data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "Xiaopang arranges the 50 integers from 1 to 50 in ascending order without any spaces in between. Then, he inserts a \"+\" sign between each pair of adjacent digits, resulting in an addition expression: \\(1+2+3+4+5+6+7+8+9+1+0+1+1+\\cdots+4+9+5+0\\). Please calculate the sum of... | math | {
"style": "rule",
"ground_truth": "330"
} | {
"index": 39000,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Xiaopang, Xiaodingding, Xiaoya, and Xiaoqiao have a total of 8 parents and 4 children in their four families. They are going to an amusement park together. The ticket pricing is as follows: Adult tickets are 100 yuan per person, children's tickets are 50 yuan per person. If the... | math | {
"style": "rule",
"ground_truth": "800"
} | {
"index": 39001,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Xiaoqiang conducts an experiment while drinking a beverage. He inserts a chopstick vertically into the bottom of the cup and measures the wetted part, which is exactly 8 centimeters. He then turns the chopstick around and inserts the other end straight into the bottom of the cu... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 39002,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Xiaoting's average score for five math tests is 85, the median is 86, and the mode is 88. What is the sum of the scores of the two lowest tests?"
}
] | math | {
"style": "rule",
"ground_truth": "163"
} | {
"index": 39003,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Xiaoying goes home at noon to cook noodles by herself, which involves the following steps: ① Wash the pot and fill it with water, taking 2 minutes; ② Wash the vegetables, taking 3 minutes; ③ Prepare the noodles and seasonings, taking 2 minutes; ④ Boil the water in the pot, taki... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 39004,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Xibing is a local specialty in Haiyang, with a unique flavor, symbolizing joy and reunion. Person A and person B went to the market to purchase the same kind of gift box filled with Xibing at the same price. Person A bought $2400$ yuan worth of Xibing, which was $10$ boxes less... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"index": 39005,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Xinjiang region has a dry climate and is one of the three major cotton-producing areas in China, producing high-quality long-staple cotton. In an experiment on the germination rate of a certain variety of long-staple cotton seeds, research institute staff selected experimental ... | math | {
"style": "rule",
"ground_truth": "0.95"
} | {
"index": 39006,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Xinyi is a beautiful city with abundant tourism resources. The Malingshan Scenic Area is a $4A$-rated tourist attraction in our city. The scenic area has developed a souvenir that costs $30$ yuan to produce and is sold. The selling price is set not to be lower than the cost and... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"index": 39007,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Yan is somewhere between his home and the stadium. To get to the stadium he can walk directly to the stadium, or else he can walk home and then ride his bicycle to the stadium. He rides 7 times as fast as he walks, and both choices require the same amount of time. What is the... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"index": 39008,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Yan is at a point between his house and a park. He has two options to reach the park: He can either walk directly to the park or he can walk back to his house and use his scooter to reach the park. He scoots 10 times faster than he walks, and both routes take the same amount of... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{11}"
} | {
"index": 39009,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Yan is between his home and the library. To get to the library, he can either walk directly to the library or walk home and then ride his bicycle to the library. He rides 5 times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yan's d... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"index": 39010,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Yan is somewhere between his office and a concert hall. To get to the concert hall, he can either walk directly there, or walk to his office and then take a scooter to the concert hall. He rides 5 times as fast as he walks, and both choices take the same amount of time. What is... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"index": 39011,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Yangyang leaves home for school. If she walks 60 meters per minute, she arrives at school at 6:53. If she walks 75 meters per minute, she arrives at school at 6:45. What time does Yangyang leave home?"
}
] | math | {
"style": "rule",
"ground_truth": "6:13"
} | {
"index": 39012,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Yann writes down the first $n$ consecutive positive integers, $1,2,3,4, \\ldots, n-1, n$. He removes four different integers $p, q, r, s$ from the list. At least three of $p, q, r, s$ are consecutive and $100<p<q<r<s$. The average of the integers remaining in the list is 89.562... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"index": 39013,
"solution": "When Yann removes 4 of the $n$ integers from his list, there are $n-4$ integers left. Suppose that the sum of the $n-4$ integers left is $T$. The average of these $n-4$ integers is $89.5625=89.5+0.0625=89+\\frac{1}{2}+\\frac{1}{16}=89 \\frac{9}{16}=\\frac{1433}{16}$. Since the sum of ... |
DeepScaleR | [
{
"role": "user",
"content": "Yannick has a bicycle lock with a 4-digit passcode whose digits are between 0 and 9 inclusive. (Leading zeroes are allowed.) The dials on the lock is currently set at 0000. To unlock the lock, every second he picks a contiguous set of dials, and increases or decreases all of th... | math | {
"style": "rule",
"ground_truth": "(12,2)"
} | {
"index": 39014,
"solution": "To simplify the solution, we instead consider the equivalent problem of reducing a passcode to 0000 using the given move. Given a passcode $a_{1} a_{2} a_{3} a_{4}$, define a differential of the passcode to be a quintuple ( $d_{1}, d_{2}, d_{3}, d_{4}, d_{5}$ ) such that $d_{i} \\equi... |
DeepScaleR | [
{
"role": "user",
"content": "Yannick picks a number $N$ randomly from the set of positive integers such that the probability that $n$ is selected is $2^{-n}$ for each positive integer $n$. He then puts $N$ identical slips of paper numbered 1 through $N$ into a hat and gives the hat to Annie. Annie does not... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2 \\ln 2-1}"
} | {
"index": 39015,
"solution": "Let $S$ denote the value drawn from the hat. The probability that 2 is picked is $\\frac{1}{n}$ if $n \\geq 2$ and 0 if $n=1$. Thus, the total probability $X$ that 2 is picked is $$P(S=2)=\\sum_{k=2}^{\\infty} \\frac{2^{-k}}{k}$$ By the definition of conditional probability, $P(N=n \\... |
DeepScaleR | [
{
"role": "user",
"content": "Yao Ming has a free throw shooting percentage of 90% during games. What is the probability that he misses one free throw out of three attempts?"
