data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Given the integers a and b, where a consists of a sequence of 1986 nines and b consists of a sequence of 1986 fours, calculate the sum of the digits of the base 10 representation of 9ab. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15880"
} | {
"split": "train",
"index": 17349,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute $\\sin 315^\\circ$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 17350,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a cone with a base radius of $1$ and a height of $\\sqrt{3}$, both the apex of the cone and the base circle are on the surface of a sphere $O$, calculate the surface area of this sphere. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{16\\pi}{3}"
} | {
"split": "train",
"index": 17351,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Josh writes the numbers $1,2,3,\\dots,99,100$. He marks out $1$, skips the next number $(2)$, marks out $3$, and continues skipping and marking out the next number to the end of the list. Then he goes back to the start of his list, marks out the first remaining number $(2)$, sk... | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 17352,
"solution": "Josh's method of marking out numbers can be understood as a process of elimination where in each round, every second number from the remaining list is marked out. Let's analyze the pattern step by step:\n\n1. **First Pass:**\n - Josh marks out every second number... |
deepscaler | [
{
"role": "user",
"content": "Quadrilateral $ABCD$ has right angles at $A$ and $C$, with diagonal $AC = 5$. If $AB = BC$ and sides $AD$ and $DC$ are of distinct integer lengths, what is the area of quadrilateral $ABCD$? Express your answer in simplest radical form. Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "12.25"
} | {
"split": "train",
"index": 17353,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the remainder when $9^{1995}$ is divided by 7? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 17354,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each of the twelve letters in \"STATISTICS\" is written on its own square tile and placed in a bag. What is the probability that a tile randomly selected from the bag will have a letter on it that is in the word \"TEST\"? Express your answer as a common fraction. Let's think st... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 17355,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The base of a rectangular parallelepiped is a square with a side length of \\(2 \\sqrt{3}\\). The diagonal of a lateral face forms an angle of \\(30^\\circ\\) with the plane of an adjacent lateral face. Find the volume of the parallelepiped. Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 17356,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the angle $D A C$ given that $A B = B C$ and $A C = C D$, and the lines on which points $A, B, C, D$ lie are parallel with equal distances between adjacent lines. Point $A$ is to the left of $B$, $C$ is to the left of $B$, and $D$ is to the right of $C$. Let's think step b... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 17357,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the period of $y = \\tan x + \\cot x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\pi"
} | {
"split": "train",
"index": 17358,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many distinct arrangements of the letters in the word \"balloon\" are there? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1260"
} | {
"split": "train",
"index": 17359,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the triangular pyramid $P-ABC$, $PA\\bot $ plane $ABC$, $\\triangle ABC$ is an isosceles triangle, where $AB=BC=2$, $\\angle ABC=120{}^\\circ $, and $PA=4$. The surface area of the circumscribed sphere of the triangular pyramid $P-ABC$ is __________. Let's think step by step... | math | {
"style": "rule",
"ground_truth": "32\\pi"
} | {
"split": "train",
"index": 17360,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate plane \\( xOy \\), the coordinates of point \\( F \\) are \\((1,0)\\), and points \\( A \\) and \\( B \\) lie on the parabola \\( y^2 = 4x \\). It is given that \\( \\overrightarrow{OA} \\cdot \\overrightarrow{OB} = -4 \\) and \\( |\\overrightarrow{F... | math | {
"style": "rule",
"ground_truth": "-11"
} | {
"split": "train",
"index": 17361,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A finite sequence of three-digit integers has the property that the tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first t... | math | {
"style": "rule",
"ground_truth": "37"
} | {
