data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "At HappyTails Training Center, cats can learn to do three tricks: jump, fetch, and spin. Of the cats at the center:\n- 40 cats can jump\n- 25 cats can fetch\n- 30 cats can spin\n- 15 cats can jump and fetch\n- 10 cats can fetch and spin\n- 12 cats can jump and spin\n- 5 cats ca... | math | {
"style": "rule",
"ground_truth": "70"
} | {
"index": 5200,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At Jefferson High School, there are 500 students enrolled. One hundred twenty students are in the orchestra, 190 are in band, and 220 are in chorus. If only 400 students are in orchestra, band, and/or chorus, how many students are in exactly two of these groups?"
}
] | math | {
"style": "rule",
"ground_truth": "130"
} | {
"index": 5201,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At Jefferson Summer Camp, $60\\%$ of the children play soccer, $30\\%$ of the children swim, and $40\\%$ of the soccer players swim. To the nearest whole percent, what percent of the non-swimmers play soccer?"
}
] | math | {
"style": "rule",
"ground_truth": "51\\%"
} | {
"index": 5202,
"solution": "Let's denote the total number of children at the camp as $N$. We are given the following percentages:\n- $60\\%$ of the children play soccer, which translates to $0.6N$ children.\n- $30\\%$ of the children swim, which translates to $0.3N$ children.\n- $40\\%$ of the soccer players also... |
DeepScaleR | [
{
"role": "user",
"content": "At McDonald's restaurants, we can order Chicken McNuggets in packages of 6, 9, or 20 pieces. (For example, we can order 21 pieces because $21=6+6+9$, but there is no way to get 19 pieces.) What is the largest number of pieces that we cannot order?"
}
] | math | {
"style": "rule",
"ground_truth": "43"
} | {
"index": 5203,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At Megapolis Hospital one year, multiple-birth statistics were as follows: Sets of twins, triplets, and quadruplets accounted for $1000$ of the babies born. There were four times as many sets of triplets as sets of quadruplets, and there was three times as many sets of twins as... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 5204,
"solution": "1. **Define Variables:**\n Let $a$ be the number of sets of twins, $b$ be the number of sets of triplets, and $c$ be the number of sets of quadruplets.\n\n2. **Set Up Equations:**\n From the problem, we have the following relationships:\n - There are four times as many sets of tr... |
DeepScaleR | [
{
"role": "user",
"content": "At Pine Ridge Elementary School, one third of the students ride the school bus home. One fifth of the students are picked up by car. One eighth of the students go home on their skateboards. Another one tenth of the students share rides with classmates. The rest of the students ... | math | {
"style": "rule",
"ground_truth": "\\frac{29}{120}"
} | {
"index": 5205,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At Rachelle's school, an A counts $4$ points, a B $3$ points, a C $2$ points, and a D $1$ point. Her GPA in the four classes she is taking is computed as the total sum of points divided by 4. She is certain that she will get A's in both Mathematics and Science and at least a C ... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{24}"
} | {
"index": 5206,
"solution": "1. **Calculate the probability of getting each grade in English and History:**\n - For English:\n - Probability of A: $\\frac{1}{6}$\n - Probability of B: $\\frac{1}{4}$\n - Probability of C: $1 - \\frac{1}{6} - \\frac{1}{4} = 1 - \\frac{5}{12} = \\frac{7}{12}$\n - For ... |
DeepScaleR | [
{
"role": "user",
"content": "At Rosa's Rose Shop, a bouquet containing a dozen roses costs $\\$20$. If the price of a bouquet is directly proportional to the number of roses it contains, how many dollars will a bouquet of 39 roses cost?"
}
] | math | {
"style": "rule",
"ground_truth": "65"
} | {
"index": 5207,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At Stanford in 1988, human calculator Shakuntala Devi was asked to compute $m = \\sqrt[3]{61{,}629{,}875}$ and $n = \\sqrt[7]{170{,}859{,}375}$ . Given that $m$ and $n$ are both integers, compute $100m+n$ .\n\n*Proposed by Evan Chen*"
}
] | math | {
"style": "rule",
"ground_truth": "39515"
} | {
"index": 5208,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At Typico High School, $60\\%$ of the students like dancing, and the rest dislike it. Of those who like dancing, $80\\%$ say that they like it, and the rest say that they dislike it. Of those who dislike dancing, $90\\%$ say that they dislike it, and the rest say that they like... | math | {
"style": "rule",
"ground_truth": "$25\\%$"
} | {
"index": 5209,
"solution": "1. **Assume Total Number of Students**: Let's assume there are 100 students at Typico High School for simplicity in calculation.\n\n2. **Students Who Like Dancing**: \n - Given that 60% of the students like dancing.\n - Therefore, $60\\% \\times 100 = 60$ students like dancing.\n\n... |
DeepScaleR | [
{
"role": "user",
"content": "At Wednesday's basketball game, the Cayley Comets scored 90 points. At Friday's game, they scored $80\\%$ as many points as they scored on Wednesday. How many points did they score on Friday?"
