data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "In right triangle $XYZ$, we have $\\angle X = \\angle Z$ and $XZ = 8\\sqrt{2}$. 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": 22149,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The table below gives the percent of students in each grade at Annville and Cleona elementary schools:\n\\[\\begin{tabular}{rccccccc}&\\textbf{\\underline{K}}&\\textbf{\\underline{1}}&\\textbf{\\underline{2}}&\\textbf{\\underline{3}}&\\textbf{\\underline{4}}&\\textbf{\\underlin... | math | {
"style": "rule",
"ground_truth": "15\\%"
} | {
"split": "train",
"index": 22150,
"solution": "1. **Calculate the number of 6th graders in Annville:**\n - Annville has 100 students in total.\n - The percentage of 6th graders in Annville is 11%.\n - Therefore, the number of 6th graders in Annville is:\n \\[\n \\frac{11\\% \\times 100}{100} = 11 ... |
deepscaler | [
{
"role": "user",
"content": "Let \\( a_{1}, a_{2}, \\cdots, a_{n} \\) be distinct positive integers such that \\( a_{1} + a_{2} + \\cdots + a_{n} = 2014 \\), where \\( n \\) is some integer greater than 1. Let \\( d \\) be the greatest common divisor of \\( a_{1}, a_{2}, \\cdots, a_{n} \\). For all values ... | math | {
"style": "rule",
"ground_truth": "530"
} | {
"split": "train",
"index": 22151,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The volume of the parallelepiped generated by $\\begin{pmatrix} 2 \\\\ 3 \\\\ 4 \\end{pmatrix},$ $\\begin{pmatrix} 1 \\\\ k \\\\ 2 \\end{pmatrix},$ and $\\begin{pmatrix} 1 \\\\ 2 \\\\ k \\end{pmatrix}$ is 15. Find $k,$ where $k > 0.$ Let's think step by step and put only the f... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{2}"
} | {
"split": "train",
"index": 22152,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $f(\\alpha)= \\dfrac {\\sin (\\alpha- \\dfrac {5\\pi}{2})\\cos ( \\dfrac {3\\pi}{2}+\\alpha)\\tan (\\pi-\\alpha)}{\\tan (-\\alpha-\\pi)\\sin (\\pi-\\alpha)}$.\n(1) Simplify $f(\\alpha)$\n(2) If $\\cos (\\alpha+ \\dfrac {3\\pi}{2})= \\dfrac {1}{5}$ and $\\alpha$ is an angl... | math | {
"style": "rule",
"ground_truth": "\\dfrac{2\\sqrt{6}}{5}"
} | {
"split": "train",
"index": 22153,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A plane intersects a right circular cylinder of radius $2$ forming an ellipse. If the major axis of the ellipse is $30\\%$ longer than the minor axis, what is the length of the major axis? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5.2"
} | {
"split": "train",
"index": 22154,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, \\(p, q, r, s\\), and \\(t\\) represent five consecutive integers, not necessarily in order. The two integers in the leftmost circle add to 63. The two integers in the rightmost circle add to 57. What is the value of \\(r\\)? Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 22155,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the variables $a$ and $b$ satisfying $b=-\\frac{1}{2}a^2+3\\ln(a)$ (with $a>0$), if point $Q(m,n)$ is on the line $y=2x+\\frac{1}{2}$, calculate the minimum value of $(a-m)^2+(b-n)^2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9}{5}"
} | {
"split": "train",
"index": 22156,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(a\\), \\(b\\), and \\(c\\) be nonnegative real numbers such that \\(a^2 + b^2 + c^2 = 1\\). Find the maximum value of\n\\[2ab \\sqrt{3} + 2ac.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 22157,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given point $A(3,0)$, $\\overrightarrow{EA}=(2,1)$, $\\overrightarrow{EF}=(1,2)$, and point $P(2,0)$ satisfies $\\overrightarrow{EP}=λ \\overrightarrow{EA}+μ \\overrightarrow{EF}$, find the value of $λ+μ$. Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 22158,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the value of $x$ between 0 and 180 such that\n\\[\\tan (120^\\circ - x^\\circ) = \\frac{\\sin 120^\\circ - \\sin x^\\circ}{\\cos 120^\\circ - \\cos x^\\circ}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 22159,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 18 identical cars in a train. In some cars, exactly half of the seats are free, in others, exactly one-third of the seats are free, and in the remaining cars, all seats are occupied. At the same time, exactly one-ninth of all seats in the whole train are free. How man... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 22160,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive value of $x$ such that $x + 4321$ results in a palindrome? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 22161,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a triangle $ABC$ , the median $AD$ divides $\\angle{BAC}$ in the ratio $1:2$ . Extend $AD$ to $E$ such that $EB$ is perpendicular $AB$ . Given that $BE=3,BA=4$ , find the integer nearest to $BC^2$ . Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "29"
