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 12 ordered pairs of integers $(x,y)$ that satisfy $x^2 + y^2 = 25$. What is the greatest possible sum $x+y$?"
}
] | math | {
"style": "rule",
"ground_truth": "7"
} | {
"index": 35000,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 12 sprinters in an international track event final, including 5 Americans. Gold, silver, and bronze medals are awarded to the first, second, and third place finishers respectively. Determine the number of ways the medals can be awarded if no more than two Americans re... | math | {
"style": "rule",
"ground_truth": "1260"
} | {
"index": 35001,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 12 students in a classroom; 6 of them are Democrats and 6 of them are Republicans. Every hour the students are randomly separated into four groups of three for political debates. If a group contains students from both parties, the minority in the group will change his... | math | {
"style": "rule",
"ground_truth": "\\frac{341}{55}"
} | {
"index": 35002,
"solution": "When the party distribution is $6-6$, the situation can change (to $3-9$ ) only when a group of three contains three people from the same party, and the remaining three are distributed evenly across the other three groups (to be converted). To compute the probability, we assume that t... |
DeepScaleR | [
{
"role": "user",
"content": "There are 120 different five-digit numbers composed of the digits 1, 2, 3, 4, and 5. Arrange them in descending order. The 95th number is $\\quad$"
}
] | math | {
"style": "rule",
"ground_truth": "21354"
} | {
"index": 35003,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 120 five-digit numbers formed by the digits 1, 2, 3, 4, 5, arranged in descending order. The 95th number is ______."
}
] | math | {
"style": "rule",
"ground_truth": "21354"
} | {
"index": 35004,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 1235 numbers written on a board. One of them appears more frequently than the others - 10 times. What is the smallest possible number of different numbers that can be written on the board?"
}
] | math | {
"style": "rule",
"ground_truth": "138"
} | {
"index": 35005,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 128 players in a single elimination tennis tournament, where exactly 32 players receive a bye in the first round. Calculate the total number of matches played in this tournament."
}
] | math | {
"style": "rule",
"ground_truth": "126"
} | {
"index": 35006,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 13 students in a class (one of them being the monitor) and 13 seats in the classroom. Every day, the 13 students line up in random order and then enter the classroom one by one. Except for the monitor, each student will randomly choose an unoccupied seat and sit down.... | math | {
"style": "rule",
"ground_truth": "7/13"
} | {
"index": 35007,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 13 weights arranged in a row on a table, ordered by mass (the lightest on the left, the heaviest on the right). It is known that the mass of each weight is an integer number of grams, the masses of any two adjacent weights differ by no more than 5 grams, and the total... | math | {
"style": "rule",
"ground_truth": "185"
} | {
"index": 35008,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 15 cards, each with 3 different Chinese characters. No two cards have the exact same set of Chinese characters, and in any set of 6 cards, there are always at least 2 cards that share a common Chinese character. What is the maximum number of different Chinese characte... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"index": 35009,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 15 different-colored crayons in a box. Karl wants to first select three crayons for his art project and then select four crayons for his friend's project. How many ways can Karl select these seven crayons if the order of selection does not matter for each set?"
}
] | math | {
"style": "rule",
"ground_truth": "225225"
} | {
"index": 35010,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 15 girls in a class of 27 students. The ratio of boys to girls in this class is:"
}
] | math | {
"style": "rule",
"ground_truth": "4:5"
} | {
"index": 35011,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 15 married couples among 30 people. Calculate the total number of handshakes that occurred among these people."
}
] | math | {
"style": "rule",
"ground_truth": "301"
} | {
"index": 35012,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 15 rectangular sheets of paper. In each move, one of the sheets is chosen and cut with a straight line, not passing through its vertices, into two sheets. After 60 moves, it turned out that all the sheets are triangles or hexagons. How many hexagons are there?"
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 35013,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 150 different cards on the table with the numbers $2, 4, 6, \\ldots, 298, 300$ (each card has exactly one number, and each number appears exactly once). In how many ways can you choose 2 cards so that the sum of the numbers on the chosen cards is divisible by $5$?"