}
] | math | {
"style": "rule",
"ground_truth": "72"
} | {
"index": 5210,
"solution": "On Friday, the Cayley Comets scored $80\\%$ of 90 points. This is equal to $\\frac{80}{100} \\times 90 = \\frac{8}{10} \\times 90 = 8 \\times 9 = 72$ points. Alternatively, since $80\\%$ is equivalent to 0.8, then $80\\%$ of 90 is equal to $0.8 \\times 90 = 72$."
} |
DeepScaleR | [
{
"role": "user",
"content": "At a ball, there were 29 boys and 15 girls. Some boys danced with some girls (no more than once with each partner). After the ball, each person told their parents how many times they danced. What is the maximum number of different numbers the children could have mentioned?"
}... | math | {
"style": "rule",
"ground_truth": "29"
} | {
"index": 5211,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a bus station, there are three buses departing to a school between 6:30 AM and 7:30 AM each day. The ticket prices for the buses are the same, but the comfort levels vary. Xiao Jie, a student, observes before boarding. When the first bus arrives, he does not get on but caref... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 5212,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a bus stop near Absent-Minded Scientist's house, two bus routes stop: #152 and #251. Both go to the subway station. The interval between bus #152 is exactly 5 minutes, and the interval between bus #251 is exactly 7 minutes. The intervals are strictly observed, but these two ... | math | {
"style": "rule",
"ground_truth": "5/14"
} | {
"index": 5213,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a certain crosswalk, the pedestrian signal alternates between red and green lights, with the red light lasting for $40s$. If a pedestrian arrives at the crosswalk and encounters a red light, the probability that they need to wait at least $15s$ for the green light to appear ... | math | {
"style": "rule",
"ground_truth": "\\dfrac{5}{8}"
} | {
"index": 5214,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a certain grocery store, cookies may be bought in boxes of $10$ or $21.$ What is the minimum positive number of cookies that must be bought so that the cookies may be split evenly among $13$ people?\n\n*Author: Ray Li*"
}
] | math | {
"style": "rule",
"ground_truth": "52"
} | {
"index": 5215,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a certain meeting, a total of \\(12k\\) people attended. Each person greeted exactly \\(3k+6\\) other people. For any two individuals, the number of people who greeted both of them is the same. How many people attended the meeting?"
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 5216,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a certain university, the division of mathematical sciences consists of the departments of mathematics, statistics, and computer science. There are two male and two female professors in each department. A committee of six professors is to contain three men and three women an... | math | {
"style": "rule",
"ground_truth": "88"
} | {
"index": 5217,
"solution": "Use generating functions. For each department, there is 1 way to pick 2 males, 4 ways to pick one of each, and 1 way to pick 2 females. Since there are three departments in total, and we wish for three males and three females, the answer will be equal to the coefficient of $x^3y^3$ in ... |
DeepScaleR | [
{
"role": "user",
"content": "At a circular table, there are 5 people seated: Arnaldo, Bernaldo, Cernaldo, Dernaldo, and Ernaldo, each in a chair. Analyzing clockwise, we have:\n\nI. There is 1 empty chair between Arnaldo and Bernaldo;\n\nII. There are 5 chairs between Bernaldo and Cernaldo;\n\nIII. There a... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 5218,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a club, twenty gentlemen met. Some of them were wearing hats, and some were without hats. From time to time, one of the gentlemen took off his hat and put it on one of those who did not have a hat at that moment. In the end, ten gentlemen counted that each of them had given ... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 5219,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a community gathering there are only single women and married men with their wives. The probability that a randomly selected woman is single is $\\frac{3}{7}$. Calculate the fraction of the people in the gathering who are married men."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{11}"
} | {
"index": 5220,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a conference of $40$ people, there are $25$ people who each know each other, and among them, $5$ people do not know $3$ other specific individuals in their group. The remaining $15$ people do not know anyone at the conference. People who know each other hug, and people who d... | math | {
"style": "rule",
"ground_truth": "495"
} | {
"index": 5221,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a conference there are $n$ mathematicians. Each of them knows exactly $k$ fellow mathematicians. Find the smallest value of $k$ such that there are at least three mathematicians that are acquainted each with the other two.\n\n[color=#BF0000]Rewording of the last line for cla... | math | {
"style": "rule",
"ground_truth": "\\left\\lfloor \\frac{n}{2} \\right\\rfloor +1"
} | {
"index": 5222,
"solution": "\nLet \\( n \\) be the number of mathematicians at the conference. We are tasked with finding the smallest value of \\( k \\) such that there are at least three mathematicians, say \\( X, Y, \\) and \\( Z \\), who are all acquainted with each other (i.e., each knows the other two).\n\n... |
DeepScaleR | [
{
"role": "user",
"content": "At a conference with 35 businessmen, 18 businessmen drank coffee, 15 businessmen drank tea, and 8 businessmen drank juice. Six businessmen drank both coffee and tea, four drank both tea and juice, and three drank both coffee and juice. Two businessmen drank all three beverages.... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"index": 5223,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a conference, the 2016 participants were registered from P1 to P2016. Each participant from P1 to P2015 shook hands with exactly the same number of participants as the number on their registration form. How many hands did the 2016th participant shake?"
