data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "What is the least positive integer value of $x$ such that $(2x)^2 + 2\\cdot 37\\cdot 2x + 37^2$ is a multiple of 47? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 35849,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given positive real numbers $x$, $y$, and $z$, find the minimum value of $\\frac{x^2+2y^2+z^2}{xy+3yz}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{5}}{5}"
} | {
"split": "train",
"index": 35850,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A right circular cone has a base with radius $600$ and height $200\\sqrt{7}.$ A fly starts at a point on the surface of the cone whose distance from the vertex of the cone is $125$, and crawls along the surface of the cone to a point on the exact opposite side of the cone whose... | math | {
"style": "rule",
"ground_truth": "625"
} | {
"split": "train",
"index": 35851,
"solution": "The easiest way is to unwrap the cone into a circular sector. Center the sector at the origin with one radius on the positive $x$-axis and the angle $\\theta$ going counterclockwise. The circumference of the base is $C=1200\\pi$. The sector's radius (cone's sweep) ... |
deepscaler | [
{
"role": "user",
"content": "Find the sum of the roots, real and non-real, of the equation $x^{2001}+\\left(\\frac 12-x\\right)^{2001}=0$, given that there are no multiple roots. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "500"
} | {
"split": "train",
"index": 35852,
"solution": "We find that the given equation has a $2000^{\\text{th}}$ degree polynomial. Note that there are no multiple roots. Thus, if $\\frac{1}{2} - x$ is a root, $x$ is also a root. Thus, we pair up $1000$ pairs of roots that sum to $\\frac{1}{2}$ to get a sum of $\\boxed... |
deepscaler | [
{
"role": "user",
"content": "If $\\left( r + \\frac{1}{r} \\right)^2 = 5,$ then find $r^3 + \\frac{1}{r^3}.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{5}"
} | {
"split": "train",
"index": 35853,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The quadratic $8x^2 - 48x - 320$ can be written in the form $a(x+b)^2+c$, where $a$, $b$, and $c$ are constants. What is $a+b+c$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-387"
} | {
"split": "train",
"index": 35854,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many zeros are in the expansion of $999,\\!999,\\!999,\\!998^2$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 35855,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that\n\\begin{eqnarray*}&(1)& x\\text{ and }y\\text{ are both integers between 100 and 999, inclusive;}\\qquad \\qquad \\qquad \\qquad \\qquad \\\\ &(2)& y\\text{ is the number formed by reversing the digits of }x\\text{; and}\\\\ &(3)& z=|x-y|. \\end{eqnarray*}\n How man... | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 35856,
"solution": "We express the numbers as $x=100a+10b+c$ and $y=100c+10b+a$. From this, we have \\begin{eqnarray*}z&=&|100a+10b+c-100c-10b-a|\\\\&=&|99a-99c|\\\\&=&99|a-c|\\\\ \\end{eqnarray*} Because $a$ and $c$ are digits, and $a$ and $c$ are both between 1 and 9 (from condition... |
deepscaler | [
{
"role": "user",
"content": "\nCalculate the definite integral:\n\n$$\n\\int_{0}^{2} e^{\\sqrt{(2-x) /(2+x)}} \\cdot \\frac{d x}{(2+x) \\sqrt{4-x^{2}}}\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{e-1}{2}"
} | {
"split": "train",
"index": 35857,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\( e^{i \\theta} = \\frac{3 + i \\sqrt{2}}{4}, \\) then find \\( \\cos 3\\theta. \\) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9}{64}"
} | {
"split": "train",
"index": 35858,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest result that can be obtained from the following process?\n\nChoose three different numbers from the set $\\{3,5,7,11,13,17\\}$.\nAdd two of these numbers.\nMultiply their sum by the third number. Let's think step by step and put only the final answer within ... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 35859,
"solution": "To find the smallest result from the given process, we need to consider the operations involved: addition and multiplication. Both operations are increasing functions when dealing with positive integers. Therefore, to minimize the result, we should ideally start wi... |
deepscaler | [
{
"role": "user",
"content": "Let \\( a, b, c \\) be pairwise distinct positive integers such that \\( a+b, b+c \\) and \\( c+a \\) are all square numbers. Find the smallest possible value of \\( a+b+c \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "55"
} | {
"split": "train",
"index": 35860,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the coefficient of $x^3y^5$ in the expansion of $\\left(\\frac{2}{3}x - \\frac{y}{3}\\right)^8$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{448}{6561}"
