data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "Distinct ways to distribute $7$ identical balls into $4$ distinct boxes such that no box is empty."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 8000,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Distribute 10 volunteer positions among 4 schools, with the requirement that each school receives at least one position. How many different ways can the positions be distributed? (Answer with a number.)"
}
] | math | {
"style": "rule",
"ground_truth": "84"
} | {
"index": 8001,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Distribute 16 identical books among 4 students so that each student gets at least one book, and each student gets a different number of books. How many distinct ways can this be done? (Answer with a number.)"
}
] | math | {
"style": "rule",
"ground_truth": "216"
} | {
"index": 8002,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Distribute 3 male and 2 female freshmen, a total of 5 students, into two classes, Class A and Class B, with each class receiving no fewer than 2 students, and Class A must have at least 1 female student. The number of different distribution schemes is ______."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 8003,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Distribute 4 college students to three factories A, B, and C for internship activities. Factory A can only arrange for 1 college student, the other factories must arrange for at least 1 student each, and student A cannot be assigned to factory C. The number of different distrib... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 8004,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Distribute 5 students into 3 groups: Group A, Group B, and Group C, with Group A having at least two people, and Groups B and C having at least one person each, and calculate the number of different distribution schemes."
}
] | math | {
"style": "rule",
"ground_truth": "80"
} | {
"index": 8005,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Distribute 5 students into 3 groups: Group A, Group B, and Group C, with the condition that Group A must have at least two people, and Groups B and C must have at least one person each. How many different distribution schemes exist?"
}
] | math | {
"style": "rule",
"ground_truth": "80"
} | {
"index": 8006,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Distribute 5 students into dormitories A, B, and C, with each dormitory having at least 1 and at most 2 students. Among these, the number of different ways to distribute them without student A going to dormitory A is \\_\\_\\_\\_\\_\\_."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 8007,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Distribute 5 students into three groups: A, B, and C. Group A must have at least two students, while groups B and C must have at least one student each. Determine the number of different distribution schemes."
}
] | math | {
"style": "rule",
"ground_truth": "80"
} | {
"index": 8008,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Distribute 5 students into two dormitories, A and B, with each dormitory accommodating at least 2 students. Find the number of distinct arrangements."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 8009,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Distribute 5 volunteers from the Shanghai World Expo to work in the pavilions of China, the United States, and the United Kingdom. Each pavilion must have at least one volunteer, with the requirement that two specific volunteers, A and B, do not work in the same pavilion. How m... | math | {
"style": "rule",
"ground_truth": "114"
} | {
"index": 8010,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Distribute 6 volunteers into 4 groups, with each group having at least 1 and at most 2 people, and assign them to four different exhibition areas of the fifth Asia-Europe Expo. The number of different allocation schemes is ______ (answer with a number)."
}
] | math | {
"style": "rule",
"ground_truth": "1080"
} | {
"index": 8011,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Distribute 61 books to a class of students. If at least one person must receive at least 3 books, what is the maximum number of students in the class?"
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 8012,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Distribute 7 students into two dormitories, A and B, with each dormitory having at least 2 students. How many different distribution plans are there?"
}
] | math | {
"style": "rule",
"ground_truth": "112"
} | {
"index": 8013,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Distribute five students, namely A, B, C, D, and E, to Peking University, Tsinghua University, and Renmin University of China for recommendation, with the condition that each university gets at least one student and student A cannot be recommended to Peking University. How many... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 8014,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divers extracted a certain number of pearls, not exceeding 1000. The distribution of the pearls happens as follows: each diver in turn approaches the heap of pearls and takes either exactly half or exactly one-third of the remaining pearls. After all divers have taken their sha... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 8015,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide 2 teachers and 6 students into 2 groups, each group consisting of 1 teacher and 3 students. Calculate the total number of different arrangements to assign them to locations A and B to participate in social practice activities."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 8016,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide 6 volunteers into 4 groups for service at four different venues of the 2012 London Olympics. Among these groups, 2 groups will have 2 people each, and the other 2 groups will have 1 person each. How many different allocation schemes are there? (Answer with a number)"
}... | math | {
"style": "rule",
"ground_truth": "540"
} | {
"index": 8017,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide 6 volunteers into 4 groups, with two groups having 2 people each and the other two groups having 1 person each, to serve at four different pavilions of the World Expo. How many different allocation schemes are there? (Answer with a number)."