"split": "train",
"index": 17362,
"solution": "1. **Understanding the Sequence Property**: The sequence is such that the tens and units digits of each term become the hundreds and tens digits of the next term. This implies that each digit in a position (hundreds, tens, units) of one term will appear in the next... |
deepscaler | [
{
"role": "user",
"content": "Six distinguishable players are participating in a tennis tournament. Each player plays one match of tennis against every other player. There are no ties in this tournament; each tennis match results in a win for one player and a loss for the other. Suppose that whenever $A$ an... | math | {
"style": "rule",
"ground_truth": "2048"
} | {
"split": "train",
"index": 17363,
"solution": "We first group the players by wins, so let $G_{1}$ be the set of all players with the most wins, $G_{2}$ be the set of all players with the second most wins, $\\ldots, G_{n}$ be the set of all players with the least wins. By the condition in the problem, everyone i... |
deepscaler | [
{
"role": "user",
"content": "Let \\( f(x) = x^2 + px + q \\). It is known that the inequality \\( |f(x)| > \\frac{1}{2} \\) has no solutions on the interval \\([2, 4]\\). Find \\( \\underbrace{f(f(\\ldots f}_{2017}\\left(\\frac{5-\\sqrt{11}}{2}\\right)) \\ldots) \\). Round your answer to the nearest hundre... | math | {
"style": "rule",
"ground_truth": "4.16"
} | {
"split": "train",
"index": 17364,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If line $l_1: ax+2y+6=0$ is parallel to line $l_2: x+(a-1)y+(a^2-1)=0$, then the real number $a=$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 17365,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( g(x) \\) be the function defined on \\(-2 \\le x \\le 2\\) by the formula \n\\[ g(x) = 2 - \\sqrt{4 - x^2}. \\]\nIf a graph of \\( x = g(y) \\) is overlaid on the graph of \\( y = g(x) \\), then one fully enclosed region is formed by the two graphs. What is the area of ... | math | {
"style": "rule",
"ground_truth": "2.28"
} | {
"split": "train",
"index": 17366,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer with exactly 20 positive divisors? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "432"
} | {
"split": "train",
"index": 17367,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all the roots of the equation\n\n\\[ 1 - \\frac{x}{1} + \\frac{x(x-1)}{2!} - \\frac{x(x-1)(x-2)}{3!} + \\frac{x(x-1)(x-2)(x-3)}{4!} - \\frac{x(x-1)(x-2)(x-3)(x-4)}{5!} + \\frac{x(x-1)(x-2)(x-3)(x-4)(x-5)}{6!} = 0 \\]\n\n(Where \\( n! = 1 \\cdot 2 \\cdot 3 \\cdots n \\))\n\... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 17368,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = \\log_{m}(m - x)$, if the maximum value in the interval $[3, 5]$ is 1 greater than the minimum value, determine the real number $m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3 + \\sqrt{6}"
} | {
"split": "train",
"index": 17369,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $XYZ$, $XY=12$, $YZ=16$, and $XZ=20$. Point $M$ is on $\\overline{XY}$, $N$ is on $\\overline{YZ}$, and $O$ is on $\\overline{XZ}$. Let $XM = p \\cdot XY$, $YN = q \\cdot YZ$, and $ZO = r \\cdot XZ$, where $p$, $q$, and $r$ are positive and satisfy $p+q+r=3/4$ and $... | math | {
"style": "rule",
"ground_truth": "41"
} | {
"split": "train",
"index": 17370,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Express twenty-three in base 2. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10111_2"
} | {
"split": "train",
"index": 17371,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\(1 \\leq x^{2}+y^{2} \\leq 4\\), find the sum of the maximum and minimum values of \\(x^{2}-xy+y^{2}\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6.5"
} | {
"split": "train",
"index": 17372,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( a \\in \\mathbf{R} \\). A complex number is given by \\(\\omega = 1 + a\\mathrm{i}\\). A complex number \\( z \\) satisfies \\( \\overline{\\omega} z - \\omega = 0 \\). Determine the value of \\( a \\) such that \\(|z^2 - z + 2|\\) is minimized, and find this minimum va... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{14}}{4}"
} | {
"split": "train",
"index": 17373,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given complex numbers $w$ and $z$ such that $|w+z|=3$ and $|w^2+z^2|=18,$ find the smallest possible value of $|w^3+z^3|.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{81}{2}"
} | {
"split": "train",