} | {
"split": "train",
"index": 35861,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a particular game, each of $4$ players rolls a standard $8$-sided die. The winner is the player who rolls the highest number. If there is a tie for the highest roll, those involved in the tie will roll again continuing until one player wins. Hugo is one of the players. What ... | math | {
"style": "rule",
"ground_truth": "\\frac{27}{128}"
} | {
"split": "train",
"index": 35862,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the equation of the oblique asymptote of the graph of $\\frac{2x^2+7x+10}{2x+3}$?\n\nEnter your answer in the form $y = mx + b.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "y = x+2"
} | {
"split": "train",
"index": 35863,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On November 1, 2019, at exactly noon, two students, Gavrila and Glafira, set their watches (both have standard watches where the hands make a full rotation in 12 hours) accurately. It is known that Glafira's watch gains 12 seconds per day, and Gavrila's watch loses 18 seconds p... | math | {
"style": "rule",
"ground_truth": "1440"
} | {
"split": "train",
"index": 35864,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the minimum value of the function \\( f(x)=\\cos 3x + 4 \\cos 2x + 8 \\cos x \\) for \\( x \\in \\mathbb{R} \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-5"
} | {
"split": "train",
"index": 35865,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the area enclosed by the graph of $|3x|+|4y|=12$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 35866,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the constant term in the expansion of $\\left(1+x+\\frac{1}{x^{2}}\\right)^{10}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4351"
} | {
"split": "train",
"index": 35867,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the random variable $\\xi$ follows a normal distribution $N(0,\\sigma^{2})$, and $P(\\xi > 2)=0.023$, determine $P(-2\\leqslant \\xi\\leqslant 2)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.954"
} | {
"split": "train",
"index": 35868,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 (a > b > 0)$, its left focus is $F$, left vertex is $A$, and point $B$ is a point on the ellipse in the first quadrant. The line $OB$ intersects the ellipse at another point $C$. If the line $BF$ bisects the line segment... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 35869,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer that is both a multiple of $7$ and a multiple of $4$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 35870,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A polynomial with integer coefficients is of the form\n\\[9x^4 + a_3 x^3 + a_2 x^2 + a_1 x + 15 = 0.\\]Find the number of different possible rational roots of this polynomial. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 35871,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the line $y=kx+t$ is a tangent line to the curve $y=e^x+2$ and also a tangent line to the curve $y=e^{x+1}$, find the value of $t$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4-2\\ln 2"
} | {
"split": "train",
"index": 35872,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The repeating decimals $0.abab\\overline{ab}$ and $0.abcabc\\overline{abc}$ satisfy\n\\[0.abab\\overline{ab}+0.abcabc\\overline{abc}=\\frac{33}{37},\\]\n where $a$, $b$, and $c$ are (not necessarily distinct) digits. Find the three digit number $abc$. Let's think step by step a... | math | {
"style": "rule",
"ground_truth": "447"
} | {
"split": "train",
"index": 35873,
"solution": "Note that $\\frac{33}{37}=\\frac{891}{999} = 0.\\overline{891}$. Also note that the period of $0.abab\\overline{ab}+0.abcabc\\overline{abc}$ is at most $6$. Therefore, we only need to worry about the sum $0.ababab+ 0.abcabc$. Adding the two, we get \\[\\begin{array... |
deepscaler | [
{
"role": "user",
"content": "Given a triangle \\(ABC\\) with an area of 1. The first player chooses a point \\(X\\) on side \\(AB\\), the second player chooses a point \\(Y\\) on side \\(BC\\), and then the first player chooses a point \\(Z\\) on side \\(AC\\). The first player's goal is to maximize the ar... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 35874,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the number $ABCC$ (written in decimal system) given that\n\n$$\nABCC = (DD - E) \\cdot 100 + DD \\cdot E\n$$\n\nwhere $A, B, C, D,$ and $E$ are distinct digits. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1966"
} | {
"split": "train",