}
] | math | {
"style": "rule",
"ground_truth": "1080"
} | {
"index": 8018,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide a 7-meter-long rope into 8 equal parts, each part is meters, and each part is of the whole rope. (Fill in the fraction)"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{8}"
} | {
"index": 8019,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide a circle with a circumference of 24 into 24 equal segments. Select 8 points from the 24 segment points such that the arc length between any two chosen points is not equal to 3 or 8. How many different ways are there to choose such a set of 8 points? Provide reasoning."
... | math | {
"style": "rule",
"ground_truth": "258"
} | {
"index": 8020,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide a square into 25 smaller squares, where 24 of these smaller squares are unit squares, and the remaining piece can also be divided into squares with a side length of 1. Find the area of the original square."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 8021,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide all coins into two parts of 20 coins each and weigh them. Since the number of fake coins is odd, one of the piles will be heavier. Thus, there is at most one fake coin in that pile. Divide it into two piles of 10 coins and weigh them. If the balance is even, then all 20 ... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 8022,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide an $m$-by-$n$ rectangle into $m n$ nonoverlapping 1-by-1 squares. A polyomino of this rectangle is a subset of these unit squares such that for any two unit squares $S, T$ in the polyomino, either (1) $S$ and $T$ share an edge or (2) there exists a positive integer $n$ s... | math | {
"style": "rule",
"ground_truth": "470"
} | {
"index": 8023,
"solution": "To span an $a \\times b$ rectangle, we need at least $a+b-1$ squares. Indeed, consider a square of the polyomino bordering the left edge of the rectangle and one bordering the right edge. There exists a path connecting these squares; suppose it runs through $c$ different rows. Then the... |
DeepScaleR | [
{
"role": "user",
"content": "Divide each natural number by the sum of the squares of its digits (for single-digit numbers, divide by the square of the number). Is there a smallest quotient among the obtained quotients, and if so, which one is it?"
}
] | math | {
"style": "rule",
"ground_truth": "1/9"
} | {
"index": 8024,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide every natural number with at least two digits by the sum of its digits! When will the quotient be the largest, and when will it be the smallest?"
}
] | math | {
"style": "rule",
"ground_truth": "1.9"
} | {
"index": 8025,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide the natural numbers from 1 to 30 into two groups such that the product $A$ of all numbers in the first group is divisible by the product $B$ of all numbers in the second group. What is the minimum value of $\\frac{A}{B}$?"
}
] | math | {
"style": "rule",
"ground_truth": "1077205"
} | {
"index": 8026,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide the natural numbers from 1 to 8 into two groups such that the product of all numbers in the first group is divisible by the product of all numbers in the second group. What is the minimum value of the quotient of the product of the first group divided by the product of t... | math | {
"style": "rule",
"ground_truth": "70"
} | {
"index": 8027,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide the numbers 1 through 10 into three groups such that the difference between any two numbers within the same group does not appear in that group. If one of the groups is {2, 5, 9}, then the sum of all the numbers in the group that contains 10 is $\\qquad$."
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"index": 8028,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide the product of the first five positive composite integers by the product of the next five composite integers. Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{42}"
} | {
"index": 8029,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide the product of the first six positive composite integers by the product of the next six composite integers. Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{49}"
} | {
"index": 8030,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide the sequence $\\{2n+1\\}$ cyclically into one-term, two-term, three-term, four-term groups as follows: $(3), (5,7), (9,11,13), (15,17,19,21), (23), (25,27), (29,31,33), (35,37,39,41), (43), \\cdots$. What is the sum of the numbers in the 100th group?"
