data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "A point is chosen at random on the number line between 0 and 1, and the point is colored red. Then, another point is chosen at random on the number line between 0 and 1, and this point is colored blue. What is the probability that the number of the blue point is greater than th... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 5700,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In right triangle $ABC$, $AB=10$, $AC=6$ and $BC=8$ units. What is the distance from $C$ to the midpoint of segment $AB$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 5701,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Real numbers \\(x\\) and \\(y\\) satisfy the following equations: \\(x=\\log_{10}(10^{y-1}+1)-1\\) and \\(y=\\log_{10}(10^{x}+1)-1\\). Compute \\(10^{x-y}\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{101}{110}"
} | {
"split": "train",
"index": 5702,
"solution": "Taking 10 to the power of both sides in each equation, these equations become: \\(10^{x}=\\left(10^{y-1}+1\\right) \\cdot 10^{-1}\\) and \\(10^{y}=\\left(10^{x}+1\\right) \\cdot 10^{-1}\\). Let \\(a=10^{x}\\) and \\(b=10^{y}\\). Our equations become: \\(10a=b/10+1\\... |
deepscaler | [
{
"role": "user",
"content": "Let $N$ denote the number of all natural numbers $n$ such that $n$ is divisible by a prime $p> \\sqrt{n}$ and $p<20$ . What is the value of $N$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "69"
} | {
"split": "train",
"index": 5703,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the tens digit of $7^{2011}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 5704,
"solution": "1. **Identify the goal:** We need to find the tens digit of $7^{2011}$. This is equivalent to finding $7^{2011} \\mod 100$ because the tens digit of a number is the second last digit from the right.\n\n2. **Use modular arithmetic to simplify the problem:** We start ... |
deepscaler | [
{
"role": "user",
"content": "If $8^{2x} = 11$, evaluate $2^{x + 1.5}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11^{1/6} \\cdot 2 \\sqrt{2}"
} | {
"split": "train",
"index": 5705,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the probability that Claudia gets at least 2 more heads than tails if she flips 12 coins? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{793}{2048}"
} | {
"split": "train",
"index": 5706,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a modified SHORT BINGO, a $5\\times5$ card uses a WILD square in the middle and places 24 other numbers in the remaining squares. Numbers are placed as follows: 5 distinct numbers from $1-15$ in the first column, 5 distinct numbers from $16-30$ in the second column, 4 distin... | math | {
"style": "rule",
"ground_truth": "360360"
} | {
"split": "train",
"index": 5707,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The function $f(x)$ satisfies\n\\[f(x + y) = f(x) + f(y)\\]for all real numbers $x$ and $y,$ and $f(4) = 5.$ Find $f(5).$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{25}{4}"
} | {
"split": "train",
"index": 5708,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $|$$\\overrightarrow {a}$$ $|=1$, $\\overrightarrow {b}$ $=$ ($ $\\frac { \\sqrt {3}}{3} $, $ \\frac { \\sqrt {3}}{3}$), and $|$ $\\overrightarrow {a}$ $+3 \\overrightarrow {b}$ $|=2$, find the projection of $\\overrightarrow {b}$ in the direction of $\\overrig... | math | {
"style": "rule",
"ground_truth": "- \\frac {1}{2}"
} | {
"split": "train",
"index": 5709,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For what value of $n$ does $|6 + ni| = 6\\sqrt{5}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 5710,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $T$ denote the sum of all four-digit positive integers where each digit is distinct and ranges from 1 to 9. Compute the remainder when $T$ is divided by $1000$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "320"
} | {
"split": "train",
"index": 5711,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=4\\cos (ωx- \\frac {π}{6})\\sin (π-ωx)-\\sin (2ωx- \\frac {π}{2})$, where $ω > 0$.\n(1) Find the range of the function $f(x)$.\n(2) If $y=f(x)$ is an increasing function in the interval $[- \\frac {3π}{2}, \\frac {π}{2}]$, find the maximum value of $ω$.... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"split": "train",
"index": 5712,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A factory has two branches, one in location A and the other in location B, producing 12 and 6 machines respectively. Now, they need to distribute 10 machines to area A and 8 machines to area B. It is known that the transportation cost for moving one machine from location A to a... | math | {