"index": 35875,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A basket of apples is divided into two parts, A and B. The ratio of the number of apples in A to the number of apples in B is $27: 25$. Part A has more apples than Part B. If at least 4 apples are taken from A and added to B, then Part B will have more apples than Part A. How m... | math | {
"style": "rule",
"ground_truth": "156"
} | {
"split": "train",
"index": 35876,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If four different positive integers $m$, $n$, $p$, $q$ satisfy $(7-m)(7-n)(7-p)(7-q)=4$, find the value of $m+n+p+q$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 35877,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The value of the expression \\[(3^{1001}+4^{1002})^2-(3^{1001}-4^{1002})^2\\]is $k\\cdot12^{1001}$ for some positive integer $k$. What is $k$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 35878,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = x^3 - 6x + 5, x \\in \\mathbb{R}$.\n\n(1) Find the equation of the tangent line to the function $f(x)$ at $x = 1$;\n\n(2) Find the extreme values of $f(x)$ in the interval $[-2, 2]$. Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "5 - 4\\sqrt{2}"
} | {
"split": "train",
"index": 35879,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $ab \\gt 0$, then the value of $\\frac{a}{|a|}+\\frac{b}{|b|}+\\frac{ab}{{|{ab}|}}$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 35880,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that $A, B, C, D$ are four points in the plane, and let $Q, R, S, T, U, V$ be the respective midpoints of $A B, A C, A D, B C, B D, C D$. If $Q R=2001, S U=2002, T V=$ 2003, find the distance between the midpoints of $Q U$ and $R V$. Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "2001"
} | {
"split": "train",
"index": 35881,
"solution": "This problem has far more information than necessary: $Q R$ and $U V$ are both parallel to $B C$, and $Q U$ and $R V$ are both parallel to $A D$. Hence, $Q U V R$ is a parallelogram, and the desired distance is simply the same as the side length $Q R$, namely 2001.... |
deepscaler | [
{
"role": "user",
"content": "The degree measure of angle $A$ is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 35882,
"solution": "\n#### Detailed Steps for Solution 1:\n1. **Identify the first angle**: Given that one angle in the diagram is $110^\\circ$, the adjacent angle on a straight line must be $180^\\circ - 110^\\circ = 70^\\circ$ due to the linear pair property (sum of angles on a stra... |
deepscaler | [
{
"role": "user",
"content": "In the polygon shown, each side is perpendicular to its adjacent sides, and all 28 of the sides are congruent. The perimeter of the polygon is 56. Find the area of the polygon.\n\n[asy]\nunitsize(0.5 cm);\n\ndraw((3,0)--(4,0)--(4,1)--(5,1)--(5,2)--(6,2)--(6,3)--(7,3)--(7,4)--... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 35883,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a city, from 7:00 to 8:00, is a peak traffic period, during which all vehicles travel at half their normal speed. Every morning at 6:50, two people, A and B, start from points A and B respectively and travel towards each other. They meet at a point 24 kilometers from point A... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 35884,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be a set. We say $S$ is $D^\\ast$ *-finite* if there exists a function $f : S \\to S$ such that for every nonempty proper subset $Y \\subsetneq S$ , there exists a $y \\in Y$ such that $f(y) \\notin Y$ . The function $f$ is called a *witness* of $S$ . Ho... | math | {
"style": "rule",
"ground_truth": "120"
} | {
"split": "train",
"index": 35885,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Butch and Sundance need to get out of Dodge. To travel as quickly as possible, each alternates walking and riding their only horse, Sparky, as follows. Butch begins by walking while Sundance rides. When Sundance reaches the first of the hitching posts that are conveniently loca... | math | {
"style": "rule",
"ground_truth": "279"
} | {
"split": "train",
"index": 35886,
"solution": "When they meet at the milepost, Sparky has been ridden for $n$ miles total. Assume Butch rides Sparky for $a$ miles, and Sundance rides for $n-a$ miles. Thus, we can set up an equation, given that Sparky takes $\\frac{1}{6}$ hours per mile, Butch takes $\\frac{1}{4... |
deepscaler | [
{
"role": "user",
"content": "If the graph of the power function $f(x)=x^{\\alpha}$ ($\\alpha$ is a constant) always passes through point $A$, and the line ${kx}{-}y{+}2k{+}1{+}\\sqrt{3}{=}0$ always passes through point $B$, then the angle of inclination of line $AB$ is _____. Let's think step by step and p... | math | {
"style": "rule",
"ground_truth": "\\frac{5\\pi}{6}"
} | {
"split": "train",
