data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "A gives 24 apples to B and C, and each of the three people has at least two apples. How many different ways are there to distribute the apples?"
}
] | math | {
"style": "rule",
"ground_truth": "190"
} | {
"index": 1900,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A gives B as many cents as B has and C as many cents as C has. Similarly, B then gives A and C as many cents as each then has. C, similarly, then gives A and B as many cents as each then has. After this, each person gives half of what they have to each other person. If each fin... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 1901,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A glass is filled to the brim with salty water. Fresh ice with mass \\( m = 502 \\) floats on the surface. What volume \\( \\Delta V \\) of water will spill out of the glass by the time the ice melts? Neglect surface tension. The density of fresh ice is \\( \\rho_{n} = 0.92 \\,... | math | {
"style": "rule",
"ground_truth": "2.63"
} | {
"index": 1902,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A gold coin is worth $x\\%$ more than a silver coin. The silver coin is worth $y\\%$ less than the gold coin. Both $x$ and $y$ are positive integers. How many possible values for $x$ are there?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 1903,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A graduating high school class has $45$ people. Each student writes a graduation message to every other student, with each pair writing only one message between them. How many graduation messages are written in total? (Answer with a number)"
}
] | math | {
"style": "rule",
"ground_truth": "1980"
} | {
"index": 1904,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A granary has collected 1536 shi of rice, and upon inspection, it is found that out of 224 grains, 28 are weeds. Determine the approximate amount of weeds in this batch of rice."
}
] | math | {
"style": "rule",
"ground_truth": "192"
} | {
"index": 1905,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A granite pedestal. When constructing a square foundation and a cubic pedestal for a monument, granite cubic blocks of size \\(1 \\times 1\\) meter were used. The pedestal used exactly as many blocks as the square foundation upon which it stood. All the blocks were used whole a... | math | {
"style": "rule",
"ground_truth": "128"
} | {
"index": 1906,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A graph $G(V,E)$ is triangle-free, but adding any edges to the graph will form a triangle. It's given that $|V|=2019$, $|E|>2018$, find the minimum of $|E|$ ."
}
] | math | {
"style": "rule",
"ground_truth": "4033"
} | {
"index": 1907,
"solution": "\nGiven a graph \\( G(V, E) \\) that is triangle-free, but adding any edges to the graph will form a triangle, and with \\( |V| = 2019 \\) and \\( |E| > 2018 \\), we need to find the minimum number of edges \\( |E| \\).\n\nWe claim that the minimum number of edges is \\( 2n - 5 \\) whe... |
DeepScaleR | [
{
"role": "user",
"content": "A graph has $ 30$ vertices, $ 105$ edges and $ 4822$ unordered edge pairs whose endpoints are disjoint. Find the maximal possible difference of degrees of two vertices in this graph."
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"index": 1908,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A graph has 1982 points. Given any four points, there is at least one joined to the other three. What is the smallest number of points which are joined to 1981 points?"
}
] | math | {
"style": "rule",
"ground_truth": "1979"
} | {
"index": 1909,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A graph shows the number of books read in June by the top readers in a school library. The data points given are:\n- 4 readers read 3 books each\n- 5 readers read 5 books each\n- 2 readers read 7 books each\n- 1 reader read 10 books\nDetermine the mean (average) number of books... | math | {
"style": "rule",
"ground_truth": "5.0833"
} | {
"index": 1910,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A green chameleon always tells the truth, while a brown chameleon lies and immediately turns green after lying. In a group of 2019 chameleons (both green and brown), each chameleon, in turn, answered the question, \"How many of them are green right now?\" The answers were the n... | math | {
"style": "rule",
"ground_truth": "1010"
} | {
"index": 1911,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A green point and a purple point are chosen at random on the number line between 0 and 1. What is the probability that the purple point is greater than the green point but less than three times the green point?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"index": 1912,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A grid consists of multiple squares, as shown below. Count the different squares possible using the lines in the grid.\n\n[asy]\nunitsize(0.5 cm);\nint i, j;\nfor(i = 0; i <= 5; ++i) {\n draw((0,i)--(5,i));\n draw((i,0)--(i,5));\n}\nfor(i = 1; i <= 4; ++i) {\n for (j =... | math | {
"style": "rule",
"ground_truth": "54"
} | {
"index": 1913,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A grocer arranges a display of cans where the top row has three cans, and each lower row has two more cans than the row above it. The total number of cans in the display is 169. How many rows does the display contain?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 1914,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A grocer creates a display of cans where the top row contains two cans and each subsequent lower row has three more cans than the row preceding it. If the total number of cans used in the display is 120, how many rows are there in the display?"
