data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Determine how many \"super prime dates\" occurred in 2007, where a \"super prime date\" is defined as a date where both the month and day are prime numbers, and additionally, the day is less than or equal to the typical maximum number of days in the respective prime month. Let'... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 32549,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Sandwiches at Joe's Fast Food cost $3 each and sodas cost $2 each. How many dollars will it cost to purchase 5 sandwiches and 8 sodas? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 32550,
"solution": "1. **Calculate the cost of sandwiches**: Each sandwich costs $3$ dollars. Therefore, the cost for $5$ sandwiches is calculated by multiplying the number of sandwiches by the cost per sandwich:\n \\[\n 5 \\times 3 = 15 \\text{ dollars}\n \\]\n\n2. **Calculate ... |
deepscaler | [
{
"role": "user",
"content": "The coefficient of $x^{3}$ in the expansion of $(2x^{2}+x-1)^{5}$ is _______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-30"
} | {
"split": "train",
"index": 32551,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of different numbers of the form $\\left\\lfloor\\frac{i^2}{2015} \\right\\rfloor$ , with $i = 1,2, ..., 2015$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2016"
} | {
"split": "train",
"index": 32552,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Estimate the probability of a rifle student hitting the target using a random simulation method by analyzing the ratio of the number of sets of three random numbers where exactly one represents a hit to the total number of sets of three random numbers. Let's think step by step ... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{20}"
} | {
"split": "train",
"index": 32553,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Prince Gvidon had three sons. Among his descendants, 93 each had two sons and no daughters, while the rest died childless. How many total descendants did Prince Gvidon have? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "189"
} | {
"split": "train",
"index": 32554,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( a \\) be a real number, and let \\( m(a) \\) denote the minimum value of the function \\( f(x) = x^2 - ax + \\frac{a}{2} \\) for \\( 0 \\leq x \\leq 1 \\). Find the maximum value of \\( m(a) \\) as \\( a \\) varies. Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 32555,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Sasha wrote down numbers from one to one hundred, and Misha erased some of them. Among the remaining numbers, 20 have the digit one in their recording, 19 have the digit two in their recording, and 30 numbers have neither the digit one nor the digit two. How many numbers did Mi... | math | {
"style": "rule",
"ground_truth": "33"
} | {
"split": "train",
"index": 32556,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a rectangular coordinate system, what is the number of units in the distance from the origin to the point (7, -24)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 32557,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Seven sticks with lengths 2, 3, 5, 7, 11, 13 and 17 inches are placed in a box. Three of the sticks are randomly selected. What is the probability that a triangle can be formed by joining the endpoints of the sticks? Express your answer as a common fraction. Let's think step by... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{35}"
} | {
"split": "train",
"index": 32558,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a grid, identify the rectangles and squares, and describe their properties and characteristics. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 32559,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $4:x^2 = x:16$, 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": "4"
} | {
"split": "train",
"index": 32560,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A school organizes a table tennis competition. Class A has 5 male students and 3 female students registered; Class B has 6 male students and 2 female students registered. If 2 students are selected from each of Class A and Class B, there are a total of $\\boxed{345}$ different ... | math | {
"style": "rule",
"ground_truth": "345"
} | {
"split": "train",
"index": 32561,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\(\\alpha\\) is an acute angle and \\(\\beta\\) is an obtuse angle, and \\(\\sec (\\alpha - 2\\beta)\\), \\(\\sec \\alpha\\), and \\(\\sec (\\alpha + 2\\beta)\\) form an arithmetic sequence, find the value of \\(\\frac{\\cos \\alpha}{\\cos \\beta}\\). Let's think st... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 32562,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sports conference has 12 teams in two divisions of 6 each. How many games are in a complete season for the conference if each team must play every other team in its own division three times and every team in the other division twice? Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "162"
} | {
"split": "train",
"index": 32563,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $i=\\sqrt{-1}$. The product of the real parts of the roots of $z^2-z=5-5i$ is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-6"
} | {
"split": "train",
"index": 32564,