"index": 35887,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle \\( ABC \\), side \\( AC \\) is the largest. Points \\( M \\) and \\( N \\) on side \\( AC \\) are such that \\( AM = AB \\) and \\( CN = CB \\). It is known that angle \\( \\angle NBM \\) is three times smaller than angle \\( \\angle ABC \\). Find \\( \\angle ABC \... | math | {
"style": "rule",
"ground_truth": "108"
} | {
"split": "train",
"index": 35888,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In Mr. Smith's science class, there are 3 boys for every 4 girls. If there are 42 students in total in his class, what percent of them are boys? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "42.857\\%"
} | {
"split": "train",
"index": 35889,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Select 4 out of the numbers $1, 2, 3, 4, 5$ to form a four-digit number. What is the average value of these four-digit numbers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3333"
} | {
"split": "train",
"index": 35890,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "David and Evan are playing a game. Evan thinks of a positive integer $N$ between 1 and 59, inclusive, and David tries to guess it. Each time David makes a guess, Evan will tell him whether the guess is greater than, equal to, or less than $N$. David wants to devise a strategy t... | math | {
"style": "rule",
"ground_truth": "36440"
} | {
"split": "train",
"index": 35891,
"solution": "We can represent each strategy as a binary tree labeled with the integers from 1 to 59, where David starts at the root and moves to the right child if he is too low and to the left child if he is too high. Our tree must have at most 6 layers as David must guess at ... |
deepscaler | [
{
"role": "user",
"content": "Given the function \\( f(x) = \\sqrt{1 + x \\sqrt{1 + (x+1) \\sqrt{1 + (x+2) \\sqrt{1 + (x+3) \\sqrt{\\cdots}}}}} \\) for \\( x > 1 \\), \\( x \\in \\mathbf{N}^{*} \\), find \\( f(2008) \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2009"
} | {
"split": "train",
"index": 35892,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $ABC$ is isosceles with angle $B$ congruent to angle $C$. The measure of angle $C$ is four times the measure of angle $A$. What is the number of degrees in the measure of angle $B$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "80"
} | {
"split": "train",
"index": 35893,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three ants begin on three different vertices of a tetrahedron. Every second, they choose one of the three edges connecting to the vertex they are on with equal probability and travel to the other vertex on that edge. They all stop when any two ants reach the same vertex at the ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{16}"
} | {
"split": "train",
"index": 35894,
"solution": "At every second, each ant can travel to any of the three vertices they are not currently on. Given that, at one second, the three ants are on different vertices, the probability of them all going to the same vertex is $\\frac{1}{27}$ and the probability of them all... |
deepscaler | [
{
"role": "user",
"content": "Let\n\\[f(x) = \\left\\{\n\\begin{array}{cl}\nx^2 + 3 & \\text{if $x < 15$}, \\\\\n3x - 2 & \\text{if $x \\ge 15$}.\n\\end{array}\n\\right.\\]\nFind $f^{-1}(10) + f^{-1}(49).$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{7} + 17"
} | {
"split": "train",
"index": 35895,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given distinct prime numbers $p$ and $q$ and a natural number $n \\geq 3$, find all $a \\in \\mathbb{Z}$ such that the polynomial $f(x) = x^n + ax^{n-1} + pq$ can be factored into 2 integral polynomials of degree at least 1. Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "-1 - pq \\text{ and } 1 + pq"
} | {
"split": "train",
"index": 35896,
"solution": "\nGiven distinct prime numbers \\( p \\) and \\( q \\) and a natural number \\( n \\geq 3 \\), we aim to find all \\( a \\in \\mathbb{Z} \\) such that the polynomial \\( f(x) = x^n + ax^{n-1} + pq \\) can be factored into two integral polynomials of degree at least... |
deepscaler | [
{
"role": "user",
"content": "The volume of a given sphere is \\( 72\\pi \\) cubic inches. Calculate the surface area of the sphere in terms of \\( \\pi \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36\\pi 2^{2/3}"
} | {
"split": "train",
"index": 35897,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\( f(u) = u^{2} + au + (b-2) \\), where \\( u = x + \\frac{1}{x} \\) (with \\( x \\in \\mathbb{R} \\) and \\( x \\neq 0 \\)). If \\( a \\) and \\( b \\) are real numbers such that the equation \\( f(u) = 0 \\) has at least one real root, find the minimum value of \\( a^{... | math | {
"style": "rule",
"ground_truth": "4/5"
} | {
"split": "train",