}
] | math | {
"style": "rule",
"ground_truth": "n = 9"
} | {
"index": 1915,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains 100 cans, how many rows does it contain?"
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 1916,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A grocer sets up a pyramid display for a store promotion, where the topmost row has three cans and each succeeding row below has three more cans than the row immediately above it. If the grocer uses 225 cans in total for this display, how many rows are there in the display?"
... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 1917,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A grocer stacks oranges in a pyramid-like stack whose rectangular base is $5$ oranges by $8$ oranges. Each orange above the first level rests in a pocket formed by four oranges below. The stack is completed by a single row of oranges. How many oranges are in the stack?"
}
... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 1918,
"solution": "1. **Calculate the number of oranges in each layer**:\n - The base layer (1st layer) is a rectangle of $5$ oranges by $8$ oranges. Thus, the number of oranges in the 1st layer is:\n \\[\n 5 \\times 8 = 40\n \\]\n - Each subsequent layer reduces in size by one orange in ... |
DeepScaleR | [
{
"role": "user",
"content": "A grocery store manager decides to design a more compact pyramid-like stack of apples with a rectangular base of 4 apples by 6 apples. Each apple above the first level still rests in a pocket formed by four apples below, and the stack is completed with a double row of apples on... | math | {
"style": "rule",
"ground_truth": "53"
} | {
"index": 1919,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group consists of 4 boys and 3 girls.\n(1) If one boy and one girl are each chosen to host a program, how many different selections are possible?\n(2) If two boys and two girls are chosen to form a small choir, and are to be arranged in a row with the requirement that the two... | math | {
"style": "rule",
"ground_truth": "216"
} | {
"index": 1920,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group consists of 4 male students and 3 female students. From this group, 4 people are selected to complete three different tasks, with the condition that at least two of the selected individuals must be female, and each task must have at least one person assigned to it. The ... | math | {
"style": "rule",
"ground_truth": "792"
} | {
"index": 1921,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group consists of 5 girls and 5 boys. The members of the same gender do not know each other, and there are no two girls who have two mutual boy acquaintances. What is the maximum number of acquaintanceships within the group? How does the answer change if the group consists of... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"index": 1922,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of $6$ friends are to be seated in the back row of an otherwise empty movie theater with $8$ seats in a row. Euler and Gauss are best friends and must sit next to each other with no empty seat between them, while Lagrange cannot sit in an adjacent seat to either Eul... | math | {
"style": "rule",
"ground_truth": "3360"
} | {
"index": 1923,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of $10$ students from Class 9(1) of a certain school are doing \"pull-up\" training. The number of times they have done it is recorded in the table below. Find the median of the number of times these $10$ students have done.\n\n| Times | $4$ | $5$ | $6$ | $7$ | $8$ |\n|... | math | {
"style": "rule",
"ground_truth": "5.5"
} | {
"index": 1924,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of $12$ pirates agree to divide a treasure chest of gold coins among themselves as follows. The $k^{\\text{th}}$ pirate to take a share takes $\\frac{k}{12}$ of the coins that remain in the chest. The number of coins initially in the chest is the smallest number for whi... | math | {
"style": "rule",
"ground_truth": "1925"
} | {
"index": 1925,
"solution": "To solve this problem, we need to determine the smallest number of coins in the chest initially, such that each pirate receives a whole number of coins when taking their share according to the given rule. The rule states that the $k^{\\text{th}}$ pirate takes $\\frac{k}{12}$ of the rem... |
DeepScaleR | [
{
"role": "user",
"content": "A group of 101 Dalmathians participate in an election, where they each vote independently on either candidate \\(A\\) or \\(B\\) with equal probability. If \\(X\\) Dalmathians voted for the winning candidate, the expected value of \\(X^{2}\\) can be expressed as \\(\\frac{a}{b}... | math | {
"style": "rule",
"ground_truth": "51"
} | {
"index": 1926,
"solution": "Claim: with 101 replaced with \\(2k+1\\), the expectation of \\(X^{2}\\) is \\(\\frac{\\binom{2k}{k}}{2^{2k+1}}(2k+1)^{2}+\\frac{(2k+1)(2k+2)}{4}\\). The answer is this value taken modulo 103, which can be calculated by noting that the integers modulo 103 form a finite field. Note that... |
DeepScaleR | [
{
"role": "user",
"content": "A group of 11 people, including Ivanov and Petrov, are seated in a random order around a circular table. Find the probability that there will be exactly 3 people sitting between Ivanov and Petrov."
