data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "How many ways are there to put 7 balls in 2 boxes if the balls are distinguishable but the boxes are not? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 31549,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system $xOy$, $\\alpha$ is an angle in the fourth quadrant. The terminal side of angle $\\alpha$ intersects the unit circle $O$ at point $P(x_{0}, y_{0})$. If $\\cos(\\alpha - \\frac{\\pi}{3}) = -\\frac{\\sqrt{3}}{3}$, determine the $y_{0}$ coordinat... | math | {
"style": "rule",
"ground_truth": "\\frac{-\\sqrt{6}-3}{6}"
} | {
"split": "train",
"index": 31550,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given 12 points in a diagram, calculate the number of groups of 3 points that can be formed to create a triangle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "200"
} | {
"split": "train",
"index": 31551,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate:\n$$\n202.2 \\times 89.8 - 20.22 \\times 186 + 2.022 \\times 3570 - 0.2022 \\times 16900\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18198"
} | {
"split": "train",
"index": 31552,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define $p(n)$ to be th product of all non-zero digits of $n$ . For instance $p(5)=5$ , $p(27)=14$ , $p(101)=1$ and so on. Find the greatest prime divisor of the following expression:\n\\[p(1)+p(2)+p(3)+...+p(999).\\] Let's think step by step and put only the final answer... | math | {
"style": "rule",
"ground_truth": "103"
} | {
"split": "train",
"index": 31553,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A $6$-inch and $18$-inch diameter poles are placed together and bound together with wire.\nThe length of the shortest wire that will go around them is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12\\sqrt{3}+14\\pi"
} | {
"split": "train",
"index": 31554,
"solution": "1. **Understanding the Setup**: We have two poles with diameters of $6$ inches and $18$ inches, respectively. This means the radii are $3$ inches and $9$ inches. When bound together, the wire will wrap around the outer edges of both poles.\n\n2. **Visualizing the G... |
deepscaler | [
{
"role": "user",
"content": "Given that $40\\%$ of the birds were pigeons, $20\\%$ were sparrows, $15\\%$ were crows, and the remaining were parakeets, calculate the percent of the birds that were not sparrows and were crows. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18.75\\%"
} | {
"split": "train",
"index": 31555,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given: $A=2a^{2}-5ab+3b$, $B=4a^{2}+6ab+8a$. \n$(1)$ Simplify: $2A-B$; \n$(2)$ If $a=-1$, $b=2$, find the value of $2A-B$; \n$(3)$ If the value of the algebraic expression $2A-B$ is independent of $a$, find the value of $b$. Let's think step by step and put only the final an... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{2}"
} | {
"split": "train",
"index": 31556,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The functions $p(x),$ $q(x),$ and $r(x)$ are all invertible. We set\n\\[f = q \\circ p \\circ r.\\]Which is the correct expression for $f^{-1}$?\n\nA. $r^{-1} \\circ q^{-1} \\circ p^{-1}$\n\nB. $p^{-1} \\circ q^{-1} \\circ r^{-1}$\n\nC. $r^{-1} \\circ p^{-1} \\circ q^{-1}$\n\n... | math | {
"style": "rule",
"ground_truth": "\\text{C}"
} | {
"split": "train",
"index": 31557,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Daniel works at an electronics store, and he claims that the popularity of a toaster (measured in number of sales) is inversely proportional to its cost. If 12 customers buy a toaster that costs $\\$500$, according to Daniel's theory, how many customers would buy a toaster that... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 31558,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let line $l_1: x + my + 6 = 0$ and line $l_2: (m - 2)x + 3y + 2m = 0$. When $m = \\_\\_\\_\\_\\_\\_$, $l_1 \\parallel l_2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 31559,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the number $2 * 0 * 1 * 6 * 0 * 2 *$, each of the 6 asterisks must be replaced with any of the digits $0, 2, 4, 5, 7, 9$ (digits may be repeated) so that the resulting 12-digit number is divisible by 12. How many ways can this be done? Let's think step by step and put only t... | math | {
"style": "rule",
"ground_truth": "5184"
} | {
"split": "train",
"index": 31560,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many numbers are in the list $$ 1, 4, 7, \\ldots, 2005, 2008 ?$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "670"
} | {
"split": "train",