"style": "rule",
"ground_truth": "8600"
} | {
"split": "train",
"index": 5713,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "To enhance and beautify the city, all seven streetlights on a road are to be changed to colored lights. If there are three colors available for the colored lights - red, yellow, and blue - and the installation requires that no two adjacent streetlights are of the same color, wi... | math | {
"style": "rule",
"ground_truth": "114"
} | {
"split": "train",
"index": 5714,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An apartment building consists of 20 rooms numbered $1,2, \\ldots, 20$ arranged clockwise in a circle. To move from one room to another, one can either walk to the next room clockwise (i.e. from room $i$ to room $(i+1)(\\bmod 20))$ or walk across the center to the opposite room... | math | {
"style": "rule",
"ground_truth": "257"
} | {
"split": "train",
"index": 5715,
"solution": "One way is to walk directly from room 10 to 20 . Else, divide the rooms into 10 pairs $A_{0}=(10,20), A_{1}=(1,11), A_{2}=(2,12), \\ldots, A_{9}=(9,19)$. Notice that - each move is either between rooms in $A_{i}$ and $A_{(i+1)(\\bmod 10)}$ for some $i \\in\\{0,1, \\... |
deepscaler | [
{
"role": "user",
"content": "In a pocket, there are several balls of three different colors (enough in quantity), and each time 2 balls are drawn. To ensure that the result of drawing is the same 5 times, at least how many times must one draw? Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 5716,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In how many ways can you rearrange the letters of \"HMMTHMMT\" such that the consecutive substring \"HMMT\" does not appear? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "361"
} | {
"split": "train",
"index": 5717,
"solution": "There are $8!/(4!2!2!)=420$ ways to order the letters. If the permuted letters contain \"HMMT\", there are $5 \\cdot 4!/ 2!=60$ ways to order the other letters, so we subtract these. However, we have subtracted \"HMMTHMMT\" twice, so we add it back once to obtain 36... |
deepscaler | [
{
"role": "user",
"content": "Find all real numbers $x$ such that \\[\\frac{x^3+2x^2}{x^2+3x+2} + x = -6.\\]Enter all the solutions, separated by commas. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\tfrac32"
} | {
"split": "train",
"index": 5718,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate plane $xOy$, an ellipse $(E)$ has its center at the origin, passes through the point $A(0,1)$, and its left and right foci are $F_{1}$ and $F_{2}$, respectively, with $\\overrightarrow{AF_{1}} \\cdot \\overrightarrow{AF_{2}} = 0$.\n\n(I) Find the equ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 5719,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $$f(x)=4\\sin(x- \\frac {π}{6})\\cos x+1$$.\n(Ⅰ) Find the smallest positive period of f(x);\n(Ⅱ) Find the maximum and minimum values of f(x) in the interval $$\\[-\\frac {π}{4}, \\frac {π}{4}\\]$$ . Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 5720,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of an infinite geometric series is 64 times the series that results if the first four terms of the original series are removed. What is the value of the series' common ratio? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 5721,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many positive integer multiples of $1001$ can be expressed in the form $10^{j} - 10^{i}$, where $i$ and $j$ are integers and $0\\leq i < j \\leq 99$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "784"
} | {
"split": "train",
"index": 5722,
"solution": "Note that $1001=7\\cdot 11\\cdot 13,$ and note that $10^3 \\equiv \\pmod{p}$ for prime $p | 1001$; therefore, the order of 10 modulo $7,11$, and $13$ must divide 6. A quick check on 7 reveals that it is indeed 6. Therefore we note that $i-j=6k$ for some natural numb... |
deepscaler | [
{
"role": "user",
"content": "Five squares and two right-angled triangles are positioned as shown. The areas of three squares are \\(3 \\, \\mathrm{m}^{2}, 7 \\, \\mathrm{m}^{2}\\), and \\(22 \\, \\mathrm{m}^{2}\\). What is the area, in \\(\\mathrm{m}^{2}\\), of the square with the question mark?\nA) 18\nB)... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 5723,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $P = \\sqrt{1988 \\cdot 1989 \\cdot 1990 \\cdot 1991 + 1} + \\left(-1989^{2}\\right)$, calculate the value of $P$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1988"
} | {
"split": "train",