"index": 35898,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate:<br/>$(1)3-\\left(-2\\right)$;<br/>$(2)\\left(-4\\right)\\times \\left(-3\\right)$;<br/>$(3)0\\div \\left(-3\\right)$;<br/>$(4)|-12|+\\left(-4\\right)$;<br/>$(5)\\left(+3\\right)-14-\\left(-5\\right)+\\left(-16\\right)$;<br/>$(6)(-5)÷(-\\frac{1}{5})×(-5)$;<br/>$(7)-24... | math | {
"style": "rule",
"ground_truth": "-399\\frac{3}{4}"
} | {
"split": "train",
"index": 35899,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the sequence $\\{a_{n}\\}$, the sum of the first $n$ terms is $S_{n}=2^{n}+2$. Find the sum $T_{20}$ of the first 20 terms in the sequence $\\{\\log _{2}a_{n}\\}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "192"
} | {
"split": "train",
"index": 35900,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many even integers $n$ between 1 and 200 is the greatest common divisor of 18 and $n$ equal to 4? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "34"
} | {
"split": "train",
"index": 35901,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the expression: \\[ M = \\frac{\\sqrt{\\sqrt{7} + 3} + \\sqrt{\\sqrt{7} - 3}}{\\sqrt{\\sqrt{7} + 2}} + \\sqrt{5 - 2\\sqrt{6}}, \\]\nand determine the value of $M$.\nA) $\\sqrt{9}$\nB) $\\sqrt{2} - 1$\nC) $2\\sqrt{2} - 1$\nD) $\\sqrt{\\frac{7}{2}}$\nE) $1$ Let's think s... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2} - 1"
} | {
"split": "train",
"index": 35902,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the set $X=\\left\\{1,2,3,4\\right\\}$, consider a function $f:X\\to X$ where $f^1=f$ and $f^{k+1}=\\left(f\\circ f^k\\right)$ for $k\\geq1$. Determine the number of functions $f$ that satisfy $f^{2014}\\left(x\\right)=x$ for all $x$ in $X$. Let's think step... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 35903,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In an isosceles right triangle \\( \\triangle ABC \\), \\( \\angle A = 90^\\circ \\), \\( AB = 1 \\). \\( D \\) is the midpoint of \\( BC \\), \\( E \\) and \\( F \\) are two other points on \\( BC \\). \\( M \\) is the other intersection point of the circumcircles of \\( \\tri... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 35904,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram below, how many distinct paths are there from January 1 to December 31, moving from one adjacent dot to the next either to the right, down, or diagonally down to the right? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "372"
} | {
"split": "train",
"index": 35905,
"solution": "For each dot in the diagram, we can count the number of paths from January 1 to it by adding the number of ways to get to the dots to the left of it, above it, and above and to the left of it, starting from the topmost leftmost dot. This yields the following number... |
deepscaler | [
{
"role": "user",
"content": "Let the complex numbers \\(z\\) and \\(w\\) satisfy \\(|z| = 3\\) and \\((z + \\bar{w})(\\bar{z} - w) = 7 + 4i\\), where \\(i\\) is the imaginary unit and \\(\\bar{z}\\), \\(\\bar{w}\\) denote the conjugates of \\(z\\) and \\(w\\) respectively. Find the modulus of \\((z + 2\\ba... | math | {
"style": "rule",
"ground_truth": "\\sqrt{65}"
} | {
"split": "train",
"index": 35906,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The operation $\\#$ is defined as $a \\# b = a + \\frac{a}{b}$. What is the value of $6 \\# 2$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 35907,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $α$ is an angle in the second quadrant, let point $P(x, \\sqrt {5})$ be a point on the terminal side of $α$, and $\\cos α= \\frac { \\sqrt {2}}{4}x$. Find the value of $4\\cos (α+ \\frac {π}{2})-3\\tan α$. Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "\\sqrt {15}- \\sqrt {10}"
} | {
"split": "train",
"index": 35908,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $p_1,p_2,p_3,p_4$ be four distinct primes, and let $1=d_1<d_2<\\ldots<d_{16}=n$ be the divisors of $n=p_1p_2p_3p_4$ . Determine all $n<2001$ with the property that $d_9-d_8=22$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1995"
} | {
"split": "train",
"index": 35909,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=e^{ax}-x-1$, where $a\\neq 0$. If $f(x)\\geqslant 0$ holds true for all $x\\in R$, then the set of possible values for $a$ is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\{1\\}"
} | {
"split": "train",
"index": 35910,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC, AB = 360, BC = 507,$ and $CA = 780.$ Let $M$ be the midpoint of $\\overline{CA},$ and let $D$ be the point on $\\overline{CA}$ such that $\\overline{BD}$ bisects angle $ABC.$ Let $F$ be the point on $\\overline{BC}$ such that $\\overline{DF} \\perp \\overlin... | math | {
"style": "rule",
"ground_truth": "289"