"index": 31561,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Point $O$ is the center of an ellipse with major axis $\\overline{AB}$ and minor axis $\\overline{CD}.$ Point $F$ is one focus of the ellipse. If $OF = 6$ and the diameter of the inscribed circle of triangle $OCF$ is 2, compute the product $(AB)(CD).$ Let's think step by step... | math | {
"style": "rule",
"ground_truth": "65"
} | {
"split": "train",
"index": 31562,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If 700 were expressed as a sum of at least three distinct powers of 2, what would be the least possible sum of the exponents of these powers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 31563,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sequence of numbers \\(a_1, a_2, \\cdots, a_n, \\cdots\\) is defined. Let \\(S(a_i)\\) be the sum of all the digits of \\(a_i\\). For example, \\(S(22) = 2 + 2 = 4\\). If \\(a_1 = 2017\\), \\(a_2 = 22\\), and \\(a_n = S(a_{n-1}) + S(a_{n-2})\\), what is the value of \\(a_{201... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 31564,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an isosceles triangle $PQR$ with $PQ=QR$ and the angle at the vertex $108^\\circ$. Point $O$ is located inside the triangle $PQR$ such that $\\angle ORP=30^\\circ$ and $\\angle OPR=24^\\circ$. Find the measure of the angle $\\angle QOR$. Let's think step by step and put o... | math | {
"style": "rule",
"ground_truth": "126"
} | {
"split": "train",
"index": 31565,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\(\\alpha, \\beta \\in \\left(0, \\frac{\\pi}{2}\\right)\\), \\(\\sin \\beta = 2 \\cos (\\alpha + \\beta) \\cdot \\sin \\alpha \\left(\\alpha + \\beta \\neq \\frac{\\pi}{2}\\right)\\), find the maximum value of \\(\\tan \\beta\\). Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{3}"
} | {
"split": "train",
"index": 31566,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the smallest integral value of $n$ such that the quadratic equation\n\\[3x(nx+3)-2x^2-9=0\\]\nhas no real roots.\nA) -2\nB) -1\nC) 0\nD) 1 Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 31567,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The legs \\( AC \\) and \\( CB \\) of the right triangle \\( ABC \\) are 15 and 8, respectively. A circular arc with radius \\( CB \\) is drawn from center \\( C \\), cutting off a part \\( BD \\) from the hypotenuse. Find \\( BD \\). Let's think step by step and put only the f... | math | {
"style": "rule",
"ground_truth": "\\frac{128}{17}"
} | {
"split": "train",
"index": 31568,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangles $ABC$ and $AFG$ have areas $3012$ and $10004$, respectively, with $B=(0,0),$ $C=(335,0),$ $F=(1020, 570),$ and $G=(1030, 580).$ Find the sum of all possible $x$-coordinates of $A$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1800"
} | {
"split": "train",
"index": 31569,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Dots are placed two units apart both horizontally and vertically on a coordinate grid. Calculate the number of square units enclosed by the polygon formed by connecting these dots: \n[asy]\nsize(90);\npair a=(0,0), b=(20,0), c=(20,20), d=(40,20), e=(40,40), f=(20,40), g=(0,40),... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 31570,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $n = 2^{10} \\cdot 3^{14} \\cdot 5^{8}$, how many of the natural-number factors of $n$ are multiples of 150? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "980"
} | {
"split": "train",
"index": 31571,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that positive real numbers a and b satisfy $a^{2}+2ab+4b^{2}=6$, calculate the maximum value of a+2b. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2}"
} | {
"split": "train",
"index": 31572,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=2\\sqrt{3}\\sin^2{x}-\\sin\\left(2x-\\frac{\\pi}{3}\\right)$,\n(Ⅰ) Find the smallest positive period of the function $f(x)$ and the intervals where $f(x)$ is monotonically increasing;\n(Ⅱ) Suppose $\\alpha\\in(0,\\pi)$ and $f\\left(\\frac{\\alpha}{2}\\r... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}+1"
} | {
"split": "train",
"index": 31573,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\left(a + \\frac{1}{a}\\right)^2 = 5$, find the value of $a^3 + \\frac{1}{a^3}$. 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": 31574,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The arithmetic mean of seven numbers is 42. If three new numbers \\( x, y, \\) and \\( z \\) are added to the list, the mean of the ten-member list becomes 50. What is the mean of \\( x, y, \\) and \\( z \\)? Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "\\frac{206}{3}"
} | {
"split": "train",