"index": 5724,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the domains of functions f(x) and g(x) are both $\\mathbb{R}$, and $f(x) + g(2-x) = 5$, $g(x) - f(x-4) = 7$. If the graph of $y = g(x)$ is symmetric about the line $x = 2$, $g(2) = 4$, calculate the value of $\\sum _{k=1}^{22}f(k)$. Let's think step by step and put o... | math | {
"style": "rule",
"ground_truth": "-24"
} | {
"split": "train",
"index": 5725,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify the expression given by \\(\\frac{a^{-1} - b^{-1}}{a^{-3} + b^{-3}} : \\frac{a^{2} b^{2}}{(a+b)^{2} - 3ab} \\cdot \\left(\\frac{a^{2} - b^{2}}{ab}\\right)^{-1}\\) for \\( a = 1 - \\sqrt{2} \\) and \\( b = 1 + \\sqrt{2} \\). Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 5726,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For a real number \\( x \\), find the maximum value of\n\\[\n\\frac{x^6}{x^{12} + 3x^8 - 6x^6 + 12x^4 + 36}\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{18}"
} | {
"split": "train",
"index": 5727,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token in the discard pile. The game ends when some player runs out of tokens. Players $A$, $B$, and $... | math | {
"style": "rule",
"ground_truth": "37"
} | {
"split": "train",
"index": 5728,
"solution": "\nWe will analyze the game by observing the token distribution and the rules of the game. The key observation is that in each round, the player with the most tokens gives one token to each of the other two players and one token to the discard pile, effectively losin... |
deepscaler | [
{
"role": "user",
"content": "Add $45.23$ to $78.569$ and round your answer to the nearest tenth. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "123.8"
} | {
"split": "train",
"index": 5729,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the vector $\\mathbf{v}$ such that\n\\[\\operatorname{proj}_{\\begin{pmatrix} 2 \\\\ 1 \\end{pmatrix}} \\mathbf{v} = \\begin{pmatrix} \\frac{38}{5} \\\\ \\frac{19}{5} \\end{pmatrix}\\]and\n\\[\\operatorname{proj}_{\\begin{pmatrix} 2 \\\\ 3 \\end{pmatrix}} \\mathbf{v} = \\b... | math | {
"style": "rule",
"ground_truth": "\\begin{pmatrix} 7 \\\\ 5 \\end{pmatrix}"
} | {
"split": "train",
"index": 5730,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A B C$ be a triangle, and let $D, E$, and $F$ be the midpoints of sides $B C, C A$, and $A B$, respectively. Let the angle bisectors of $\\angle F D E$ and $\\angle F B D$ meet at $P$. Given that $\\angle B A C=37^{\\circ}$ and $\\angle C B A=85^{\\circ}$, determine the de... | math | {
"style": "rule",
"ground_truth": "61^{\\circ}"
} | {
"split": "train",
"index": 5731,
"solution": "Because $D, E, F$ are midpoints, we have $A B C \\sim D E F$. Furthermore, we know that $F D \\| A C$ and $D E \\| A B$, so we have $$\\angle B D F=\\angle B C A=180-37-85=58^{\\circ}$$ Also, $\\angle F D E=\\angle B A C=37^{\\circ}$. Hence, we have $$\\angle B P D=... |
deepscaler | [
{
"role": "user",
"content": "Every day, 12 tons of potatoes are delivered to the city using one type of transport from three collective farms. The price per ton is 4 rubles from the first farm, 3 rubles from the second farm, and 1 ruble from the third farm. To ensure timely delivery, the loading process fo... | math | {
"style": "rule",
"ground_truth": "24.6667"
} | {
"split": "train",
"index": 5732,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the value of the expression $\\frac{\\log \\sqrt{27}+\\log 8-3 \\log \\sqrt{10}}{\\log 1.2}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}"
} | {
"split": "train",
"index": 5733,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$A B C D$ is a regular tetrahedron of volume 1. Maria glues regular tetrahedra $A^{\\prime} B C D, A B^{\\prime} C D$, $A B C^{\\prime} D$, and $A B C D^{\\prime}$ to the faces of $A B C D$. What is the volume of the tetrahedron $A^{\\prime} B^{\\prime} C^{\\prime} D^{\\prime}$... | math | {
"style": "rule",
"ground_truth": "\\frac{125}{27}"
} | {
"split": "train",
"index": 5734,
"solution": "Consider the tetrahedron with vertices at $W=(1,0,0), X=(0,1,0), Y=(0,0,1)$, and $Z=(1,1,1)$. This tetrahedron is similar to $A B C D$. It has center $O=\\left(\\frac{1}{2}, \\frac{1}{2}, \\frac{1}{2}\\right)$. We can construct a tetrahedron $W^{\\prime} X^{\\prime}... |
deepscaler | [
{
"role": "user",
"content": "How many edges does a square-based pyramid have? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 5735,
"solution": "A square-based pyramid has 8 edges: 4 edges that form the square base and 1 edge that joins each of the four vertices of the square base to the top vertex."