... | math | {
"style": "rule",
"ground_truth": "2235"
} | {
"index": 35014,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 16 different cards, including 4 red, 4 yellow, 4 blue, and 4 green cards. If 3 cards are drawn at random, the requirement is that these 3 cards cannot all be of the same color, and at most 1 red card is allowed. The number of different ways to draw the cards is \\_\\_... | math | {
"style": "rule",
"ground_truth": "472"
} | {
"index": 35015,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 16 people standing in a circle: each of them is either truthful (always tells the truth) or a liar (always lies). Everyone said that both of their neighbors are liars. What is the maximum number of liars that can be in this circle?"
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 35016,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 16 students who form a $4 \\times 4$ square matrix. In an examination, their scores are all different. After the scores are published, each student compares their score with the scores of their adjacent classmates (adjacent refers to those directly in front, behind, l... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 35017,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 17 people at a party, and each has a reputation that is either $1,2,3,4$, or 5. Some of them split into pairs under the condition that within each pair, the two people's reputations differ by at most 1. Compute the largest value of $k$ such that no matter what the rep... | math | {
"style": "rule",
"ground_truth": "7"
} | {
"index": 35018,
"solution": "First, note that $k=8$ fails when there are $15,0,1,0,1$ people of reputation 1, 2, 3, 4, 5, respectively. This is because the two people with reputation 3 and 5 cannot pair with anyone, and there can only be at maximum $\\left\\lfloor\\frac{15}{2}\\right\\rfloor=7$ pairs of people wi... |
DeepScaleR | [
{
"role": "user",
"content": "There are 17 people standing in a circle: each of them is either truthful (always tells the truth) or a liar (always lies). All of them said that both of their neighbors are liars. What is the maximum number of liars that can be in this circle?"
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 35019,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 18 identical cars in a train. In some cars, exactly half of the seats are free, in others, exactly one-third of the seats are free, and in the remaining cars, all seats are occupied. At the same time, exactly one-ninth of all seats in the whole train are free. How man... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 35020,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 18 teams participating in the opening ceremony of a competition. When entering, the 1st team has 27 members, the 2nd team has 26 members, and the 18th team has 10 members. If they enter in a single file, and all 18 teams' members are assigned numbers from 1 to 333 in ... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 35021,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 19 candy boxes arranged in a row, with the middle box containing $a$ candies. Moving to the right, each box contains $m$ more candies than the previous one; moving to the left, each box contains $n$ more candies than the previous one ($a$, $m$, and $n$ are all positiv... | math | {
"style": "rule",
"ground_truth": "105"
} | {
"index": 35022,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 19 weights with values $1, 2, 3, \\ldots, 19$ grams: nine iron, nine bronze, and one gold. It is known that the total weight of all the iron weights is 90 grams more than the total weight of the bronze weights. Find the weight of the gold weight."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 35023,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 196 students numbered from 1 to 196 arranged in a line. Students at odd-numbered positions (1, 3, 5, ...) leave the line. The remaining students are renumbered starting from 1 in order. Then, again, students at odd-numbered positions leave the line. This process repea... | math | {
"style": "rule",
"ground_truth": "128"
} | {
"index": 35024,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 1987 sets, each with 45 elements. The union of any two sets has 89 elements. How many elements are there in the union of all 1987 sets?"
}
] | math | {
"style": "rule",
"ground_truth": "87429"
} | {
"index": 35025,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 1991 participants at a sporting event. Each participant knows at least $n$ other participants (the acquaintance is mutual). What is the minimum value of $n$ for which there necessarily exists a group of 6 participants who all know each other?"
}
] | math | {
"style": "rule",
"ground_truth": "1593"
} | {
"index": 35026,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2 boys and 3 girls, a total of 5 students standing in a row. If boy A does not stand at either end, and among the 3 girls, exactly 2 girls stand next to each other, calculate the number of different arrangements."
}
] | math | {
"style": "rule",
"ground_truth": "72"
} | {
"index": 35027,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2 dimes of Chinese currency, how many ways can they be exchanged into coins (1 cent, 2 cents, and 5 cents)?"