}
] | math | {
"style": "rule",
"ground_truth": "1008"
} | {
"index": 5224,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a conference, there are only single women and married men with their wives. The probability that a randomly selected woman is single is $\\frac{3}{7}$. What fraction of the people in the conference are married men?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{11}"
} | {
"index": 5225,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a crossroads, if vehicles are not allowed to turn back, calculate the total number of possible driving routes."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 5226,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a dog show, each dog was assigned a sequential number from 1 to 24. Due to health reasons, one of the dogs was unable to participate in the competition. It turns out that among the remaining 23 dogs, one has a number equal to the arithmetic mean of the remaining dogs' number... | math | {
"style": "rule",
"ground_truth": "124"
} | {
"index": 5227,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a family outing to a theme park, the Thomas family, comprising three generations, plans to purchase tickets. The two youngest members, categorized as children, get a 40% discount. The two oldest members, recognized as seniors, enjoy a 30% discount. The middle generation no l... | math | {
"style": "rule",
"ground_truth": "49.27"
} | {
"index": 5228,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a gathering of $30$ people, there are $20$ people who all know each other and $10$ people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur within the group?"
}
] | math | {
"style": "rule",
"ground_truth": "245"
} | {
"index": 5229,
"solution": "1. **Identify the groups and their interactions**: We have two distinct groups at the gathering:\n - Group A: 20 people who all know each other.\n - Group B: 10 people who know no one in the gathering.\n\n2. **Calculate handshakes between Group A and Group B**: \n - Each person i... |
DeepScaleR | [
{
"role": "user",
"content": "At a hypothetical school, there are three departments in the faculty of sciences: biology, physics and chemistry. Each department has three male and one female professor. A committee of six professors is to be formed containing three men and three women, and each department mus... | math | {
"style": "rule",
"ground_truth": "27"
} | {
"index": 5230,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a large gathering hosted by Benjamin Franklin, each man shakes hands with every other attendee except their own spouse and except Benjamin Franklin, who is also present. No handshakes take place between women, and Franklin only shakes hands with the women. If 15 married coup... | math | {
"style": "rule",
"ground_truth": "225"
} | {
"index": 5231,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a math competition, a team of $8$ students has $2$ hours to solve $30$ problems. If each problem needs to be solved by $2$ students, on average how many minutes can a student spend on a problem?"
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 5232,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a math contest, $57$ students are wearing blue shirts, and another $75$ students are wearing yellow shirts. The $132$ students are assigned into $66$ pairs. In exactly $23$ of these pairs, both students are wearing blue shirts. In how many pairs are both students wearing yel... | math | {
"style": "rule",
"ground_truth": "32"
} | {
"index": 5233,
"solution": "1. **Total number of students and pairs:**\n Given that there are $57$ students wearing blue shirts and $75$ students wearing yellow shirts, the total number of students is $57 + 75 = 132$. These students are divided into $66$ pairs.\n\n2. **Pairs with both students wearing blue shir... |
DeepScaleR | [
{
"role": "user",
"content": "At a meeting of $ 12k$ people, each person exchanges greetings with exactly $ 3k\\plus{}6$ others. For any two people, the number who exchange greetings with both is the same. How many people are at the meeting?"
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 5234,
"solution": "\nLet the total number of people at the meeting be \\( n = 12k \\). Each person exchanges greetings with exactly \\( 3k + 6 \\) others. We need to determine the value of \\( n \\).\n\nGiven that for any two people, the number of people who exchange greetings with both is the same, this... |
DeepScaleR | [
{
"role": "user",
"content": "At a meeting of cactus enthusiasts, 80 cactophiles presented their collections, each consisting of cacti of different species. It turned out that no single species of cactus is found in all collections simultaneously, but any 15 people have cacti of the same species. What is th... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 5235,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a meeting with $25$ businessmen, twelve businessmen drank coffee, and ten businessmen drank tea. Five businessmen drank both coffee and tea. How many businessmen drank neither coffee nor tea?"