}
] | math | {
"style": "rule",
"ground_truth": "1/10"
} | {
"index": 1927,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of 12 friends decides to form a committee of 5. Calculate the number of different committees that can be formed. Additionally, if there are 4 friends who refuse to work together, how many committees can be formed without any of these 4 friends?"
}
] | math | {
"style": "rule",
"ground_truth": "56"
} | {
"index": 1928,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of 25 friends were discussing a large positive integer. ``It can be divided by 1,'' said the first friend. ``It can be divided by 2,'' said the second friend. ``And by 3,'' said the third friend. ``And by 4,'' added the fourth friend. This continued until everyone had m... | math | {
"style": "rule",
"ground_truth": "787386600"
} | {
"index": 1929,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of 40 boys and 28 girls stand hand in hand in a circle facing inwards. Exactly 18 of the boys give their right hand to a girl. How many boys give their left hand to a girl?"
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 1930,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of 50 girls sit in a circle. They throw a ball around the circle. Each girl who gets the ball throws it to the girl sitting six places anticlockwise from her, who catches it. Freda catches the ball 100 times. In that time, how many girls never get to catch the ball?"
... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 1931,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of 8 boys and 8 girls was paired up randomly. Find the probability that there is at least one pair with two girls. Round your answer to the nearest hundredth."
}
] | math | {
"style": "rule",
"ground_truth": "0.98"
} | {
"index": 1932,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of adventurers displays their loot. It is known that exactly 9 adventurers have rubies; exactly 8 have emeralds; exactly 2 have sapphires; exactly 11 have diamonds. Additionally, it is known that:\n\n- If an adventurer has diamonds, they either have rubies or sapphires ... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"index": 1933,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of adventurers is showing their loot. It is known that exactly 5 adventurers have rubies; exactly 11 have emeralds; exactly 10 have sapphires; exactly 6 have diamonds. Additionally, it is known that:\n\n- If an adventurer has diamonds, then they have either emeralds or ... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 1934,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of children held a grape-eating contest. When the contest was over, the winner had eaten $n$ grapes, and the child in $k$-th place had eaten $n+2-2k$ grapes. The total number of grapes eaten in the contest was $2009$. Find the smallest possible value of $n$."
}
] | math | {
"style": "rule",
"ground_truth": "89"
} | {
"index": 1935,
"solution": "If the first child ate $n=2m$ grapes, then the maximum number of grapes eaten by all the children together is $2m + (2m-2) + (2m-4) + \\cdots + 4 + 2 = m(m+1)$. Similarly, if the first child ate $2m-1$ grapes, the maximum total number of grapes eaten is $(2m-1)+(2m-3)+\\cdots+3+1 = m^2... |
DeepScaleR | [
{
"role": "user",
"content": "A group of children riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted $7$ children and $19$ wheels. How many tricycles were there?"