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"index": 35028,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2 teachers, 3 male students, and 4 female students taking a photo together. How many different standing arrangements are there under the following conditions? (Show the process, and represent the final result with numbers) \n(1) The male students must stand together;... | math | {
"style": "rule",
"ground_truth": "1728"
} | {
"index": 35029,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 20 cards with numbers $1, 2, \\cdots, 19, 20$ on them. These cards are placed in a box, and 4 people each draw one card. The two people who draw the smaller numbers will be in one group, and the two who draw the larger numbers will be in another group. If two of the p... | math | {
"style": "rule",
"ground_truth": "$\\frac{7}{51}$"
} | {
"index": 35030,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 20 cards, each with a number from 1 to 20. These cards are placed in a box, and 4 people each draw one card without replacement. The two people who draw the smaller numbers form one group, and the two people who draw the larger numbers form another group. If two peopl... | math | {
"style": "rule",
"ground_truth": "7/51"
} | {
"index": 35031,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 20 chairs arranged in a circle. There are \\(n\\) people sitting in \\(n\\) different chairs. These \\(n\\) people stand, move \\(k\\) chairs clockwise, and then sit again. After this happens, exactly the same set of chairs is occupied. For how many pairs \\((n, k)\\)... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"index": 35032,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 20 people in my club. 8 of them are left-handed. 15 of them like jazz music. 2 of them are right-handed and dislike jazz music. How many club members are left-handed and like jazz music? Assume people are either left-handed or right-handed, but not both."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"index": 35033,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 20 points, each pair of adjacent points are equally spaced. By connecting four points with straight lines, you can form a square. Using this method, you can form _ squares."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 35034,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 20 rooms, some with lights on and some with lights off. The occupants of these rooms prefer to match the majority of the rooms. Starting from room one, if the majority of the remaining 19 rooms have their lights on, the occupant will turn the light on; otherwise, they... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 35035,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 20 rooms, with some lights on and some lights off. The people in these rooms want to have their lights in the same state as the majority of the other rooms. Starting with the first room, if the majority of the remaining 19 rooms have their lights on, the person will t... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 35036,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 20 students in a class. In total, 10 of them have black hair, 5 of them wear glasses, and 3 of them both have black hair and wear glasses. How many of the students have black hair but do not wear glasses?"
}
] | math | {
"style": "rule",
"ground_truth": "7"
} | {
"index": 35037,
"solution": "Since 10 students have black hair and 3 students have black hair and wear glasses, then a total of $10-3=7$ students have black hair but do not wear glasses."
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 200 candies. What is the minimum number of schoolchildren that these candies can be distributed to so that, no matter how the candies are distributed, there are always at least two schoolchildren who receive the same number of candies (possibly none)?"
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"index": 35038,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 200 computers in a computer center, some of which are connected by cables in pairs, with a total of 345 cables used. We call a \"cluster\" a set of computers such that any computer in this set can send a signal to all others through the cables. Initially, all computer... | math | {
"style": "rule",
"ground_truth": "153"
} | {
"index": 35039,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 200 matches. How many ways are there to form, using all the matches, a square and (separately) an equilateral triangle? (Different ways are distinguished by the sizes of the square and the triangle)."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 35040,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 200 students enrolled at Memorial Middle School. Seventy of the students are in band and 95 are in chorus. If only 150 students are in band and/or chorus, how many students are in both band and chorus?"
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 35041,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2006 positive integers \\( a_{1}, a_{2}, \\cdots, a_{2006} \\) (which can be the same) such that the ratios \\( \\frac{a_{1}}{a_{2}}, \\frac{a_{2}}{a_{3}}, \\cdots, \\frac{a_{2005}}{a_{2006}} \\) are all distinct. What is the minimum number of distinct numbers among \... | math | {
"style": "rule",
"ground_truth": "46"
} | {
"index": 35042,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2008 congruent circles on a plane such that no two are tangent to each other and each circle intersects at least three other circles. Let $ N$ be the total number of intersection points of these circles. Determine the smallest possible values of $ N$ ."
}
] | math | {
"style": "rule",
"ground_truth": "3012"
} | {
"index": 35043,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2008 distinct points on a circle. If you connect two of these points to form a line and then connect another two points (distinct from the first two) to form another line, what is the probability that the two lines intersect inside the circle?"
