data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "There are 4 boys and 3 girls standing in a row. (You must write down the formula before calculating the result to score points) \n(Ⅰ) If the 3 girls must stand together, how many different arrangements are there? \n(Ⅱ) If no two girls are next to each other, how many differen... | math | {
"style": "rule",
"ground_truth": "720"
} | {
"index": 35100,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 children and 2 coaches in the Chess Interest Group of Hongxing Primary School. The ages of the 4 children differ by 2 years sequentially, and the ages of the 2 coaches differ by 2 years. The sum of the squares of the ages of the 6 people is 2796 years. What is the s... | math | {
"style": "rule",
"ground_truth": "106"
} | {
"index": 35101,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 college entrance examination candidates entering the school through 2 different intelligent security gates. Each security gate can only allow 1 person to pass at a time. It is required that each security gate must have someone passing through. Then there are ______ ... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"index": 35102,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 different colors of light bulbs, with each color representing a different signal. Assuming there is an ample supply of each color, we need to install one light bulb at each vertex $P, A, B, C, A_{1}, B_{1}, C_{1}$ of an airport signal tower (as shown in the diagram)... | math | {
"style": "rule",
"ground_truth": "2916"
} | {
"index": 35103,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 different digits that can form 18 different four-digit numbers arranged in ascending order. The first four-digit number is a perfect square, and the second-last four-digit number is also a perfect square. What is the sum of these two numbers?"
}
] | math | {
"style": "rule",
"ground_truth": "10890"
} | {
"index": 35104,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 different points \\( A, B, C, D \\) on two non-perpendicular skew lines \\( a \\) and \\( b \\), where \\( A \\in a \\), \\( B \\in a \\), \\( C \\in b \\), and \\( D \\in b \\). Consider the following two propositions:\n(1) Line \\( AC \\) and line \\( BD \\) are a... | math | {
"style": "rule",
"ground_truth": "(1)(2)"
} | {
"index": 35105,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 distinct balls and 4 distinct boxes. All the balls need to be placed into the boxes.\n(1) If exactly one box remains empty, how many different arrangements are possible?\n(2) If exactly two boxes remain empty, how many different arrangements are possible?"
}
] | math | {
"style": "rule",
"ground_truth": "84"
} | {
"index": 35106,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 male and 2 female volunteers, a total of 6 volunteers, and 2 elderly people standing in a row for a group photo. The photographer requests that the two elderly people stand next to each other in the very center, with the two female volunteers standing immediately to... | math | {
"style": "rule",
"ground_truth": "96"
} | {
"index": 35107,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 male students and 2 female students taking the photo. The male student named \"甲\" cannot stand at either end, and the female students must stand next to each other. Find the number of ways to arrange the students."
}
] | math | {
"style": "rule",
"ground_truth": "144"
} | {
"index": 35108,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 people in the family. If Masha's scholarship is doubled, the total family income will increase by 5%. If the mother's salary is doubled instead, the total family income will increase by 15%. If the father's salary is doubled, the total family income will increase by... | math | {
"style": "rule",
"ground_truth": "55"
} | {
"index": 35109,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 pieces of part $A$ weighing 5 tons each, 6 pieces of part $B$ weighing 4 tons each, 11 pieces of part $C$ weighing 3 tons each, and 7 pieces of part $D$ weighing 1 ton each. If all the parts are to be transported at once, what is the minimum number of trucks, each w... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 35110,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 problems in a mathematics competition. The scores are allocated as follows: 2 marks for a correct answer, -1 mark for a wrong answer, and 0 marks for a blank answer. To ensure that 3 candidates will have the same scores, how many candidates, denoted as $S$, must the... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 35111,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 representatives from each of 4 companies at a convention. At the start of the convention, every person shakes hands once with every person except the other representatives from their company. How many handshakes are there?"
}
] | math | {
"style": "rule",
"ground_truth": "96"
} | {
"index": 35112,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 spheres in space with radii 2, 2, 3, and 3, respectively. Each sphere is externally tangent to the other 3 spheres. Additionally, there is a small sphere that is externally tangent to all 4 of these spheres. Find the radius of the small sphere."