"solution": "1. **Identify the quadratic equation and apply the quadratic formula**:\n The given equation is $z^2 - z = 5 - 5i$. Rearranging, we have:\n \\[\n z^2 - z - (5 - 5i) = 0\n \\]\n Applying the quadratic formula, $z = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$, w... |
deepscaler | [
{
"role": "user",
"content": "Given a triangle $\\triangle ABC$ with an area of $S$, and $\\overrightarrow{AB} \\cdot \\overrightarrow{AC} = S$.\n\n(I) Find the value of $\\tan 2A$;\n\n(II) If $\\cos C = \\frac{3}{5}$, and $|\\overrightarrow{AC} - \\overrightarrow{AB}| = 2$, find the area $S$ of $\\triangle... | math | {
"style": "rule",
"ground_truth": "\\frac{8}{5}"
} | {
"split": "train",
"index": 32565,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A point in space $(x,y,z)$ is randomly selected so that $-1\\le x \\le 1$,$-1\\le y \\le 1$,$-1\\le z \\le 1$. What is the probability that $x^2+y^2+z^2\\le 1$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{6}"
} | {
"split": "train",
"index": 32566,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)= \\sqrt {3}\\sin ^{2}x+\\sin x\\cos x- \\frac { \\sqrt {3}}{2}$ $(x\\in\\mathbb{R})$.\n$(1)$ If $x\\in(0, \\frac {\\pi}{2})$, find the maximum value of $f(x)$;\n$(2)$ In $\\triangle ABC$, if $A < B$ and $f(A)=f(B)= \\frac {1}{2}$, find the value of $\\f... | math | {
"style": "rule",
"ground_truth": "\\sqrt {2}"
} | {
"split": "train",
"index": 32567,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When a certain biased coin is flipped five times, the probability of getting heads exactly once is not equal to $0$ and is the same as that of getting heads exactly twice. Let $\\frac ij$, in lowest terms, be the probability that the coin comes up heads in exactly $3$ out of $5... | math | {
"style": "rule",
"ground_truth": "283"
} | {
"split": "train",
"index": 32568,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "John has two identical cups. Initially, he puts 6 ounces of tea into the first cup and 6 ounces of milk into the second cup. He then pours one-third of the tea from the first cup into the second cup and mixes thoroughly. After stirring, John then pours half of the mixture from ... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{8}"
} | {
"split": "train",
"index": 32569,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the parabola $y^2 = 4x$, a line passing through point $P(4, 0)$ intersects the parabola at points $A(x_1, y_1)$ and $B(x_2, y_2)$. Find the minimum value of $y_1^2 + y_2^2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 32570,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given vectors $\\overrightarrow {a}$ = (4, 3) and $\\overrightarrow {b}$ = (-1, 2), with $\\overrightarrow {m}$ = $\\overrightarrow {a}$ - $λ \\overrightarrow {b}$ and $\\overrightarrow {n}$ = 2$\\overrightarrow {a}$ + $\\overrightarrow {b}$, find the values of $λ$ such that $\... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{2}"
} | {
"split": "train",
"index": 32571,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A subset $B$ of $\\{1, 2, \\dots, 2017\\}$ is said to have property $T$ if any three elements of $B$ are the sides of a nondegenerate triangle. Find the maximum number of elements that a set with property $T$ may contain. Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "1009"
} | {
"split": "train",
"index": 32572,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$ , $\\angle ACB=50^{\\circ}$ and $\\angle CBA=70^{\\circ}$ . Let $D$ be a foot of perpendicular from point $A$ to side $BC$ , $O$ circumcenter of $ABC$ and $E$ antipode of $A$ in circumcircle $ABC$ . Find $\\angle DAE$ Let's think step by st... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 32573,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a class organizing a cultural evening, they plan to select 4 programs from 8 programs, with the requirement that at least one of the programs A or B must be selected, and when both A and B are selected, their performance order cannot be adjacent. Express the number of differ... | math | {
"style": "rule",
"ground_truth": "1140"
} | {
"split": "train",
"index": 32574,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find $\\frac{1}{3}+\\frac{2}{7}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{13}{21}"
} | {
"split": "train",
"index": 32575,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Points \\( K \\) and \\( N \\) are located on the sides \\( AB \\) and \\( AC \\) of triangle \\( ABC \\) respectively, such that \\( AK = BK \\) and \\( AN = 2NC \\).\n\nIn what ratio does the segment \\( KN \\) divide the median \\( AM \\) of triangle \\( ABC \\)? Let's think... | math | {
"style": "rule",
"ground_truth": "4:3"
} | {
"split": "train",
"index": 32576,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Andrea flips a fair coin repeatedly, continuing until she either flips two heads in a row (the sequence $H H$ ) or flips tails followed by heads (the sequence $T H$ ). What is the probability that she will stop after flipping $H H$ ? Let's think step by step and put only the fi... | math | {
"style": "rule",
"ground_truth": "1/4"
} | {
"split": "train",
"index": 32577,
"solution": "The only way that Andrea can ever flip $H H$ is if she never flips $T$, in which case she must flip two heads immediately at the beginning. This happens with probability $\\frac{1}{4}$."