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"index": 1936,
"solution": "\nWe are given that there are 7 children and 19 wheels. Each child is riding either a bicycle (which has 2 wheels) or a tricycle (which has 3 wheels). We need to determine the number of tricycles.\n\n#### Solution 1: Using a substitution method\n1. Let $b$ be the number of bicycles and... |
DeepScaleR | [
{
"role": "user",
"content": "A group of children, numbering between 50 and 70, attended a spring math camp. To celebrate Pi Day (March 14), they decided to give each other squares if they were just acquaintances and circles if they were friends. Andrey noted that each boy received 3 circles and 8 squares, ... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 1937,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of clerks is assigned the task of sorting $1775$ files. Each clerk sorts at a constant rate of $30$ files per hour. At the end of the first hour, some of the clerks are reassigned to another task; at the end of the second hour, the same number of the remaining clerks ar... | math | {
"style": "rule",
"ground_truth": "945"
} | {
"index": 1938,
"solution": "We start with the same approach as solution 1 to get $19x-21t=355$. Then notice that $21t + 355 \\equiv 0 \\pmod{19}$, or $2t-6 \\equiv 0 \\pmod{19}$, giving the smallest solution at $t=3$. We find that $x=22$. Then the number of files they sorted will be $30x+15(x-t)=660+285=\\boxed{9... |
DeepScaleR | [
{
"role": "user",
"content": "A group of cows and horses are randomly divided into two equal rows. Each animal in one row is directly opposite an animal in the other row. If 75 of the animals are horses and the number of cows opposite cows is 10 more than the number of horses opposite horses, determine the ... | math | {
"style": "rule",
"ground_truth": "170"
} | {
"index": 1939,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of dancers are arranged in a rectangular formation. When they are arranged in 12 rows, there are 5 positions unoccupied in the formation. When they are arranged in 10 rows, there are 5 positions unoccupied. How many dancers are in the group if the total number is betwee... | math | {
"style": "rule",
"ground_truth": "295"
} | {
"index": 1940,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of friends are sharing a bag of candy. On the first day, they eat $\frac{1}{2}$ of the candies in the bag. On the second day, they eat $\frac{2}{3}$ of the remaining candies. On the third day, they eat $\frac{3}{4}$ of the remaining candies. On the fourth day, they eat ... | math | {
"style": "rule",
"ground_truth": "720"
} | {
"index": 1941,
"solution": "We work backwards through the given information. At the end, there is 1 candy remaining. Since $\frac{5}{6}$ of the candies are removed on the fifth day, this 1 candy represents $\frac{1}{6}$ of the candies left at the end of the fourth day. Thus, there were $6 \times 1=6$ candies left... |
DeepScaleR | [
{
"role": "user",
"content": "A group of n friends wrote a math contest consisting of eight short-answer problem $S_1, S_2, S_3, S_4, S_5, S_6, S_7, S_8$ , and four full-solution problems $F_1, F_2, F_3, F_4$ . Each person in the group correctly solved exactly 11 of the 12 problems. We create an 8 x 4 t... | math | {
"style": "rule",
"ground_truth": "32"
} | {
"index": 1942,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of one hundred friends, including Petya and Vasya, live in several cities. Petya found the distance from his city to the city of each of the other 99 friends and summed these 99 distances, obtaining a total of 1000 km. What is the maximum possible total distance that Va... | math | {
"style": "rule",
"ground_truth": "99000"
} | {
"index": 1943,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of schoolchildren, heading to a school camp, was planned to be seated in buses so that there would be an equal number of passengers in each bus. Initially, 22 people were seated in each bus, but it turned out that three schoolchildren could not be seated. However, when ... | math | {
"style": "rule",
"ground_truth": "135"
} | {
"index": 1944,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of students during a sports meeting lined up for a team photo. When they lined up in rows of 5, there were two students left over. When they formed rows of 6 students, there were three extra students, and when they lined up in rows of 8, there were four students left ov... | math | {
"style": "rule",
"ground_truth": "59"
} | {
"index": 1945,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of toddlers in a kindergarten collectively has 90 teeth. Any two toddlers together have no more than 9 teeth. What is the minimum number of toddlers that can be in the group?"
}
] | math | {
"style": "rule",
"ground_truth": "23"
} | {
"index": 1946,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group of women working together at the same rate can build a wall in $45$ hours. When the work started, all the women did not start working together. They joined the worked over a period of time, one by one, at equal intervals. Once at work, each one stayed till the work wa... | math | {
"style": "rule",
"ground_truth": "75"
} | {
"index": 1947,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A group with 7 young men and 7 young women was divided into pairs randomly. Find the probability that at least one pair consists of two women. Round the answer to two decimal places."
}
] | math | {
"style": "rule",
"ground_truth": "0.96"
} | {
"index": 1948,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A gumball machine contains $9$ red, $7$ white, and $8$ blue gumballs. The least number of gumballs a person must buy to be sure of getting four gumballs of the same color is"
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 1949,
"solution": "To determine the least number of gumballs a person must buy to be sure of getting four gumballs of the same color, we consider the worst-case scenario where the gumballs are picked in such a way that it takes the maximum number of picks to get four gumballs of the same color.\n\n1. **T... |
DeepScaleR | [
{
"role": "user",
"content": "A gymnastics team consists of 48 members. To form a square formation, they need to add at least ____ people or remove at least ____ people."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 1950,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hairdresser moved from Vienna to Debrecen to continue his trade. Over the course of 3 years, he became impoverished despite having some money originally. In the first year, he had to spend half of his money. In the second year, he spent a third of what he initially took with ... | math | {
"style": "rule",
"ground_truth": "1500"
} | {
"index": 1951,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hall is organizing seats in rows for a lecture. Each complete row must contain $13$ chairs. Initially, the hall has $169$ chairs arranged. To maintain fully occupied rows with minimal empty seats, if $100$ students are expected to attend, how many chairs should be removed or ... | math | {
"style": "rule",
"ground_truth": "65"
} | {
"index": 1952,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hare is jumping in one direction on a strip divided into cells. In one jump, it can move either one cell or two cells. How many ways can the hare get from the 1st cell to the 12th cell?"