"index": 17374,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $11^{-1} \\equiv 3 \\pmod{31}$, find $20^{-1} \\pmod{31}$. Provide the result as a residue modulo 31 (a number between 0 and 30, inclusive). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 17375,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a unique quadruple of positive integers $(a, b, c, k)$ such that $c$ is not a perfect square and $a+\\sqrt{b+\\sqrt{c}}$ is a root of the polynomial $x^{4}-20 x^{3}+108 x^{2}-k x+9$. Compute $c$. Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 17376,
"solution": "The four roots are $a \\pm \\sqrt{b \\pm \\sqrt{c}}$, so the sum of roots is 20 , so $a=5$. Next, we compute the sum of squares of roots: $$(a+\\sqrt{b \\pm \\sqrt{c}})^{2}+(a-\\sqrt{b \\pm \\sqrt{c}})^{2}=2 a^{2}+2 b \\pm 2 \\sqrt{c}$$ so the sum of squares of roo... |
deepscaler | [
{
"role": "user",
"content": "Let $c$ be a real number randomly selected from the interval $[-20,20]$. Then, $p$ and $q$ are two relatively prime positive integers such that $\\frac{p}{q}$ is the probability that the equation $x^4 + 36c^2 = (9c^2 - 15c)x^2$ has at least two distinct real solutions. Find the... | math | {
"style": "rule",
"ground_truth": "29"
} | {
"split": "train",
"index": 17377,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the set $M=\\{m\\in \\mathbb{Z} | x^2+mx-36=0 \\text{ has integer solutions}\\}$, a non-empty set $A$ satisfies the conditions: \n(1) $A \\subseteq M$, \n(2) If $a \\in A$, then $-a \\in A$, the number of all such sets $A$ is. Let's think step by step and put only the f... | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 17378,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In an isosceles triangle, the center of the inscribed circle divides the altitude in the ratio $17: 15$. The base is 60. Find the radius of this circle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7.5"
} | {
"split": "train",
"index": 17379,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Fifty numbers have an average of 76. Forty of these numbers have an average of 80. What is the average of the other ten numbers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 17380,
"solution": "If 50 numbers have an average of 76, then the sum of these 50 numbers is $50(76)=3800$. If 40 numbers have an average of 80, then the sum of these 40 numbers is $40(80)=3200$. Therefore, the sum of the 10 remaining numbers is $3800-3200=600$, and so the average of ... |
deepscaler | [
{
"role": "user",
"content": "Find the sum of the rational roots of $g(x)=x^3-9x^2+16x-4$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 17381,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the volume of the region in three-dimensional space defined by the inequalities $|x|+|y|+|z|\\le1$ and $|x|+|y|+|z-1|\\le1$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"split": "train",
"index": 17382,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\cos \\alpha =\\dfrac{4}{5}$ and $\\cos (\\alpha +\\beta )=\\dfrac{5}{13}$, where $\\alpha$ and $\\beta$ are acute angles.\n1. Find the value of $\\sin 2\\alpha$.\n2. Find the value of $\\sin \\beta$. Let's think step by step and put only the final answer within \\... | math | {
"style": "rule",
"ground_truth": "\\dfrac{33}{65}"
} | {
"split": "train",
"index": 17383,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, if median $\\overline{AD}$ makes an angle of $30^\\circ$ with side $\\overline{BC},$ then find the value of $|\\cot B - \\cot C|.$ 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": 17384,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\dfrac {\\pi}{2} < \\alpha < \\pi$ and $\\sin (\\alpha+ \\dfrac {\\pi}{6})= \\dfrac {3}{5}$, find the value of $\\cos (\\alpha- \\dfrac {\\pi}{6})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac {3\\sqrt {3}-4}{10}"
} | {
"split": "train",
"index": 17385,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Among the 9 natural numbers $1,2,3, \\cdots, 9$, if 3 numbers are chosen, let $x$ be the number of pairs of adjacent numbers among the chosen 3 numbers (for example, if the 3 chosen numbers are $1,2,3$, there are 2 pairs of adjacent numbers: 1,2 and 2,3, so the value of $x$ is ... | math | {
"style": "rule",
"ground_truth": "2/3"
} | {
"split": "train",
"index": 17386,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Schools A and B are having a sports competition with three events. In each event, the winner gets 10 points and the loser gets 0 points, with no draws. The school with the highest total score after the three events wins the championship. It is known that the probabilities of sc... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 17387,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(a_{1}, a_{2}, \\cdots, a_{10}\\) be any 10 distinct positive integers such that \\(a_{1} + a_{2} + \\cdots + a_{10} = 1995\\). Find the minimum value of \\(a_{1} a_{2} + a_{2} a_{3} + \\cdots + a_{10} a_{1}\\). Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "6044"