}
] | math | {
"style": "rule",
"ground_truth": "0.243"
} | {
"index": 39016,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Yasmine makes her own chocolate beverage by mixing volumes of milk and syrup in the ratio \\(5: 2\\). Milk comes in \\(2 \\text{ L}\\) bottles and syrup comes in \\(1.4 \\text{ L}\\) bottles. Yasmine has a limitless supply of full bottles of milk and of syrup. Determine the sma... | math | {
"style": "rule",
"ground_truth": "19.6"
} | {
"index": 39017,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Yesterday Han drove 1 hour longer than Ian at an average speed 5 miles per hour faster than Ian. Jan drove 2 hours longer than Ian at an average speed 10 miles per hour faster than Ian. Han drove 70 miles more than Ian. How many more miles did Jan drive than Ian?"
}
] | math | {
"style": "rule",
"ground_truth": "150"
} | {
"index": 39018,
"solution": "1. **Define Variables:**\n Let $d$ be the distance Ian drove, $t$ be the time Ian drove, and $s$ be Ian's speed. Thus, Ian's equation is:\n \\[\n d = s \\cdot t\n \\]\n This is equation (1).\n\n2. **Set Up Han's Equation:**\n Han drove 1 hour longer than Ian and at a speed... |
DeepScaleR | [
{
"role": "user",
"content": "Yesterday, Sasha cooked soup and added too little salt, requiring additional seasoning. Today, he added twice as much salt as yesterday, but still had to season the soup additionally, though with half the amount of salt he used for additional seasoning yesterday. By what factor... | math | {
"style": "rule",
"ground_truth": "1.5"
} | {
"index": 39019,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Yesterday, Sasha cooked soup and added too little salt, so he had to add more salt later. Today he doubled the amount of salt, but still had to add more salt, though only half as much as yesterday. By what factor does Sasha need to increase today's portion of salt so that tomor... | math | {
"style": "rule",
"ground_truth": "1.5"
} | {
"index": 39020,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You and five friends need to raise $1500$ dollars in donations for a charity, dividing the fundraising equally. How many dollars will each of you need to raise?"
}
] | math | {
"style": "rule",
"ground_truth": "250"
} | {
"index": 39021,
"solution": "1. **Identify the total amount to be raised and the number of people involved:**\n - Total amount to be raised: $1500$ dollars.\n - Number of people involved: $6$ (you and five friends).\n\n2. **Calculate the amount each person needs to raise:**\n - To find out how much each per... |
DeepScaleR | [
{
"role": "user",
"content": "You are given 10 numbers - one one and nine zeros. You are allowed to select two numbers and replace each of them with their arithmetic mean.\n\nWhat is the smallest number that can end up in the place of the one?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{512}"
} | {
"index": 39022,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You are given 16 pieces of paper numbered $16,15, \\ldots, 2,1$ in that order. You want to put them in the order $1,2, \\ldots, 15,16$ switching only two adjacent pieces of paper at a time. What is the minimum number of switches necessary?"
}
] | math | {
"style": "rule",
"ground_truth": "120"
} | {
"index": 39023,
"solution": "Piece 16 has to move to the back 15 times, piece 15 has to move to the back 14 times, ..., piece 2 has to move to the back 1 time, piece 1 has to move to the back 0 times. Since only one piece can move back in each switch, we must have at least $15+14+\\ldots+1=\\mathbf{120}$ switches... |
DeepScaleR | [
{
"role": "user",
"content": "You are given a $10 \\times 2$ grid of unit squares. Two different squares are adjacent if they share a side. How many ways can one mark exactly nine of the squares so that no two marked squares are adjacent?"
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 39024,
"solution": "Since each row has only two squares, it is impossible for two marked squares to be in the same row. Therefore, exactly nine of the ten rows contain marked squares. Consider two cases: Case 1: The first or last row is empty. These two cases are symmetrical, so assume without loss of ge... |
DeepScaleR | [
{
"role": "user",
"content": "You are given a number composed of three different non-zero digits, 7, 8, and a third digit which is not 7 or 8. Find the minimum value of the quotient of this number divided by the sum of its digits."