"index": 31575,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the sequence $(a_k)_{k\\ge 1}$ of positive rational numbers defined by $a_1 = \\frac{2020}{2021}$ and for $k\\ge 1$, if $a_k = \\frac{m}{n}$ for relatively prime positive integers $m$ and $n$, then\n\\[a_{k+1} = \\frac{m + 18}{n+19}.\\]Determine the sum of all positive... | math | {
"style": "rule",
"ground_truth": "59"
} | {
"split": "train",
"index": 31576,
"solution": "We know that $a_{1}=\\tfrac{t}{t+1}$ when $t=2020$ so $1$ is a possible value of $j$. Note also that $a_{2}=\\tfrac{2038}{2040}=\\tfrac{1019}{1020}=\\tfrac{t}{t+1}$ for $t=1019$. Then $a_{2+q}=\\tfrac{1019+18q}{1020+19q}$ unless $1019+18q$ and $1020+19q$ are not re... |
deepscaler | [
{
"role": "user",
"content": "For any positive integer $x_{}$, let $S(x)$ be the sum of the digits of $x_{}$, and let $T(x)$ be $|S(x+2)-S(x)|.$ For example, $T(199)=|S(201)-S(199)|=|3-19|=16.$ How many values of $T(x)$ do not exceed 1999? Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "223"
} | {
"split": "train",
"index": 31577,
"solution": "For most values of $x$, $T(x)$ will equal $2$. For those that don't, the difference must be bumping the number up a ten, a hundred, etc. If we take $T(a999)$ as an example, \\[|(a + 1) + 0 + 0 + 1 - (a + 9 + 9 + 9)| = |2 - 9(3)|\\] And in general, the values of $T(... |
deepscaler | [
{
"role": "user",
"content": "Given the function \\( f(n) \\) defined on the set of natural numbers \\(\\mathbf{N}\\), and satisfies:\n\n\\[\n\\begin{array}{l}\nf(1) = f(2) = 1, \\\\\nf(3n) = 3 f(n) - 2, \\\\\nf(3n+1) = 3 f(n) + 1, \\\\\nf(3n+2) = 3 f(n) + 4 \\quad (n \\in \\mathbf{N}).\n\\end{array}\n\\]\n... | math | {
"style": "rule",
"ground_truth": "1093"
} | {
"split": "train",
"index": 31578,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute $95^2$ in your head. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9025"
} | {
"split": "train",
"index": 31579,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that each side of a triangle is an integer and none exceeds 4, determine the number of such distinct triangles. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 31580,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many times does the digit 0 appear in the integer equal to \\( 20^{10} \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 31581,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many three-digit numbers can you subtract 297 and obtain a second three-digit number which is the original three-digit number reversed? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 31582,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain school sends two students, A and B, to form a \"youth team\" to participate in a shooting competition. In each round of the competition, A and B each shoot once. It is known that the probability of A hitting the target in each round is $\\frac{1}{2}$, and the probabil... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{24}"
} | {
"split": "train",
"index": 31583,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\{1, a, \\frac{b}{a}\\} = \\{0, a^2, a+b\\}$, find the value of $a^{2015} + b^{2014}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 31584,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rubber band is 4 inches long. An ant begins at the left end. Every minute, the ant walks one inch along rightwards along the rubber band, but then the band is stretched (uniformly) by one inch. For what value of $n$ will the ant reach the right end during the $n$th minute? Le... | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 31585,
"solution": "7 The ant traverses $1 / 4$ of the band's length in the first minute, $1 / 5$ of the length in the second minute (the stretching does not affect its position as a fraction of the band's length), $1 / 6$ of the length in the third minute, and so on. Since $$1 / 4+1 ... |
deepscaler | [
{
"role": "user",
"content": "Given $a \\gt 0$, $b \\gt 0$, and $a+2b=1$, find the minimum value of $\\frac{{b}^{2}+a+1}{ab}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{10} + 6"
} | {
"split": "train",
"index": 31586,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each edge length of a rectangular solid is a prime number. If the volume of the rectangular solid is 385 cubic units, what is the total surface area, in square units, of the rectangular solid? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "334"
} | {
"split": "train",
"index": 31587,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are two lathes processing parts of the same model. The yield rate of the first lathe is $15\\%$, and the yield rate of the second lathe is $10\\%$. Assuming that the yield rates of the two lathes do not affect each other, the probability of both lathes producing excellent... | math | {
"style": "rule",
"ground_truth": "13\\%"
} | {