} |
deepscaler | [
{
"role": "user",
"content": "A circle with radius $r$ is contained within the region bounded by a circle with radius $R$. The area bounded by the larger circle is $\\frac{a}{b}$ times the area of the region outside the smaller circle and inside the larger circle. Then $R:r$ equals: Let's think step by step... | math | {
"style": "rule",
"ground_truth": "\\sqrt{a}:\\sqrt{a-b}"
} | {
"split": "train",
"index": 32578,
"solution": "1. **Identify the areas involved**: \n - The area of the larger circle is $\\pi R^2$.\n - The area of the smaller circle is $\\pi r^2$.\n - The area of the region outside the smaller circle and inside the larger circle is $\\pi R^2 - \\pi r^2$.\n\n2. **Set up... |
deepscaler | [
{
"role": "user",
"content": "The inclination angle of the line $x-y+1=0$ can be calculated. 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": 32579,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$12 \\cos ^{4} \\frac{\\pi}{8}+\\cos ^{4} \\frac{3 \\pi}{8}+\\cos ^{4} \\frac{5 \\pi}{8}+\\cos ^{4} \\frac{7 \\pi}{8}=$ 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": 32580,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x$, $y$, $z$, $u$, and $v$ be positive integers with $x+y+z+u+v=2505$. Let $N$ be the largest of the sums $x+y$, $y+z$, $z+u$, and $u+v$. Determine the smallest possible value of $N$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1253"
} | {
"split": "train",
"index": 32581,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute $\\tan 75^\\circ.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2 + \\sqrt{3}"
} | {
"split": "train",
"index": 32582,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Julie is preparing a speech for her class. Her speech must last between one-half hour and three-quarters of an hour. The ideal rate of speech is 150 words per minute. If Julie speaks at the ideal rate, what number of words would be an appropriate length for her speech? Let's... | math | {
"style": "rule",
"ground_truth": "5650"
} | {
"split": "train",
"index": 32583,
"solution": "1. **Convert Time to Minutes**: \n - One-half hour is $\\frac{1}{2} \\times 60 = 30$ minutes.\n - Three-quarters of an hour is $\\frac{3}{4} \\times 60 = 45$ minutes.\n\n2. **Calculate the Range of Words**:\n - At the ideal rate of 150 words per minute, the m... |
deepscaler | [
{
"role": "user",
"content": "Given a nonnegative real number $x$, let $\\langle x\\rangle$ denote the fractional part of $x$; that is, $\\langle x\\rangle=x-\\lfloor x\\rfloor$, where $\\lfloor x\\rfloor$ denotes the greatest integer less than or equal to $x$. Suppose that $a$ is positive, $\\langle a^{-1}... | math | {
"style": "rule",
"ground_truth": "233"
} | {
"split": "train",
"index": 32584,
"solution": "Find $a$ as shown above. Note that $a$ satisfies the equation $a^2 = a+1$ (this is the equation we solved to get it). Then, we can simplify $a^{12}$ as follows using the fibonacci numbers:\n$a^{12} = a^{11}+a^{10}= 2a^{10} + a^{9} = 3a^8+ 2a^9 = ... = 144a^1+89a^0 ... |
deepscaler | [
{
"role": "user",
"content": "Find the largest positive integer $n>10$ such that the residue of $n$ when divided by each perfect square between $2$ and $\\dfrac n2$ is an odd number. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "505"
} | {
"split": "train",
"index": 32585,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A$, $M$, and $C$ be nonnegative integers such that $A+M+C=12$. What is the maximum value of \\[A\\cdot M\\cdot C+A\\cdot M+M\\cdot\nC+C\\cdot A?\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "112"
} | {
"split": "train",
"index": 32586,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A hall is organizing seats in rows for a lecture. Each complete row must contain $13$ chairs. Initially, the hall has $169$ chairs arranged. To maintain fully occupied rows with minimal empty seats, if $100$ students are expected to attend, how many chairs should be removed or ... | math | {
"style": "rule",
"ground_truth": "65"
} | {
"split": "train",
"index": 32587,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle \\(XYZ,\\) \\(XY = 5,\\) \\(XZ = 7,\\) \\(YZ = 9,\\) and \\(W\\) lies on \\(\\overline{YZ}\\) such that \\(\\overline{XW}\\) bisects \\(\\angle YXZ.\\) Find \\(\\cos \\angle YXW.\\) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3\\sqrt{5}}{10}"
} | {
"split": "train",
"index": 32588,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Isosceles trapezoid \\(ABCD\\) with bases \\(AB\\) and \\(CD\\) has a point \\(P\\) on \\(AB\\) with \\(AP=11, BP=27\\), \\(CD=34\\), and \\(\\angle CPD=90^{\\circ}\\). Compute the height of isosceles trapezoid \\(ABCD\\). Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 32589,
"solution": "Drop projections of \\(A, P, B\\) onto \\(CD\\) to get \\(A', P', B'\\). Since \\(A'B'=38\\) and \\(CD=34\\), we get that \\(DA'=CB'=2\\). Thus, \\(P'D=9\\) and \\(P'C=25\\). Hence, the answer is \\(PP'=\\sqrt{P'D \\cdot P'C}=15\\)."