}
] | math | {
"style": "rule",
"ground_truth": "144"
} | {
"index": 1953,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A haunted house has six windows. In how many ways can Georgie the Ghost enter the house by one window and leave by a different window?"
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 1954,
"solution": "1. **Choosing the Entry Window:** Georgie the Ghost has 6 different windows to choose from when deciding where to enter the haunted house. This gives him 6 options for entry.\n\n2. **Choosing the Exit Window:** After entering through one window, there are 5 remaining windows that Georg... |
DeepScaleR | [
{
"role": "user",
"content": "A heavy concrete platform anchored to the seabed in the North Sea supported an oil rig that stood 40 m above the calm water surface. During a severe storm, the rig toppled over. The catastrophe was captured from a nearby platform, and it was observed that the top of the rig dis... | math | {
"style": "rule",
"ground_truth": "68.2"
} | {
"index": 1955,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hectoliter barrel is full of wine; 1 liter of liquid flows out in 24 hours, which is replaced by the inflow of 1 liter of water. After how much time will the contents of the barrel be half wine and half water?"
}
] | math | {
"style": "rule",
"ground_truth": "69"
} | {
"index": 1956,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hemisphere is placed on a sphere of radius \\(100 \\text{ cm}\\). The second hemisphere is placed on the first one, and the third hemisphere is placed on the second one (as shown below). Find the maximum height of the tower (in cm)."
}
] | math | {
"style": "rule",
"ground_truth": "300"
} | {
"index": 1957,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hemisphere-shaped bowl with radius 1 foot is filled full with chocolate. All of the chocolate is then evenly distributed between 27 congruent, smaller hemisphere-shaped molds. What is the radius of each of the smaller molds, in feet?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"index": 1958,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hemisphere-shaped bowl with radius 1 foot is filled full with chocolate. All of the chocolate is then evenly distributed between 36 cylindrical molds, each having a height equal to their diameter. What is the diameter of each cylinder?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2^{1/3}}{3}"
} | {
"index": 1959,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A heptagonal prism has ____ faces and ____ vertices."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 1960,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A herd of 183 elephants could drink the lake in 1 day, and a herd of 37 elephants could do it in 5 days.\n\nIn how many days will one elephant drink the lake?"
}
] | math | {
"style": "rule",
"ground_truth": "365"
} | {
"index": 1961,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A herd of elephants. Springs are bubbling at the bottom of the lake. A herd of 183 elephants could drink it dry in one day, and a herd of 37 elephants could do so in 5 days. How many days will it take for 1 elephant to drink the lake dry?"
}
] | math | {
"style": "rule",
"ground_truth": "365"
} | {
"index": 1962,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A herder has forgotten the number of cows she has, and does not want to count them all of them. She remembers these four facts about the number of cows: \n\n\n- It has $3$ digits.\n- It is a palindrome.\n- The middle digit is a multiple of $4$ .\n- It is divisible by $11$ .... | math | {
"style": "rule",
"ground_truth": "726"
} | {
"index": 1963,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hexagon has its vertices alternately on two concentric circles with radii 3 units and 5 units and centered at the origin on a Cartesian plane. Each alternate vertex starting from the origin extends radially outward to the larger circle. Calculate the area of this hexagon."
... | math | {
"style": "rule",
"ground_truth": "\\frac{51\\sqrt{3}}{2}"
} | {
"index": 1964,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hexagon inscribed in a circle has three consecutive sides, each of length 3, and three consecutive sides, each of length 5. The chord of the circle that divides the hexagon into two trapezoids, one with three sides, each of length 3, and the other with three sides, each of le... | math | {
"style": "rule",
"ground_truth": "409"
} | {
"index": 1965,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hexagon inscribed in a circle has three consecutive sides, each of length 4, and three consecutive sides, each of length 7. The chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length 4, and the other with three sides each of leng... | math | {
"style": "rule",
"ground_truth": "1017"
} | {
"index": 1966,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hexagon is inscribed in a circle. Five of the sides have length $81$ and the sixth, denoted by $\\overline{AB}$, has length $31$. Find the sum of the lengths of the three diagonals that can be drawn from $A$."