"split": "train",
"index": 31588,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The left focus of the hyperbola $C$: $\\dfrac{x^2}{a^2} - \\dfrac{y^2}{b^2} = 1 \\, (a > 0, b > 0)$ is $F$. If the symmetric point $A$ of $F$ with respect to the line $\\sqrt{3}x + y = 0$ is a point on the hyperbola $C$, then the eccentricity of the hyperbola $C$ is \\_\\_\\_\\... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3} + 1"
} | {
"split": "train",
"index": 31589,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four circles $\\omega,$ $\\omega_{A},$ $\\omega_{B},$ and $\\omega_{C}$ with the same radius are drawn in the interior of triangle $ABC$ such that $\\omega_{A}$ is tangent to sides $AB$ and $AC$, $\\omega_{B}$ to $BC$ and $BA$, $\\omega_{C}$ to $CA$ and $CB$, and $\\omega$ is e... | math | {
"style": "rule",
"ground_truth": "389"
} | {
"split": "train",
"index": 31590,
"solution": "Consider a 13-14-15 triangle. $A=84.$ [By Heron's Formula or by 5-12-13 and 9-12-15 right triangles.]\n The inradius is $r=\\frac{A}{s}=\\frac{84}{21}=4$, where $s$ is the semiperimeter. Scale the triangle with the inradius by a linear scale factor, $u.$\n The circ... |
deepscaler | [
{
"role": "user",
"content": "A spherical scoop of vanilla ice cream with radius of 2 inches is dropped onto the surface of a dish of hot chocolate sauce. As it melts, the ice cream spreads out uniformly forming a cylindrical region 8 inches in radius. Assuming the density of the ice cream remains constant,... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"split": "train",
"index": 31591,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the greatest common divisor of 91 and 72. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 31592,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $A*B$ means $\\frac{A+B}{2}$, then $(3*5)*8$ is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 31593,
"solution": "1. **Interpret the operation $*$**: Given that $A*B = \\frac{A+B}{2}$, we need to apply this operation to the numbers in the expression $(3*5)*8$.\n\n2. **Evaluate $3*5$**:\n \\[\n 3*5 = \\frac{3+5}{2} = \\frac{8}{2} = 4\n \\]\n Here, we added 3 and 5, then... |
deepscaler | [
{
"role": "user",
"content": "The fraction \\(\\frac{p}{q}\\) is in its simplest form. If \\(\\frac{7}{10} < \\frac{p}{q} < \\frac{11}{15}\\), where \\(q\\) is the smallest possible positive integer and \\(c = pq\\), find the value of \\(c\\). Let's think step by step and put only the final answer within \\... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 31594,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, $\\angle ABC = \\angle ACB = 40^\\circ$, and $P$ is a point inside the triangle such that $\\angle PAC = 20^\\circ$ and $\\angle PCB = 30^\\circ$. Find the measure of $\\angle PBC$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 31595,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x=1$ is an extremum point of the function $f(x)=(x^{2}+ax-1)e^{x-1}$, determine the maximum value of $f(x)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5e^{-3}"
} | {
"split": "train",
"index": 31596,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that $f$ is a function from $\\mathbb{R}$ to $\\mathbb{R}$ such that \\[ f(x) + f\\left( 1 - \\frac{1}{x} \\right) = \\arctan x \\] for all real $x \\neq 0$. (As usual, $y = \\arctan x$ means $-\\pi/2 < y < \\pi/2$ and $\\tan y = x$.) Find \\[ \\int_0^1 f(x)\\,dx. \\] L... | math | {
"style": "rule",
"ground_truth": "\\frac{3\\pi}{8}"
} | {
"split": "train",
"index": 31597,
"solution": "The given functional equation, along with the same equation but with $x$ replaced by $\\frac{x-1}{x}$ and $\\frac{1}{1-x}$ respectively, yields: \\[ f(x) + f\\left(1-\\frac{1}{x}\\right) = \\tan^{-1}(x) \\] \\[ f\\left(\\frac{x-1}{x}\\right) + f\\left(\\frac{1}{1-x... |
deepscaler | [
{
"role": "user",
"content": "\nFor what values of the parameter \\( a \\in \\mathbb{R} \\) does the maximum distance between the roots of the equation\n\n\\[ a \\tan^{3} x + \\left(2-a-a^{2}\\right) \\tan^{2} x + \\left(a^{2}-2a-2\\right) \\tan x + 2a = 0 \\]\n\nbelonging to the interval \\(\\left(-\\frac{... | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{4}"
} | {
"split": "train",
"index": 31598,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the numbers $1, 4, 7, 10, 13$ are placed in five squares such that the sum of the three numbers in the horizontal row equals the sum of the three numbers in the vertical column, determine the largest possible value for the horizontal or vertical sum. Let's think step... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 31599,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The Incredible Hulk can double the distance he jumps with each succeeding jump. If his first jump is 1 meter, the second jump is 2 meters, the third jump is 4 meters, and so on, then on which jump will he first be able to jump more than 1 kilometer (1,000 meters)? Let's think s... | math | {