}
] | math | {
"style": "rule",
"ground_truth": "1992"
} | {
"index": 8031,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide the sequence successively into groups with the first parenthesis containing one number, the second parenthesis two numbers, the third parenthesis three numbers, the fourth parenthesis four numbers, the fifth parenthesis one number, and so on in a cycle: $(3)$, $(5,7)$, $... | math | {
"style": "rule",
"ground_truth": "2072"
} | {
"index": 8032,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Divide the sides of a unit square \\(ABCD\\) into 5 equal parts. Let \\(D'\\) denote the second division point from \\(A\\) on side \\(AB\\), and similarly, let the second division points from \\(B\\) on side \\(BC\\), from \\(C\\) on side \\(CD\\), and from \\(D\\) on side \\(... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{29}"
} | {
"index": 8033,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Dizzy Daisy is standing on the point $(0,0)$ on the $xy$-plane and is trying to get to the point $(6,6)$. She starts facing rightward and takes a step 1 unit forward. On each subsequent second, she either takes a step 1 unit forward or turns 90 degrees counterclockwise then tak... | math | {
"style": "rule",
"ground_truth": "131922"
} | {
"index": 8034,
"solution": "Because Daisy can only turn in one direction and never goes to the same square twice, we see that she must travel in an increasing spiral about the origin. Clearly, she must arrive at $(6,6)$ coming from below. To count her paths, it therefore suffices to consider the horizontal and ve... |
DeepScaleR | [
{
"role": "user",
"content": "Does there exist a fraction equivalent to $\\frac{7}{13}$ such that the difference between the denominator and the numerator is 24?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{28}{52}"
} | {
"index": 8035,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Does there exist a natural number \\( n \\), greater than 1, such that the value of the expression \\(\\sqrt{n \\sqrt{n \\sqrt{n}}}\\) is a natural number?"
}
] | math | {
"style": "rule",
"ground_truth": "256"
} | {
"index": 8036,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Does there exist a point \\( M \\) on the parabola \\( y^{2} = 2px \\) such that the ratio of the distance from point \\( M \\) to the vertex and the distance from point \\( M \\) to the focus is maximized? If such a point \\( M \\) exists, find its coordinates and the maximum ... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{\\sqrt{3}}"
} | {
"index": 8037,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Does there exist a positive integer \\( m \\) such that the equation \\(\\frac{1}{a} + \\frac{1}{b} + \\frac{1}{c} + \\frac{1}{abc} = \\frac{m}{a+b+c}\\) has infinitely many solutions in positive integers \\( (a, b, c) \\)?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 8038,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Does there exist a six-digit number that increases by 6 times if its first three digits, without changing their order, are moved to the end of the number?"
}
] | math | {
"style": "rule",
"ground_truth": "142857"
} | {
"index": 8039,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Does there exist a three-digit number whose cube ends in three sevens?"
}
] | math | {
"style": "rule",
"ground_truth": "753"
} | {
"index": 8040,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Does there exist an integer \\( n \\) such that \\( 21n \\equiv 1 \\mod 74 \\)?"
}
] | math | {
"style": "rule",
"ground_truth": "67"
} | {
"index": 8041,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Dolly, Molly and Polly each can walk at $6 \\mathrm{~km} / \\mathrm{h}$. Their one motorcycle, which travels at $90 \\mathrm{~km} / \\mathrm{h}$, can accommodate at most two of them at once (and cannot drive by itself!). Let $t$ hours be the time taken for all three of them to ... | math | {
"style": "rule",
"ground_truth": "t<3.9"
} | {
"index": 8042,
"solution": "First, we note that the three people are interchangeable in this problem, so it does not matter who rides and who walks at any given moment. We abbreviate the three people as D, M and P. We call their starting point $A$ and their ending point $B$. Here is a strategy where all three peo... |
DeepScaleR | [
{
"role": "user",
"content": "Dolly, Molly, and Polly each can walk at $6 \\mathrm{~km} / \\mathrm{h}$. Their one motorcycle, which travels at $90 \\mathrm{~km} / \\mathrm{h}$, can accommodate at most two of them at once. What is true about the smallest possible time $t$ for all three of them to reach a poi... | math | {
"style": "rule",
"ground_truth": "t < 3.9"
} | {
"index": 8043,
"solution": "First, we note that the three people are interchangeable in this problem, so it does not matter who rides and who walks at any given moment. We abbreviate the three people as D, M, and P. We call their starting point $A$ and their ending point $B$. Here is a strategy where all three pe... |
DeepScaleR | [
{
"role": "user",
"content": "Don has a bottle of milk with $\\frac{1}{5}$ of a gallon of milk in it. Don's friend Rachel drinks $\\frac{2}{3}$ of the milk he has. How many gallons of milk did Rachel drink?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{15}"
} | {
"index": 8044,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Done with her new problems, Wendy takes a break from math. Still without any fresh reading material, she feels a bit antsy. She starts to feel annoyed that Michael's loose papers clutter the family van. Several of them are ripped, and bits of paper litter the floor. Tired of tr... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 8045,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Donna has $n$ boxes of doughnuts. Each box contains $13$ doughnuts.\n\nAfter eating one doughnut, Donna is able to rearrange the remaining doughnuts into bags so that each bag contains $9$ doughnuts, and none are left over. What is the smallest possible value of $n$?"