}
] | math | {
"style": "rule",
"ground_truth": "11.125"
} | {
"index": 39025,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You are given a positive integer $k$ and not necessarily distinct positive integers $a_1, a_2 , a_3 , \\ldots,\na_k$ . It turned out that for any coloring of all positive integers from $1$ to $2021$ in one of the $k$ colors so that there are exactly $a_1$ numbers of ... | math | {
"style": "rule",
"ground_truth": "2021"
} | {
"index": 39026,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You are given a set of cards labeled from 1 to 100. You wish to make piles of three cards such that in any pile, the number on one of the cards is the product of the numbers on the other two cards. However, no card can be in more than one pile. What is the maximum number of pil... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"index": 39027,
"solution": "Certainly, the two factors in any pile cannot both be at least 10, since then the product would be at least $10 \\times 11>100$. Also, the number 1 can not appear in any pile, since then the other two cards in the pile would have to be the same. So each pile must use one of the number... |
DeepScaleR | [
{
"role": "user",
"content": "You are given an unlimited supply of red, blue, and yellow cards to form a hand. Each card has a point value and your score is the sum of the point values of those cards. The point values are as follows: the value of each red card is 1 , the value of each blue card is equal to ... | math | {
"style": "rule",
"ground_truth": "168"
} | {
"index": 39028,
"solution": "If there are $B$ blue cards, then each red card contributes $1+2 B$ points (one for itself and two for each blue card) and each yellow card contributes $3 B$ points. Thus, if $B>1$, it is optimal to change all red cards to yellow cards. When $B=0$, the maximum number of points is 15 .... |
DeepScaleR | [
{
"role": "user",
"content": "You are given that $3^{400}\\equiv 1\\pmod{1000}$. What are the last three digits of $3^{12000}$?"
}
] | math | {
"style": "rule",
"ground_truth": "001"
} | {
"index": 39029,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You are given that $x$ is directly proportional to $y^3$, and $y$ is inversely proportional to $\\sqrt{z}$. If the value of $x$ is 3 when $z$ is $12$, what is the value of $x$ when $z$ is equal to $75$? Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{24}{125}"
} | {
"index": 39030,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You are given the digits $0$, $1$, $2$, $3$, $4$, $5$. Form a four-digit number with no repeating digits.\n\n(I) How many different four-digit numbers can be formed?\n\n(II) How many of these four-digit numbers have a tens digit that is larger than both the units digit and the ... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 39031,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You are given the numbers $0$, $2$, $3$, $4$, $6$. Use these numbers to form different combinations and calculate the following:\n $(1)$ How many unique three-digit numbers can be formed?\n $(2)$ How many unique three-digit numbers that can be divided by $3$ can be formed? ... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 39032,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You are given the numbers 1, 2, 3, 4, 5, 6, 7, 8 to be placed at the eight vertices of a cube, such that the sum of any three numbers on each face of the cube is at least 10. Find the minimum possible sum of the four numbers on any face."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 39033,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You are in a completely dark room with a drawer containing 10 red, 20 blue, 30 green, and 40 khaki socks. What is the smallest number of socks you must randomly pull out in order to be sure of having at least one of each color?"
}
] | math | {
"style": "rule",
"ground_truth": "91"
} | {
"index": 39034,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You are in a place where 99% of the inhabitants are vampires and 1% are regular humans. On average, 90% of the vampires are correctly identified as vampires, and 90% of humans are correctly identified as humans. What is the probability that someone identified as a human is actu... | math | {
"style": "rule",
"ground_truth": "1/12"
} | {
"index": 39035,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You are playing a game in which you have $3$ envelopes, each containing a uniformly random amount of money between $0$ and $1000$ dollars. (That is, for any real $0 \\leq a < b \\leq 1000$ , the probability that the amount of money in a given envelope is between $a$ an... | math | {
"style": "rule",
"ground_truth": "695"
} | {
"index": 39036,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You are standing at a pole and a snail is moving directly away from the pole at $1 \\mathrm{~cm} / \\mathrm{s}$. When the snail is 1 meter away, you start 'Round 1'. In Round $n(n \\geq 1)$, you move directly toward the snail at $n+1 \\mathrm{~cm} / \\mathrm{s}$. When you reach... | math | {
"style": "rule",
"ground_truth": "5050"
} | {
"index": 39037,
"solution": "Suppose the snail is $x_{n}$ meters away at the start of round $n$, so $x_{1}=1$, and the runner takes $\\frac{100 x_{n}}{(n+1)-1}=\\frac{100 x_{n}}{n}$ seconds to catch up to the snail. But the runner takes the same amount of time to run back to the start, so during round $n$, the sn... |
DeepScaleR | [
{
"role": "user",
"content": "You are standing at the edge of a river which is $1$ km wide. You have to go to your camp on the opposite bank . The distance to the camp from the point on the opposite bank directly across you is $1$ km . You can swim at $2$ km/hr and walk at $3$ km-hr . What is the sh... | math | {