}
] | math | {
"style": "rule",
"ground_truth": "1/3"
} | {
"index": 35044,
"solution": "Given four of these points, there are 3 ways in which to connect two of them and then connect the other two, and of these possibilities exactly one will intersect inside the circle. Thus $1 / 3$ of all the ways to connect two lines and then connect two others have an intersection poin... |
DeepScaleR | [
{
"role": "user",
"content": "There are 2008 red cards and 2008 white cards. 2008 players sit down in circular toward the inside of the circle in situation that 2 red cards and 2 white cards from each card are delivered to each person. Each person conducts the following procedure in one turn as follows.\r\... | math | {
"style": "rule",
"ground_truth": "1004"
} | {
"index": 35045,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2009 numbers arranged in a circle, each of which is either 1 or -1, and not all numbers are the same. Consider all possible consecutive groups of ten numbers. Compute the product of the numbers in each group of ten and sum these products. What is the maximum possible ... | math | {
"style": "rule",
"ground_truth": "2005"
} | {
"index": 35046,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2010 boxes labeled $B_1, B_2, \\dots, B_{2010}$, and $2010n$ balls have been distributed\namong them, for some positive integer $n$. You may redistribute the balls by a sequence of moves,\neach of which consists of choosing an $i$ and moving \\emph{exactly} $i$ balls ... | math | {
"style": "rule",
"ground_truth": "n \\geq 1005"
} | {
"index": 35047,
"solution": "It is possible if and only if $n \\geq 1005$.\nSince\n\\[\n1 + \\cdots + 2009 = \\frac{2009 \\times 2010}{2} = 2010 \\times 1004.5,\n\\]\nfor $n \\leq 1004$, we can start with an initial distribution in which each box\n$B_i$ starts with at most $i-1$ balls (so in particular $B_1$ is e... |
DeepScaleR | [
{
"role": "user",
"content": "There are 2011 positive numbers with both their sum and the sum of their reciprocals equal to 2012. Let $x$ be one of these numbers. Find the maximum value of $x + \\frac{1}{x}.$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{8045}{2012}"
} | {
"index": 35048,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2012 distinct points in the plane, each of which is to be coloured using one of \\( n \\) colours so that the number of points of each colour are distinct. A set of \\( n \\) points is said to be multi-coloured if their colours are distinct. Determine \\( n \\) that m... | math | {
"style": "rule",
"ground_truth": "61"
} | {
"index": 35049,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2014 points marked on a circle. A grasshopper sits on one of these points and makes jumps either 57 divisions or 10 divisions clockwise. It is known that he visited all the marked points, making the minimum number of jumps."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 35050,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2016 points arranged on a circle. We are allowed to jump 2 or 3 points clockwise at will.\n\nHow many jumps must we make at least to reach all the points and return to the starting point again?"
}
] | math | {
"style": "rule",
"ground_truth": "2017"
} | {
"index": 35051,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2017 jars in a row on a table, initially empty. Each day, a nice man picks ten consecutive jars and deposits one coin in each of the ten jars. Later, Kelvin the Frog comes back to see that $N$ of the jars all contain the same positive integer number of coins (i.e. the... | math | {
"style": "rule",
"ground_truth": "2014"
} | {
"index": 35052,
"solution": "Label the jars $1,2, \\ldots, 2017$. I claim that the answer is 2014. To show this, we need both a construction and an upper bound. For the construction, for $1 \\leq i \\leq 201$, put a coin in the jars $10 i+1,10 i+2, \\ldots, 10 i+10$. After this, each of the jars $1,2, \\ldots, 20... |
DeepScaleR | [
{
"role": "user",
"content": "There are 2019 bags, each bag containing 2019 beads with a total weight of 1 kilogram. The beads in each bag are numbered \\(1, 2, \\cdots, 2019\\). A selection is considered proper if and only if beads with different numbers are selected from different bags (at most one bead f... | math | {
"style": "rule",
"ground_truth": "2018!"
} | {
"index": 35053,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2019 numbers written on the board. One of them occurs more frequently than the others - 10 times. What is the minimum number of different numbers that could be written on the board?"
}
] | math | {
"style": "rule",
"ground_truth": "225"
} | {
"index": 35054,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2019 students in a school, and some of these students are members of different student clubs. Each student club has an advisory board consisting of 12 students who are members of that particular club. An {\\em advisory meeting} (for a particular club) can be realized ... | math | {
"style": "rule",
"ground_truth": "\\binom{2003}{11}"
} | {
"index": 35055,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2020 quadratic equations written on the board:\n\n$$\n\\begin{gathered}\n2020 x^{2}+b x+2021=0 \\\\\n2019 x^{2}+b x+2020=0 \\\\\n2018 x^{2}+b x+2019=0 \\\\\n\\ldots \\\\\nx^{2}+b x+2=0\n\\end{gathered}\n$$\n\n(each subsequent equation is obtained from the previous one... | math | {
"style": "rule",
"ground_truth": "2021"
} | {
"index": 35056,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 2021 balls in a crate, numbered from 1 to 2021. Erica calculates the digit sum for each ball. For example, the digit sum of 2021 is 5, since \\(2+0+2+1=5\\). Balls with equal digit sums have the same color and balls with different digit sums have different colors. How... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"index": 35057,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 203 students in the third grade, which is 125 fewer than the fourth grade. How many students are there in total in the third and fourth grades?"