}
] | math | {
"style": "rule",
"ground_truth": "6/11"
} | {
"index": 35113,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 white tiles, 4 yellow tiles, and 8 green tiles, all of which are square tiles with a side length of 1. These tiles are used to create square patterns with a side length of 4. How many different patterns can be created?"
}
] | math | {
"style": "rule",
"ground_truth": "900900"
} | {
"index": 35114,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 willow trees and 4 poplar trees planted in a row. How many ways can they be planted alternately?"
}
] | math | {
"style": "rule",
"ground_truth": "1152"
} | {
"index": 35115,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 40 identical looking coins, among which 3 are counterfeit - they weigh the same and are lighter than the genuine coins (the genuine coins also weigh the same). How can you use three weighings on a balance scale without weights to select 16 genuine coins?"
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 35116,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 400 students at Pascal H.S., where the ratio of boys to girls is $3: 2$. There are 600 students at Fermat C.I., where the ratio of boys to girls is $2: 3$. What is the ratio of boys to girls when considering all students from both schools?"
}
] | math | {
"style": "rule",
"ground_truth": "12:13"
} | {
"index": 35117,
"solution": "Since the ratio of boys to girls at Pascal H.S. is $3: 2$, then $\frac{3}{3+2}=\frac{3}{5}$ of the students at Pascal H.S. are boys. Thus, there are $\frac{3}{5}(400)=\frac{1200}{5}=240$ boys at Pascal H.S. Since the ratio of boys to girls at Fermat C.I. is $2: 3$, then $\frac{2}{2+3}... |
DeepScaleR | [
{
"role": "user",
"content": "There are 42 stepping stones in a pond, arranged along a circle. You are standing on one of the stones. You would like to jump among the stones so that you move counterclockwise by either 1 stone or 7 stones at each jump. Moreover, you would like to do this in such a way that y... | math | {
"style": "rule",
"ground_truth": "63"
} | {
"index": 35118,
"solution": "Number the stones $0,1, \\ldots, 41$, treating the numbers as values modulo 42, and let $r_{n}$ be the length of your jump from stone $n$. If you jump from stone $n$ to $n+7$, then you cannot jump from stone $n+6$ to $n+7$ and so must jump from $n+6$ to $n+13$. That is, if $r_{n}=7$, ... |
DeepScaleR | [
{
"role": "user",
"content": "There are 456 natives on an island, each of whom is either a knight who always tells the truth or a liar who always lies. All residents have different heights. Once, each native said, \"All other residents are shorter than me!\" What is the maximum number of natives who could h... | math | {
"style": "rule",
"ground_truth": "454"
} | {
"index": 35119,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 46 ones written on the board. Each minute, Carlson erases any two numbers and writes their sum on the board, then eats a number of candies equal to the product of the two erased numbers. What is the maximum number of candies he could eat in 46 minutes?"
}
] | math | {
"style": "rule",
"ground_truth": "1035"
} | {
"index": 35120,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 49 children, each wearing a unique number from 1 to 49 on their chest. Select several children and arrange them in a circle such that the product of the numbers of any two adjacent children is less than 100. What is the maximum number of children you can select?"
}
... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 35121,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 49 ones written on a board. Each minute, Karlson erases any two numbers and writes their sum on the board, then he eats a number of candies equal to the product of the two erased numbers. What is the maximum number of candies he could eat in 49 minutes?"
}
] | math | {
"style": "rule",
"ground_truth": "1176"
} | {
"index": 35122,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 balls numbered $(1)$, $(2)$, $(3)$, $(4)$, $(5)$ and 5 boxes numbered $(1)$, $(2)$, $(3)$, $(4)$, $(5)$. Each box contains one ball. The number of ways in which at most two balls have the same number as their respective boxes is $\\_\\_\\_\\_\\_\\_$."