"style": "rule",
"ground_truth": "11^{\\text{th}}"
} | {
"split": "train",
"index": 31600,
"solution": "1. **Identify the sequence**: The problem describes a geometric sequence where the first term \\(a_1 = 1\\) meter and each subsequent term doubles the previous term. This can be expressed as:\n \\[\n a_n = 2^{n-1}\n \\]\n where \\(n\\) is the jump number.\n... |
deepscaler | [
{
"role": "user",
"content": "In square \\(R S T U\\), a quarter-circle arc with center \\(S\\) is drawn from \\(T\\) to \\(R\\). A point \\(P\\) on this arc is 1 unit from \\(TU\\) and 8 units from \\(RU\\). What is the length of the side of square \\(RSTU\\)? Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 31601,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the probability that the same number will be facing up on each of three standard six-sided dice that are tossed simultaneously? 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{1}{36}"
} | {
"split": "train",
"index": 31602,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $T$ be a subset of $\\{1,2,3,...,40\\}$ such that no pair of distinct elements in $T$ has a sum divisible by $5$. What is the maximum number of elements in $T$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 31603,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the sum: $\\sum_{n=1}^{99} \\left(n^{3}+3n^{2}+3n\\right)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25502400"
} | {
"split": "train",
"index": 31604,
"solution": "The sum is calculated as follows: $$\\begin{aligned} & \\left(1^{3}+3 \\cdot 1^{2}+3 \\cdot 1\\right)+\\left(2^{3}+3 \\cdot 2^{2}+3 \\cdot 2\\right)+\\cdots+\\left(99^{3}+3 \\cdot 99^{2}+3 \\cdot 99\\right) \\\\ & =\\left(1^{3}+3 \\cdot 1^{2}+3 \\cdot 1+1\\right)+\... |
deepscaler | [
{
"role": "user",
"content": "In rectangle $ABCD$, $AB = 3$ and $BC = 9$. The rectangle is folded so that points $A$ and $C$ coincide, forming the pentagon $ABEFD$. What is the length of segment $EF$? Express your answer in simplest radical form.\n\n[asy]\nsize(200);\ndefaultpen(linewidth(.8pt)+fontsize(10p... | math | {
"style": "rule",
"ground_truth": "\\sqrt{10}"
} | {
"split": "train",
"index": 31605,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest whole number that has a remainder of 1 when divided by 4, a remainder of 1 when divided by 3, and a remainder of 2 when divided by 5? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "37"
} | {
"split": "train",
"index": 31606,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a nursery group, there are two small Christmas trees and five children. The caregivers want to split the children into two dance circles around each tree, with at least one child in each circle. The caregivers distinguish between the children but not between the trees: two s... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 31607,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $f(x) = \\log_a x$, its inverse function is $g(x)$. \n(1) Solve the equation for $x$: $f(x-1) = f(a-x) - f(5-x)$; \n(2) Let $F(x) = (2m-1)g(x) + \\left( \\frac{1}{m} - \\frac{1}{2} \\right)g(-x)$. If $F(x)$ has a minimum value, find the expression for $h(m)$; \n(3) Fin... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 31608,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the maximum value of the function \\( f(x) \\), which is defined as the minimum of the three functions \\( 4x + 1 \\), \\( x + 2 \\), and \\( -2x + 4 \\) for each real number \\( x \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{8}{3}"
} | {
"split": "train",
"index": 31609,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Kelvin the frog currently sits at $(0,0)$ in the coordinate plane. If Kelvin is at $(x, y)$, either he can walk to any of $(x, y+1),(x+1, y)$, or $(x+1, y+1)$, or he can jump to any of $(x, y+2),(x+2, y)$ or $(x+1, y+1)$. Walking and jumping from $(x, y)$ to $(x+1, y+1)$ are co... | math | {
"style": "rule",
"ground_truth": "1831830"
} | {
"split": "train",
"index": 31610,
"solution": "Observe there are $\\binom{14}{6}=3003$ up-right paths from $(0,0)$ to $(6,8)$, each of which are 14 steps long. Any two of these steps can be combined into one: $UU, RR$, and $RU$ as jumps, and $UR$ as walking from $(x, y)$ to $(x+1, y+1)$. The number of ways to c... |
deepscaler | [
{
"role": "user",
"content": "Let $x, y, z$ be real numbers such that:\n\\begin{align*}\ny+z & = 16, \\\\\nz+x & = 18, \\\\\nx+y & = 20.\n\\end{align*}\nFind $\\sqrt{xyz(x+y+z)}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9\\sqrt{77}"