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"index": 5236,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a national competition, 31 participants are accommodated in a hotel where each participant gets his/her own room. The rooms are numbered from 1 to 31. When all participants have arrived, except those assigned to rooms 15, 16, and 17, what is the median room number of the rem... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 5237,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a nursery, 2006 babies sit in a circle. Suddenly each baby pokes the baby immediately to either its left or its right, with equal probability. What is the expected number of unpoked babies?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1003}{2}"
} | {
"index": 5238,
"solution": "The probability that any given baby goes unpoked is $1 / 4$. So the answer is $2006 / 4=1003 / 2$."
} |
DeepScaleR | [
{
"role": "user",
"content": "At a painting club meeting, 7 friends are present. They need to create two separate teams: one team of 4 members, and another team of 2 members for different competitions. How many distinct ways can they form these teams?"
}
] | math | {
"style": "rule",
"ground_truth": "105"
} | {
"index": 5239,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a particular school with 43 students, each student takes chemistry, biology, or both. The chemistry class is three times as large as the biology class, and 5 students are taking both classes. How many people are in the chemistry class?"
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 5240,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a party, Ted's age is 15 years less than twice Sally's age. The sum of their ages is 54. How old is Ted?"
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"index": 5241,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a party, each man danced with exactly three women and each woman danced with exactly two men. Twelve men attended the party. How many women attended the party?"
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 5242,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a physical education lesson, 29 seventh graders attended, some of whom brought one ball each. During the lesson, sometimes one seventh grader would give their ball to another seventh grader who did not have a ball.\n\nAt the end of the lesson, $N$ seventh graders said, \"I r... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 5243,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a recent math contest, Evan was asked to find $2^{2016}(\\bmod p)$ for a given prime number $p$ with $100<p<500$. Evan has forgotten what the prime $p$ was, but still remembers how he solved it: - Evan first tried taking 2016 modulo $p-1$, but got a value $e$ larger than 100... | math | {
"style": "rule",
"ground_truth": "211"
} | {
"index": 5244,
"solution": "Answer is $p=211$. Let $p=2d+1,50<d<250$. The information in the problem boils down to $2016=d+21 \\quad(\\bmod 2d)$. From this we can at least read off $d \\mid 1995$. Now factor $1995=3 \\cdot 5 \\cdot 7 \\cdot 19$. The values of $d$ in this interval are $57,95,105,133$. The prime va... |
DeepScaleR | [
{
"role": "user",
"content": "At a regional science fair, 25 participants each have their own room in the same hotel, with room numbers from 1 to 25. All participants have arrived except those assigned to rooms 14 and 20. What is the median room number of the other 23 participants?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 5245,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a robot racing competition, a certain number of mechanisms were presented. The robots were paired to race the same distance. The protocol recorded the differences in the finishing times between the winner and the loser in each of the races. All the differences were distinct:... | math | {
"style": "rule",
"ground_truth": "63"
} | {
"index": 5246,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a school cafeteria, Jenny wants to buy a meal consisting of one main dish, one drink, one dessert, and one side dish. The list below contains Jenny's preferred choices available:\n\n\\begin{tabular}{ |c|c|c|c| }\n\\hline\n\\textbf{Main Dishes} & \\textbf{Drinks} & \\textbf{D... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"index": 5247,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a school cafeteria, Sam wants to buy a lunch consisting of one main course, one beverage, and one snack. The table below lists Sam's options available in the cafeteria. How many different lunch combinations can Sam choose from?\n\n\\begin{tabular}{ |c | c | c | }\n\\hline \\... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 5248,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a school cafeteria, Sam wants to buy a lunch consisting of one main dish, one beverage, and one snack. The table below lists Sam's choices in the cafeteria. How many distinct possible lunches can he buy if he avoids pairing Fish and Chips with Soda due to dietary restriction... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 5249,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a school fundraiser, $3109 was raised. The money was shared equally among 25 charities. The amount received by each charity from the school was:"
}
] | math | {
"style": "rule",
"ground_truth": "$124.36"
} | {
"index": 5250,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a school trip, there are 8 students and a teacher. They want to take pictures in groups where each group consists of either 4 or 5 students. How many different group combinations can they make?"
}
] | math | {
"style": "rule",
"ground_truth": "126"
} | {
"index": 5251,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a state contest, 21 Mathletes stay in the same hotel. Each Mathlete gets his/her own room and the room numbers are 1 through 21. When all the Mathletes have arrived, except the ones staying in rooms 12 and 13, what is the median room number of the other 19 Mathletes?"