}
] | math | {
"style": "rule",
"ground_truth": "109"
} | {
"index": 35123,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 balls of the same shape and size in a bag, including 3 red balls and 2 yellow balls. Now, balls are randomly drawn from the bag one at a time until two different colors of balls are drawn. Let the random variable $\\xi$ be the number of balls drawn at this time. Fin... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{2}"
} | {
"index": 35124,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 blue chips and 3 yellow chips in a bag. One chip is drawn from the bag. That chip is placed back into the bag. A second chip is then drawn. What is the probability that the two selected chips are of different colors? Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{15}{32}"
} | {
"index": 35125,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 blue chips, 4 red chips and 3 yellow chips in a bag. One chip is drawn from the bag. That chip is placed back into the bag, and a second chip is drawn. What is the probability that the two selected chips are of different colors? Express your answer as a common fract... | math | {
"style": "rule",
"ground_truth": "\\frac{47}{72}"
} | {
"index": 35126,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 different books to be distributed among three people, with each person receiving at least 1 book and at most 2 books. Calculate the total number of different distribution methods."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"index": 35127,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 different types of books, with at least 3 copies of each. If we want to buy 3 books to gift to 3 students, with each student receiving one book, how many different ways are there to do this?"
}
] | math | {
"style": "rule",
"ground_truth": "125"
} | {
"index": 35128,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 female students and 2 male students in a class. Find the number of different distribution schemes in which they can be divided into two groups, with each group having both female and male students."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 35129,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 girls sitting in a row on five chairs, and opposite them, on five chairs, there are 5 boys sitting. It was decided that the boys would switch places with the girls. In how many ways can this be done?"
}
] | math | {
"style": "rule",
"ground_truth": "14400"
} | {
"index": 35130,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 integers written on a board. By summing them pairwise, the following set of 10 numbers is obtained: \\( 5, 9, 10, 11, 12, 16, 16, 17, 21, 23 \\). Determine which numbers are written on the board. Provide the product of these numbers in your answer."
}
] | math | {
"style": "rule",
"ground_truth": "5292"
} | {
"index": 35131,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 integers written on the board. By summing them in pairs, the following set of 10 numbers is obtained: 2, 6, 10, 10, 12, 14, 16, 18, 20, 24. Determine which numbers are written on the board and write their product as the answer."
}
] | math | {
"style": "rule",
"ground_truth": "-3003"
} | {
"index": 35132,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 integers written on the board. The sums of these integers taken in pairs resulted in the following set of 10 numbers: $6, 9, 10, 13, 13, 14, 17, 17, 20, 21$. Determine which numbers are written on the board. Provide their product as the answer."
}
] | math | {
"style": "rule",
"ground_truth": "4320"
} | {
"index": 35133,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 people seated at a circular table. What is the probability that Angie and Carlos are seated directly opposite each other?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 35134,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 people standing in a row, where A and B must stand next to each other, and C and D cannot stand next to each other. How many different arrangements are there?"
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 35135,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 people standing in a row. If person A is not at the left end and not adjacent to person B, determine the number of possible arrangements."
}
] | math | {
"style": "rule",
"ground_truth": "54"
} | {
"index": 35136,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 people standing in a row. The number of ways to arrange them so that there is exactly one person between A and B."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 35137,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 students on a team for a math competition. The math competition has 5 subject tests. Each student on the team must choose 2 distinct tests, and each test must be taken by exactly two people. In how many ways can this be done?"
}
] | math | {
"style": "rule",
"ground_truth": "2040"
} | {
"index": 35138,
"solution": "We can model the situation as a bipartite graph on 10 vertices, with 5 nodes representing the students and the other 5 representing the tests. We now simply want to count the number of bipartite graphs on these two sets such that there are two edges incident on each vertex. Notice tha... |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 students taking a test, and each student's score ($a, b, c, d, e$) is an integer between 0 and 100 inclusive. It is known that $a \\leq b \\leq c \\leq d \\leq e$. If the average score of the 5 students is $p$, then the median score $c$ is at least $\\qquad$ ."
}
... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 35139,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 students who signed up to participate in a two-day volunteer activity at the summer district science museum. Each day, two students are needed for the activity. The probability that exactly 1 person will participate in the volunteer activity for two consecutive days... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"index": 35140,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 weights. Their masses are 1000 g, 1001 g, 1002 g, 1004 g, and 1007 g, but they have no markings and are visually indistinguishable. There is a scale with a pointer that shows the mass in grams. How can you determine the 1000 g weight using three weighings?"