} |
deepscaler | [
{
"role": "user",
"content": "Pedro wrote a list of all positive integers less than 10000 in which each of the digits 1 and 2 appear exactly once. For example, 1234, 231, and 102 were written on the list, but 1102 and 235 are not on the list. How many numbers are there on Pedro's list? Let's think step by s... | math | {
"style": "rule",
"ground_truth": "336"
} | {
"split": "train",
"index": 5736,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate $6 \\cdot 8\\frac{1}{3}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 5737,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the set $$ \\mathcal{S}=\\{(a, b, c, d, e): 0<a<b<c<d<e<100\\} $$ where $a, b, c, d, e$ are integers. If $D$ is the average value of the fourth element of such a tuple in the set, taken over all the elements of $\\mathcal{S}$ , find the largest integer less than... | math | {
"style": "rule",
"ground_truth": "66"
} | {
"split": "train",
"index": 5738,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a rational number, write it as a fraction in lowest terms and calculate the product of the resulting numerator and denominator. For how many rational numbers between $0$ and $1$ will $20_{}^{}!$ be the resulting product? Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "128"
} | {
"split": "train",
"index": 5739,
"solution": "If the fraction is in the form $\\frac{a}{b}$, then $a < b$ and $\\gcd(a,b) = 1$. There are 8 prime numbers less than 20 ($2, 3, 5, 7, 11, 13, 17, 19$), and each can only be a factor of one of $a$ or $b$. There are $2^8$ ways of selecting some combination of numbers... |
deepscaler | [
{
"role": "user",
"content": "Find the number of all natural numbers in which each subsequent digit is less than the previous one. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1013"
} | {
"split": "train",
"index": 5740,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the tetrahedron \\( ABCD \\), \\( AC = 8 \\), \\( AB = CD = 7 \\), \\( BC = AD = 5 \\), and \\( BD = 6 \\). Given a point \\( P \\) on \\( AC \\), find the minimum value of \\( BP + PD \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{21}"
} | {
"split": "train",
"index": 5741,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The value of $2x+10$ is half of the value of $5x+30$. What is the value of $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-10"
} | {
"split": "train",
"index": 5742,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the small country of Mathland, all automobile license plates have four symbols. The first must be a vowel (A, E, I, O, or U), the second and third must be two different letters among the 21 non-vowels, and the fourth must be a digit (0 through 9). If the symbols are chosen a... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{21,000}"
} | {
"split": "train",
"index": 5743,
"solution": "To solve this problem, we need to calculate the total number of possible license plates and then determine the probability of the specific license plate \"AMC8\".\n\n1. **Calculate the total number of possible license plates:**\n - **First symbol (vowel):** There ... |
deepscaler | [
{
"role": "user",
"content": "Given $\\alpha $, $\\beta \\in (0, \\frac{π}{2})$, $\\sin \\alpha = \\frac{{\\sqrt{5}}}{5}$, $\\cos \\beta = \\frac{1}{{\\sqrt{10}}}$, find the value of $\\alpha - \\beta$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{\\pi}{4}"
} | {
"split": "train",
"index": 5744,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In an arithmetic sequence $\\{a_n\\}$, it is known that $a_1 + a_3 = 0$ and $a_2 + a_4 = -2$. Find the sum of the first 10 terms of the sequence $\\left\\{ \\frac{a_n}{2^{n-1}} \\right\\}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{256}"
} | {
"split": "train",
"index": 5745,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many positive four-digit integers are divisible by both 7 and 6? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "215"
} | {
"split": "train",
"index": 5746,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "After Sally takes 20 shots, she has made $55\\%$ of her shots. After she takes 5 more shots, she raises her percentage to $56\\%$. How many of the last 5 shots did she make? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 5747,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Barry picks infinitely many points inside a unit circle, each independently and uniformly at random, $P_{1}, P_{2}, \\ldots$ Compute the expected value of $N$, where $N$ is the smallest integer such that $P_{N+1}$ is inside the convex hull formed by the points $P_{1}, P_{2}, \\... | math | {
"style": "rule",
"ground_truth": "6.54"
} | {
"split": "train",
"index": 5748,
"solution": "Clearly, $N \\geq 3$, and let's scale the circle to have area 1. We can see that the probability to not reach $N=4$ is equal to the probability that the fourth point is inside the convex hull of the past three points. That is, the probability is just one minus the e... |
deepscaler | [
{
"role": "user",
"content": "Given the set $P={x|1≦x≦6,x∈N}$, for its non-empty subset $A$, multiply each element $k$ in $A$ by $(-1)^k$ and then sum them up. (For example, if $A={1,3,6}$, the sum would be $(-1)⋅1+(-1)^3⋅3+(-1)^6⋅6=2$.) The total sum of these sums for all non-empty subsets of $M$ is \\_\\_... | math | {
"style": "rule",
"ground_truth": "96"
} | {
"split": "train",