}
] | math | {
"style": "rule",
"ground_truth": "7"
} | {
"index": 8046,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Doraemon and Nobita are playing the game \"rock, paper, scissors.\" The rules state that the winner of each round receives two dorayakis, while the loser gets none. If there is a tie, each player receives one dorayaki. Nobita knows that Doraemon can only play \"rock,\" but he s... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 8047,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Dorothea has a $3 \\times 4$ grid of dots. She colors each dot red, blue, or dark gray. Compute the number of ways Dorothea can color the grid such that there is no rectangle whose sides are parallel to the grid lines and whose vertices all have the same color."
}
] | math | {
"style": "rule",
"ground_truth": "284688"
} | {
"index": 8048,
"solution": "To find an appropriate estimate, we will lower bound the number of rectangles. Let $P(R)$ be the probability a random 3 by 4 grid will have a rectangle with all the same color in the grid. Let $P(r)$ be the probability that a specific rectangle in the grid will have the same color. Not... |
DeepScaleR | [
{
"role": "user",
"content": "Dots are placed two units apart both horizontally and vertically on a coordinate grid. Calculate the number of square units enclosed by the polygon formed by connecting these dots: \n[asy]\nsize(90);\npair a=(0,0), b=(20,0), c=(20,20), d=(40,20), e=(40,40), f=(20,40), g=(0,40),... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 8049,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Dots are spaced one unit part, horizontally and vertically. What is the number of square units enclosed by the polygon?\n[asy]\n/* AMC8 1998 #6P */\nsize(1inch,1inch);\npair a=(0,0), b=(10,0), c=(20,0), d=(30, 0);\npair e=(0,10), f=(10,10), g=(20,10), h=(30,10);\npair i=(0,20),... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"index": 8050,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Doug and Dave shared a pizza with $8$ equally-sized slices. Doug wanted a plain pizza, but Dave wanted anchovies on half the pizza. The cost of a plain pizza was $8$ dollars, and there was an additional cost of $2$ dollars for putting anchovies on one half. Dave ate all the sli... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"index": 8051,
"solution": "1. **Calculate the total cost of the pizza:** \n The pizza is plain and costs $8$ dollars. Adding anchovies to half of it costs an additional $2$ dollars. Therefore, the total cost of the pizza is:\n \\[\n 8 + 2 = 10 \\text{ dollars}\n \\]\n\n2. **Determine the cost per slice:... |
DeepScaleR | [
{
"role": "user",
"content": "Doug and Ryan are competing in the 2005 Wiffle Ball Home Run Derby. In each round, each player takes a series of swings. Each swing results in either a home run or an out, and an out ends the series. When Doug swings, the probability that he will hit a home run is $1 / 3$. When... | math | {
"style": "rule",
"ground_truth": "1/5"
} | {
"index": 8052,
"solution": "Denote this probability by $p$. Doug hits more home runs if he hits a home run on his first try when Ryan does not, or if they both hit home runs on their first try and Doug hits more home runs thereafter. The probability of the first case occurring is $\\frac{1}{3} \\cdot \\frac{1}{2}... |
DeepScaleR | [
{
"role": "user",
"content": "Doug constructs a square window using $8$ equal-size panes of glass. The ratio of the height to width for each pane is $5 : 2$, and the borders around and between the panes are $2$ inches wide. In inches, what is the side length of the square window?"