}
] | math | {
"style": "rule",
"ground_truth": "384"
} | {
"index": 1967,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hexagon is inscribed in a circle. Five of the sides have length $81$ and the sixth, denoted by $\\overline{AB}$, has length $31$. Find the sum of the lengths of the three diagonals that can be drawn from $A_{}^{}$."
}
] | math | {
"style": "rule",
"ground_truth": "384"
} | {
"index": 1968,
"solution": "[asy]defaultpen(fontsize(9)); pair A=expi(-pi/2-acos(475/486)), B=expi(-pi/2+acos(475/486)), C=expi(-pi/2+acos(475/486)+acos(7/18)), D=expi(-pi/2+acos(475/486)+2*acos(7/18)), E=expi(-pi/2+acos(475/486)+3*acos(7/18)), F=expi(-pi/2-acos(475/486)-acos(7/18)); draw(unitcircle);draw(A--B--C... |
DeepScaleR | [
{
"role": "user",
"content": "A hexagon is obtained by joining, in order, the points $(0,1)$, $(1,2)$, $(2,2)$, $(2,1)$, $(3,1)$, $(2,0)$, and $(0,1)$. The perimeter of the hexagon can be written in the form $a+b\\sqrt{2}+c\\sqrt{5}$, where $a$, $b$ and $c$ are whole numbers. Find $a+b+c$."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"index": 1969,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hexagon that is inscribed in a circle has side lengths $22$, $22$, $20$, $22$, $22$, and $20$ in that order. The radius of the circle can be written as $p+\\sqrt{q}$, where $p$ and $q$ are positive integers. Find $p+q$."
}
] | math | {
"style": "rule",
"ground_truth": "272"
} | {
"index": 1970,
"solution": "Using the trapezoid $ABCD$ mentioned above, draw an altitude of the trapezoid passing through point $B$ onto $AD$ at point $J$. Now, we can use the pythagorean theorem: $(22^2-(r-10)^2)+10^2=r^2$. Expanding and combining like terms gives us the quadratic \\[r^2-10r-242=0\\] and solving... |
DeepScaleR | [
{
"role": "user",
"content": "A hexagonal lattice now consists of 13 points where each point is one unit distance from its nearest neighbors. Points are arranged with one center point, six points forming a hexagon around the center, and an additional outer layer of six points forming a larger hexagon. How m... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 1971,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hexagonal prism has a height of 165 cm. Its two hexagonal faces are regular hexagons with sides of length 30 cm. Its other six faces are rectangles. A fly and an ant start at point \\(X\\) on the bottom face and travel to point \\(Y\\) on the top face. The fly flies directly ... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"index": 1972,
"solution": "Throughout this solution, we remove the units (cm) as each length is in these same units. First, we calculate the distance flown by the fly, which we call \\(f\\). Let \\(Z\\) be the point on the base on the prism directly underneath \\(Y\\). Since the hexagonal base has side length 30... |
DeepScaleR | [
{
"role": "user",
"content": "A hexagonal prism has a regular hexagonal base, and its lateral edges are perpendicular to the base. It is known that all the vertices of the hexagonal prism are on the same spherical surface, and the volume of the hexagonal prism is $\\frac{9}{8}$, with a base perimeter of 3. ... | math | {
"style": "rule",
"ground_truth": "\\frac{4\\pi}{3}"
} | {
"index": 1973,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A high school basketball game between the Raiders and Wildcats was tied at the end of the first quarter. The number of points scored by the Raiders in each of the four quarters formed an increasing geometric sequence, and the number of points scored by the Wildcats in each of t... | math | {
"style": "rule",
"ground_truth": "34"
} | {
"index": 1974,
"solution": "1. **Define the sequences**: Let the quarterly scores for the Raiders be $a, ar, ar^2, ar^3$ and for the Wildcats be $b, b+d, b+2d, b+3d$. Given that the sequences are increasing and the Raiders' sequence is geometric while the Wildcats' sequence is arithmetic.\n\n2. **Initial conditio... |
DeepScaleR | [
{
"role": "user",
"content": "A high school basketball team has 12 players, including a set of twins, John and James. In how many ways can we choose a starting lineup of 5 players if exactly one of the twins must be in the lineup?"