} |
deepscaler | [
{
"role": "user",
"content": "The complex numbers corresponding to the vertices $O$, $A$, and $C$ of the parallelogram $OABC$ are $0$, $3+2i$, and $-2+4i$, respectively.<br/>$(1)$ Find the complex number corresponding to point $B$;<br/>$(2)$ In triangle $OAB$, find the height $h$ on side $OB$. Let's think s... | math | {
"style": "rule",
"ground_truth": "\\frac{16\\sqrt{37}}{37}"
} | {
"split": "train",
"index": 32590,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nCompute the definite integral:\n\n$$\n\\int_{1}^{2} \\frac{x+\\sqrt{3 x-2}-10}{\\sqrt{3 x-2}+7} d x\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{22}{27}"
} | {
"split": "train",
"index": 32591,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that a high school senior year has 12 classes, with exactly 8 classes to be proctored by their own homeroom teachers, find the number of different proctoring arrangements for the math exam. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4455"
} | {
"split": "train",
"index": 32592,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Vertex E of equilateral triangle ∆ABE is inside square ABCD. F is the intersection point of diagonal BD and line segment AE. If AB has length √(1+√3), calculate the area of ∆ABF. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{2}"
} | {
"split": "train",
"index": 32593,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A flagpole is originally $5$ meters tall. A hurricane snaps the flagpole at a point $x$ meters above the ground so that the upper part, still attached to the stump, touches the ground $1$ meter away from the base. What is $x$? Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "2.4"
} | {
"split": "train",
"index": 32594,
"solution": "1. **Identify the problem setup**: Let $AB$ represent the flagpole, which is $5$ meters tall. The flagpole breaks at point $D$, and the top part touches the ground at point $C$, $1$ meter away from the base $B$. We need to find the height $x = AD$ where the flagpol... |
deepscaler | [
{
"role": "user",
"content": "Let $x_1,$ $x_2,$ $x_3,$ $\\dots,$ $x_{100}$ be positive real numbers such that $x_1^2 + x_2^2 + x_3^2 + \\dots + x_{100}^2 = 1.$ Find the minimum value of\n\\[\\frac{x_1}{1 - x_1^2} + \\frac{x_2}{1 - x_2^2} + \\frac{x_3}{1 - x_3^2} + \\dots + \\frac{x_{100}}{1 - x_{100}^2}.\\... | math | {
"style": "rule",
"ground_truth": "\\frac{3 \\sqrt{3}}{2}"
} | {
"split": "train",
"index": 32595,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A wishing well is located at the point $(11,11)$ in the $xy$ -plane. Rachelle randomly selects an integer $y$ from the set $\\left\\{ 0, 1, \\dots, 10 \\right\\}$ . Then she randomly selects, with replacement, two integers $a,b$ from the set $\\left\\{ 1,2,\\dots,10 \... | math | {
"style": "rule",
"ground_truth": "111"
} | {
"split": "train",
"index": 32596,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $ABC$ is an isosceles triangle with $AB=BC$. Point $D$ is the midpoint of both $\\overline{BC}$ and $\\overline{AE}$, and $\\overline{CE}$ is 11 units long. What is the length of $\\overline{BD}$? Express your answer as a decimal to the nearest tenth.\n\n[asy]\ndraw((... | math | {
"style": "rule",
"ground_truth": "5.5"
} | {
"split": "train",
"index": 32597,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Dave walks to school and averages 85 steps per minute, with each step being 80 cm long. It now takes him 15 minutes to get to school. Jack, walking the same route to school, takes steps that are 72 cm long and averages 104 steps per minute. Find the time it takes Jack to reach ... | math | {
"style": "rule",
"ground_truth": "13.62"
} | {
"split": "train",
"index": 32598,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, three circles each with a radius of 5 units intersect at exactly one common point, which is the origin. Calculate the total area in square units of the shaded region formed within the triangular intersection of the three circles. Express your answer in terms of ... | math | {
"style": "rule",
"ground_truth": "\\frac{150\\pi - 75\\sqrt{3}}{12}"
} | {
"split": "train",
"index": 32599,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Multiply \\(333\\) by \\(111\\) and express the result. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36963"
} | {
"split": "train",