} | {
"split": "train",
"index": 35911,
"solution": "Firstly, angle bisector theorem yields $\\frac{CD}{AD} = \\frac{507}{360} = \\frac{169}{120}$. We're given that $AM=MC$. Therefore, the cross ratio\n\\[(A,C;M,D) = \\frac{AM(CD)}{AD(MC)} = \\frac{169}{120}\\]\n We need a fourth point for this cross ratio to be usef... |
deepscaler | [
{
"role": "user",
"content": "Given an ellipse $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1$ (where $a > b > 0$) with its left focus at F and the eccentricity $e = \\frac{\\sqrt{2}}{2}$, the line segment cut by the ellipse from the line passing through F and perpendicular to the x-axis has length $\\sqrt{2}$.\n... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}"
} | {
"split": "train",
"index": 35912,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jeff decides to play with a Magic 8 Ball. Each time he asks it a question, it has a 1/3 chance of giving him a positive answer. If he asks it 7 questions, what is the probability that it gives him exactly 3 positive answers? Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "\\frac{560}{2187}"
} | {
"split": "train",
"index": 35913,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each row of a $24 \\times 8$ table contains some permutation of the numbers $1, 2, \\cdots , 8.$ In each column the numbers are multiplied. What is the minimum possible sum of all the products?\n*(C. Wu)* Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "8 * (8!)^3"
} | {
"split": "train",
"index": 35914,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the constant term of the expansion of $\\left(5x + \\frac{2}{5x}\\right)^8$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1120"
} | {
"split": "train",
"index": 35915,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a hypothetical math competition, contestants are given the problem to find three distinct positive integers $X$, $Y$, and $Z$ such that their product $X \\cdot Y \\cdot Z = 399$. What is the largest possible value of the sum $X+Y+Z$? Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "29"
} | {
"split": "train",
"index": 35916,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A council consists of nine women and three men. During their meetings, they sit around a round table with the women in indistinguishable rocking chairs and the men on indistinguishable stools. How many distinct ways can the nine chairs and three stools be arranged around the ro... | math | {
"style": "rule",
"ground_truth": "55"
} | {
"split": "train",
"index": 35917,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let the sequence $a_{i}$ be defined as $a_{i+1}=2^{a_{i}}$. Find the number of integers $1 \\leq n \\leq 1000$ such that if $a_{0}=n$, then 100 divides $a_{1000}-a_{1}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 35918,
"solution": "We claim that $a_{1000}$ is constant $\\bmod 100$. $a_{997}$ is divisible by 2. This means that $a_{998}$ is divisible by 4. Thus $a_{999}$ is constant $\\bmod 5$. Since it is also divisible by 4, it is constant $\\bmod 20$. Thus $a_{1000}$ is constant $\\bmod 25$,... |
deepscaler | [
{
"role": "user",
"content": "Winnie-the-Pooh eats 3 cans of condensed milk and a jar of honey in 25 minutes, while Piglet eats them in 55 minutes. Pooh eats one can of condensed milk and 3 jars of honey in 35 minutes, while Piglet eats them in 1 hour 25 minutes. How long will it take for them to eat 6 cans... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 35919,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A point $P$ is randomly selected from the square region with vertices at $(\\pm 2, \\pm 2)$. What is the probability that $P$ is within one unit of the origin? Express your answer as a common fraction in terms of $\\pi$. Let's think step by step and put only the final answer wi... | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{16}"
} | {
"split": "train",
"index": 35920,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the sequence $\\{a_n\\}$ is a non-zero arithmetic sequence, $S_n$ denotes the sum of the first $n$ terms, and $S_{2n-1} = a_n^2$ for any $n \\in \\mathbb{N^*}$. If the inequality $\\dfrac{1}{a_1a_2} + \\dfrac{1}{a_2a_3} + \\ldots + \\dfrac{1}{a_na_{n+1}} \\leqslant n\\log... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 35921,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve the quadratic equation $(x-h)^2 + 4h = 5 + x$ and find the sum of the squares of its roots. If the sum is equal to $20$, what is the absolute value of $h$?\n**A)** $\\frac{\\sqrt{22}}{2}$ \n**B)** $\\sqrt{22}$ \n**C)** $\\frac{\\sqrt{44}}{2}$ \n**D)** $2$ \n**E)** Non... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{22}}{2}"
} | {
"split": "train",
