both starting and finishing at the same point. The rabbit ran clockwise at a speed of 10 m/s and the hedgehog ran anticlockwise at a speed of 1 m/s. When they met, the rabbit continued as before, but the hedgeho... | math | {
"ground_truth": "545",
"style": "rule"
} | {
"difficulty": 99.21875,
"index": 1737,
"split": "train"
} | 545 |
deepscaler | [
{
"content": "In a pocket, there are several balls of three different colors (enough in quantity), and each time 2 balls are drawn. To ensure that the result of drawing is the same 5 times, at least how many times must one draw? Let's think step by step and output the final answer within \\boxed{}.",
"role"... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"difficulty": 40.625,
"index": 10039,
"split": "train"
} | 25 |
deepscaler | [
{
"content": "At around 8 o'clock in the morning, two cars left the fertilizer plant one after another, heading toward Happy Village. Both cars travel at a speed of 60 kilometers per hour. At 8:32, the distance the first car had traveled from the fertilizer plant was three times the distance traveled by the sec... | math | {
"ground_truth": "8:11",
"style": "rule"
} | {
"difficulty": 89.0625,
"index": 2972,
"split": "train"
} | 8:11 |
deepscaler | [
{
"content": "In the picture, there is a grid consisting of 25 small equilateral triangles. How many rhombuses can be made from two adjacent small triangles? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "30",
"style": "rule"
} | {
"difficulty": 85.15625,
"index": 3267,
"split": "train"
} | 30 |
deepscaler | [
{
"content": "A thief on a bus gets off at a bus stop and walks in the direction opposite to the bus’s travel direction. The bus continues its journey, and a passenger realizes they have been robbed. The passenger gets off at the next stop and starts chasing the thief. If the passenger's speed is twice that of ... | math | {
"ground_truth": "440",
"style": "rule"
} | {
"difficulty": 94.53125,
"index": 1777,
"split": "train"
} | 440 |
deepscaler | [
{
"content": "Define a natural number to be \"super-nice\" if it is either the product of exactly three distinct prime numbers or the fourth power of a prime number. What is the sum of the first eight super-nice numbers? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"... | math | {
"ground_truth": "520",
"style": "rule"
} | {
"difficulty": 99.21875,
"index": 544,
"split": "train"
} | 520 |
deepscaler | [
{
"content": "On the side \\(AB\\) of an equilateral triangle \\(\\mathrm{ABC}\\), a right triangle \\(\\mathrm{AHB}\\) is constructed (\\(\\mathrm{H}\\) is the vertex of the right angle) such that \\(\\angle \\mathrm{HBA}=60^{\\circ}\\). Let the point \\(K\\) lie on the ray \\(\\mathrm{BC}\\) beyond the point ... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"difficulty": 78.90625,
"index": 4035,
"split": "train"
} | 15 |
deepscaler | [
{
"content": "The angle $A$ at the vertex of the isosceles triangle $ABC$ is $100^{\\circ}$. On the ray $AB$, a segment $AM$ is laid off, equal to the base $BC$. Find the measure of the angle $BCM$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"difficulty": 67.1875,
"index": 6631,
"split": "train"
} | 10 |
deepscaler | [
{
"content": "If you set the clock back by 10 minutes, the number of radians the minute hand has turned is \\_\\_\\_\\_\\_\\_. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\pi}{3}",
"style": "rule"
} | {
"difficulty": 20.3125,
"index": 13231,
"split": "train"
} | \frac{\pi}{3} |
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