} | {
"split": "train",
"index": 22162,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( m \\) be the product of all positive integer divisors of 360,000. Suppose the prime factors of \\( m \\) are \\( p_{1}, p_{2}, \\ldots, p_{k} \\), for some positive integer \\( k \\), and \\( m = p_{1}^{e_{1}} p_{2}^{e_{2}} \\cdot \\ldots \\cdot p_{k}^{e_{k}} \\), for s... | math | {
"style": "rule",
"ground_truth": "630"
} | {
"split": "train",
"index": 22163,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many positive divisors of $150$ are not divisible by 5? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 22164,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $f(x) = x^2$ and $g(x) = |x - 1|$, let $f_1(x) = g(f(x))$, $f_{n+1}(x) = g(f_n(x))$, calculate the number of solutions to the equation $f_{2015}(x) = 1$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2017"
} | {
"split": "train",
"index": 22165,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Sara makes a staircase out of toothpicks as shown:\n[asy] size(150); defaultpen(linewidth(0.8)); path h = ellipse((0.5,0),0.45,0.015), v = ellipse((0,0.5),0.015,0.45); for(int i=0;i<=2;i=i+1) { for(int j=0;j<=3-i;j=j+1) { filldraw(shift((i,j))*h,black); filldraw(shift((j,i))*v,... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 22166,
"solution": "\nTo solve this problem, we need to determine the number of steps, $n$, in a staircase that uses 180 toothpicks. We will derive a formula for the number of toothpicks used in a staircase with $n$ steps and then solve for $n$.\n\n#### Step 1: Establish the pattern\n... |
deepscaler | [
{
"role": "user",
"content": "Let $n$ be a positive integer. Find, with proof, the least positive integer $d_{n}$ which cannot be expressed in the form \\[\\sum_{i=1}^{n}(-1)^{a_{i}}2^{b_{i}},\\]\nwhere $a_{i}$ and $b_{i}$ are nonnegative integers for each $i.$ Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "2 \\left( \\frac{4^n - 1}{3} \\right) + 1"
} | {
"split": "train",
"index": 22167,
"solution": "\nLet \\( n \\) be a positive integer. We aim to find the least positive integer \\( d_n \\) which cannot be expressed in the form \n\\[\n\\sum_{i=1}^{n}(-1)^{a_{i}}2^{b_{i}},\n\\]\nwhere \\( a_i \\) and \\( b_i \\) are nonnegative integers for each \\( i \\).\n\nW... |
deepscaler | [
{
"role": "user",
"content": "The addition below is incorrect. The display can be made correct by changing one digit $d$, wherever it occurs, to another digit $e$. Find the sum of $d$ and $e$.\n$\\begin{tabular}{ccccccc} & 7 & 4 & 2 & 5 & 8 & 6 \\\\ + & 8 & 2 & 9 & 4 & 3 & 0 \\\\ \\hline 1 & 2 & 1 & 2 & 0 &... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 22168,
"solution": "1. **Identify the Incorrect Sum**: First, we add the given numbers without changing any digits:\n - $742586 + 829430 = 1572016$\n - The provided sum is $1212016$.\n\n2. **Analyze the Incorrectness**: The provided sum $1212016$ differs significantly from the act... |
deepscaler | [
{
"role": "user",
"content": "A steamboat, 2 hours after departing from dock $A$, stops for 1 hour and then continues its journey at a speed that is 0.8 times its initial speed. As a result, it arrives at dock $B$ 3.5 hours late. If the stop had occurred 180 km further, and all other conditions remained the... | math | {
"style": "rule",
"ground_truth": "270"
} | {
"split": "train",
"index": 22169,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a bag, there are 70 balls which differ only in color: 20 red, 20 blue, 20 yellow, and the rest are black and white.\n\nWhat is the minimum number of balls that must be drawn from the bag, without seeing them, to ensure that there are at least 10 balls of one color among them... | math | {
"style": "rule",
"ground_truth": "38"
} | {
"split": "train",
"index": 22170,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many positive integers less than $201$ are multiples of either $8$ or $11$, but not both at once? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "39"
} | {
"split": "train",
"index": 22171,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given squares $ABCD$ and $EFGH$ are congruent, $AB=12$, and $H$ is located at vertex $D$ of square $ABCD$. Calculate the total area of the region in the plane covered by these squares. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "252"
} | {
"split": "train",