"index": 5749,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "To stabilize housing prices, a local government decided to build a batch of affordable housing for the community. The plan is to purchase a piece of land for 16 million yuan and build a residential community with 10 buildings on it. Each building has the same number of floors, ... | math | {
"style": "rule",
"ground_truth": "1225"
} | {
"split": "train",
"index": 5750,
"solution": ""
} |
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"
} | {
"split": "train",
"index": 5751,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given two functions $f(x) = e^{2x-3}$ and $g(x) = \\frac{1}{4} + \\ln \\frac{x}{2}$, if $f(m) = g(n)$ holds, calculate the minimum value of $n-m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2} + \\ln 2"
} | {
"split": "train",
"index": 5752,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given Jones traveled 100 miles on his first trip and 500 miles on a subsequent trip at a speed four times as fast, compare his new time to the old time. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1.25"
} | {
"split": "train",
"index": 5753,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nA client of a brokerage company deposited 12,000 rubles into a brokerage account at a rate of 60 rubles per dollar with instructions to the broker to invest the amount in bonds of foreign banks, which have a guaranteed return of 12% per annum in dollars.\n\n(a) Determine the ... | math | {
"style": "rule",
"ground_truth": "39.52\\%"
} | {
"split": "train",
"index": 5754,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the cube ABCD-A<sub>1</sub>B<sub>1</sub>C<sub>1</sub>D<sub>1</sub>, the angle formed by the skew lines A<sub>1</sub>B and AC is \\_\\_\\_\\_\\_\\_°; the angle formed by the line A<sub>1</sub>B and the plane A<sub>1</sub>B<sub>1</sub>CD is \\_\\_\\_\\_\\_\\_\\_\\_\\_°. Let's ... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 5755,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For the function $f(x)=\\sin \\left(2x+ \\frac {\\pi}{6}\\right)$, consider the following statements: \n$(1)$ The graph of the function is symmetric about the line $x=- \\frac {\\pi}{12}$; \n$(2)$ The graph of the function is symmetric about the point $\\left( \\frac {5\\... | math | {
"style": "rule",
"ground_truth": "(2)(4)"
} | {
"split": "train",
"index": 5756,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Cagney can frost a cupcake every 15 seconds, while Lacey can frost every 40 seconds. They take a 10-second break after every 10 cupcakes. Calculate the number of cupcakes that they can frost together in 10 minutes. Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 5757,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A four-digit integer \\( p \\) and the four-digit integer obtained by reversing the order of the digits of \\( p \\) are both divisible by \\( 63 \\) (product of primes \\( 7 \\) and \\( 9 \\)). Additionally, \\( p \\) must be divisible by \\( 19 \\). Determine the greatest pos... | math | {
"style": "rule",
"ground_truth": "5985"
} | {
"split": "train",
"index": 5758,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The probability it will rain on Saturday is $60\\%$, and the probability it will rain on Sunday is $25\\%$. If the probability of rain on a given day is independent of the weather on any other day, what is the probability it will rain on both days, expressed as a percent? Let's... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 5759,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle can be circumscribed around the quadrilateral $ABCD$. Additionally, $AB = 3$, $BC = 4$, $CD = 5$, and $AD = 2$. \n\nFind $AC$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{\\frac{299}{11}}"
} | {
"split": "train",
"index": 5760,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The robot vacuum cleaner is programmed to move on the floor according to the law:\n\n$$\\left\\{\\begin{array}{l} x = t(t-6)^2 \\\\ y = 0, \\quad 0 \\leq t \\leq 7 \\\\ y = (t-7)^2, \\quad t \\geq 7 \\end{array}\\right.$$\n\nwhere the axes are chosen parallel to the walls and t... | math | {
"style": "rule",
"ground_truth": "\\sqrt{445}"
} | {
"split": "train",
"index": 5761,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find $\\sec 120^\\circ.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 5762,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the ratio $AC:CB$ is $2:3$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). Determine the ratio $PA:AB$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2:1"
} | {
"split": "train",
"index": 5763,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\(100^a = 4\\) and \\(100^b = 5\\), then find \\(20^{(1 - a - b)/(2(1 - b))}\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{5}"
} | {
"split": "train",
"index": 5764,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jerry's favorite number is $97$ . He knows all kinds of interesting facts about $97$ :\n\n\n- $97$ is the largest two-digit prime.\n- Reversing the order of its digits results in another prime.\n- There is only one way in which $97$ can be written as a difference of two p... | math | {
"style": "rule",
"ground_truth": "96"
} | {
"split": "train",
"index": 5765,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A=H_{1}, B=H_{6}+1$. A real number $x$ is chosen randomly and uniformly in the interval $[A, B]$. Find the probability that $x^{2}>x^{3}>x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 5766,
"solution": "$A=-1, B=3$. For $x^{3}>x$, either $x>1$ or $-1<x<0$. However, for $x>1, x^{2}<x^{3}$, so there are no solutions. $-1<x<0$ also satisfies $x^{2}>x^{3}$, so our answer is $1 / 4$."