}
] | math | {
"style": "rule",
"ground_truth": "1000"
} | {
"index": 35141,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 5 yellow pegs, 4 red pegs, 3 green pegs, 2 blue pegs, and 1 orange peg to be placed on a triangular peg board. In how many ways can the pegs be placed so that no (horizontal) row or (vertical) column contains two or more pegs of the same color? (Any two pegs of the s... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 35142,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 500 machines, each using 6 parts of the same type. These parts must be replaced by the end of the week if they fail. Out of all new parts, 10% fail by the end of the first week, 30% fail by the end of the second week, and the remaining 60% fail by the end of the third... | math | {
"style": "rule",
"ground_truth": "3000"
} | {
"index": 35143,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 52 students in a class. Now, using the systematic sampling method, a sample of size 4 is drawn. It is known that the seat numbers in the sample are 6, X, 30, and 42. What should be the seat number X?"
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 35144,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 54 chips in a box. Each chip is either small or large. If the number of small chips is greater than the number of large chips by a prime number of chips, what is the greatest possible number of large chips?"
}
] | math | {
"style": "rule",
"ground_truth": "26"
} | {
"index": 35145,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 54 students in a class, and there are 4 tickets for the Shanghai World Expo. Now, according to the students' ID numbers, the tickets are distributed to 4 students through systematic sampling. If it is known that students with ID numbers 3, 29, and 42 have been selecte... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 35146,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 55 points marked on a plane: the vertices of a regular 54-gon and its center. Petya wants to color a set of three marked points in red so that the colored points form the vertices of a regular triangle. In how many ways can Petya do this?"
}
] | math | {
"style": "rule",
"ground_truth": "72"
} | {
"index": 35147,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 552 weights with masses of 1g, 2g, 3g, ..., 552g. Divide them into three equal weight piles."
}
] | math | {
"style": "rule",
"ground_truth": "50876"
} | {
"index": 35148,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 6 balls of each of the four colors: red, blue, yellow, and green. Each set of 6 balls of the same color is numbered from 1 to 6. If 3 balls with different numbers are randomly selected, and these 3 balls have different colors and their numbers are not consecutive, the... | math | {
"style": "rule",
"ground_truth": "96"
} | {
"index": 35149,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 6 blue, 7 red, and 9 white light bulbs. In how many ways can you arrange them (using all the light bulbs) in a garland so that no two white light bulbs are consecutive?"
}
] | math | {
"style": "rule",
"ground_truth": "3435432"
} | {
"index": 35150,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 6 boxes, each containing a key that cannot be used interchangeably. If one key is placed in each box and all the boxes are locked, and it is required that after breaking open one box, the remaining 5 boxes can still be opened with the keys, then the number of ways to ... | math | {
"style": "rule",
"ground_truth": "120"
} | {
"index": 35151,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"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 f... | math | {
"style": "rule",
"ground_truth": "96"
} | {
"index": 35152,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"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 suitcases are opened? How many attempts are needed if there are 10 suitcases and 10 keys?"
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"index": 35153,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 6 male doctors and 4 female doctors. From them, 3 male doctors and 2 female doctors are selected to provide medical services in 5 different regions. It is specified that male doctor A cannot go to region A. How many different assignment plans are there in total?"
}
... | math | {
"style": "rule",
"ground_truth": "12960"
} | {
"index": 35154,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 6 married couples at a party. At the start of the party, every person shakes hands once with every other person except his or her spouse. How many handshakes are there?"
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 35155,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 6 people including A, B, and C standing in a row for a photo, where A cannot stand at either end, and B and C must stand next to each other. How many such arrangements are there?"
}
] | math | {
"style": "rule",
"ground_truth": "144"
} | {
"index": 35156,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 6 rectangular prisms with edge lengths of \\(3 \\text{ cm}\\), \\(4 \\text{ cm}\\), and \\(5 \\text{ cm}\\). The faces of these prisms are painted red in such a way that one prism has only one face painted, another has exactly two faces painted, a third prism has exac... | math | {
"style": "rule",
"ground_truth": "177"
} | {
"index": 35157,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 6 seats in a row and 3 people taking their seats, find the number of different ways of seating them such that there are exactly two adjacent empty seats."