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 5252,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a store, when a length or a width is reported as $x$ inches that means it is at least $x - 0.5$ inches and at most $x + 0.5$ inches. Suppose the dimensions of a rectangular tile are reported as $2$ inches by $3$ inches. In square inches, what is the minimum area for the rect... | math | {
"style": "rule",
"ground_truth": "3.75"
} | {
"index": 5253,
"solution": "1. **Understanding the Problem:**\n The problem states that when a dimension is reported as $x$ inches, the actual dimension is between $x - 0.5$ inches and $x + 0.5$ inches. For a rectangle reported to have dimensions $2$ inches by $3$ inches, the actual dimensions are:\n - Length... |
DeepScaleR | [
{
"role": "user",
"content": "At a sumo wrestling tournament, 20 sumo wrestlers participated. After weighing, it was found that the average weight of the wrestlers is 125 kg. What is the maximum possible number of wrestlers weighing more than 131 kg, given that according to the rules, individuals weighing l... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"index": 5254,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a tennis tournament there were $2n$ boys and $n$ girls participating. Every player played every other player. The boys won $\\frac 75$ times as many matches as the girls. It is knowns that there were no draws. Find $n$ ."
}
] | math | {
"style": "rule",
"ground_truth": "\\[ n \\in \\{ \\mathbf{N} \\equiv 0, 3 \\pmod{8} \\} \\]"
} | {
"index": 5255,
"solution": "The total number of games played in the tournament is $\\tfrac{3n(3n-1)}{2}.$ Since the boys won $\\tfrac75$ as many matches as the girls, the boys won $\\tfrac{7}{12}$ of all the games played, so the total number of games that a boy won is $\\tfrac{7}{12} \\cdot \\tfrac{3n(3n-1)}{2} =... |
DeepScaleR | [
{
"role": "user",
"content": "At a tribal council meeting, 60 people spoke in turn. Each of them said only one phrase. The first three speakers all said the same thing: \"I always tell the truth!\" The next 57 speakers also said the same phrase: \"Among the previous three speakers, exactly two of them told ... | math | {
"style": "rule",
"ground_truth": "45"
} | {
"index": 5256,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a twins and triplets convention, there were $9$ sets of twins and $6$ sets of triplets, all from different families. Each twin shook hands with all the twins except his/her siblings and with half the triplets. Each triplet shook hands with all the triplets except his/her sib... | math | {
"style": "rule",
"ground_truth": "441"
} | {
"index": 5257,
"solution": "1. **Count the total number of twins and triplets:**\n - There are $9$ sets of twins, with $2$ twins per set, giving a total of $9 \\times 2 = 18$ twins.\n - There are $6$ sets of triplets, with $3$ triplets per set, giving a total of $6 \\times 3 = 18$ triplets.\n\n2. **Calculate ... |
DeepScaleR | [
{
"role": "user",
"content": "At a university dinner, there are 2017 mathematicians who each order two distinct entrées, with no two mathematicians ordering the same pair of entrées. The cost of each entrée is equal to the number of mathematicians who ordered it, and the university pays for each mathematici... | math | {
"style": "rule",
"ground_truth": "127009"
} | {
"index": 5258,
"solution": "\nTo determine the maximum total amount the university could have paid, we can model the problem using graph theory. Consider a graph \\( G \\) with 2017 edges, where each edge represents a pair of distinct entrées ordered by a mathematician. The cost of each entrée is equal to the num... |
DeepScaleR | [
{
"role": "user",
"content": "At a variety show, there are seven acts: dance, comic dialogue, sketch, singing, magic, acrobatics, and opera. When arranging the program order, the conditions are that dance, comic dialogue, and sketch cannot be adjacent to each other. How many different arrangements of the pr... | math | {
"style": "rule",
"ground_truth": "1440"
} | {
"index": 5259,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At a women's doubles tennis tournament, there were three teams of two women. After the tournament, each woman shook hands once with each of the other players except her partner. What is the number of handshakes that occurred?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 5260,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of $12$, $15$, and $10$ minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the aver... | math | {
"style": "rule",
"ground_truth": "\\frac{88}{7}"
} | {
"index": 5261,
"solution": "1. **Define the number of students in each grade**:\n Let the number of fifth graders be $f$. According to the problem, there are twice as many fourth graders as fifth graders, and twice as many third graders as fourth graders. Therefore, the number of fourth graders is $2f$ and the ... |
DeepScaleR | [
{
"role": "user",
"content": "At an exchange point, there are two types of transactions:\n1) Give 2 euros - receive 3 dollars and a candy as a gift.\n2) Give 5 dollars - receive 3 euros and a candy as a gift.\n\nWhen the wealthy Buratino came to the exchange point, he only had dollars. When he left, he had ... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 5262,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At an international table tennis championship, 200 participants arrived. The tournament follows a single-elimination format, meaning that in each match two players compete, the loser is eliminated from the championship, and the winner remains. Find the maximum possible number o... | math | {
"style": "rule",
"ground_truth": "66"
} | {
"index": 5263,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At an observation station $C$, the distances to two lighthouses $A$ and $B$ are $300$ meters and $500$ meters, respectively. Lighthouse $A$ is observed at $30^{\\circ}$ north by east from station $C$, and lighthouse $B$ is due west of station $C$. Calculate the distance between... | math | {
"style": "rule",
"ground_truth": "700"
} | {
"index": 5264,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At an old estate, the house is surrounded in a circle by tall trees: spruces, pines, and birches. There are a total of 96 trees. These trees have a strange property: from any coniferous tree, if you take two trees skipping one tree in between, one of them is coniferous and the ... | math | {
"style": "rule",
"ground_truth": "32"
} | {
"index": 5265,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"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... | math | {
"style": "rule",
"ground_truth": "8:11"
} | {
"index": 5266,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At breakfast, lunch, and dinner, Joe randomly chooses with equal probabilities either an apple, an orange, or a banana to eat. On a given day, what is the probability that Joe will eat at least two different kinds of fruit?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{8}{9}"
} | {
"index": 5267,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At constant temperature, the pressure of a sample of gas is inversely proportional to its volume. I have some oxygen in a 2.28 liter container with a pressure of 5 kPa. If I move all of it to a 5.7 liter container at the same temperature, what will the new pressure be in kPa?"
... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 5268,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At each of the sixteen circles in the network below stands a student. A total of $3360$ coins are distributed among the sixteen students. All at once, all students give away all their coins by passing an equal number of coins to each of their neighbors in the network. After the... | math | {
"style": "rule",
"ground_truth": "280"
} | {
"index": 5269,
"solution": "Since the students give the same number of gifts of coins as they receive and still end up the same number of coins, we can assume that every gift of coins has the same number of coins. Let $x$ be the number of coins in each gift of coins. There $10$ people who give $4$ gifts of coins,... |
DeepScaleR | [
{
"role": "user",
"content": "At each vertex of a cube with an edge length of 1, there is the center of a sphere. All the spheres are identical, and each touches three neighboring spheres. Find the length of the part of the space diagonal of the cube that lies outside the spheres."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3} - 1"
} | {
"index": 5270,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At exactly noon, Anna Kuzminichna looked out the window and saw Klava, the village shop clerk, going on a break. Two minutes past twelve, Anna Kuzminichna looked out the window again, and no one was at the closed store. Klava was absent for exactly 10 minutes, and when she retu... | math | {
"style": "rule",
"ground_truth": "1/2"
} | {
"index": 5271,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At exactly noon, Anna Kuzminichna looked out the window and saw that Klava, the shop assistant of the countryside shop, was leaving for a break. At two minutes past one, Anna Kuzminichna looked out the window again and saw that no one was in front of the closed shop. Klava was ... | math | {
"style": "rule",
"ground_truth": "0.75"
} | {
"index": 5272,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At his usual rate a man rows 15 miles downstream in five hours less time than it takes him to return. If he doubles his usual rate, the time downstream is only one hour less than the time upstream. In miles per hour, the rate of the stream's current is:"
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 5273,
"solution": "Let $r$ be the man's rowing speed in still water (in miles per hour) and $w$ be the speed of the stream's current (in miles per hour).\n\n1. **Formulate the equations based on the problem statement:**\n - The time taken to row 15 miles downstream (where the speed is $r+w$) is 5 hours... |
DeepScaleR | [
{
"role": "user",
"content": "At lunch, $60\\%$ of the students selected soda while $20\\%$ selected milk. If 72 students selected soda, how many students selected milk?"
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 5274,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At lunch, Abby, Bart, Carl, Dana, and Evan share a pizza divided radially into 16 slices. Each one takes takes one slice of pizza uniformly at random, leaving 11 slices. The remaining slices of pizza form \"sectors\" broken up by the taken slices, e.g. if they take five consecu... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{3}"
} | {
"index": 5275,
"solution": "Consider the more general case where there are $N$ slices and $M>0$ slices are taken. Let $S$ denote the number of adjacent pairs of slices of pizza which still remain. There are $N-M$ slices and a sector of $k$ slices contributes $k-1$ pairs to $S$. Hence the number of sectors is $N-M... |
DeepScaleR | [
{
"role": "user",
"content": "At most, how many interior angles greater than $180^\\circ$ can a 2006-sided polygon have?"
}
] | math | {
"style": "rule",
"ground_truth": "2003"
} | {
"index": 5276,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At night, there was a heavy snowfall. In the morning, Xiao Long and his father measured the length of a circular path in the garden by walking. They started from the same point and walked in the same direction. Xiao Long's step length is 54 cm, and his father's step length is 7... | math | {
"style": "rule",
"ground_truth": "21.6"
} | {
"index": 5277,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At noon on a certain day, Minneapolis is $N$ degrees warmer than St. Louis. At $4{:}00$ the temperature in Minneapolis has fallen by $5$ degrees while the temperature in St. Louis has risen by $3$ degrees, at which time the temperatures in the two cities differ by $2$ degrees. ... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 5278,
"solution": "1. **Define the variables:**\n Let $M$ represent the temperature in Minneapolis at noon, and $L$ represent the temperature in St. Louis at noon. Given that Minneapolis is $N$ degrees warmer than St. Louis at noon, we can express this relationship as:\n \\[\n M = L + N\n \\]\n\n... |
DeepScaleR | [
{
"role": "user",
"content": "At one of George Washington's parties, each man shook hands with everyone except his spouse, and no handshakes took place between women. If $13$ married couples attended, how many handshakes were there among these $26$ people?"