}
] | math | {
"style": "rule",
"ground_truth": "660"
} | {
"index": 1975,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A high school basketball team has 16 players, including a set of twins named Bob and Bill, and another set of twins named Tom and Tim. How many ways can we choose 5 starters if no more than one player from each set of twins can be chosen?"
}
] | math | {
"style": "rule",
"ground_truth": "3652"
} | {
"index": 1976,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A high school has three math teachers. To facilitate students, math teachers are scheduled for duty from Monday to Friday, with two teachers on duty on Monday. If each teacher is on duty for two days a week, then there are ________ possible duty schedules for a week."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 1977,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A high school is holding a speech contest with 10 participants. There are 3 students from Class 1, 2 students from Class 2, and 5 students from other classes. Using a draw to determine the speaking order, what is the probability that the 3 students from Class 1 are placed conse... | math | {
"style": "rule",
"ground_truth": "$\\frac{1}{20}$"
} | {
"index": 1978,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A high school math preparation group consists of six science teachers and two liberal arts teachers. During a three-day period of smog-related class suspensions, they need to arrange teachers to be on duty for question-answering sessions. The requirement is that each day, there... | math | {
"style": "rule",
"ground_truth": "540"
} | {
"index": 1979,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A high school math team received 5 college students for a teaching internship, who are about to graduate. They need to be assigned to three freshman classes: 1, 2, and 3, with at least one and at most two interns per class. Calculate the number of different allocation schemes."... | math | {
"style": "rule",
"ground_truth": "90"
} | {
"index": 1980,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A high school offers three separate elective classes for the senior two-grade mathematics course. After the selection process, four students request to change their math class. However, each class can accept at most two more students. Determine the number of different ways the ... | math | {
"style": "rule",
"ground_truth": "54"
} | {
"index": 1981,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A high school second-year class has a total of 1000 students. To investigate the vision condition of the students in this grade, if 50 samples are selected using the systematic sampling method, and all students are randomly numbered from 000, 001, 002, …, to 999, if it is deter... | math | {
"style": "rule",
"ground_truth": "101"
} | {
"index": 1982,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A high school with 2000 students held a \"May Fourth\" running and mountain climbing competition in response to the call for \"Sunshine Sports\". Each student participated in only one of the competitions. The number of students from the first, second, and third grades participa... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 1983,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A high school's 11th-grade class 1 has 45 male students and 15 female students. The teacher uses stratified sampling to form a 4-person extracurricular interest group. Calculate the probability of a student being selected for this group and the number of male and female student... | math | {
"style": "rule",
"ground_truth": "0.5"
} | {
"index": 1984,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A high school's second-year students are studying the relationship between students' math and Chinese scores. They conducted a simple random sampling with replacement and obtained a sample of size $200$ from the second-year students. The sample observation data of math scores a... | math | {
"style": "rule",
"ground_truth": "\\frac{15}{7}"
} | {
"index": 1985,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A high-tech Japanese company has presented a unique robot capable of producing construction blocks that can be sold for 90 monetary units each. Due to a shortage of special chips, it is impossible to replicate or even repair this robot if it goes out of order in the near future... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 1986,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hiker is exploring a trail. The trail has three sections: the first $25 \\%$ of the trail is along a river, the next $\\frac{5}{8}$ of the trail is through a forest, and the remaining 3 km of the trail is up a hill. How long is the trail?"
}
] | math | {
"style": "rule",
"ground_truth": "24 \\text{ km}"
} | {
"index": 1987,
"solution": "Since $25 \\%$ is equivalent to $\\frac{1}{4}$, then the fraction of the trail covered by the section along the river and the section through the forest is $\\frac{1}{4}+\\frac{5}{8}=\\frac{2}{8}+\\frac{5}{8}=\\frac{7}{8}$. This means that the final section up a hill represents $1-\\fr... |
DeepScaleR | [
{
"role": "user",
"content": "A hockey team has 6 more red helmets than blue helmets. The ratio of red helmets to blue helmets is $5:3$. What is the total number of red helmets and blue helmets?"