}
] | math | {
"style": "rule",
"ground_truth": "72"
} | {
"index": 35158,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 60 empty boxes $B_1,\\ldots,B_{60}$ in a row on a table and an unlimited supply of pebbles. Given a positive integer $n$, Alice and Bob play the following game.\nIn the first round, Alice takes $n$ pebbles and distributes them into the 60 boxes as she wishes. Each sub... | math | {
"style": "rule",
"ground_truth": "960"
} | {
"index": 35159,
"solution": "To solve this problem, we need to find the smallest integer \\( n \\) such that Alice can always prevent Bob from winning regardless of how the game progresses. The setup is as follows:\n\n1. Alice and Bob are playing a game with 60 boxes, \\( B_1, B_2, \\ldots, B_{60} \\), and an unl... |
DeepScaleR | [
{
"role": "user",
"content": "There are 7 balls of each of the three colors: red, blue, and yellow. When randomly selecting 3 balls with different numbers, determine the total number of ways to pick such that the 3 balls are of different colors and their numbers are not consecutive."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 35160,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 7 cards, each with a number written on it: 1, 2, 2, 3, 4, 5, 6. Three cards are randomly drawn from these 7 cards. Let the minimum value of the numbers on the drawn cards be $\\xi$. Find $P\\left(\\xi =2\\right)=$____ and $E\\left(\\xi \\right)=$____."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{12}{7}"
} | {
"index": 35161,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 7 cylindrical logs with a diameter of 5 decimeters each. They are tied together at two places using a rope. How many decimeters of rope are needed at least (excluding the rope length at the knots, and using $\\pi$ as 3.14)?"
}
] | math | {
"style": "rule",
"ground_truth": "91.4"
} | {
"index": 35162,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 7 light bulbs arranged in a row. It is required to light up at least 3 of the bulbs, and adjacent bulbs cannot be lit at the same time. Determine the total number of different ways to light up the bulbs."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 35163,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 7 line segments with integer lengths in centimeters: $a_1$, $a_2$, $a_3$, $a_4$, $a_5$, $a_6$, $a_7$, satisfying $a_1 < a_2 < a_3 < a_4 < a_5 < a_6 < a_7$, and any three of these line segments cannot form a triangle. If $a_1 = 1$ cm and $a_7 = 21$ cm, then $a_6 = \\ $... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 35164,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 7 parking spaces in a row in a parking lot, and now 4 cars need to be parked. If 3 empty spaces need to be together, calculate the number of different parking methods."
}
] | math | {
"style": "rule",
"ground_truth": "120"
} | {
"index": 35165,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 7 people standing in a row. How many different arrangements are there according to the following requirements?\n\n(1) Among them, A cannot stand at the head, and B cannot stand at the tail;\n(2) Among them, A, B, and C must stand next to each other;\n(3) Among them, A... | math | {
"style": "rule",
"ground_truth": "840"
} | {
"index": 35166,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 7 people standing in a row. How many different arrangements are there according to the following requirements?\n(1) Among them, A, B, and C cannot stand next to each other;\n(2) Among them, A and B have exactly one person between them;\n(3) A does not stand at the hea... | math | {
"style": "rule",
"ground_truth": "3720"
} | {
"index": 35167,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 7 students participating in 5 sports events. Students A and B cannot participate in the same event. Each event must have participants, and each student can only participate in one event. How many different arrangements satisfy these conditions? (Answer in numbers)"
... | math | {
"style": "rule",
"ground_truth": "15000"
} | {
"index": 35168,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 7 students standing in a row. How many different arrangements are there in the following situations? \n(1) A and B must stand together; \n(2) A is not at the head of the line, and B is not at the end of the line; \n(3) There must be exactly one person between A and... | math | {
"style": "rule",
"ground_truth": "1200"
} | {
"index": 35169,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 7 volunteers to be arranged for community service activities on Saturday and Sunday, with 3 people arranged for each day, calculate the total number of different arrangements."