}
] | math | {
"style": "rule",
"ground_truth": "26"
} | {
"index": 8053,
"solution": "1. **Identify the dimensions of each pane**: Given that the ratio of the height to the width of each pane is $5:2$, let the height of each pane be $5x$ inches and the width be $2x$ inches.\n\n2. **Calculate the total dimensions of the window**: The window is constructed with $8$ panes ... |
DeepScaleR | [
{
"role": "user",
"content": "Doug constructs a square window using $8$ equal-size panes of glass. The ratio of the height to width for each pane is $5 : 2$, and the borders around and between the panes are $2$ inches wide. In inches, what is the side length of the square window?"
}
] | math | {
"style": "rule",
"ground_truth": "26"
} | {
"index": 8054,
"solution": "1. **Identify the dimensions of each pane**: Given that the ratio of the height to width for each pane is $5:2$, let the width of each pane be $2x$ and the height be $5x$.\n\n2. **Calculate the total width and height of the window**: The window is composed of $4$ panes across and $2$ p... |
DeepScaleR | [
{
"role": "user",
"content": "Dr. Fu Manchu has a bank account that has an annual interest rate of 6 percent, but it compounds monthly. If this is equivalent to a bank account that compounds annually at a rate of $r$ percent, then what is $r$? (Give your answer to the nearest hundredth.)"
}
] | math | {
"style": "rule",
"ground_truth": "6.17"
} | {
"index": 8055,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Dr. Green gives bonus points on a test for students who score above the class average. In a class of 150 students, what is the maximum number of students who can score above the average if their scores are integers?"
}
] | math | {
"style": "rule",
"ground_truth": "149"
} | {
"index": 8056,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Dr. Math's four-digit house number $ABCD$ contains no zeroes and can be split into two different two-digit primes ``$AB$'' and ``$CD$'' where the digits $A$, $B$, $C$ and $D$ are not necessarily distinct. If each of the two-digit primes is less than 40, how many such house numb... | math | {
"style": "rule",
"ground_truth": "56"
} | {
"index": 8057,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Dr. Math's four-digit house number $ABCD$ contains no zeroes and can be split into two different two-digit primes ``$AB$'' and ``$CD$''. Moreover, both these two-digit primes are greater than 50 but less than 100. Find the total number of possible house numbers for Dr. Math."
... | math | {
"style": "rule",
"ground_truth": "90"
} | {
"index": 8058,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Dr. Math's four-digit house number $WXYZ$ contains no zeroes and can be split into two different two-digit primes ``$WX$'' and ``$YZ$'' where the digits $W$, $X$, $Y$, and $Z$ are not necessarily distinct. If each of the two-digit primes is less than 50, how many such house num... | math | {
"style": "rule",
"ground_truth": "110"
} | {
"index": 8059,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Dr. Math's four-digit house number $WXYZ$ contains no zeroes and can be split into two different two-digit primes ``$WX$'' and ``$YZ$'' where the digits $W$, $X$, $Y$, and $Z$ are not necessarily distinct. If each of the two-digit primes is less than 60, how many such house num... | math | {
"style": "rule",
"ground_truth": "156"
} | {
"index": 8060,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Dr. Math's house number $WXYZ$ is a four-digit number where each digit $W$, $X$, $Y$, and $Z$ is non-zero, and the two portions of the house number, $WX$ and $YZ$, form two-digit primes. Every prime number selected must be less than 50. Additionally, the sum of the digits in $Y... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 8061,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Dragoons take up \\(1 \\times 1\\) squares in the plane with sides parallel to the coordinate axes such that the interiors of the squares do not intersect. A dragoon can fire at another dragoon if the difference in the \\(x\\)-coordinates of their centers and the difference in ... | math | {
"style": "rule",
"ground_truth": "168"
} | {
"index": 8062,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Draw a $2004 \\times 2004$ array of points. What is the largest integer $n$ for which it is possible to draw a convex $n$-gon whose vertices are chosen from the points in the array?"