} | {
"split": "train",
"index": 17388,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given positive integers \\( n \\) and \\( m \\), let \\( A = \\{1, 2, \\cdots, n\\} \\) and define \\( B_{n}^{m} = \\left\\{\\left(a_{1}, a_{2}, \\cdots, a_{m}\\right) \\mid a_{i} \\in A, i=1,2, \\cdots, m\\} \\right. \\) satisfying:\n1. \\( \\left|a_{i} - a_{i+1}\\right| \\neq... | math | {
"style": "rule",
"ground_truth": "104"
} | {
"split": "train",
"index": 17389,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the sum of all odd terms in the first 10 terms of a geometric sequence is $85 \\frac{1}{4}$, and the sum of all even terms is $170 \\frac{1}{2}$, find the value of $S=a_{3}+a_{6}+a_{9}+a_{12}$. Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "585"
} | {
"split": "train",
"index": 17390,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Convert $199_{10}$ to base 2. Let $x$ be the number of zeros and $y$ be the number of ones in base 2. What is the value of $y-x?$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 17391,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Convex hexagon $ABCDEF$ has exactly two distinct side lengths. Side $AB$ measures 5 units, and side $BC$ measures 6 units. The perimeter of hexagon $ABCDEF$ is 34 units. How many sides of hexagon $ABCDEF$ have measure 6 units? Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 17392,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Alice picks a number uniformly at random from the first $5$ even positive integers, and Palice picks a number uniformly at random from the first $5$ odd positive integers. If Alice picks a larger number than Palice with probability $\\frac{m}{n}$ for relatively prime posi... | math | {
"style": "rule",
"ground_truth": "39"
} | {
"split": "train",
"index": 17393,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ella walks to her university library, averaging 80 steps per minute, with each of her steps covering 80 cm. It takes her 20 minutes to get to the library. Her friend Tia, going to the same library by the same route, averages 120 steps per minute, but her steps are only 70 cm lo... | math | {
"style": "rule",
"ground_truth": "15.24"
} | {
"split": "train",
"index": 17394,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A_{10}$ denote the answer to problem 10. Two circles lie in the plane; denote the lengths of the internal and external tangents between these two circles by $x$ and $y$, respectively. Given that the product of the radii of these two circles is $15 / 2$, and that the distan... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 17395,
"solution": "Suppose the circles have radii $r_{1}$ and $r_{2}$. Then using the tangents to build right triangles, we have $x^{2}+\\left(r_{1}+r_{2}\\right)^{2}=A_{10}^{2}=y^{2}+\\left(r_{1}-r_{2}\\right)^{2}$. Thus, $y^{2}-x^{2}=\\left(r_{1}+r_{2}\\right)^{2}-\\left(r_{1}-r_{2... |
deepscaler | [
{
"role": "user",
"content": "In trapezoid $ABCD$, leg $\\overline{BC}$ is perpendicular to bases $\\overline{AB}$ and $\\overline{CD}$, and diagonals $\\overline{AC}$ and $\\overline{BD}$ are perpendicular. Given that $AB=\\sqrt{11}$ and $AD=\\sqrt{1001}$, find $BC^2$. Let's think step by step and put only... | math | {
"style": "rule",
"ground_truth": "110"
} | {
"split": "train",
"index": 17396,
"solution": "Let $BC=x$ and $CD=y+\\sqrt{11}$. From Pythagoras with $AD$, we obtain $x^2+y^2=1001$. Since $AC$ and $BD$ are perpendicular diagonals of a quadrilateral, then $AB^2+CD^2=BC^2+AD^2$, so we have \\[\\left(y+\\sqrt{11}\\right)^2+11=x^2+1001.\\] Substituting $x^2=1001... |
deepscaler | [
{
"role": "user",
"content": "There exists a constant $k$ so that the minimum value of\n\\[4x^2 - 6kxy + (3k^2 + 2) y^2 - 4x - 4y + 6\\]over all real numbers $x$ and $y$ is 0. Find $k.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 17397,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two circles, both with the same radius $r$ , are placed in the plane without intersecting each other. A line in the plane intersects the first circle at the points $A,B$ and the other at points $C,D$ , so that $|AB|=|BC|=|CD|=14\\text{cm}$ . Another line intersects the cir... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 17398,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine how many integer values of $x$ satisfy $\\lceil{\\sqrt{x}}\\rceil = 20$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "39"
} | {
"split": "train",