"index": 32600,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the sum and product of all values of $x$ such that $x^2 = 18x - 16$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 32601,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The domain of the function $f(x)=\\log_{\\frac{1}{2}}(\\log_4(\\log_{\\frac{1}{4}}(\\log_{16}(\\log_{\\frac{1}{16}}x))))$ is an interval of length $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$? Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "271"
} | {
"split": "train",
"index": 32602,
"solution": "To find the domain of the function \n\\[ f(x) = \\log_{\\frac{1}{2}}\\left(\\log_4\\left(\\log_{\\frac{1}{4}}\\left(\\log_{16}\\left(\\log_{\\frac{1}{16}}x\\right)\\right)\\right)\\right), \\]\nwe need to ensure that each logarithm in the nested expression is defin... |
deepscaler | [
{
"role": "user",
"content": "Given the sets\n\n$$\n\\begin{array}{l}\nM=\\{x, x y, \\lg (x y)\\} \\\\\nN=\\{0,|x|, y\\},\n\\end{array}\n$$\n\nand $M=N$, determine the value of:\n\n$$\\left(x+\\frac{1}{y}\\right)+\\left(x^{2}+\\frac{1}{y^{2}}\\right)+\\left(x^{3}+\\frac{1}{y^{3}}\\right)+\\cdots+\\left(x^{2... | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 32603,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Rectangle $ABCD$ has area $2006.$ An ellipse with area $2006\\pi$ passes through $A$ and $C$ and has foci at $B$ and $D$. What is the perimeter of the rectangle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8\\sqrt{1003}"
} | {
"split": "train",
"index": 32604,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a school, a dodgeball tournament was held. Each game was between two teams. A win awarded 15 points, a draw awarded 11 points, and a loss awarded no points. Each team played every other team exactly once. At the end of the tournament, it turned out that the total number of p... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 32605,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many different triangles can be formed having a perimeter of 7 units if each side must have integral length? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 32606,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On a blackboard a stranger writes the values of $s_{7}(n)^{2}$ for $n=0,1, \\ldots, 7^{20}-1$, where $s_{7}(n)$ denotes the sum of digits of $n$ in base 7 . Compute the average value of all the numbers on the board. Let's think step by step and put only the final answer within ... | math | {
"style": "rule",
"ground_truth": "3680"
} | {
"split": "train",
"index": 32607,
"solution": "Solution 1: We solve for 0 to $b^{n}-1$ and $s_{b}(n)^{2}$ (i.e. base $b$ ). Let $n=d_{1} \\ldots d_{n}$ in base $b$, where there may be leading zeros. Then $s_{b}(n)=d_{1}+\\cdots+d_{n}$, regardless of the leading zeros. $$\\mathbb{E}\\left[s_{d}(n)^{2}\\right]=\\... |
deepscaler | [
{
"role": "user",
"content": "A person bought a bond for 1000 yuan with a maturity of one year. After the bond matured, he spent 440 yuan and then used the remaining money to buy the same type of bond again for another year. After the bond matured the second time, he received 624 yuan. Calculate the annual ... | math | {
"style": "rule",
"ground_truth": "4\\%"
} | {
"split": "train",
"index": 32608,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the number of integers $D$ such that whenever $a$ and $b$ are both real numbers with $-1 / 4<a, b<1 / 4$, then $\\left|a^{2}-D b^{2}\\right|<1$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 32609,
"solution": "We have $$-1<a^{2}-D b^{2}<1 \\Rightarrow \\frac{a^{2}-1}{b^{2}}<D<\\frac{a^{2}+1}{b^{2}}$$ We have $\\frac{a^{2}-1}{b^{2}}$ is maximal at $-15=\\frac{.25^{2}-1}{.25^{2}}$ and $\\frac{a^{2}+1}{b^{2}}$ is minimal at $\\frac{0^{2}+1}{.25^{2}}=16$. However, since we c... |
deepscaler | [
{
"role": "user",
"content": "If a triangle has two sides of lengths 5 and 7 units, then how many different integer lengths can the third side be? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 32610,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $\\angle B=60^{\\circ}$, $AC=2\\sqrt{3}$, $BC=4$, then the area of $\\triangle ABC$ is $\\_\\_\\_\\_\\_\\_$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{3}"
} | {
"split": "train",
"index": 32611,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the least possible value of $(xy-1)^2+(x+y)^2$ for real numbers $x$ and $y$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 32612,
"solution": "1. **Expand and simplify the expression**: Start by expanding the given expression:\n \\[\n (xy-1)^2 + (x+y)^2 = (xy-1)^2 + x^2 + 2xy + y^2.\n \\]\n Expanding $(xy-1)^2$ gives:\n \\[\n (xy-1)^2 = x^2y^2 - 2xy + 1.\n \\]\n Substituting this into the ... |