"style": "rule",
"ground_truth": "\\frac{2 + \\sqrt{5}}{6}"
} | {
"index": 39038,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You are the general of an army. You and the opposing general both have an equal number of troops to distribute among three battlefields. Whoever has more troops on a battlefield always wins (you win ties). An order is an ordered triple of non-negative real numbers $(x, y, z)$ s... | math | {
"style": "rule",
"ground_truth": "\\sqrt[5]{8}"
} | {
"index": 39039,
"solution": "Let $x$ be the portion of soldiers the opposing general sends to the first battlefield, and $y$ the portion he sends to the second. Then $1-x-y$ is the portion he sends to the third. Then $x \\geq 0$, $y \\geq 0$, and $x+y \\leq 1$. Furthermore, you win if one of the three conditions ... |
DeepScaleR | [
{
"role": "user",
"content": "You are trapped in a room with only one exit, a long hallway with a series of doors and land mines. To get out you must open all the doors and disarm all the mines. In the room is a panel with 3 buttons, which conveniently contains an instruction manual. The red button arms a m... | math | {
"style": "rule",
"ground_truth": "9"
} | {
"index": 39040,
"solution": "Clearly we do not want to reset the system at any time. After pressing the red button $r$ times, the yellow button $y$ times, and the green button $g$ times, there will be $3+r-2 y$ armed mines and $3+y-2 g$ closed doors, so we want the values of $r, y$, and $g$ that make both of thes... |
DeepScaleR | [
{
"role": "user",
"content": "You are trapped in ancient Japan, and a giant enemy crab is approaching! You must defeat it by cutting off its two claws and six legs and attacking its weak point for massive damage. You cannot cut off any of its claws until you cut off at least three of its legs, and you canno... | math | {
"style": "rule",
"ground_truth": "14400"
} | {
"index": 39041,
"solution": "The answer is given by $6!2!\\binom{5}{2}$, because we can cut off the claws and legs in any order and there are $\\binom{5}{2}$ ways to decide when to cut off the two claws (since we can do it at any time among the last 5 cuts)."
} |
DeepScaleR | [
{
"role": "user",
"content": "You are trying to cross a 400 foot wide river. You can jump at most 4 feet, but you have many stones you can throw into the river. You will stop throwing stones and cross the river once you have placed enough stones to be able to do so. You can throw straight, but you can't jud... | math | {
"style": "rule",
"ground_truth": "712.811"
} | {
"index": 39042,
"solution": "If we divide the river into 1004-foot sections, then to be able to cross we need to get at least one stone into each section. On average, this takes $$\\frac{100}{100}+\\frac{100}{99}+\\cdots+\\frac{100}{1} \\approx 100 \\ln 100$$ stone throws (it takes $\\frac{100}{100-k}$ moves on a... |
DeepScaleR | [
{
"role": "user",
"content": "You are trying to cross a 6 foot wide river. You can jump at most 4 feet, but you have one stone you can throw into the river; after it is placed, you may jump to that stone and, if possible, from there to the other side of the river. However, you are not very accurate and the ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"index": 39043,
"solution": "To be able to cross, the stone must land between 2 and 4 feet from the river bank you are standing on. Therefore the probability is $\\frac{2}{6}=\\frac{1}{3}$."
} |
DeepScaleR | [
{
"role": "user",
"content": "You can arrange 15 balls in the shape of a triangle, but you cannot arrange 96 balls in the shape of a square (missing one ball). Out of how many balls, not exceeding 50, can you arrange them both in the shape of a triangle and a square?"
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 39044,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You flip a fair coin which results in heads ( $\\text{H}$ ) or tails ( $\\text{T}$ ) with equal probability. What is the probability that you see the consecutive sequence $\\text{THH}$ before the sequence $\\text{HHH}$ ?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{8}"
} | {
"index": 39045,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have $5$ red shirts, $5$ green shirts, $6$ pairs of pants, $8$ green hats and $8$ red hats, all of which are distinct. How many outfits can you make consisting of one shirt, one pair of pants, and one hat without having the same color of shirts and hats?"
}
] | math | {
"style": "rule",
"ground_truth": "480"
} | {
"index": 39046,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have $7$ red shirts, $8$ green shirts, $10$ pairs of pants, $10$ blue hats, $10$ red hats, and $5$ scarves (each distinct). How many outfits can you make consisting of one shirt, one pair of pants, one hat, and one scarf, without having the same color of shirts and hats?"
... | math | {
"style": "rule",
"ground_truth": "7500"
} | {
"index": 39047,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have 128 teams in a single elimination tournament. The Engineers and the Crimson are two of these teams. Each of the 128 teams in the tournament is equally strong, so during each match, each team has an equal probability of winning. Now, the 128 teams are randomly put into ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{64}"
} | {
"index": 39048,
"solution": "There are $\\binom{128}{2}=127 \\cdot 64$ pairs of teams. In each tournament, 127 of these pairs play. By symmetry, the answer is $\\frac{127}{127 \\cdot 64}=\\frac{1}{64}$."