} |
deepscaler | [
{
"role": "user",
"content": "For dinner, Priya is eating grilled pineapple spears. Each spear is in the shape of the quadrilateral PINE, with $P I=6 \\mathrm{~cm}, I N=15 \\mathrm{~cm}, N E=6 \\mathrm{~cm}, E P=25 \\mathrm{~cm}$, and \\angle N E P+\\angle E P I=60^{\\circ}$. What is the area of each spear,... | math | {
"style": "rule",
"ground_truth": "\\frac{100 \\sqrt{3}}{3}"
} | {
"split": "train",
"index": 5767,
"solution": "We consider a configuration composed of 2 more quadrilaterals congruent to PINE. Let them be $P^{\\prime} I^{\\prime} N^{\\prime} E^{\\prime}$, with $E^{\\prime}=P$ and $N^{\\prime}=I$, and $P^{\\prime \\prime} I^{\\prime \\prime} N^{\\prime \\prime} E^{\\prime \\pr... |
deepscaler | [
{
"role": "user",
"content": "A set $\\mathcal{S}$ of distinct positive integers has the following property: for every integer $x$ in $\\mathcal{S},$ the arithmetic mean of the set of values obtained by deleting $x$ from $\\mathcal{S}$ is an integer. Given that 1 belongs to $\\mathcal{S}$ and that 2002 is t... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 5768,
"solution": "Let the sum of the integers in $\\mathcal{S}$ be $N$, and let the size of $|\\mathcal{S}|$ be $n+1$. After any element $x$ is removed, we are given that $n|N-x$, so $x\\equiv N\\pmod{n}$. Since $1\\in\\mathcal{S}$, $N\\equiv1\\pmod{n}$, and all elements are congruen... |
deepscaler | [
{
"role": "user",
"content": "The number of rounds of golf played by each golfer of an amateur golf association is shown in the chart below. What is the average number of rounds played by each golfer? Express your answer to the nearest whole number. [asy]\nsize(150);\ndraw((0,7)--(0,0)--(10,0));\nfor(int i ... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 5769,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the matrix \n\\[\\mathbf{N} = \\begin{pmatrix} 2x & -y & z \\\\ y & x & -2z \\\\ y & -x & z \\end{pmatrix}\\]\nand it is known that $\\mathbf{N}^T \\mathbf{N} = \\mathbf{I}$. Find $x^2 + y^2 + z^2$. Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 5770,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the sequence $\\{a_n\\}$ is defined by\n$a_1=2$\n$a_{n+1}=a_n+2n$\nwhere $n\\geq1$.\nThen $a_{100}$ equals Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9902"
} | {
"split": "train",
"index": 5771,
"solution": "1. **Define the sequence and initial conditions**: The sequence $\\{a_n\\}$ is defined by:\n - $a_1 = 2$\n - $a_{n+1} = a_n + 2n$ for $n \\geq 1$.\n\n2. **Identify the pattern in the sequence**: Calculate the first few terms to observe any pattern:\n - $a_1 = ... |
deepscaler | [
{
"role": "user",
"content": "Given the ellipse $C$: $\\frac{x^{2}}{a^{2}}+ \\frac{y^{2}}{b^{2}}=1(a > b > 0)$, its right focus $F$, and the line passing through $F$ with a slope of $1$ intersects the ellipse at points $M$ and $N$. The perpendicular bisector of $MN$ intersects the $x$-axis at point $P$. If ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 5772,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many positive odd integers greater than 1 and less than $200$ are square-free? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "82"
} | {
"split": "train",
"index": 5773,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\alpha$ and $\\beta$ be real numbers. Find the minimum value of\n\\[(3 \\cos \\alpha + 4 \\sin \\beta - 10)^2 + (3 \\sin \\alpha + 4 \\cos \\beta - 12)^2.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(\\sqrt{244} - 7)^2"
} | {
"split": "train",
"index": 5774,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of the first $n$ terms of a geometric sequence $\\{a_n\\}$, where each term is positive, is $S_n$. Given that $S_n = 2$ and $S_{3n} = 14$, calculate $S_{4n}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 5775,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Abigail chooses an integer at random from the set $\\{2,4,6,8,10\\}$. Bill chooses an integer at random from the set $\\{2,4,6,8,10\\}$. Charlie chooses an integer at random from the set $\\{2,4,6,8,10\\}$. What is the probability that the product of their three integers is not... | math | {