} | {
"split": "train",
"index": 31611,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We wrote the reciprocals of natural numbers from 2 to 2011 on a board. In one step, we erase two numbers, \\( x \\) and \\( y \\), and replace them with the number\n\n$$\n\\frac{xy}{xy + (1 - x)(1 - y)}\n$$\n\nBy repeating this process 2009 times, only one number remains. What ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2010! + 1}"
} | {
"split": "train",
"index": 31612,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle has an area of $M\\text{ cm}^2$ and a circumference of $N\\text{ cm}$. If $\\dfrac{M}{N}=20$, what is the radius of the circle, in cm? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 31613,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four mathletes and two coaches sit at a circular table. How many distinct arrangements are there of these six people if the two coaches sit opposite each other? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 31614,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the plane rectangular coordinate system xOy, the origin is taken as the pole, the positive semi-axis of the x-axis is taken as the polar axis, and the polar coordinate system is established. The same unit length is adopted in both coordinate systems. The polar coordinate equ... | math | {
"style": "rule",
"ground_truth": "\\frac { \\sqrt {31}}{7}"
} | {
"split": "train",
"index": 31615,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the integral $$\\int_{ -2 }^{ 2 }$$($$\\sqrt {16-x^{2}}$$+sinx)dx=\\_\\_\\_\\_\\_\\_ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4\\sqrt{3} + \\frac{8\\pi}{3}"
} | {
"split": "train",
"index": 31616,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathbb{N}_{\\geqslant 1}$ be the set of positive integers. \nFind all functions $f \\colon \\mathbb{N}_{\\geqslant 1} \\to \\mathbb{N}_{\\geqslant 1}$ such that, for all positive integers $m$ and $n$:\n\\[\\mathrm{GCD}\\left(f(m),n\\right) + \\mathrm{LCM}\\left(m,f(n)\\r... | math | {
"style": "rule",
"ground_truth": "f(n) = n"
} | {
"split": "train",
"index": 31617,
"solution": "\nGiven the problem, we seek all functions \\( f: \\mathbb{N}_{\\geq 1} \\to \\mathbb{N}_{\\geq 1} \\) such that for all positive integers \\( m \\) and \\( n \\), the following holds:\n\n\\[\n\\mathrm{GCD}(f(m), n) + \\mathrm{LCM}(m, f(n)) = \\mathrm{GCD}(m, f(n))... |
deepscaler | [
{
"role": "user",
"content": "**\nHow many non-similar regular 500-pointed stars are there?\n\n** Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "99"
} | {
"split": "train",
"index": 31618,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many times do you have to subtract 8 from 792 to get 0? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "99"
} | {
"split": "train",
"index": 31619,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\cos^2x-\\sin^2x+\\frac{1}{2}, x \\in (0,\\pi)$.\n\n$(1)$ Find the interval of monotonic increase for $f(x)$;\n\n$(2)$ Suppose $\\triangle ABC$ is an acute triangle, with the side opposite to angle $A$ being $a=\\sqrt{19}$, and the side opposite to ang... | math | {
"style": "rule",
"ground_truth": "\\frac{15\\sqrt{3}}{4}"
} | {
"split": "train",
"index": 31620,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given positive numbers $x$ and $y$ satisfying $x^2+y^2=1$, find the maximum value of $\\frac {1}{x}+ \\frac {1}{y}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{2}"
} | {
"split": "train",
"index": 31621,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a circle of radius $\\sqrt{13}$, let $A$ be a point at a distance $4 + \\sqrt{13}$ from the center $O$ of the circle. Let $B$ be the point on the circle nearest to point $A$. A line passing through the point $A$ intersects the circle at points $K$ and $L$. The maximum pos... | math | {
"style": "rule",
"ground_truth": "146"
} | {
"split": "train",
"index": 31622,
"solution": "Let $N,M$ les on $AL$ such that $BM\\bot AL, ON\\bot AL$, call $BM=h, ON=k,LN=KN=d$ We call $\\angle{LON}=\\alpha$ By similar triangle, we have $\\frac{h}{k}=\\frac{4}{4+\\sqrt{13}}, h=\\frac{4k}{4+\\sqrt{13}}$. Then, we realize the area is just $dh=d\\cdot \\frac{... |
deepscaler | [
{
"role": "user",
"content": "Four cubes with edge lengths $1$, $2$, $3$, and $4$ are stacked as shown. What is the length of the portion of $\\overline{XY}$ contained in the cube with edge length $3$? 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": 31623,
"solution": "1. **Identify the coordinates of points $X$ and $Y$:**\n - Assume the cubes are stacked such that the bottom face of each cube lies on the $xy$-plane and one vertex of each cube is at the origin $(0,0,0)$.\n - The cube with edge length $1$ is entirely within th... |