}
] | math | {
"style": "rule",
"ground_truth": "234"
} | {
"index": 5279,
"solution": "To solve this problem, we need to calculate the total number of handshakes at the party under the given conditions: each man shakes hands with every other man and with every woman except his own spouse. No handshakes occur between women.\n\n1. **Calculate handshakes among men:**\n Ea... |
DeepScaleR | [
{
"role": "user",
"content": "At some time between 9:30 and 10 o'clock, the triangle determined by the minute hand and the hour hand is an isosceles triangle. If the two equal angles in this triangle are each twice as large as the third angle, what is the time?"
}
] | math | {
"style": "rule",
"ground_truth": "9:36"
} | {
"index": 5280,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the \"Economics and Law\" congress, a \"Best of the Best\" tournament was held, in which more than 220 but fewer than 254 delegates—economists and lawyers—participated. During one match, participants had to ask each other questions within a limited time and record correct an... | math | {
"style": "rule",
"ground_truth": "105"
} | {
"index": 5281,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the 2007 Math Olympics, Team Canada won $17$ out of a possible $100$ medals. Which one of the following is closest to the fraction of medals that they won? $$\n\\frac{1}{4} \\qquad \\frac{1}{5} \\qquad \\frac{1}{6} \\qquad \\frac{1}{7} \\qquad \\frac{1}{8}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"index": 5282,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the 2013 Winnebago County Fair a vendor is offering a \"fair special\" on sandals. If you buy one pair of sandals at the regular price of $50, you get a second pair at a 40% discount, and a third pair at half the regular price. Javier took advantage of the \"fair special\" t... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 5283,
"solution": "1. **Calculate the total cost without any discounts:** \n The regular price for one pair of sandals is $50. Therefore, the cost for three pairs of sandals at the regular price is:\n \\[\n 3 \\times 50 = 150 \\text{ dollars}\n \\]\n\n2. **Calculate the total cost with the \"fai... |
DeepScaleR | [
{
"role": "user",
"content": "At the 4 PM show, all the seats in the theater were taken, and 65 percent of the audience was children. At the 6 PM show, again, all the seats were taken, but this time only 50 percent of the audience was children. Of all the people who attended either of the shows, 57 percent ... | math | {
"style": "rule",
"ground_truth": "520"
} | {
"index": 5284,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the CleverCat Academy, cats can learn to do three tricks: jump, play dead, and fetch. Of the cats at the academy:\n- 60 cats can jump\n- 35 cats can play dead\n- 40 cats can fetch\n- 20 cats can jump and play dead\n- 15 cats can play dead and fetch\n- 22 cats can jump and fe... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 5285,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the CleverCat Academy, there are three skills that the cats can learn: jump, climb, and hunt. Out of the cats enrolled in the school:\n- 40 cats can jump.\n- 25 cats can climb.\n- 30 cats can hunt.\n- 10 cats can jump and climb.\n- 15 cats can climb and hunt.\n- 12 cats can ... | math | {
"style": "rule",
"ground_truth": "69"
} | {
"index": 5286,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the Gooddog Obedience School, dogs can learn to do three tricks: sit, stay, and roll over. Of the dogs at the school: \\begin{tabular}{l@{\\qquad}l}\n50 dogs can sit & 17 dogs can sit and stay \\\\\n29 dogs can stay & 12 dogs can stay and roll over \\\\\n34 dogs can roll ove... | math | {
"style": "rule",
"ground_truth": "84"
} | {
"index": 5287,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the Hardey Fitness Center, the management did a survey of their membership. The average age of the female members was 40 years old. The average age of the male members was 25 years old. The average age of the entire membership was 30 years old. What is the ratio of the femal... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 5288,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the Lacsap Hospital, Emily is a doctor and Robert is a nurse. Not including Emily, there are five doctors and three nurses at the hospital. Not including Robert, there are $d$ doctors and $n$ nurses at the hospital. What is the product of $d$ and $n$?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 5289,
"solution": "Since Emily is a doctor and there are 5 doctors and 3 nurses aside from Emily at the hospital, then there are 6 doctors and 3 nurses in total. Since Robert is a nurse, then aside from Robert, there are 6 doctors and 2 nurses. Therefore, $d=6$ and $n=2$, so $dn=12$."