"index": 35922,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the sum of all two-digit positive integers whose squares end with the digits 01? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "199"
} | {
"split": "train",
"index": 35923,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On the game show $\\text{\\emph{Wheel of Fortunes}}$, you encounter a spinner divided equally into 6 regions labeled as follows: \"Bankrupt,\" \"$600\", \"$100\", \"$2000\", \"$150\", \"$700\". What is the probability that you will accumulate exactly $1450$ in your first three ... | math | {
"style": "rule",
"ground_truth": "\\frac{6}{125}"
} | {
"split": "train",
"index": 35924,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A store received a cistern of milk. The seller has a balance scale without weights (you can place cans on the pans of the scale) and three identical cans, two of which are empty and the third contains 1 liter of milk. How can you measure exactly 85 liters of milk into one can u... | math | {
"style": "rule",
"ground_truth": "85"
} | {
"split": "train",
"index": 35925,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the sum of the $x$-coordinates of the solutions to the system of equations $y=|x^2-8x+12|$ and $y=\\frac{20}{3}-x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 35926,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many zeros are at the end of the product $s(1) \\cdot s(2) \\cdot \\ldots \\cdot s(100)$, where $s(n)$ denotes the sum of the digits of the natural number $n$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 35927,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle is circumscribed around a unit square \\(ABCD\\), and a point \\(M\\) is selected on the circle.\n\nWhat is the maximum value that the product \\(MA \\cdot MB \\cdot MC \\cdot MD\\) can take? Let's think step by step and put only the final answer within \\boxed{}."
}... | math | {
"style": "rule",
"ground_truth": "0.5"
} | {
"split": "train",
"index": 35928,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\left( r + \\frac{1}{r} \\right)^2 = 3,$ then find $r^3 + \\frac{1}{r^3}.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 35929,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Seven distinct integers are picked at random from the set {1,2,3,...,12}. What is the probability that among those selected, the second smallest number is 4? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{33}"
} | {
"split": "train",
"index": 35930,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $x+\\sin y=2008$ and $x+2008 \\cos y=2007$, where $0 \\leq y \\leq \\frac{\\pi}{2}$, find the value of $x+y$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2007 + \\frac\\pi 2"
} | {
"split": "train",
"index": 35931,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given vectors $$\\overrightarrow {m}=( \\sqrt {3}\\sin x+\\cos x,1), \\overrightarrow {n}=(\\cos x,-f(x)), \\overrightarrow {m}\\perp \\overrightarrow {n}$$.\n(1) Find the monotonic intervals of $f(x)$;\n(2) Given that $A$ is an internal angle of $\\triangle ABC$, and $$f\\left... | math | {
"style": "rule",
"ground_truth": "\\frac { \\sqrt {3}-1}{4}"
} | {
"split": "train",
"index": 35932,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sequence $a_1, a_2, \\ldots$ is geometric with $a_1=a$ and common ratio $r,$ where $a$ and $r$ are positive integers. Given that $\\log_8 a_1+\\log_8 a_2+\\cdots+\\log_8 a_{12} = 2006,$ find the number of possible ordered pairs $(a,r).$ Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "46"
} | {
"split": "train",
"index": 35933,
"solution": "Using the above method, we can derive that $a^{2}r^{11} = 2^{1003}$. Now, think about what happens when r is an even power of 2. Then $a^{2}$ must be an odd power of 2 in order to satisfy the equation which is clearly not possible. Thus the only restriction r has i... |
deepscaler | [
{
"role": "user",
"content": "What is the value of $x$ if $P Q S$ is a straight line and $\\angle P Q R=110^{\\circ}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 35934,
"solution": "Since $P Q S$ is a straight line and $\\angle P Q R=110^{\\circ}$, then $\\angle R Q S=180^{\\circ}-\\angle P Q R=70^{\\circ}$. Since the sum of the angles in $\\triangle Q R S$ is $180^{\\circ}$, then $70^{\\circ}+(3 x)^{\\circ}+(x+14)^{\\circ} =180^{\\circ}$. Sol... |
deepscaler | [
{
"role": "user",
"content": "Given the lengths of the three sides of $\\triangle ABC$ are $AB=7$, $BC=5$, and $CA=6$, the value of $\\overrightarrow {AB}\\cdot \\overrightarrow {BC}$ is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-19"
} | {
"split": "train",