"index": 17399,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many natural numbers greater than 10 but less than 100 are relatively prime to 21? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "51"
} | {
"split": "train",
"index": 17400,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A plastic snap-together cube has a protruding snap on one side and receptacle holes on the other five sides as shown. What is the smallest number of these cubes that can be snapped together so that only receptacle holes are showing?\n[asy] draw((0,0)--(4,0)--(4,4)--(0,4)--cycl... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 17401,
"solution": "To solve this problem, we need to determine the smallest number of cubes that can be snapped together such that all the protruding snaps are hidden and only the receptacle holes are visible.\n\n1. **Understanding the Cube Configuration**: Each cube has one protrudi... |
deepscaler | [
{
"role": "user",
"content": "Below is pictured a regular seven-pointed star. Find the measure of angle \\( a \\) in radians. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5\\pi}{7}"
} | {
"split": "train",
"index": 17402,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the numbers 1, 3, 5 and 2, 4, 6, calculate the total number of different three-digit numbers that can be formed when arranging these numbers on three cards. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 17403,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The mean of the numbers 3, 7, 10, and 15 is twice the mean of $x$, 20, and 6. 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": "-12.875"
} | {
"split": "train",
"index": 17404,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a large square of side length 60 units, subdivided into a grid with non-uniform rows and columns. The rows are divided into segments of 20, 20, and 20 units, and the columns are divided into segments of 15, 15, 15, and 15 units. A shaded region is created by connecting... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 17405,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S$ be the set of all positive integers whose prime factorizations only contain powers of the primes 2 and 2017 (1, powers of 2, and powers of 2017 are thus contained in $S$). Compute $\\sum_{s \\in S} \\frac{1}{s}$. Let's think step by step and put only the final answer wi... | math | {
"style": "rule",
"ground_truth": "\\frac{2017}{1008}"
} | {
"split": "train",
"index": 17406,
"solution": "Since every $s$ can be written as $2^{i} \\cdot 2017^{j}$ for non-negative integers $i$ and $j$, the given sum can be written as $\\left(\\sum_{i=0}^{\\infty} \\frac{1}{2^{i}}\\right)\\left(\\sum_{j=0}^{\\infty} \\frac{1}{2017^{j}}\\right)$. We can easily find the ... |
deepscaler | [
{
"role": "user",
"content": "Given two random variables $X$ and $Y$, where $X\\sim B(8, \\frac{1}{2})$ and $Y\\sim N(\\mu, \\sigma^2)$, find the probability $P(4 \\leq Y \\leq 8)$, given that $\\mu = E(X)$ and $P(Y < 0) = 0.2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.3"
} | {
"split": "train",
"index": 17407,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Sides $\\overline{AB}$ and $\\overline{AC}$ of equilateral triangle $ABC$ are tangent to a circle at points $B$ and $C$ respectively. What fraction of the area of $\\triangle ABC$ lies outside the circle? Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{3}-\\frac{4\\sqrt{3}\\pi}{27}"
} | {
"split": "train",
"index": 17408,
"solution": "1. **Identify the Geometry and Relationships**:\n - Let the radius of the circle be $r$, and its center be $O$.\n - Since $\\overline{AB}$ and $\\overline{AC}$ are tangent to the circle at points $B$ and $C$, respectively, $\\angle OBA = \\angle OCA = 90^\\circ... |
deepscaler | [
{
"role": "user",
"content": "Margie bought $3$ apples at a cost of $50$ cents per apple. She paid with a 5-dollar bill. How much change did Margie receive? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "$3.50"
} | {
"split": "train",
"index": 17409,
"solution": "1. **Convert the cost per apple to dollars:** \n Since $50$ cents is equivalent to $\\textdollar 0.50$, the cost per apple in dollars is $\\textdollar 0.50$.\n\n2. **Calculate the total cost for three apples:** \n The total cost for three apples is calculated... |
deepscaler | [
{
"role": "user",
"content": "Find all functions $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ such that\n$$f(x^2 + y) \\ge (\\frac{1}{x} + 1)f(y)$$\nholds for all $x \\in \\mathbb{R} \\setminus \\{0\\}$ and all $y \\in \\mathbb{R}$. Let's think step by step and put only the final answer within \\boxed{}."