}
] | math | {
"style": "rule",
"ground_truth": "140"
} | {
"index": 35170,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 7 volunteers to be arranged to participate in the promotional activities for the Shanghai World Expo on Saturday and Sunday, with 6 people participating each day and 3 people arranged for each day. There are __________ different arrangements possible (answer with a nu... | math | {
"style": "rule",
"ground_truth": "140"
} | {
"index": 35171,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 7 volunteers, among which 3 people only speak Russian, and 4 people speak both Russian and English. From these, 4 people are to be selected to serve as translators for the opening ceremony of the \"Belt and Road\" summit, with 2 people serving as English translators a... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 35172,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 700 cards in a box, in six colors: red, orange, yellow, green, blue, and white. The ratio of the number of red, orange, and yellow cards is $1: 3: 4$, and the ratio of the number of green, blue, and white cards is $3:1:6$. Given that there are 50 more yellow cards tha... | math | {
"style": "rule",
"ground_truth": "312"
} | {
"index": 35173,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 Olympic volunteers, among them volunteers $A_{1}$, $A_{2}$, $A_{3}$ are proficient in Japanese, $B_{1}$, $B_{2}$, $B_{3}$ are proficient in Russian, and $C_{1}$, $C_{2}$ are proficient in Korean. One volunteer proficient in Japanese, Russian, and Korean is to be sel... | math | {
"style": "rule",
"ground_truth": "\\dfrac {5}{6}"
} | {
"index": 35174,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 blue, 7 red, and 12 white light bulbs. In how many ways can they all be arranged to form a garland such that no two white light bulbs are next to each other?"
}
] | math | {
"style": "rule",
"ground_truth": "11711700"
} | {
"index": 35175,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 books on a shelf, which include a trilogy that must be selected together. In how many ways can 5 books be selected from this shelf if the order in which the books are selected does not matter?"
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 35176,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 cards; one side of each card is blank, and the other side has the letters И, Я, Л, З, Г, О, О, О written on them. The cards are placed on the table with the blank side up, shuffled, and then turned over one by one in sequence. What is the probability that the letter... | math | {
"style": "rule",
"ground_truth": "1/6720"
} | {
"index": 35177,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 different positive integers. Among them, at least 6 are multiples of 2, at least 5 are multiples of 3, at least 3 are multiples of 5, and at least 1 is a multiple of 7. To minimize the largest number among these 8 integers, what is this largest number?"
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 35178,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 identical balls in a box, consisting of three balls numbered 1, three balls numbered 2, and two balls numbered 3. A ball is randomly drawn from the box, returned, and then another ball is randomly drawn. The product of the numbers on the balls drawn first and second... | math | {
"style": "rule",
"ground_truth": "225/64"
} | {
"index": 35179,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 keys numbered 1 to 8 and 8 boxes numbered 1 to 8. Each key can only open the box with the same number. All keys are placed in these boxes and locked up so that each box contains one key. How many different ways are there to place the keys in the boxes such that at l... | math | {
"style": "rule",
"ground_truth": "35280"
} | {
"index": 35180,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 lily pads in a pond numbered $1,2, \\ldots, 8$. A frog starts on lily pad 1. During the $i$-th second, the frog jumps from lily pad $i$ to $i+1$, falling into the water with probability $\\frac{1}{i+1}$. The probability that the frog lands safely on lily pad 8 witho... | math | {
"style": "rule",
"ground_truth": "108"
} | {
"index": 35181,
"solution": "The probability the frog lands safely on lily pad $i+1$ given that the frog safely landed on lily pad $i$ is $\\frac{i}{i+1}$. The probability the frog make it to lily pad 8 safely is simply the product of the probabilities of the frog making it to each of the lily pads 2 through 8 gi... |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 participants in a performance, with a total of $m$ shows. In each show, 4 people perform on stage. It is required that any two of the 8 people perform together the same number of times. Find the minimum value of $m$."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 35182,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 seats in a row, and 3 people are sitting in the same row. If there are empty seats on both sides of each person, the number of different seating arrangements is \\_\\_\\_\\_\\_\\_\\_\\_\\_."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 35183,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 sprinters in the Olympic 100-meter finals. Three of the sprinters are Americans. The gold medal goes to first place, silver to second, and bronze to third. In how many ways can the medals be awarded if at most one American gets a medal?"