deepscaler | [
{
"role": "user",
"content": "Determine the base seven product of the numbers $321_7$ and $13_7$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4503_7"
} | {
"split": "train",
"index": 31624,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the eighth term of the sequence $1440,$ $1716,$ $1848,\\ldots,$ whose terms are formed by multiplying the corresponding terms of two arithmetic sequences. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "348"
} | {
"split": "train",
"index": 31625,
"solution": "If you multiply the corresponding terms of two arithmetic sequences, you get the terms of a quadratic function. Thus, we have a quadratic $ax^2+bx+c$ such that $f(1)=1440$, $f(2)=1716$, and $f(3)=1848$. Plugging in the values for x gives us a system of three equati... |
deepscaler | [
{
"role": "user",
"content": "Two real numbers are selected independently at random from the interval $[-20, 10]$. What is the probability that the product of those numbers is greater than zero? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{9}"
} | {
"split": "train",
"index": 31626,
"solution": "1. **Define the intervals for positive and negative numbers**:\n - The interval $[-20, 10]$ can be split into two parts: $[-20, 0)$ for negative numbers and $(0, 10]$ for positive numbers.\n - The length of the interval $[-20, 0)$ is $20$ units.\n - The lengt... |
deepscaler | [
{
"role": "user",
"content": "Let $f(n)$ be the integer closest to $\\sqrt[4]{n}.$ Find $\\sum_{k=1}^{1995}\\frac 1{f(k)}.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "400"
} | {
"split": "train",
"index": 31627,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of $\\frac{1}{4} + \\frac{3}{8}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{8}"
} | {
"split": "train",
"index": 31628,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the minimum number of children required in a school to be sure that at least 3 of them have their birthday on the same day? (Keep in mind that some people are born on February 29.) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "733"
} | {
"split": "train",
"index": 31629,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is a Jack, the second card is a Queen, and the third card is a King? Assuming the dealing is done without replacement. Let's think step by step and put only the final ... | math | {
"style": "rule",
"ground_truth": "\\frac{8}{16575}"
} | {
"split": "train",
"index": 31630,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rectangular grazing area is to be fenced off on three sides using part of a $100$ meter rock wall as the fourth side. Fence posts are to be placed every $12$ meters along the fence including the two posts where the fence meets the rock wall. What is the fewest number of pos... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 31631,
"solution": "1. **Identify the dimensions and orientation of the grazing area**: The grazing area is a rectangle with dimensions $36$ m and $60$ m. To minimize the number of fence posts, we use the longer side ($60$ m) along the existing rock wall. This means the two $36$ m sid... |
deepscaler | [
{
"role": "user",
"content": "A painting $18$\" X $24$\" is to be placed into a wooden frame with the longer dimension vertical. The wood at the top and bottom is twice as wide as the wood on the sides. If the frame area equals that of the painting itself, the ratio of the smaller to the larger dimension of... | math | {
"style": "rule",
"ground_truth": "2:3"
} | {
"split": "train",
"index": 31632,
"solution": "1. **Define the variables:**\n Let the width of the frame on the sides be $x$ inches. Then, the width of the frame on the top and bottom is $2x$ inches, since it is twice as wide.\n\n2. **Determine the overall dimensions of the framed painting:**\n - The width ... |
deepscaler | [
{
"role": "user",
"content": "The necessary and sufficient condition for the lines $ax+2y+1=0$ and $3x+(a-1)y+1=0$ to be parallel is \"$a=$ ______\". Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 31633,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the sequence $\\{a_n\\}$ is an arithmetic sequence and satisfies $a_1=1$, $a_3=7$, let $S_n$ be the sum of the first $n$ terms of the sequence $\\{(-1)^n a_n\\}$. Find the value of $S_{2017}$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "-3025"
} | {
"split": "train",
"index": 31634,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\sin x = \\frac{3}{5}$, with $x \\in \\left( \\frac{\\pi}{2}, \\pi \\right)$, find the values of $\\cos 2x$ and $\\tan\\left( x + \\frac{\\pi}{4} \\right)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{7}"
} | {
"split": "train",