}
] | math | {
"style": "rule",
"ground_truth": "531"
} | {
"index": 35058,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 21 competitors with distinct skill levels numbered $1,2, \\ldots, 21$. They participate in a pingpong tournament as follows. First, a random competitor is chosen to be \"active\", while the rest are \"inactive.\" Every round, a random inactive competitor is chosen to ... | math | {
"style": "rule",
"ground_truth": "\\frac{47}{42}"
} | {
"index": 35059,
"solution": "Solution 1: Insert a player with skill level 0, who will be the first active player (and lose their first game). If Alice plays after any of the players with skill level $12,13, \\ldots, 21$, which happens with probability $\\frac{10}{11}$, then she will play exactly 1 game. If Alice ... |
DeepScaleR | [
{
"role": "user",
"content": "There are 21 different pairs of digits (a, b) such that $\\overline{5a68} \\times \\overline{865b}$ is divisible by 824."
}
] | math | {
"style": "rule",
"ground_truth": "19"
} | {
"index": 35060,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 21 nonzero numbers. For each pair of these numbers, their sum and product are calculated. It turns out that half of all the sums are positive and half are negative. What is the maximum possible number of positive products?"
}
] | math | {
"style": "rule",
"ground_truth": "120"
} | {
"index": 35061,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 21 students in Class 3(1), with student numbers ranging from 1 to 21. They are arranged in a circle. The differences between the student numbers of each adjacent pair are recorded as positive values, calculated as the larger number minus the smaller number. What is th... | math | {
"style": "rule",
"ground_truth": "220"
} | {
"index": 35062,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 22 black and 3 blue balls in a bag. Ahmet chooses an integer $ n$ in between 1 and 25. Betül draws $ n$ balls from the bag one by one such that no ball is put back to the bag after it is drawn. If exactly 2 of the $ n$ balls are blue and the second blue ball is ... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 35063,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 22 people standing in a circle, and each of them is either a knight (who always tells the truth) or a liar (who always lies). Each person says: \"The next 10 people clockwise from me are liars.\" How many liars are there among these 22 people?"
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 35064,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 23 socks in a drawer: 8 white and 15 black. Every minute, Marina goes to the drawer and pulls out a sock. If at any moment Marina has pulled out more black socks than white ones, she exclaims, \"Finally!\" and stops the process.\n\nWhat is the maximum number of socks ... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"index": 35065,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 24 four-digit whole numbers that use each of the four digits 2, 4, 5 and 7 exactly once. Only one of these four-digit numbers is a multiple of another one. What is it?"
}
] | math | {
"style": "rule",
"ground_truth": "7425"
} | {
"index": 35066,
"solution": "To solve this problem, we need to determine which of the given four-digit numbers is a multiple of another four-digit number formed using the digits 2, 4, 5, and 7 exactly once.\n\n1. **Identify the Range of Numbers**: The numbers formed by the digits 2, 4, 5, and 7 are between the sm... |
DeepScaleR | [
{
"role": "user",
"content": "There are 256 players in a tennis tournament who are ranked from 1 to 256, with 1 corresponding to the highest rank and 256 corresponding to the lowest rank. When two players play a match in the tournament, the player whose rank is higher wins the match with probability \\(\\fr... | math | {
"style": "rule",
"ground_truth": "103"
} | {
"index": 35067,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 26 bricks, and two brothers are vying to take them. The younger brother arrives first and arranges the bricks. The elder brother arrives and thinks the younger brother has taken too many, so he takes half of the bricks from the younger brother. The younger brother, fe... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 35068,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 29 ones written on a board. Each minute, Karlson 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 29 minutes?"