}
] | math | {
"style": "rule",
"ground_truth": "561"
} | {
"index": 8063,
"solution": "\nTo determine the largest integer \\( n \\) for which it is possible to draw a convex \\( n \\)-gon whose vertices are chosen from the points in a \\( 2004 \\times 2004 \\) array, we need to consider the properties of the convex hull and the arrangement of points.\n\nGiven the array o... |
DeepScaleR | [
{
"role": "user",
"content": "Draw a perpendicular line from the left focus $F_1$ of the ellipse $\\frac {x^{2}}{a^{2}}+ \\frac {y^{2}}{b^{2}}=1 (a > b > 0)$ to the $x$-axis meeting the ellipse at point $P$, and let $F_2$ be the right focus. If $\\angle F_{1}PF_{2}=60^{\\circ}$, calculate the eccentricity o... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{3}"
} | {
"index": 8064,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Draw a rectangle. Connect the midpoints of the opposite sides to get 4 congruent rectangles. Connect the midpoints of the lower right rectangle for a total of 7 rectangles. Repeat this process infinitely. Let $n$ be the minimum number of colors we can assign to the rectangles s... | math | {
"style": "rule",
"ground_truth": "(3,4)"
} | {
"index": 8065,
"solution": "$(3,4) \\text {. }$"
} |
DeepScaleR | [
{
"role": "user",
"content": "Draw a square of side length 1. Connect its sides' midpoints to form a second square. Connect the midpoints of the sides of the second square to form a third square. Connect the midpoints of the sides of the third square to form a fourth square. And so forth. What is the sum of... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 8066,
"solution": "The area of the first square is 1, the area of the second is $\\frac{1}{2}$, the area of the third is $\\frac{1}{4}$, etc., so the answer is $1+\\frac{1}{2}+\\frac{1}{4}+\\frac{1}{8}+\\cdots=2$."
} |
DeepScaleR | [
{
"role": "user",
"content": "Draw a tangent line MN to the circle $(x-2)^2+(y-2)^2=1$ at point N, where N is the point of tangency. If $|MN|=|MO|$ (where O is the origin), then the minimum value of $|MN|$ is \\_\\_\\_\\_\\_\\_."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7\\sqrt{2}}{8}"
} | {
"index": 8067,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Draw five lines \\( l_1, l_2, \\cdots, l_5 \\) on a plane such that no two lines are parallel and no three lines pass through the same point.\n(1) How many intersection points are there in total among these five lines? How many intersection points are there on each line? How ma... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 8068,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Driving along a highway, Megan noticed that her odometer showed $15951$ (miles). This number is a palindrome-it reads the same forward and backward. Then $2$ hours later, the odometer displayed the next higher palindrome. What was her average speed, in miles per hour, during th... | math | {
"style": "rule",
"ground_truth": "55"
} | {
"index": 8069,
"solution": "1. **Identify the initial and final odometer readings**: Megan's odometer initially reads $15951$, a palindrome. After $2$ hours, it shows the next higher palindrome.\n\n2. **Determine the next palindrome**: To find the smallest palindrome greater than $15951$, we consider the structur... |
DeepScaleR | [
{
"role": "user",
"content": "Driving at a constant speed, Sharon usually takes $180$ minutes to drive from her house to her mother's house. One day Sharon begins the drive at her usual speed, but after driving $\\frac{1}{3}$ of the way, she hits a bad snowstorm and reduces her speed by $20$ miles per hour.... | math | {
"style": "rule",
"ground_truth": "135"
} | {
"index": 8070,
"solution": "1. **Define Variables:**\n Let the total distance from Sharon's house to her mother's house be $x$ miles. \n\n2. **Calculate Speeds:**\n Sharon's usual speed is $\\frac{x}{180}$ miles per minute, since she normally takes 180 minutes to cover $x$ miles.\n\n3. **Distance and Speed Ad... |
DeepScaleR | [
{
"role": "user",
"content": "Druv has a $33 \\times 33$ grid of unit squares, and he wants to color each unit square with exactly one of three distinct colors such that he uses all three colors and the number of unit squares with each color is the same. However, he realizes that there are internal sides,... | math | {
"style": "rule",
"ground_truth": "66"
} | {
"index": 8071,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Due to a snow and ice disaster, a citrus orchard suffered severe damage. To address this, experts proposed a rescue plan for the fruit trees, which needs to be implemented over two years and is independent each year. The plan estimates that in the first year, the probability of... | math | {
"style": "rule",
"ground_truth": "0.2"
} | {
"index": 8072,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Due to the increasing personnel exchanges between Hefei and Nanjing as a result of urban development, there is a plan to build a dedicated railway to alleviate traffic pressure, using a train as a shuttle service. It is known that the daily round-trip frequency $y$ of the train... | math | {
"style": "rule",
"ground_truth": "7920"
} | {
"index": 8073,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During a break between voyages, a sailor turned 20 years old. All six crew members gathered in the cabin to celebrate. \"I am twice the age of the cabin boy and 6 years older than the engineer,\" said the helmsman. \"And I am as much older than the cabin boy as I am younger tha... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 8074,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During a break, a fly entered the math classroom and began crawling on a poster depicting the graph of a quadratic function \\( y = f(x) \\) with a leading coefficient of -1. Initially, the fly moved exactly along the parabola to the point with an abscissa of 2, but then starte... | math | {
"style": "rule",
"ground_truth": "6070"
} | {
"index": 8075,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During a class's May Day gathering, the original program schedule included 5 events. Just before the performance, 2 additional events were added. If these 2 new events are to be inserted into the original schedule, how many different insertion methods are there?"