} |
DeepScaleR | [
{
"role": "user",
"content": "You have 2 six-sided dice. One is a normal fair die, while the other has 2 ones, 2 threes, and 2 fives. You pick a die and roll it. Because of some secret magnetic attraction of the unfair die, you have a 75% chance of picking the unfair die and a 25% chance of picking the fair ... | math | {
"style": "rule",
"ground_truth": "1/7"
} | {
"index": 39049,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have 5 identical buckets, each with a maximum capacity of some integer number of liters, and a 30-liter barrel containing an integer number of liters of water. All the water from the barrel was poured into the buckets, with the first bucket being half full, the second one-t... | math | {
"style": "rule",
"ground_truth": "29"
} | {
"index": 39050,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have 50 dimes and 20 quarters. What percent of the value of your money is in quarters?"
}
] | math | {
"style": "rule",
"ground_truth": "50\\%"
} | {
"index": 39051,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have 68 coins of different weights. Using 100 weighings on a balance scale without weights, find the heaviest and the lightest coin."
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 39052,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have a \\(2 \\times 3\\) grid filled with integers between 1 and 9. The numbers in each row and column are distinct. The first row sums to 23, and the columns sum to 14, 16, and 17 respectively.\n\nGiven the following grid:\n\\[\n\\begin{array}{c|c|c|c|}\n & 14 & 16 & 17... | math | {
"style": "rule",
"ground_truth": "49"
} | {
"index": 39053,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have a length of string and 7 beads in the 7 colors of the rainbow. You place the beads on the string as follows - you randomly pick a bead that you haven't used yet, then randomly add it to either the left end or the right end of the string. What is the probability that, a... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5040}"
} | {
"index": 39054,
"solution": "The threading method does not depend on the colors of the beads, so at the end all configurations are equally likely. Since there are $7!=5040$ configurations in total, the probability of any particular configuration is $\\frac{1}{5040}$."
} |
DeepScaleR | [
{
"role": "user",
"content": "You have a number of gold coins that you were going to distribute equally among your 11 best friends. However, after dividing your gold coins into 11 equal piles, you realize that if you give away all your gold coins, 2 people will receive an extra gold coin. You have less than... | math | {
"style": "rule",
"ground_truth": "90"
} | {
"index": 39055,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have a rectangular prism box with length $x+5$ units, width $x-5$ units, and height $x^{2}+25$ units. For how many positive integer values of $x$ is the volume of the box less than 700 units?"
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 39056,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have a square with vertices at $(2,1)$, $(5,1)$, $(2,4)$, and $(5,4)$. A line joining $(2,1)$ and $(5,3)$ divides the square into two regions. What fraction of the area of the square is above this line?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"index": 39057,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have a whole cake in your pantry. On your first trip to the pantry, you eat one-third of the cake. On each successive trip, you eat one-third of the remaining cake. After four trips to the pantry, what fractional part of the cake have you eaten?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{40}{81}"
} | {
"index": 39058,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have a whole pizza in the refrigerator. On your first trip to the refrigerator, you eat half the pizza. On each successive trip, you eat half of the remaining pizza. After five trips to the refrigerator, what fractional part of the pizza have you eaten?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{31}{32}"
} | {
"index": 39059,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have four textbooks for mandatory courses numbered 1 to 4. They are randomly placed on the same shelf.\n\n1. Calculate the probability that Textbook 2 is to the left of Textbook 4.\n2. Calculate the probability that Textbook 2 is to the left of Textbook 3, and Textbook 3 is... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 39060,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have four tiles marked X and three tiles marked O. The seven tiles are randomly arranged in a row. What is the probability that no two X tiles are adjacent to each other?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{35}"
} | {
"index": 39061,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You have infinitely many boxes, and you randomly put 3 balls into them. The boxes are labeled $1,2, \\ldots$. Each ball has probability $1 / 2^{n}$ of being put into box $n$. The balls are placed independently of each other. What is the probability that some box will contain at... | math | {
"style": "rule",
"ground_truth": "5 / 7"
} | {
"index": 39062,
"solution": "Notice that the answer is the sum of the probabilities that boxes $1,2, \\ldots$, respectively, contain at least 2 balls, since those events are mutually exclusive. For box $n$, the probability of having at least 2 balls is $$3\\left[\\left(1 / 2^{n}\\right)^{2}\\left(1-1 / 2^{n}\\rig... |
DeepScaleR | [
{
"role": "user",
"content": "You have nine coins: a collection of pennies, nickels, dimes, and quarters having a total value of $1.02, with at least one coin of each type. How many dimes must you have?"