deepscaler | [
{
"role": "user",
"content": "The traffic police brigade of our county is carrying out a comprehensive road traffic safety rectification campaign \"Hundred-Day Battle\" throughout the county, which strictly requires riders of electric bicycles and motorcycles to comply with the rule of \"one helmet, one bel... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 32613,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Miyuki texted a six-digit integer to Greer. Two of the digits of the six-digit integer were 3s. Unfortunately, the two 3s that Miyuki texted did not appear and Greer instead received the four-digit integer 2022. How many possible six-digit integers could Miyuki have texted? Let... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 32614,
"solution": "The six-digit integer that Miyuki sent included the digits 2022 in that order along with two 3s. If the two 3s were consecutive digits, there are 5 possible integers: 332022, 233022, 203322, 202332, 202233. If the two 3s are not consecutive digits, there are 10 pos... |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=e^{x}-ax-1$ ($a$ is a real number), and $g(x)=\\ln x-x$.\n\n(I) Discuss the monotonic intervals of the function $f(x)$.\n\n(II) Find the extreme values of the function $g(x)$. Let's think step by step and put only the final answer within \\boxed{}."
}... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 32615,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of $x + y$ if the sequence $3, ~9, ~x, ~y, ~30$ is an arithmetic sequence? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 32616,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $a > 0$, $b > 0$, and $a + b = 1$, find the maximum value of $(-\\frac{1}{2a} - \\frac{2}{b})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{9}{2}"
} | {
"split": "train",
"index": 32617,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a cube with edge length 1, two cross-sections in the form of regular hexagons are made. Find the length of the segment at which these cross-sections intersect. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 32618,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a classroom, 34 students are seated in 5 rows of 7 chairs. The place at the center of the room is unoccupied. A teacher decides to reassign the seats such that each student will occupy a chair adjacent to his/her present one (i.e. move one desk forward, back, left or right).... | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 32619,
"solution": "Color the chairs red and black in checkerboard fashion, with the center chair black. Then all 18 red chairs are initially occupied. Also notice that adjacent chairs have different colors. It follows that we need 18 black chairs to accommodate the reassignment, but ... |
deepscaler | [
{
"role": "user",
"content": "If the following instructions are carried out by a computer, what value of \\(X\\) will be printed because of instruction \\(5\\)?\n\n1. START \\(X\\) AT \\(3\\) AND \\(S\\) AT \\(0\\). \n2. INCREASE THE VALUE OF \\(X\\) BY \\(2\\). \n3. INCREASE THE VALUE OF \\(S\\) BY THE ... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 32620,
"solution": "1. **Initialization**: The program starts with $X = 3$ and $S = 0$.\n\n2. **Loop Execution**:\n - **Instruction 2**: Increase the value of $X$ by $2$. \n - **Instruction 3**: Increase the value of $S$ by the current value of $X$.\n - **Instruction 4**: Check ... |
deepscaler | [
{
"role": "user",
"content": "A chess team has $26$ members. However, only $16$ members attended the last meeting: half of the girls attended but all of the boys attended. How many girls are on the chess team? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 32621,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 32622,
"solution": "Let $a$ be the number of $2$-point shots, $b$ be the number of $3$-point shots, and $x$ be the number of free throws. We need to find $x$.\n\nGiven:\n1. The points from two-point shots equal the points from three-point shots, so $2a = 3b$.\n2. The number of free th... |
deepscaler | [
{
"role": "user",
"content": "A bakery owner turns on his doughnut machine at 8:30 AM. At 11:10 AM the machine has completed one third of the day's job. At what time will the doughnut machine complete the job? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4:30 PM"
} | {
"split": "train",
"index": 32623,