"style": "rule",
"ground_truth": "\\frac{98}{125}"
} | {
"split": "train",
"index": 5776,
"solution": "For the product of the three integers to be a power of 2, it can have no prime factors other than 2. In each of the three sets, there are 3 powers of 2 (namely, 2,4 and 8) and 2 integers that are not a power of 2 (namely, 6 and 10). The probability that each chooses... |
deepscaler | [
{
"role": "user",
"content": "A right circular cone is inscribed in a right prism as shown. What is the ratio of the volume of the cone to the volume of the prism? Express your answer as a common fraction in terms of $\\pi$. [asy]\nimport three; import graph3;\ndefaultpen(linewidth(0.8));\nsize(200);\ndraw(... | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{12}"
} | {
"split": "train",
"index": 5777,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the ratio of the legs of a right triangle is $1: 2$, then the ratio of the corresponding segments of the hypotenuse made by a perpendicular upon it from the vertex is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1: 4"
} | {
"split": "train",
"index": 5778,
"solution": "1. **Assigning values to the legs of the triangle**: Let $\\triangle ABC$ be a right triangle with the right angle at $B$. Assume $AB = 2x$ and $BC = x$ where $x$ is a positive real number. This setup maintains the ratio of the legs as $1:2$.\n\n2. **Using the Pytha... |
deepscaler | [
{
"role": "user",
"content": "In Mr. Johnson's class, 12 out of 20 students received an 'A' grade and the rest received a 'B' grade. Mrs. Smith, teaching a different class, observed that the proportion of students getting 'A' was the same. If Mrs. Smith has 30 students total, how many students received an '... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 5779,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that five boys, A, B, C, D, and E, are randomly assigned to stay in 3 standard rooms (with at most two people per room), calculate the probability that A and B stay in the same standard room. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}"
} | {
"split": "train",
"index": 5780,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a certain exam with 50 questions, each correct answer earns 3 points, each incorrect answer deducts 1 point, and unanswered questions neither add nor deduct points. Xiaolong scored 120 points. How many questions did Xiaolong answer correctly at most? Let's think step by step... | math | {
"style": "rule",
"ground_truth": "42"
} | {
"split": "train",
"index": 5781,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A B C$ be an acute triangle with orthocenter $H$. Let $D, E$ be the feet of the $A, B$-altitudes respectively. Given that $A H=20$ and $H D=15$ and $B E=56$, find the length of $B H$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 5782,
"solution": "Let $x$ be the length of $B H$. Note that quadrilateral $A B D E$ is cyclic, so by Power of a Point, $x(56-x)=$ $20 \\cdot 15=300$. Solving for $x$, we get $x=50$ or 6 . We must have $B H>H D$ so $x=50$ is the correct length."
} |
deepscaler | [
{
"role": "user",
"content": "A circle is tangent to the lines $4x - 3y = 30$ and $4x - 3y = -10.$ The center of the circle lies on the line $2x + y = 0.$ Find the center of the circle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(1,-2)"
} | {
"split": "train",
"index": 5783,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find a quadratic with rational coefficients and quadratic term $x^2$ that has $\\sqrt{3}-2$ as a root. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x^2+4x+1"
} | {
"split": "train",
"index": 5784,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A parallelogram has 2 sides of length 20 and 15. Given that its area is a positive integer, find the minimum possible area of the parallelogram. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 5785,
"solution": "The area of the parallelogram can be made arbitrarily small, so the smallest positive integer area is 1."