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 39063,
"solution": "1. **Identify the minimum number of coins and their values**: We know that there is at least one coin of each type (penny, nickel, dime, and quarter). The minimum value from one of each type is:\n \\[\n 1 \\text{ cent (penny)} + 5 \\text{ cents (nickel)} + 10 \\text{ cents (dime)}... |
DeepScaleR | [
{
"role": "user",
"content": "You have six blocks in a row, labeled 1 through 6, each with weight 1. Call two blocks $x \\leq y$ connected when, for all $x \\leq z \\leq y$, block $z$ has not been removed. While there is still at least one block remaining, you choose a remaining block uniformly at random an... | math | {
"style": "rule",
"ground_truth": "\\frac{163}{10}"
} | {
"index": 39064,
"solution": "Note that the total cost is the total number of ordered pairs $(x, y)$ with $1 \\leq x, y \\leq 6$ such that $x$ and $y$ are connected right before $x$ gets removed. The probability that blocks $x$ and $y$ are connected just before block $x$ is removed is simply $\\frac{1}{|x-y|+1}$, ... |
DeepScaleR | [
{
"role": "user",
"content": "You have three shirts and four pairs of pants. How many outfits consisting of one shirt and one pair of pants can you make?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 39065,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You know that the Jones family has five children, and the Smith family has three children. Of the eight children you know that there are five girls and three boys. Let $\\dfrac{m}{n}$ be the probability that at least one of the families has only girls for children. Given ... | math | {
"style": "rule",
"ground_truth": "67"
} | {
"index": 39066,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You recently bought more than 100 eggs. The eggs are sorted in containers that can store exactly 12 eggs. However, upon inspecting the containers, you realize that two containers each hold only 11 eggs, while all the other containers hold 12 eggs. What is the smallest number of... | math | {
"style": "rule",
"ground_truth": "106"
} | {
"index": 39067,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You roll a fair 12-sided die repeatedly. The probability that all the prime numbers show up at least once before seeing any of the other numbers can be expressed as a fraction \\( \\frac{p}{q} \\) in lowest terms. What is \\( p+q \\)?"
}
] | math | {
"style": "rule",
"ground_truth": "793"
} | {
"index": 39068,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You start with a single piece of chalk of length 1. Every second, you choose a piece of chalk that you have uniformly at random and break it in half. You continue this until you have 8 pieces of chalk. What is the probability that they all have length $\\frac{1}{8}$ ?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{63}"
} | {
"index": 39069,
"solution": "There are 7! total ways to break the chalks. How many of these result in all having length $\\frac{1}{8}$ ? The first move gives you no choice. Then, among the remaining 6 moves, you must apply 3 breaks on the left side and 3 breaks on the right side, so there are $\\binom{6}{3}=20$ w... |
DeepScaleR | [
{
"role": "user",
"content": "You use a lock with four dials, each of which is set to a number between 0 and 9 (inclusive). You can never remember your code, so normally you just leave the lock with each dial one higher than the correct value. Unfortunately, last night someone changed all the values to 5. A... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 39070,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You walk for 90 minutes at a rate of 3 mph, then rest for 15 minutes, and then cycle for 45 minutes at a rate of 20 kph. Calculate the total distance traveled in 2 hours and 30 minutes."
}
] | math | {
"style": "rule",
"ground_truth": "13.82"
} | {
"index": 39071,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You want to arrange the numbers $1,2,3, \\ldots, 25$ in a sequence with the following property: if $n$ is divisible by $m$, then the $n$th number is divisible by the $m$ th number. How many such sequences are there?"
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 39072,
"solution": "Let the rearranged numbers be $a_{1}, \\ldots, a_{25}$. The number of pairs $(n, m)$ with $n \\mid m$ must equal the number of pairs with $a_{n} \\mid a_{m}$, but since each pair of the former type is also of the latter type, the converse must be true as well. Thus, $n \\mid m$ if and... |
DeepScaleR | [
{
"role": "user",
"content": "You want to paint some edges of a regular dodecahedron red so that each face has an even number of painted edges (which can be zero). Determine from How many ways this coloration can be done.\n\nNote: A regular dodecahedron has twelve pentagonal faces and in each vertex concur ... | math | {
"style": "rule",
"ground_truth": "2048"
} | {
"index": 39073,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "You would like to provide airline service to the 10 cities in the nation of Schizophrenia, by instituting a certain number of two-way routes between cities. Unfortunately, the government is about to divide Schizophrenia into two warring countries of five cities each, and you do... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 39074,
"solution": "Each city $C$ must be directly connected to at least 6 other cities, since otherwise the government could put $C$ in one country and all its connecting cities in the other country, and there would be no way out of $C$. This means that we have 6 routes for each of 10 cities, counted tw... |
DeepScaleR | [
{
"role": "user",
"content": "You, your friend, and two strangers are sitting at a table. A standard $52$ -card deck is randomly dealt into $4$ piles of $13$ cards each, and each person at the table takes a pile. You look through your hand and see that you have one ace. Compute the probability that you... | math | {
"style": "rule",
"ground_truth": "22/703"
} | {
"index": 39075,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Your math friend Steven rolls five fair icosahedral dice (each of which is labelled $1,2, \\ldots, 20$ on its sides). He conceals the results but tells you that at least half of the rolls are 20. Assuming that Steven is truthful, what is the probability that all three remaining... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{58}"
} | {
"index": 39076,
"solution": "The given information is equivalent to the first two dice being 20 and 19 and there being at least two 20's among the last three dice. Thus, we need to find the probability that given at least two of the last three dice are 20's, all three are. Since there is only one way to get all t... |
DeepScaleR | [
{
"role": "user",
"content": "Yu Semo and Yu Sejmo have created sequences of symbols $\\mathcal{U} = (\\text{U}_1, \\ldots, \\text{U}_6)$ and $\\mathcal{J} = (\\text{J}_1, \\ldots, \\text{J}_6)$ . These sequences satisfy the following properties.\n\n\n- Each of the twelve symbols must be $\\Sigma$ , $\... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 39077,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Yura has a calculator that allows multiplying a number by 3, adding 3 to a number, or (if the number is divisible by 3) dividing a number by 3. How can one obtain the number 11 from the number 1 using this calculator?"