}
] | math | {
"style": "rule",
"ground_truth": "406"
} | {
"index": 35069,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 29 students in a class: some are honor students who always tell the truth, and some are troublemakers who always lie.\n\nAll the students in this class sat at a round table.\n\n- Several students said: \"There is exactly one troublemaker next to me.\"\n- All other stu... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 35070,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 294 distinct cards with numbers \\(7, 11, 7^{2}, 11^{2}, \\ldots, 7^{147}, 11^{147}\\) (each card has exactly one number, and each number appears exactly once). How many ways can two cards be selected so that the product of the numbers on the selected cards is a perfe... | math | {
"style": "rule",
"ground_truth": "15987"
} | {
"index": 35071,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 boys and 3 girls, making a total of 6 students standing in a row.\n\n(1) If the three girls must stand together, find the total number of different arrangements.\n(2) If boy A cannot stand at either end, and among the 3 girls, exactly two girls stand together, find ... | math | {
"style": "rule",
"ground_truth": "288"
} | {
"index": 35072,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 boys and 4 girls, all lined up in a row. How many ways are there for the following situations?\n- $(1)$ Person A is neither at the middle nor at the ends;\n- $(2)$ Persons A and B must be at the two ends;\n- $(3)$ Boys and girls alternate."
}
] | math | {
"style": "rule",
"ground_truth": "144"
} | {
"index": 35073,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 complex numbers $a+bi$, $c+di$, and $e+fi$. If $b=1$, $e=-a-c$, and the sum of the numbers is $-i$, find $d+f$."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"index": 35074,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 complex numbers $a+bi$, $c+di$, and $e+fi$. If $b=3$, $e=-a-c$, and the sum of the numbers is $2i$, find $d+f$."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 35075,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 different balls to be placed into 5 different boxes, with at most one ball per box. How many methods are there?"
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 35076,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 different pairs of shoes in a shoe cabinet. If one shoe is picked at random from the left shoe set of 6 shoes, and then another shoe is picked at random from the right shoe set of 6 shoes, calculate the probability that the two shoes form a pair."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"index": 35077,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 female and 2 male volunteers, a total of 5 volunteers, who need to be distributed among 3 communities to participate in volunteer services. Each community can have 1 to 2 people. Female volunteers A and B must be in the same community, and male volunteers must be in... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 35078,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 females and 3 males to be arranged in a sequence of 6 contestants, with the restriction that no two males can perform consecutively and the first contestant cannot be female contestant A. Calculate the number of different sequences of contestants."
}
] | math | {
"style": "rule",
"ground_truth": "132"
} | {
"index": 35079,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 male students and 2 female students. Calculate the total number of different arrangement methods under the following different requirements: \n(1) All are arranged in a row where \"A\" can only be in the middle or on the sides. There are \\_\\_\\_\\_\\_\\_ ways to... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 35080,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 math clubs in the school district, with 5, 7, and 8 students respectively. Each club has two co-presidents. If I randomly select a club, and then randomly select three members of that club to give a copy of $\\emph{Introduction to} \\allowbreak\\ \\emph{Counting and... | math | {
"style": "rule",
"ground_truth": "\\dfrac{11}{60}"
} | {
"index": 35081,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 math teams in the area, with 5, 7, and 8 students respectively. Each team has two co-captains. If I randomly select a team, and then randomly select two members of that team to give a copy of $\\emph{Introduction to Geometry}$, what is the probability that both of t... | math | {
"style": "rule",
"ground_truth": "\\dfrac{11}{180}"
} | {
"index": 35082,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 numbers A, B, and C, such that $1001C - 2002A = 4004$, and $1001B + 3003A = 5005$. What is the average of A, B, and C?"
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 35083,
"solution": "1. **Isolate $C$ and $B$ in terms of $A$:**\n - From the equation $1001C - 2002A = 4004$, we can isolate $C$:\n \\[\n 1001C = 2002A + 4004 \\implies C = 2A + 4\n \\]\n - From the equation $1001B + 3003A = 5005$, we can isolate $B$:\n \\[\n 1001B = 5005 - 3003A ... |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 rods with several golden disks of different sizes placed on them. Initially, 5 disks are arranged on the leftmost rod (A) in descending order of size. According to the rule that only one disk can be moved at a time and a larger disk can never be placed on top of a s... | math | {
"style": "rule",
"ground_truth": "31"
} | {
"index": 35084,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 screw-in light bulbs and 5 bayonet light bulbs in the box, and light bulbs are randomly drawn without replacement until the 5th light bulb is drawn to have all the screw-in light bulbs. Calculate the probability of this event."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{28}"
} | {
"index": 35085,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 small balls of each of the red, yellow, and blue colors, with the same size. Each of the 3 balls of each color is marked with numbers 1, 2, and 3. If 3 balls are randomly drawn, find the probability that neither their colors nor their numbers are the same."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{14}"
} | {
"index": 35086,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3 teachers who have all assigned homework. Determine the number of possible situations where 4 students are doing homework at the same time."