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 1988,
"solution": "Suppose that the team has $r$ red helmets. Since the team has 6 more red helmets than blue helmets, then the team has $r-6$ blue helmets. Since the ratio of the number of red helmets to the number of blue helmets is $5:3$, then $\\frac{r}{r-6}=\\frac{5}{3}$ and so $3r=5(r-6)$ or $3r=5r... |
DeepScaleR | [
{
"role": "user",
"content": "A hollow glass sphere with uniform wall thickness and an outer diameter of $16 \\mathrm{~cm}$ floats in water in such a way that $\\frac{3}{8}$ of its surface remains dry. What is the wall thickness, given that the specific gravity of the glass is $s = 2.523$?"
}
] | math | {
"style": "rule",
"ground_truth": "0.8"
} | {
"index": 1989,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hollow silver sphere with an outer diameter of $2 R = 1 \\mathrm{dm}$ is exactly half-submerged in water. What is the thickness of the sphere's wall if the specific gravity of silver is $s = 10.5$?"
}
] | math | {
"style": "rule",
"ground_truth": "0.008"
} | {
"index": 1990,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A horse 24 feet from the center of a merry-go-round makes 32 revolutions. In order to travel the same distance, how many revolutions would a horse 8 feet from the center have to make?"
}
] | math | {
"style": "rule",
"ground_truth": "96"
} | {
"index": 1991,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hospital's internal medicine ward has 15 nurses, who work in pairs, rotating shifts every 8 hours. After two specific nurses work the same shift together, calculate the maximum number of days required for them to work the same shift again."
}
] | math | {
"style": "rule",
"ground_truth": "35"
} | {
"index": 1992,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hotel consists of a $2 \\times 8$ square grid of rooms, each occupied by one guest. All the guests are uncomfortable, so each guest would like to move to one of the adjoining rooms (horizontally or vertically). Of course, they should do this simultaneously, in such a way that... | math | {
"style": "rule",
"ground_truth": "1156"
} | {
"index": 1993,
"solution": "Imagine that the rooms are colored black and white, checkerboard-style. Each guest in a black room moves to an adjacent white room (and vice versa). If, for each such guest, we place a domino over the original room and the new room, we obtain a covering of the $2 \\times n$ grid by $n$... |
DeepScaleR | [
{
"role": "user",
"content": "A hotel has 5 distinct rooms, each with single beds for up to 2 people. The hotel has no other guests, and 5 friends want to stay there for the night. In how many ways can the 5 friends choose their rooms?"
}
] | math | {
"style": "rule",
"ground_truth": "2220"
} | {
"index": 1994,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hotel has three types of rooms available: a triple room, a double room, and a single room (each type of room can only accommodate the corresponding number of people). There are 4 adult men and 2 little boys looking for accommodation. The little boys should not stay in a room ... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 1995,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hotel packed breakfast for each of three guests. Each breakfast should have consisted of three types of rolls, one each of nut, cheese, and fruit rolls. The preparer wrapped each of the nine rolls and once wrapped, the rolls were indistinguishable from one another. She then r... | math | {
"style": "rule",
"ground_truth": "79"
} | {
"index": 1996,
"solution": "Call the three different types of rolls as A, B, and C. We need to arrange 3As, 3Bs, and 3Cs in a string such that A, B, and C appear in the first three, second three, and the third three like ABCABCABC or BCABACCAB. This can occur in $\\left(\\frac{3!}{1!1!1!}\\right)^3 = 6^3 = 216$ d... |
DeepScaleR | [
{
"role": "user",
"content": "A hotelier wanted to equip the dining room with new chairs. In the catalog, he chose a type of chair. When placing the order, he learned from the manufacturer that as part of a discount event, every fourth chair is offered at half price and that, therefore, he could save the eq... | math | {
"style": "rule",
"ground_truth": "63"
} | {
"index": 1997,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A hotpot restaurant in Chongqing operates through three methods: dining in, takeout, and setting up a stall outside (referred to as stall). In June, the ratio of revenue from dining in, takeout, and stall for this hotpot restaurant was $3:5:2$. With the introduction of policies... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{8}"
} | {
"index": 1998,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A house and store were sold for $12,000 each. The house was sold at a loss of 20% of the cost, and the store at a gain of 20% of the cost. The entire transaction resulted in:"
}
] | math | {
"style": "rule",
"ground_truth": "-$1000"
} | {
"index": 1999,
"solution": "1. **Identify the cost price of the house and store:**\n - Let $h$ be the cost price of the house and $s$ be the cost price of the store.\n - The house was sold at a loss of $20\\%$. Therefore, the selling price of the house is $80\\%$ of $h$, which is given by $\\frac{4h}{5}$.\n ... |
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