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 39078,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Yura has a calculator that allows multiplying a number by 3, adding 3 to a number, or (if the number is divisible by 3) dividing by 3. How can you obtain the number 11 from the number 1 using this calculator?"
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 39079,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Yura has unusual clocks with several minute hands, moving in different directions. Yura counted that in one hour, the minute hands coincided exactly 54 times in pairs. What is the maximum number of minute hands that Yura's clock can have?"
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"index": 39080,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Yvan and Zoé play the following game. Let \\( n \\in \\mathbb{N} \\). The integers from 1 to \\( n \\) are written on \\( n \\) cards arranged in order. Yvan removes one card. Then, Zoé removes 2 consecutive cards. Next, Yvan removes 3 consecutive cards. Finally, Zoé removes 4 ... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 39081,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Yvon has 4 different notebooks and 5 different pens. Determine the number of different possible combinations of notebooks and pens he could bring."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 39082,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Zach has twelve identical-looking chocolate eggs. Exactly three of the eggs contain a special prize inside. Zach randomly gives three of the twelve eggs to each of Vince, Wendy, Xin, and Yolanda. What is the probability that only one child will receive an egg that contains a sp... | math | {
"style": "rule",
"ground_truth": "1/55"
} | {
"index": 39083,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Zachary paid for a $\\$1$ burger with 32 coins and received no change. Each coin was either a penny or a nickel. What was the number of nickels Zachary used?"
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"index": 39084,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Zan has created this iterative rule for generating sequences of whole numbers:\n\n1) If a number is 25 or less, double the number.\n\n2) If a number is greater than 25, subtract 12 from it.\n\nLet $F$ be the first number in a sequence generated by the rule above. $F$ is a \"swe... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 39085,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Zara has a collection of $4$ marbles: an Aggie, a Bumblebee, a Steelie, and a Tiger. She wants to display them in a row on a shelf, but does not want to put the Steelie and the Tiger next to one another. In how many ways can she do this?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 39086,
"solution": "1. **Identify the total number of unrestricted arrangements:**\n Let's denote the marbles as $A$ (Aggie), $B$ (Bumblebee), $S$ (Steelie), and $T$ (Tiger). Without any restrictions, the total number of ways to arrange these four marbles is given by the factorial of the number of marb... |
DeepScaleR | [
{
"role": "user",
"content": "Zebadiah has 3 red shirts, 3 blue shirts, and 3 green shirts in a drawer. Without looking, he randomly pulls shirts from his drawer one at a time. What is the minimum number of shirts that Zebadiah has to pull out to guarantee that he has a set of shirts that includes either 3 ... | math | {
"style": "rule",
"ground_truth": "5"
} | {
"index": 39087,
"solution": "Zebadiah must remove at least 3 shirts. If he removes 3 shirts, he might remove 2 red shirts and 1 blue shirt. If he removes 4 shirts, he might remove 2 red shirts and 2 blue shirts. Therefore, if he removes fewer than 5 shirts, it is not guaranteed that he removes either 3 of the sam... |
DeepScaleR | [
{
"role": "user",
"content": "Zeus starts at the origin \\((0,0)\\) and can make repeated moves of one unit either up, down, left or right, but cannot make a move in the same direction twice in a row. What is the smallest number of moves that he can make to get to the point \\((1056,1007)\\)?"
}
] | math | {
"style": "rule",
"ground_truth": "2111"
} | {
"index": 39088,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Zhang Bing was born in 1953. In a certain year before this year, his age was a multiple of 9 and equal to the sum of the digits of that year. How old was he that year?"