"index": 35935,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the equation $|x-7| -3 = -2$, what is the product of all possible values of $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 35936,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle with center $O$ has radius $8$ units and circle $P$ has radius $2$ units. The circles are externally tangent to each other at point $Q$. Segment $TS$ is the common external tangent to circle $O$ and circle $P$ at points $T$ and $S$, respectively. What is the length ... | math | {
"style": "rule",
"ground_truth": "8\\sqrt{2}"
} | {
"split": "train",
"index": 35937,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a$ and $b$ be positive real numbers. Find the minimum value of\n\\[a^2 + b^2 + \\frac{1}{(a + b)^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": 35938,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For a positive integer $n$, let $d_n$ be the units digit of $1 + 2 + \\dots + n$. Find the remainder when \\[\\sum_{n=1}^{2017} d_n\\]is divided by $1000$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "69"
} | {
"split": "train",
"index": 35939,
"solution": "We see that $d_n$ appears in cycles of $20$ and the cycles are \\[1,3,6,0,5,1,8,6,5,5,6,8,1,5,0,6,3,1,0,0,\\] adding a total of $70$ each cycle. Since $\\left\\lfloor\\frac{2017}{20}\\right\\rfloor=100$, we know that by $2017$, there have been $100$ cycles and $700... |
deepscaler | [
{
"role": "user",
"content": "Humanity has discovered 15 habitable planets, where 7 are \"Earth-like\" and 8 are \"Mars-like\". Colonizing an Earth-like planet requires 3 units of colonization, while a Mars-like planet requires 1 unit. If humanity has 21 units available for colonization, determine how many ... | math | {
"style": "rule",
"ground_truth": "981"
} | {
"split": "train",
"index": 35940,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a press conference before the All-Star Game, eight All-Stars will be taking questions. Three are Cubs, three are Red Sox, and two are Yankees. If teammates insist on sitting together, how many ways can the eight All-Stars be seated in a row? Let's think step by step and put ... | math | {
"style": "rule",
"ground_truth": "432"
} | {
"split": "train",
"index": 35941,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In rectangle $PQRS$, $PQ=8$ and $QR=6$. Points $A$ and $B$ lie on $\\overline{PQ}$, points $C$ and $D$ lie on $\\overline{QR}$, points $E$ and $F$ lie on $\\overline{RS}$, and points $G$ and $H$ lie on $\\overline{SP}$ so that $AP=BQ<4$ and the convex octagon $ABCDEFGH$ is equi... | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 35942,
"solution": "1. **Assign Variables:**\n Let the side length of the octagon be $x$. Since $AP = BQ < 4$ and $PQ = 8$, we have $AP = BQ = \\frac{8-x}{2}$.\n\n2. **Use the Pythagorean Theorem:**\n Since $ABCDEFGH$ is equilateral, all sides are equal, and $BQ = CQ = x$. Therefo... |
deepscaler | [
{
"role": "user",
"content": "My club has 25 members. In how many ways can I choose members to form a 4-person executive committee? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12,\\!650"
} | {
"split": "train",
"index": 35943,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $V = gt + V_0$ and $S = \\frac{1}{2}gt^2 + V_0t$, then $t$ equals: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2S}{V+V_0}"
} | {
"split": "train",
"index": 35944,
"solution": "1. **Start with the given equations:**\n \\[ V = gt + V_0 \\]\n \\[ S = \\frac{1}{2}gt^2 + V_0t \\]\n\n2. **Solve for $t$ from the first equation:**\n \\[ V - V_0 = gt \\]\n \\[ t = \\frac{V - V_0}{g} \\]\n\n3. **Substitute $t$ from step 2 into the second e... |
deepscaler | [
{
"role": "user",
"content": "Let $x$ and $y$ be real numbers, where $y > x > 0$, such that\n\\[\n\\frac{x}{y} + \\frac{y}{x} = 4.\n\\]\nFind the value of\n\\[\n\\frac{x + y}{x - y}.\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 35945,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the value of $({-\\frac{4}{5}})^{2022} \\times ({\\frac{5}{4}})^{2021}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{5}"
} | {
"split": "train",
"index": 35946,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Place each of the digits 4, 5, 6, and 7 in exactly one square to make the smallest possible product. The grid placement is the same as described before. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2622"
} | {
"split": "train",
"index": 35947,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many sequences of 8 digits $x_1, x_2, \\ldots, x_8$ can we form, given the condition that no two adjacent $x_i$ have the same parity and the sequence starts with an odd digit? Leading zeroes are allowed. Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "390625"
} | {
"split": "train",
"index": 35948,
"solution": ""
} |
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