}
] | math | {
"style": "rule",
"ground_truth": "42"
} | {
"index": 8076,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During a fireworks display, a body is launched upwards with an initial velocity of $c=90 \\mathrm{m/s}$. We hear its explosion $t=5$ seconds later. At what height did it explode if the speed of sound is $a=340 \\mathrm{m/s}$? (Air resistance is neglected.)"
}
] | math | {
"style": "rule",
"ground_truth": "289"
} | {
"index": 8077,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During a journey, the distance read on the odometer was 450 miles. On the return trip, using snow tires for the same distance, the reading was 440 miles. If the original wheel radius was 15 inches, find the increase in the wheel radius, correct to the nearest hundredth of an in... | math | {
"style": "rule",
"ground_truth": "0.34"
} | {
"index": 8078,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During a long voyage of a passenger ship, it was observed that at each dock, a quarter of the passenger composition is renewed, that among the passengers leaving the ship, only one out of ten boarded at the previous dock, and finally, that the ship is always fully loaded.\n\nDe... | math | {
"style": "rule",
"ground_truth": "21/40"
} | {
"index": 8079,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During a math competition organized in a certain city, the scores of all participating students approximately follow a normal distribution $N(60, 100)$. It is known that there are 13 students who scored 90 or above.\n(1) Calculate the total number of students who participated i... | math | {
"style": "rule",
"ground_truth": "80"
} | {
"index": 8080,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During a performance, a panda named A Bao is performing on stilts. A Bao's height accounts for $\\frac{1}{4}$ of the total height when he is standing on the stilts. During the performance, A Bao accidentally breaks $20$ dm off each stilt. After the break, A Bao's height account... | math | {
"style": "rule",
"ground_truth": "160"
} | {
"index": 8081,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During a recent campaign for office, a candidate made a tour of a country which we assume lies in a plane. On the first day of the tour he went east, on the second day he went north, on the third day west, on the fourth day south, on the fifth day east, etc. If the candidate we... | math | {
"style": "rule",
"ground_truth": "580"
} | {
"index": 8082,
"solution": "On the first day, the candidate moves $[4(0) + 1]^2/2\\ \\text{east},\\, [4(0) + 2]^2/2\\ \\text{north},\\, [4(0) + 3]^2/2\\ \\text{west},\\, [4(0) + 4]^2/2\\ \\text{south}$, and so on. The E/W displacement is thus $1^2 - 3^2 + 5^2 \\ldots +37^2 - 39^2 = \\left|\\sum_{i=0}^9 \\frac{(4i... |
DeepScaleR | [
{
"role": "user",
"content": "During a secret meeting, 20 trainees elect their favorite supervisor. Each trainee votes for two supervisors. It is known that for any two trainees, there is always at least one supervisor for whom both have voted. What is the minimum number of votes received by the supervisor ... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 8083,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During a space experiment conducted by astronauts, they must implement a sequence of 6 procedures. Among them, Procedure A can only occur as the first or the last step, and Procedures B and C must be adjacent when conducted. How many different sequences are there to arrange the... | math | {
"style": "rule",
"ground_truth": "96"
} | {
"index": 8084,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During a survey of 500 people, it was found that $46\\%$ of the respondents like strawberry ice cream, $71\\%$ like vanilla ice cream, and $85\\%$ like chocolate ice cream. Are there at least six respondents who like all three types of ice cream?"