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 39089,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Zhang Hua has to go through four traffic posts A, B, C, and D on his way to school. The probability of encountering a red light at posts A and B is $\\frac{1}{2}$ each, and at posts C and D, it is $\\frac{1}{3}$ each. Assuming that the events of encountering red lights at the f... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{3}"
} | {
"index": 39090,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Zhang Hua, Li Liang, and Wang Min each sent out x, y, z New Year's cards, respectively. If it is known that the least common multiple of x, y, z is 60, the greatest common divisor of x and y is 4, and the greatest common divisor of y and z is 3, then how many New Year's cards d... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 39091,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Zhang Qiang rides a bike starting from bus stop $A$, traveling along the bus route at 250 meters per minute. After some time, a bus also departs from stop $A$, traveling at 450 meters per minute, but it needs to stop at a station for 1 minute every 6 minutes. If the bus catches... | math | {
"style": "rule",
"ground_truth": "2100"
} | {
"index": 39092,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Zhenya took a $3 \\times 3$ board and placed a column of blue and red cubes on each cell. Then he drew a diagram of the resulting arrangement: he wrote down the number of cubes of both colors in each column (the order of the cubes is unknown).\n\nWhat is the maximum number of b... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 39093,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Zou and Chou are practicing their $100$-meter sprints by running $6$ races against each other. Zou wins the first race, and after that, the probability that one of them wins a race is $\\frac23$ if they won the previous race but only $\\frac13$ if they lost the previous race. T... | math | {
"style": "rule",
"ground_truth": "97"
} | {
"index": 39094,
"solution": "Note that Zou wins one race. The probability that he wins the last race is $\\left(\\frac{2}{3}\\right)^4\\left(\\frac{1}{3}\\right)=\\frac{16}{243}.$ Now, if he doesn't win the last race, then there must be two races where the winner of the previous race loses. We can choose any $4$ ... |
DeepScaleR | [
{
"role": "user",
"content": "[asy]\ndefaultpen(linewidth(0.7)+fontsize(10));\npair A=(0,0), B=(16,0), C=(16,16), D=(0,16), E=(32,0), F=(48,0), G=(48,16), H=(32,16), I=(0,8), J=(10,8), K=(10,16), L=(32,6), M=(40,6), N=(40,16);\ndraw(A--B--C--D--A^^E--F--G--H--E^^I--J--K^^L--M--N);\nlabel(\"S\", (18,8));\nla... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 39095,
"solution": "To determine the smallest integer value of $S$ for which the table can be moved as desired without tilting it or taking it apart, we need to consider the diagonal of the table, as this is the longest dimension when the table is rotated.\n\n1. **Calculate the diagonal of the table**: T... |
DeepScaleR | [
{
"role": "user",
"content": "[asy]\ndraw((-1,-1)--(1,-1)--(1,1)--(-1,1)--cycle, black+linewidth(.75));\ndraw((0,-1)--(0,1), black+linewidth(.75));\ndraw((-1,0)--(1,0), black+linewidth(.75));\ndraw((-1,-1/sqrt(3))--(1,1/sqrt(3)), black+linewidth(.75));\ndraw((-1,1/sqrt(3))--(1,-1/sqrt(3)), black+linewidth(.... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{3}-2"
} | {
"index": 39096,
"solution": "1. **Assume the side length of the square**: Let's assume the side length of the square is 2 units for simplicity. This assumption does not affect the generality of the solution because we are interested in the ratio of areas, which is dimensionless and independent of the actual size ... |
DeepScaleR | [
{
"role": "user",
"content": "[asy]\ndraw((-7,0)--(7,0),black+linewidth(.75));\ndraw((-3*sqrt(3),0)--(-2*sqrt(3),3)--(-sqrt(3),0)--(0,3)--(sqrt(3),0)--(2*sqrt(3),3)--(3*sqrt(3),0),black+linewidth(.75));\ndraw((-2*sqrt(3),0)--(-1*sqrt(3),3)--(0,0)--(sqrt(3),3)--(2*sqrt(3),0),black+linewidth(.75));\n[/asy]\nF... | math | {
"style": "rule",
"ground_truth": "12\\sqrt{3}"
} | {
"index": 39097,
"solution": "1. **Calculate the area of one large equilateral triangle**: \n The formula for the area of an equilateral triangle with side length $s$ is given by:\n \\[\n \\text{Area} = \\frac{\\sqrt{3}}{4} s^2\n \\]\n Substituting $s = 2\\sqrt{3}$, we get:\n \\[\n \\text{Area} = \\... |
DeepScaleR | [
{
"role": "user",
"content": "[asy]\ndraw((0,1)--(4,1)--(4,2)--(0,2)--cycle);\ndraw((2,0)--(3,0)--(3,3)--(2,3)--cycle);\ndraw((1,1)--(1,2));\nlabel(\"1\",(0.5,1.5));\nlabel(\"2\",(1.5,1.5));\nlabel(\"32\",(2.5,1.5));\nlabel(\"16\",(3.5,1.5));\nlabel(\"8\",(2.5,0.5));\nlabel(\"6\",(2.5,2.5));\n[/asy]\nThe im... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 39098,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "[asy] draw((0,0)--(0,2)--(2,2)--(2,0)--cycle,dot); draw((2,2)--(0,0)--(0,1)--cycle,dot); draw((0,2)--(1,0),dot); MP(\"B\",(0,0),SW);MP(\"A\",(0,2),NW);MP(\"D\",(2,2),NE);MP(\"C\",(2,0),SE); MP(\"E\",(0,1),W);MP(\"F\",(1,0),S);MP(\"H\",(2/3,2/3),E);MP(\"I\",(2/5,6/5),N); dot((1,... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{15}"
} | {
"index": 39099,
"solution": ""
} |
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