}
... | math | {
"style": "rule",
"ground_truth": "f(x) = 0"
} | {
"split": "train",
"index": 17410,
"solution": "\nTo find all functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) that satisfy the given inequality:\n\n\\[\nf(x^2 + y) \\ge \\left(\\frac{1}{x} + 1\\right)f(y)\n\\]\n\nfor all \\( x \\in \\mathbb{R} \\setminus \\{0\\} \\) and \\( y \\in \\mathbb{R} \\), we'l... |
deepscaler | [
{
"role": "user",
"content": "How many different rectangles with sides parallel to the grid can be formed by connecting four of the dots in a $5\\times 5$ square array of dots? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 17411,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle \\(\\triangle A B C\\) has \\(A B=21, B C=55\\), and \\(C A=56\\). There are two points \\(P\\) in the plane of \\(\\triangle A B C\\) for which \\(\\angle B A P=\\angle C A P\\) and \\(\\angle B P C=90^{\\circ}\\). Find the distance between them. Let's think step by s... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{2} \\sqrt{409}"
} | {
"split": "train",
"index": 17412,
"solution": "Let \\(P_{1}\\) and \\(P_{2}\\) be the two possible points \\(P\\), with \\(A P_{1}<A P_{2}\\). Both lie on the \\(\\angle A\\)-bisector and the circle \\(\\gamma\\) with diameter \\(B C\\). Let \\(D\\) be the point where the \\(\\angle A\\)-bisector intersects \\(... |
deepscaler | [
{
"role": "user",
"content": "Given that the function $f(x)$ is an even function defined on $\\mathbb{R}$, and the odd function $g(x)$ defined on $\\mathbb{R}$ passes through the point $(-1, 1)$, and $g(x) = f(x-1)$, find the value of $f(7) + f(8)$. Let's think step by step and put only the final answer wit... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 17413,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( n \\) be a two-digit number such that the square of the sum of the digits of \\( n \\) is equal to the sum of the digits of \\( n^2 \\). Find the sum of all possible values of \\( n \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "139"
} | {
"split": "train",
"index": 17414,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute $1-2+3-4+ \\dots -100+101$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "76"
} | {
"split": "train",
"index": 17415,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Grandma Wang has 6 stools that need to be painted by a painter. Each stool needs to be painted twice. The first coat takes 2 minutes, but there must be a 10-minute wait before applying the second coat. How many minutes will it take to paint all 6 stools? Let's think step by ste... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"split": "train",
"index": 17416,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a contest with 5 participants, there were several questions. For each question, one participant gave an incorrect answer while the others answered correctly. Petya gave 10 correct answers, which is fewer than any other participant. Vasya gave 13 correct answers, which is mor... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 17417,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In right triangle $XYZ$, we have $\\angle X = \\angle Y$ and $XY = 8\\sqrt{2}$. What is the area of $\\triangle XYZ$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 17418,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( P \\) is a point on the hyperbola \\( C: \\frac{x^{2}}{4} - \\frac{y^{2}}{12} = 1 \\), and \\( F_{1} \\) and \\( F_{2} \\) are the left and right foci of the hyperbola \\( C \\), and \\( M \\) and \\( I \\) are the centroid and incenter of the triangle \\( \\tria... | math | {
"style": "rule",
"ground_truth": "\\sqrt{6}"
} | {
"split": "train",
"index": 17419,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all $x$ such that $\\lfloor \\lfloor 2x \\rfloor - 1/2 \\rfloor = \\lfloor x + 2 \\rfloor.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\left[ \\frac{5}{2}, \\frac{7}{2} \\right)"
} | {
"split": "train",
"index": 17420,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain shopping mall sells a batch of brand-name shirts, with an average daily sales of 20 pieces and a profit of $40 per piece. In order to expand sales and reduce inventory quickly, the mall decides to take appropriate price reduction measures. After investigation, it was ... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 17421,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $F_{1}$ and $F_{2}$ are the foci of a pair of related curves, and $P$ is the intersection point of the ellipse and the hyperbola in the first quadrant, when $\\angle F_{1}PF_{2}=60^{\\circ}$, determine the eccentricity of the ellipse in this pair of related curves. Let's ... | math | {
"style": "rule",
"ground_truth": "\\dfrac{\\sqrt{3}}{3}"
} | {
"split": "train",
"index": 17422,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Select 2 different numbers from 1, 3, 5, and 3 different numbers from 2, 4, 6, 8 to form a five-digit number, and determine the total number of even numbers among these five-digit numbers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "864"
} | {
"split": "train",