}
] | math | {
"style": "rule",
"ground_truth": "240"
} | {
"index": 35184,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 students arranged in two rows, with 4 people in each row. If students A and B must be arranged in the front row, and student C must be arranged in the back row, then the total number of different arrangements is ___ (answer in digits)."
}
] | math | {
"style": "rule",
"ground_truth": "5760"
} | {
"index": 35185,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 white balls and 2 red balls in a bag. Each time a ball is randomly drawn and then a white ball is put back. What is the probability that all red balls are drawn exactly at the 4th draw?"
}
] | math | {
"style": "rule",
"ground_truth": "0.0434"
} | {
"index": 35186,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 white balls and 2 red balls in a bag. Each time a ball is randomly taken out, a white ball is put back in. What is the probability that all red balls are taken out exactly by the 4th draw?"
}
] | math | {
"style": "rule",
"ground_truth": "353/5000"
} | {
"index": 35187,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 8 young people, among whom 5 are capable of doing English translation work, and 4 are capable of doing computer software design work (including one person who is capable of doing both tasks). Now, 5 young people are to be selected to undertake a task, with 3 people do... | math | {
"style": "rule",
"ground_truth": "42"
} | {
"index": 35188,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 85 beads in total on a string, arranged in the pattern \"three green, four red, one yellow, three green, four red, one yellow, ...\". How many red beads are there?"
}
] | math | {
"style": "rule",
"ground_truth": "42"
} | {
"index": 35189,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 9 digits: 0, 1, 2, …, 8. Using five cards, with the two sides respectively marked as 0/8, 1/7, 2/5, 3/4, 6/9; and 6 can be used as 9. How many different four-digit numbers can be formed with these five cards?"
}
] | math | {
"style": "rule",
"ground_truth": "1728"
} | {
"index": 35190,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 9 representatives from different countries, with 3 people from each country. They sit randomly around a round table with 9 chairs. What is the probability that each representative has at least one representative from another country sitting next to them?"
}
] | math | {
"style": "rule",
"ground_truth": "41/56"
} | {
"index": 35191,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 90 children in a chess club. During a session, they were divided into 30 groups of 3 people each, and in each group, everyone played one game with everyone else. No other games were played. A total of 30 \"boy vs. boy\" games and 14 \"girl vs. girl\" games were played... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"index": 35192,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 94 safes and 94 keys. Each key can open only one safe, and each safe can be opened by only one key. We place randomly one key into each safe. 92 safes are then randomly chosen, and then locked. What is the probability that we can open all the safes with the two keys i... | math | {
"style": "rule",
"ground_truth": "1/47"
} | {
"index": 35193,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 99 children standing in a circle, each initially holding a ball. Every minute, each child with a ball throws their ball to one of their two neighbors. If a child receives two balls, one of the balls is irrevocably lost. What is the minimum amount of time after which o... | math | {
"style": "rule",
"ground_truth": "98"
} | {
"index": 35194,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"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."
}
] | math | {
"style": "rule",
"ground_truth": "101"
} | {
"index": 35195,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 99 positive integers, and their sum is 101101. The greatest possible value of the greatest common divisor of these 99 positive integers is:"
}
] | math | {
"style": "rule",
"ground_truth": "101"
} | {
"index": 35196,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are \\( N \\geq 5 \\) natural numbers written on the board. It is known that the sum of all the numbers is 80, and the sum of any five of them is not more than 19. What is the smallest possible value of \\( N \\)?"
}
] | math | {
"style": "rule",
"ground_truth": "26"
} | {
"index": 35197,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are \\( R \\) zeros at the end of \\(\\underbrace{99\\ldots9}_{2009 \\text{ of }} \\times \\underbrace{99\\ldots9}_{2009 \\text{ of } 9 \\text{'s}} + 1 \\underbrace{99\\ldots9}_{2009 \\text{ of } 9 \\text{'s}}\\). Find the value of \\( R \\)."
}
] | math | {
"style": "rule",
"ground_truth": "4018"
} | {
"index": 35198,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are \\( k \\) people and \\( n \\) chairs in a row, where \\( 2 \\leq k < n \\). There is a couple among the \\( k \\) people. The number of ways in which all \\( k \\) people can be seated such that the couple is seated together is equal to the number of ways in which th... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 35199,
"solution": ""
} |
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