"index": 31635,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Using the digits 0, 1, 2, 3, and 4, how many even numbers can be formed without repeating any digits? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "163"
} | {
"split": "train",
"index": 31636,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The diagram below shows part of a city map. The small rectangles represent houses, and the spaces between them represent streets. A student walks daily from point $A$ to point $B$ on the streets shown in the diagram, and can only walk east or south. At each intersection, the st... | math | {
"style": "rule",
"ground_truth": "\\frac{21}{32}"
} | {
"split": "train",
"index": 31637,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a bag with 1 red ball and 2 black balls of the same size, two balls are randomly drawn. Let $\\xi$ represent the number of red balls drawn. Calculate $E\\xi$ and $D\\xi$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{9}"
} | {
"split": "train",
"index": 31638,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\sin (\\omega x-\\varphi)$ $(\\omega > 0,|\\varphi| < \\frac {\\pi}{2})$ whose graph intersects with the x-axis at points that are a distance of $\\frac {\\pi}{2}$ apart, and it passes through the point $(0,- \\frac {1}{2})$ \n$(1)$ Find the analytica... | math | {
"style": "rule",
"ground_truth": "\\frac {1}{2}"
} | {
"split": "train",
"index": 31639,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In rectangle $ABCD$, $AB=1$, $BC=2$, and points $E$, $F$, and $G$ are midpoints of $\\overline{BC}$, $\\overline{CD}$, and $\\overline{AD}$, respectively. Point $H$ is the midpoint of $\\overline{GE}$. What is the area of the shaded region? Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"split": "train",
"index": 31640,
"solution": "1. **Identify the Coordinates**: \n - Let's assign coordinates to the rectangle $ABCD$ with $A = (0, 0)$, $B = (1, 0)$, $C = (1, 2)$, and $D = (0, 2)$.\n - Midpoints are calculated as follows:\n - $E$ is the midpoint of $\\overline{BC}$, so $E = \\left(\\fr... |
deepscaler | [
{
"role": "user",
"content": "Inside triangle \\( ABC \\), a random point \\( M \\) is chosen. What is the probability that the area of one of the triangles \\( ABM \\), \\( BCM \\), or \\( CAM \\) will be greater than the sum of the areas of the other two? Let's think step by step and put only the final an... | math | {
"style": "rule",
"ground_truth": "0.75"
} | {
"split": "train",
"index": 31641,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the base of a triangle is $24$ inches, two lines are drawn parallel to the base, with one of the lines dividing the triangle exactly in half by area, and the other line dividing one of the resulting triangles further into equal areas. If the total number of areas the tria... | math | {
"style": "rule",
"ground_truth": "12\\sqrt{2}"
} | {
"split": "train",
"index": 31642,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the number of real solutions to the equation:\n\\[\n\\frac{1}{x - 1} + \\frac{2}{x - 2} + \\frac{3}{x - 3} + \\dots + \\frac{150}{x - 150} = x^2.\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "151"
} | {
"split": "train",
"index": 31643,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If 2023 were expressed as a sum of distinct powers of 2, what would be the least possible sum of the exponents of these powers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 31644,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a \\bowtie b = a+\\sqrt{b+\\sqrt{b+\\sqrt{b+...}}}$. If $7\\bowtie g = 9$, find the value of $g$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 31645,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What are the last two digits in the sum of the factorials of the first 15 positive integers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 31646,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "2022 knights and liars are lined up in a row, with the ones at the far left and right being liars. Everyone except the ones at the extremes made the statement: \"There are 42 times more liars to my right than to my left.\" Provide an example of a sequence where there is exactly... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 31647,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cuckoo clock chimes \"cuckoo\" as many times as the hour indicated by the hour hand (e.g., at 19:00, it chimes 7 times). One morning, Maxim approached the clock at 9:05 and started turning the minute hand until the clock advanced by 7 hours. How many times did the clock chime... | math | {
"style": "rule",
"ground_truth": "43"
} | {
"split": "train",
"index": 31648,
"solution": ""
} |
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