"index": 17423,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( A \\) and \\( B \\) be two moving points on the ellipse \\( x^{2}+3 y^{2}=1 \\), and \\( OA \\) is perpendicular to \\( OB \\) (where \\( O \\) is the origin). Then, the product of the maximum and minimum values of \\( |AB| \\) is ______. Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "\\frac{2 \\sqrt{3}}{3}"
} | {
"split": "train",
"index": 17424,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of $c$ if $x\\cdot(3x+1)<c$ if and only when $x\\in \\left(-\\frac{7}{3},2\\right)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 17425,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The smaller root of the equation $\\left(x- \\frac{3}{4} \\right) \\left(x - \\frac{3}{4} \\right) + \\left(x - \\frac{3}{4} \\right) \\left(x - \\frac{1}{2} \\right) = 0$ is: 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": 17426,
"solution": "1. **Identify the form of the equation**: The given equation is:\n \\[\n \\left(x-\\frac{3}{4}\\right)\\left(x-\\frac{3}{4}\\right)+\\left(x-\\frac{3}{4}\\right)\\left(x-\\frac{1}{2}\\right) = 0\n \\]\n This can be rewritten using $a = x - \\frac{3}{4}$ and... |
deepscaler | [
{
"role": "user",
"content": "A factory arranges $5$ workers to three duty positions, with each worker assigned to only one position. Each position must have at least $1$ worker. Calculate the number of ways to assign workers A and B to the same position. Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 17427,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a function f(n) defined on the set of positive integers, where f(1) = 2: For even n, f(n) = f(n-1) + 2; For odd n > 1, f(n) = f(n-2) + 2. Calculate the value of f(2017). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2018"
} | {
"split": "train",
"index": 17428,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A line is parameterized by\n\\[\\begin{pmatrix} x \\\\ y \\end{pmatrix} = \\begin{pmatrix} 2 \\\\ 1 \\end{pmatrix} + s \\begin{pmatrix} 4 \\\\ -1 \\end{pmatrix}.\\]\nA second line is parameterized by\n\\[\\begin{pmatrix} x \\\\ y \\end{pmatrix} = \\begin{pmatrix} 3 \\\\ 7 \\end... | math | {
"style": "rule",
"ground_truth": "\\frac{-13}{\\sqrt{493}}"
} | {
"split": "train",
"index": 17429,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $R$ be the rectangle in the Cartesian plane with vertices at $(0,0),(2,0),(2,1)$, and $(0,1)$. $R$ can be divided into two unit squares, as shown; the resulting figure has seven edges. Compute the number of ways to choose one or more of the seven edges such that the resulti... | math | {
"style": "rule",
"ground_truth": "61"
} | {
"split": "train",
"index": 17430,
"solution": "We have two cases, depending on whether we choose the middle edge. If so, then either all the remaining edges are either to the left of or to the right of this edge, or there are edges on both sides, or neither; in the first two cases there are 6 ways each, in the ... |
deepscaler | [
{
"role": "user",
"content": "Let $N$ be the number of ways to place the integers $1$ through $12$ in the $12$ cells of a $2 \\times 6$ grid so that for any two cells sharing a side, the difference between the numbers in those cells is not divisible by $3.$ One way to do this is shown below. Find the number... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 17431,
"solution": "We replace the numbers which are 0 mod(3) to 0, 1 mod(3) to 1, and 2 mod(3) to 2.\n Then, the problem is equivalent to arranging 4 0's,4 1's, and 4 2's into the grid (and then multiplying by $4!^3$ to account for replacing the remainder numbers with actual numbers)... |
deepscaler | [
{
"role": "user",
"content": "When Bendegúz boarded the 78-seat train car with his valid seat reservation, he was shocked to find that all seats were already taken. What had happened was that Dömötör boarded without a seat reservation. The other 77 passengers, including Elek, had purchased a seat reservatio... | math | {
"style": "rule",
"ground_truth": "1/2"
} | {
"split": "train",
"index": 17432,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the equations\n$$\nz^{2}=4+4 \\sqrt{15} i \\text { and } z^{2}=2+2 \\sqrt{3} i,\n$$\nthe roots are the coordinates of the vertices of a parallelogram in the complex plane. If the area $S$ of the parallelogram can be expressed as $p \\sqrt{q} - r \\sqrt{s}$ (where $p, q, r... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 17433,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An artist arranges 1000 dots evenly around a circle, with each dot being either red or blue. A critic counts faults: each pair of adjacent red dots counts as one fault, and each pair of blue dots exactly two apart (separated by one dot) counts as another fault. What is the smal... | math | {
"style": "rule",
"ground_truth": "250"
} | {
"split": "train",
"index": 17434,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four friends initially plan a road trip and decide to split the fuel cost equally. However, 3 more friends decide to join at the last minute. Due to the increase in the number of people sharing the cost, the amount each of the original four has to pay decreases by $\\$$8. What ... | math | {
"style": "rule",
"ground_truth": "74.67"