}
] | math | {
"style": "rule",
"ground_truth": "3^{4}"
} | {
"index": 35087,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 30 people in a room, 60\\% of whom are men. If no men enter or leave the room, how many women must enter the room so that 40\\% of the total number of people in the room are men?"
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 35088,
"solution": "Since there are 30 people in a room and 60\\% of them are men, then there are \\( \\frac{6}{10} \\times 30=18 \\) men in the room and 12 women. Since no men enter or leave the room, then these 18 men represent 40\\% of the final number in the room. Thus, 9 men represent 20\\% of the t... |
DeepScaleR | [
{
"role": "user",
"content": "There are 30 people in my math class. 12 of them have cool dads, 15 of them have cool moms, and 9 of them have cool dads and cool moms. How many people have moms and dads who are both uncool?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 35089,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 30 students in Mrs. Taylor's kindergarten class. If there are twice as many students with blond hair as with blue eyes, 6 students with blond hair and blue eyes, and 3 students with neither blond hair nor blue eyes, how many students have blue eyes?"
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 35090,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 300 children in the \"Young Photographer\" club. In a session, they divided into 100 groups of 3 people each, and in every group, each member took a photograph of the other two members in their group. No one took any additional photographs. In total, there were 100 ph... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"index": 35091,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 3012 positive numbers with both their sum and the sum of their reciprocals equal to 3013. Let $x$ be one of these numbers. Find the maximum value of $x + \\frac{1}{x}.$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{12052}{3013}"
} | {
"index": 35092,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 306 different cards with numbers \\(3, 19, 3^{2}, 19^{2}, \\ldots, 3^{153}, 19^{153}\\) (each card has exactly one number, and each number appears exactly once). How many ways can you choose 2 cards such that the product of the numbers on the selected cards is a perfe... | math | {
"style": "rule",
"ground_truth": "17328"
} | {
"index": 35093,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 32 ones written on the board. Each minute, Carlsson erases any two numbers, writes their sum on the board, and then eats an amount of candy equal to the product of the two erased numbers. What is the maximum number of candies he could eat in 32 minutes?"
}
] | math | {
"style": "rule",
"ground_truth": "496"
} | {
"index": 35094,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 35 groups of students, each group containing 3 students. Among these groups:\n- 10 groups have only 1 boy.\n- 19 groups have at least 2 boys.\n- The number of groups with 3 boys is twice the number of groups with 3 girls.\n\nHow many boys are there?"
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 35095,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 36 students at the Multiples Obfuscation Program, including a singleton, a pair of identical twins, a set of identical triplets, a set of identical quadruplets, and so on, up to a set of identical octuplets. Two students look the same if and only if they are from the ... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{17}"
} | {
"index": 35096,
"solution": "Let $X$ and $Y$ be the students Nithya encounters during the day. The number of pairs $(X, Y)$ for which $X$ and $Y$ look the same is $1 \\cdot 1+2 \\cdot 2+\\ldots+8 \\cdot 8=204$, and these pairs include all the ones in which $X$ and $Y$ are identical. As $X$ and $Y$ are chosen unif... |
DeepScaleR | [
{
"role": "user",
"content": "There are 36 students in a club. If any 33 of them attend a session, girls will always be in the majority. However, if 31 students attend, it might happen that boys are in the majority. How many girls are in the club?"
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 35097,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 37 people lined up in a row, and they are counting off one by one. The first person says 1, and each subsequent person says the number obtained by adding 3 to the previous person’s number. At one point, someone makes a mistake and subtracts 3 from the previous person'... | math | {
"style": "rule",
"ground_truth": "34"
} | {
"index": 35098,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "There are 4 boys and 3 girls lining up for a photo. The number of ways they can line up such that no two boys are adjacent is \\_\\_\\_\\_ (answer with a number), and the number of ways they can line up such that no two girls are adjacent is \\_\\_\\_\\_ (answer with a number).... | math | {
"style": "rule",
"ground_truth": "1440"
} | {
"index": 35099,
"solution": ""
} |
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