"solution": "1. **Calculate the time taken to complete one-third of the job**: \n The machine starts at $\\text{8:30 AM}$ and completes one-third of the job by $\\text{11:10 AM}$. The time duration for this is calculated as follows:\n \\[\n \\text{Time duration} = \\text... |
deepscaler | [
{
"role": "user",
"content": "The bases of an isosceles trapezoid are in the ratio 3:2. A circle is constructed on the larger base as its diameter, and this circle intersects the smaller base such that the segment cut off on the smaller base is equal to half of the smaller base. In what ratio does the circl... | math | {
"style": "rule",
"ground_truth": "1:2"
} | {
"split": "train",
"index": 32624,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two of the altitudes of an acute triangle divide the sides into segments of lengths $7, 4, 3$, and $y$ units, as shown. Calculate the value of $y$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{12}{7}"
} | {
"split": "train",
"index": 32625,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\(a_{1}, a_{2}, \\cdots, a_{n}\\) are \\(n\\) people corresponding to \\(A_{1}, A_{2}, \\cdots, A_{n}\\) cards (\\(n \\geq 2\\), \\(a_{i}\\) corresponds to \\(A_{i}\\)). Now \\(a_{1}\\) picks a card from the deck randomly, and then each person in sequence picks a ca... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 32626,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the line $y=mx+1$ intersects the ellipse $x^2+4y^2=1$ exactly once, then the value of $m^2$ is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 32627,
"solution": "1. **Substitute the line equation into the ellipse equation**: \n Given the line equation $y = mx + 1$ and the ellipse equation $x^2 + 4y^2 = 1$, substitute $y$ in the ellipse equation:\n \\[\n x^2 + 4(mx + 1)^2 = 1\n \\]\n\n2. **Expand and simplify**: \n... |
deepscaler | [
{
"role": "user",
"content": "The Seattle weather forecast suggests a 60 percent chance of rain each day of a five-day holiday. If it does not rain, then the weather will be sunny. Stella wants exactly two days to be sunny during the holidays for a gardening project. What is the probability that Stella gets... | math | {
"style": "rule",
"ground_truth": "\\frac{4320}{15625}"
} | {
"split": "train",
"index": 32628,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The function $g(x)$ satisfies\n\\[g(x) - 2 g \\left( \\frac{1}{x} \\right) = 3^x\\] for all \\( x \\neq 0 \\). Find $g(2)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{29}{9}"
} | {
"split": "train",
"index": 32629,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If we divide $2020$ by a prime $p$ , the remainder is $6$ . Determine the largest\npossible value of $p$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "53"
} | {
"split": "train",
"index": 32630,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is one odd integer \\( N \\) between 400 and 600 that is divisible by both 5 and 11. What is the sum of the digits of \\( N \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 32631,
"solution": "If \\( N \\) is divisible by both 5 and 11, then \\( N \\) is divisible by \\( 5 \\times 11=55 \\). This is because 5 and 11 have no common divisor larger than 1. Therefore, we are looking for a multiple of 55 between 400 and 600 that is odd. One way to find such a... |
deepscaler | [
{
"role": "user",
"content": "Express $0.\\overline{1}+0.\\overline{02}+0.\\overline{003}$ as a common fraction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{164}{1221}"
} | {
"split": "train",
"index": 32632,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the event \"Randomly select a point P on the side CD of rectangle ABCD, such that the longest side of ΔAPB is AB\", with a probability of 1/3, determine the ratio of AD to AB. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{5}}{3}"
} | {
"split": "train",
"index": 32633,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer with exactly 16 positive divisors? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "216"
} | {
"split": "train",
"index": 32634,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the functions $f(x)= \\begin{cases} 2^{x-2}-1,x\\geqslant 0 \\\\ x+2,x < 0 \\end{cases}$ and $g(x)= \\begin{cases} x^{2}-2x,x\\geqslant 0 \\\\ \\frac {1}{x},x < 0. \\end{cases}$, find the sum of all the zeros of the function $f[g(x)]$. Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2} + \\sqrt{3}"
} | {
"split": "train",