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 8085,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During a year when Valentine's Day, February 14, falls on a Tuesday, what day of the week is Cinco de Mayo (May 5) and how many days are between February 14 and May 5 inclusively?"
}
] | math | {
"style": "rule",
"ground_truth": "81"
} | {
"index": 8086,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During an underwater archaeological activity, a diver needs to dive $50$ meters to the bottom of the water for archaeological work. The oxygen consumption consists of the following three aspects: $(1)$ The average diving speed is $x$ meters/minute, and the oxygen consumption pe... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 8087,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During an underwater archaeology activity, a diver needs to dive 50 meters to the seabed to carry out archaeological work. The oxygen consumption includes the following three aspects: \n1. The average descent speed is $x$ meters per minute, and the oxygen consumption per minute... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 8088,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During breaks, schoolchildren played table tennis. Any two schoolchildren played no more than one game against each other. At the end of the week, it turned out that Petya played half, Kolya - a third, and Vasya - one fifth of the total number of games played during the week. W... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 8089,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During her birthday, her parents have decided to give Laura and her 2 younger brothers new cellphones. However, they are confused between the innumerable service providers. Assuming no child wants a provider that another sibling has, and that there are 20 service providers, in... | math | {
"style": "rule",
"ground_truth": "6840"
} | {
"index": 8090,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During intervals, students played table tennis. Any two students played against each other no more than one game. At the end of the week, it turned out that Petya played half, Kolya played a third, and Vasya played a fifth of all the games played during the week. How many games... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 8091,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During the \"Cool Summer Happy Shopping\" promotion held in a certain shopping mall, Xiao Yang bought $m$ items of type A goods priced at $5$ yuan each, and $n$ items of type B goods priced at $17 yuan each, spending a total of $203$ yuan. Then the maximum value of $m+n$ is ___... | math | {
"style": "rule",
"ground_truth": "31"
} | {
"index": 8092,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During the 2011 Universiade in Shenzhen, a 12-person tour group initially stood in two rows with 4 people in the front row and 8 people in the back row. The photographer plans to keep the order of the front row unchanged, and move 2 people from the back row to the front row, en... | math | {
"style": "rule",
"ground_truth": "560"
} | {
"index": 8093,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During the 2013 National Day, a city organized a large-scale group calisthenics performance involving 2013 participants, all of whom were students from the third, fourth, and fifth grades. The students wore entirely red, white, or blue sports uniforms. It was known that the fou... | math | {
"style": "rule",
"ground_truth": "213"
} | {
"index": 8094,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During the Double 11 shopping festival, a certain online store purchased two types of toys, $A$ and $B$, directly from the factory. The purchase price and selling price are as shown in the table: (Note: Profit = Selling Price - Purchase Price)\n\n| | $A$ toy | $B$ toy ... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 8095,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During the FIFA World Cup in Russia, a certain store sells a batch of football commemorative books. The cost price of each book is $40$ yuan, and the selling price is set not less than $44$ yuan, with a profit margin not exceeding $30\\%$. It was found during the sales period t... | math | {
"style": "rule",
"ground_truth": "2640"
} | {
"index": 8096,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During the National Day holiday, a fruit company organized 20 cars to transport three types of fruits, $A$, $B$, and $C$, totaling 120 tons for sale in other places. It is required that all 20 cars be fully loaded, each car can only transport the same type of fruit, and each ty... | math | {
"style": "rule",
"ground_truth": "198900"
} | {
"index": 8097,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During the National Day military parade, the marching sequences of three formations, namely A, B, and C, pass by the viewing stand in a certain order. If the order is randomly arranged, the probability that B passes before both A and C is ( )."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"index": 8098,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "During the New Year's Day holiday of 2018, 8 high school students from four different classes, each with 2 students, plan to carpool for a trip. Classes are denoted as (1), (2), (3), and (4). They will be divided between two cars, Car A and Car B, each with a capacity for 4 stu... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 8099,
"solution": ""
} |
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