} |
DeepScaleR | [
{
"role": "user",
"content": "At the MP Donut Hole Factory, Niraek, Theo, and Akshaj are coating spherical donut holes in powdered sugar. Niraek's donut holes have radius 6 mm, Theo's donut holes have radius 8 mm, and Akshaj's donut holes have radius 10 mm. All three workers coat the surface of the donut ... | math | {
"style": "rule",
"ground_truth": "400"
} | {
"index": 5290,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the New-Vasyuki currency exchange, 11 tugriks are traded for 14 dinars, 22 rupees for 21 dinars, 10 rupees for 3 thalers, and 5 crowns for 2 thalers. How many tugriks can be exchanged for 13 crowns?"
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 5291,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the beginning of a trip, the mileage odometer read $56,200$ miles. The driver filled the gas tank with $6$ gallons of gasoline. During the trip, the driver filled his tank again with $12$ gallons of gasoline when the odometer read $56,560$. At the end of the trip, the driver... | math | {
"style": "rule",
"ground_truth": "26.9"
} | {
"index": 5292,
"solution": "1. **Identify the total distance traveled**: \n The odometer readings at the start and end of the trip are given as $56,200$ miles and $57,060$ miles, respectively. Therefore, the total distance traveled during the trip is:\n \\[\n 57,060 - 56,200 = 860 \\text{ miles}\n \\]\n\n... |
DeepScaleR | [
{
"role": "user",
"content": "At the beginning of every period of British Literature, Mrs. Crabapple picks a random student to receive a crabapple as a gift, but really, as you might imagine, they are quite bitter and nasty. Given that there are 11 students in her class and her class meets four times a week... | math | {
"style": "rule",
"ground_truth": "14,\\!641"
} | {
"index": 5293,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the beginning of my bike ride I feel good, so I can travel 20 miles per hour. Later, I get tired and travel only 12 miles per hour. If I travel a total of 122 miles in a total time of 8 hours, for how many hours did I feel good? Express your answer as a common fract... | math | {
"style": "rule",
"ground_truth": "\\frac{13}{4}"
} | {
"index": 5294,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the beginning of school year in one of the first grade classes: $i)$ every student had exatly $20$ acquaintances $ii)$ every two students knowing each other had exactly $13$ mutual acquaintances $iii)$ every two students not knowing each other had exactly $12$ mutua... | math | {
"style": "rule",
"ground_truth": "31"
} | {
"index": 5295,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the beginning of the first day, a box contains 1 black ball, 1 gold ball, and no other balls. At the end of each day, for each gold ball in the box, 2 black balls and 1 gold ball are added to the box. If no balls are removed from the box, how many balls are in the box at the... | math | {
"style": "rule",
"ground_truth": "383"
} | {
"index": 5296,
"solution": "At the beginning of the first day, the box contains 1 black ball and 1 gold ball. At the end of the first day, 2 black balls and 1 gold ball are added, so the box contains 3 black balls and 2 gold balls. At the end of the second day, $2 \\times 2=4$ black balls and $2 \\times 1=2$ gold... |
DeepScaleR | [
{
"role": "user",
"content": "At the beginning of the school year, $50\\%$ of all students in Mr. Well's class answered \"Yes\" to the question \"Do you love math\", and $50\\%$ answered \"No.\" At the end of the school year, $70\\%$ answered \"Yes\" and $30\\%$ answered \"No.\" Altogether, $x\\%$ of the st... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 5297,
"solution": "Let's analyze the problem step by step to determine the minimum and maximum possible values of $x$, the percentage of students who changed their answers from the beginning to the end of the school year.\n\n1. **Initial Setup**:\n - At the beginning of the year, $50\\%$ of students an... |
DeepScaleR | [
{
"role": "user",
"content": "At the beginning of the school year, Jinshi Middle School has 17 classrooms. Teacher Dong Helong takes 17 keys to open the doors, knowing that each key can only open one door, but not knowing which key matches which door. What is the maximum number of attempts he needs to make ... | math | {
"style": "rule",
"ground_truth": "136"
} | {
"index": 5298,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the beginning of the school year, Lisa's goal was to earn an $A$ on at least $80\\%$ of her $50$ quizzes for the year. She earned an $A$ on $22$ of the first $30$ quizzes. If she is to achieve her goal, on at most how many of the remaining quizzes can she earn a grade lowe... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 5299,
"solution": "1. **Determine the total number of quizzes Lisa needs to score an A on to meet her goal:** \n Lisa's goal is to earn an A on at least 80% of her 50 quizzes. Therefore, the number of quizzes she needs to score an A on is:\n \\[\n 0.8 \\times 50 = 40\n \\]\n quizzes.\n\n2. **C... |
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