"index": 32635,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, $BC = 40$ and $\\angle C = 45^\\circ$. Let the perpendicular bisector of $BC$ intersect $BC$ at $D$ and extend to meet an extension of $AB$ at $E$. Find the length of $DE$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 32636,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, $AB = 5$, $BC = 4$, and $CA = 3$.\n\n[asy]\ndefaultpen(1);\n\npair C=(0,0), A = (0,3), B = (4,0);\ndraw(A--B--C--cycle);\n\nlabel(\"\\(A\\)\",A,N);\nlabel(\"\\(B\\)\",B,E);\nlabel(\"\\(C\\)\",C,SW);\n[/asy]\n\nPoint $P$ is randomly selected inside triangle $A... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 32637,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let point $P$ be a point on the ellipse $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 (a > b > 0)$. Let $F_1$ and $F_2$ respectively be the left and right foci of the ellipse, and let $I$ be the incenter of $\\triangle PF_1F_2$. If $S_{\\triangle IF_1P} + S_{\\triangle IPF_2} = 2S_{... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 32638,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A club has 99 members. Find the smallest positive integer $n$ such that if the number of acquaintances of each person is greater than $n$, there must exist 4 people who all know each other mutually (here it is assumed that if $A$ knows $B$, then $B$ also knows $A$). Let's think... | math | {
"style": "rule",
"ground_truth": "66"
} | {
"split": "train",
"index": 32639,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Adam and Simon start on bicycle trips from the same point at the same time. Adam travels east at 8mph and Simon travels south at 6mph. After how many hours are they 60 miles apart? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 32640,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $E$: $\\frac{x^2}{a^2}+\\frac{y^2}{b^2}=1(a>b>0)$ with left focus $F_{1}$ and right focus $F_{2}$, and the focal distance $F_{1}F_{2}$ is $2$. A line passing through $F_{1}$ intersects the ellipse $E$ at points $A$ and $B$, and the perimeter of $\\triangle ABF_... | math | {
"style": "rule",
"ground_truth": "\\frac{4\\sqrt{15}}{7}"
} | {
"split": "train",
"index": 32641,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a certain sequence, the first term is \\(a_1 = 1010\\) and the second term is \\(a_2 = 1011\\). The values of the remaining terms are chosen so that \\(a_n + a_{n+1} + a_{n+2} = 2n\\) for all \\(n \\geq 1\\). Determine \\(a_{1000}\\). Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "1676"
} | {
"split": "train",
"index": 32642,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In one month, three Wednesdays fell on even dates. On which day will the second Sunday fall in this month? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 32643,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=ax^{2}+bx+c(a\\\\neq 0)$, its graph intersects with line $l$ at two points $A(t,t^{3}-t)$, $B(2t^{2}+3t,t^{3}+t^{2})$, where $t\\\\neq 0$ and $t\\\\neq -1$. Find the value of $f{{'}}(t^{2}+2t)$. Let's think step by step and put only the final answer wit... | math | {
"style": "rule",
"ground_truth": "\\dfrac {1}{2}"
} | {
"split": "train",
"index": 32644,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Point $(x,y)$ is randomly picked from the rectangular region with vertices at $(0,0),(2023,0),(2023,2024),$ and $(0,2024)$. What is the probability that $x > 9y$? 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{2023}{36432}"
} | {
"split": "train",
"index": 32645,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( z = \\frac{1+\\mathrm{i}}{\\sqrt{2}} \\). Then calculate the value of \\( \\left(\\sum_{k=1}^{12} z^{k^{2}}\\right)\\left(\\sum_{k=1}^{12} \\frac{1}{z^{k^{2}}}\\right) \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 32646,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that in the rectangular coordinate system $(xOy)$, the origin is the pole and the positive semi-axis of $x$ is the polar axis to establish a polar coordinate system, the polar coordinate equation of the conic section $(C)$ is $p^{2}= \\frac {12}{3+\\sin ^{2}\\theta }$, th... | math | {
"style": "rule",
"ground_truth": "\\frac {12}{5}"
} | {
"split": "train",
"index": 32647,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $n$ is a positive integer, and $4^7 + 4^n + 4^{1998}$ is a perfect square, then one value of $n$ is. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3988"
} | {
"split": "train",
"index": 32648,
"solution": ""
} |
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