} | {
"split": "train",
"index": 17435,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We consider dissections of regular $n$-gons into $n - 2$ triangles by $n - 3$ diagonals which do not intersect inside the $n$-gon. A [i]bicoloured triangulation[/i] is such a dissection of an $n$-gon in which each triangle is coloured black or white and any two triangles which ... | math | {
"style": "rule",
"ground_truth": "3\\mid n"
} | {
"split": "train",
"index": 17436,
"solution": "\nTo solve the problem, we need to determine which positive integers \\( n \\ge 4 \\) allow a regular \\( n \\)-gon to be dissected into a bicoloured triangulation under the condition that, for each vertex \\( A \\), the number of black triangles having \\( A \\) a... |
deepscaler | [
{
"role": "user",
"content": "The parabola with equation $y=ax^2+bx+c$ is graphed below:\n\n[asy]\nxaxis(-3,7);\n\nyaxis(-5,32);\n\nreal g(real x)\n\n{\n\nreturn 4(x-2)^2-4;\n}\n\ndraw(graph(g,-1,5));\ndot((2,-4));\nlabel(\"Vertex: $(2,-4)$\", (2,-4), SE);\ndot((4,12));\nlabel(\"$(4,12)$\", (4,12), E);\n[/a... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 17437,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We are laying railway tracks that are $15 \\text{ meters }$ long at a temperature of $t = -8^{\\circ} \\text{C}$. What gap should we leave between each rail if the maximum expected temperature is $t = 60^{\\circ} \\text{C}$? The coefficient of expansion for the rail is $\\lambd... | math | {
"style": "rule",
"ground_truth": "12.24"
} | {
"split": "train",
"index": 17438,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The denominators of two irreducible fractions are 600 and 700. What is the smallest possible value of the denominator of their sum (when written as an irreducible fraction)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "168"
} | {
"split": "train",
"index": 17439,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the integer that is closest to $1000\\sum_{n=3}^{10000}\\frac1{n^2-4}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "521"
} | {
"split": "train",
"index": 17440,
"solution": "We know that $\\frac{1}{n^2 - 4} = \\frac{1}{(n+2)(n-2)}$. We can use the process of fractional decomposition to split this into two fractions: $\\frac{1}{(n+2)(n-2)} = \\frac{A}{(n+2)} + \\frac{B}{(n-2)}$ for some A and B.\n Solving for A and B gives $1 = (n-2)A +... |
deepscaler | [
{
"role": "user",
"content": "Find the area of trapezoid \\(ABCD\\) with a side \\(BC = 5\\), where the distances from vertices \\(A\\) and \\(D\\) to the line \\(BC\\) are 3 and 7 respectively. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 17441,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Bob chooses a $4$ -digit binary string uniformly at random, and examines an infinite sequence of uniformly and independently random binary bits. If $N$ is the least number of bits Bob has to examine in order to find his chosen string, then find the expected value of $N$ . F... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 17442,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In quadrilateral $ABCD,$ $AB = 5,$ $BC = 8$, and $CD = 20$ units. Angle $B$ and angle $C$ are both right angles. What is the length of segment $AD$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 17443,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The line $y = -\\frac{2}{3}x + 6$ crosses the $x$-axis at $P$ and the $y$-axis at $Q$. Point $T(r, s)$ is on line segment $PQ$. If the area of $\\triangle POQ$ is four times the area of $\\triangle TOP$, then what is the value of $r+s$? Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "8.25"
} | {
"split": "train",
"index": 17444,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "(1) Two poles are 6m apart with a rope tied between them, and a lamp is hung on the rope. Find the probability that the distance between the lamp and both ends is greater than 2m; \n(2) From the numbers 1, 2, 3, 4, 5, 6, if two numbers are randomly selected and added together,... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{5}"
} | {
"split": "train",
"index": 17445,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $0 < α < \\dfrac{\\pi }{2}$, $-\\dfrac{\\pi }{2} < β < 0$, $\\cos \\left( \\dfrac{\\pi }{4}+α \\right)=\\dfrac{1}{3}$, and $\\cos \\left( \\dfrac{\\pi }{4}-\\dfrac{\\beta }{2} \\right)=\\dfrac{\\sqrt{3}}{3}$, calculate the value of $\\cos \\left( α +\\dfrac{\\beta }{... | math | {
"style": "rule",
"ground_truth": "\\dfrac{5\\sqrt{3}}{9}"
} | {
"split": "train",
"index": 17446,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given unit vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfy $|\\vec{a}-\\vec{b}|=\\sqrt{3}|\\vec{a}+\\vec{b}|$, calculate the angle between $\\overrightarrow{a}$ and $\\overrightarrow{b}$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "\\dfrac{2\\pi}{3}"
} | {
"split": "train",
"index": 17447,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all values of $r$ such that $\\lfloor r \\rfloor + r = 12.2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "r=6.2"
} | {
"split": "train",
"index": 17448,
"solution": ""
} |
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