} |
deepscaler | [
{
"role": "user",
"content": "The sequence $\\{a_n\\}$ satisfies $a_n=13-3n$, $b_n=a_n⋅a_{n+1}⋅a_{n+2}$, $S_n$ is the sum of the first $n$ terms of $\\{b_n\\}$. Find the maximum value of $S_n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "310"
} | {
"split": "train",
"index": 5786,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "2^{-(2k+1)}-2^{-(2k-1)}+2^{-2k} is equal to Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2^{-(2k+1)}"
} | {
"split": "train",
"index": 5787,
"solution": "1. **Rewrite the expression with a common base:** \n We start by expressing each term in the expression $2^{-(2k+1)} - 2^{-(2k-1)} + 2^{-2k}$ using a common base. Let $x = 2^{-2k}$. Then:\n - $2^{-(2k+1)} = 2^{-2k} \\cdot 2^{-1} = x \\cdot \\frac{1}{2} = \\frac... |
deepscaler | [
{
"role": "user",
"content": "The coefficients of the polynomial\n\\[a_{10} x^{10} + a_9 x^9 + a_8 x^8 + \\dots + a_2 x^2 + a_1 x + a_0 = 0\\]are all integers, and its roots $r_1,$ $r_2,$ $\\dots,$ $r_{10}$ are all integers. Furthermore, the roots of the polynomial\n\\[a_0 x^{10} + a_1 x^9 + a_2 x^8 + \\do... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 5788,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "One material particle entered the opening of a pipe, and after 6.8 minutes, a second particle entered the same opening. Upon entering the pipe, each particle immediately began linear motion along the pipe: the first particle moved uniformly at a speed of 5 meters per minute, wh... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 5789,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An ellipse has a major axis of length 12 and a minor axis of 10. Using one focus as a center, an external circle is tangent to the ellipse. Find the radius of the circle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{11}"
} | {
"split": "train",
"index": 5790,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The UEFA Champions League playoffs is a 16-team soccer tournament in which Spanish teams always win against non-Spanish teams. In each of 4 rounds, each remaining team is randomly paired against one other team; the winner advances to the next round, and the loser is permanently... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{5}"
} | {
"split": "train",
"index": 5791,
"solution": "We note that the probability there are not two Spanish teams in the final two is the probability that the 3 of them have already competed against each other in previous rounds. Note that the random pairings in each round is equivalent, by the final round, to dividin... |
deepscaler | [
{
"role": "user",
"content": "Given \\( x, y, z \\in (0, +\\infty) \\) and \\(\\frac{x^2}{1+x^2} + \\frac{y^2}{1+y^2} + \\frac{z^2}{1+z^2} = 2 \\), find the maximum value of \\(\\frac{x}{1+x^2} + \\frac{y}{1+y^2} + \\frac{z}{1+z^2}\\). Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 5792,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A workshop produces transformers of types $A$ and $B$. One transformer of type $A$ uses 5 kg of transformer iron and 3 kg of wire, while one transformer of type $B$ uses 3 kg of iron and 2 kg of wire. The profit from selling one transformer of type $A$ is 12 thousand rubles, an... | math | {
"style": "rule",
"ground_truth": "1502"
} | {
"split": "train",
"index": 5793,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $A:B:C = 2:1:4$, what is the value of $(3A + 2B) \\div (4C - A)$? Express your answer as a common fraction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{7}"
} | {
"split": "train",
"index": 5794,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$ ($a > 0, b > 0$) and the circle $x^2 + y^2 = a^2 + b^2$ in the first quadrant, find the eccentricity of the hyperbola, where $|PF_1| = 3|PF_2|$. Let's think step by step and put only the final answer within \\boxed{}... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{10}}{2}"
} | {
"split": "train",
"index": 5795,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A bag of fruit contains 10 fruits, including an even number of apples, at most two oranges, a multiple of three bananas, and at most one pear. How many different combinations of these fruits can there be? Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 5796,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 9 representatives from different countries, with 3 people from each country. They sit randomly around a round table with 9 chairs. What is the probability that each representative has at least one representative from another country sitting next to them? Let's think s... | math | {
"style": "rule",
"ground_truth": "41/56"
} | {
"split": "train",
"index": 5797,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the sum of the series:\n\n\\[ 5(1+5(1+5(1+5(1+5(1+5(1+5(1+5(1+5(1+5(1+5(1+5)))))))))) \\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "305175780"
} | {
"split": "train",
"index": 5798,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A teacher asks her class what the value of $\\left(5^2-4^2\\right)^3$ is. What is the value of the expression? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "729"
} | {
"split": "train",
"index": 5799,
"solution": ""
} |
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