"index": 22172,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If five pairwise coprime distinct integers \\( a_{1}, a_{2}, \\cdots, a_{5} \\) are randomly selected from \\( 1, 2, \\cdots, n \\) and there is always at least one prime number among them, find the maximum value of \\( n \\). Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 22173,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a triangle with integer side lengths, one side is four times as long as a second side, and the length of the third side is 16. What is the greatest possible perimeter of the triangle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "41"
} | {
"split": "train",
"index": 22174,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two circles have centers at $(3,5)$ and $(20,15)$. Both circles are tangent to the x-axis. Determine the distance between the closest points of the two circles. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{389} - 20"
} | {
"split": "train",
"index": 22175,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\( a, b > 0 \\). Find the maximum values of \\( \\sqrt{\\frac{a}{2a+b}} + \\sqrt{\\frac{b}{2b+a}} \\) and \\( \\sqrt{\\frac{a}{a+2b}} + \\sqrt{\\frac{b}{b+2a}} \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{3}}{3}"
} | {
"split": "train",
"index": 22176,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Complete the table below, discover the patterns of square roots and cube roots, and apply the patterns to solve the problem.\n\n| $x$ | $\\ldots $ | $0.064$ | $0.64$ | $64$ | $6400$ | $64000$ | $\\ldots $ |\n|---------|-----------|---------|--------|-------|--------|------... | math | {
"style": "rule",
"ground_truth": "208.879"
} | {
"split": "train",
"index": 22177,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Mr. and Mrs. Zeta want to name their baby Zeta so that its monogram (first, middle, and last initials) will be in alphabetical order with no letter repeated. How many such monograms are possible? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "300"
} | {
"split": "train",
"index": 22178,
"solution": "To solve this problem, we need to determine the number of ways to choose three distinct letters from the alphabet such that they are in alphabetical order and the last initial is always 'Z'. The initials are for the first name, middle name, and last name, and they ... |
deepscaler | [
{
"role": "user",
"content": "A circle with a radius of 2 units has its center at $(0, 0)$. A circle with a radius of 7 units has its center at $(15, 0)$. A line tangent to both circles intersects the $x$-axis at $(x, 0)$ to the right of the origin. What is the value of $x$? Express your answer as a common ... | math | {
"style": "rule",
"ground_truth": "\\frac{10}{3}"
} | {
"split": "train",
"index": 22179,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are respectively $a$, $b$, $c$ with $a > b$, $a > c$. The radius of the circumcircle of $\\triangle ABC$ is $1$, and the area of $\\triangle ABC$ is $S= \\sqrt{3} \\sin B\\sin C$.\n\n$(1)$ Find the size of angle $A... | math | {
"style": "rule",
"ground_truth": "\\dfrac{ \\sqrt{3}}{4}"
} | {
"split": "train",
"index": 22180,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve for t: $3 \\cdot 3^t + \\sqrt{9 \\cdot 9^t} = 18$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 22181,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $cos(x+\\frac{π}{6})+sin(\\frac{2π}{3}+x)=\\frac{1}{2}$, calculate $sin(2x-\\frac{π}{6})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{8}"
} | {
"split": "train",
"index": 22182,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $z$ and $w$ be complex numbers such that $|z| = 1$ and $|w| = 3$. If $|z+w| = 2$, what is $ \\left | \\frac{1}{z} + \\frac{1}{w} \\right|$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"split": "train",
"index": 22183,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Six cards numbered $1$ through $6$ are to be lined up in a row. Find the number of arrangements of these six cards where one of the cards can be removed leaving the remaining five cards in either ascending or descending order. Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "52"
} | {
"split": "train",
"index": 22184,
"solution": "Similar to above, a $1-1$ correspondence between ascending and descending is established by subtracting each number from $7$.\n We note that the given condition is equivalent to \"cycling\" $123456$ for a contiguous subset of it. For example,\n$12(345)6 \\rightarro... |
deepscaler | [
{
"role": "user",
"content": "Let $n$ be an integer and $$m=(n-1001)(n-2001)(n-2002)(n-3001)(n-3002)(n-3003)$$ Given that $m$ is positive, find the minimum number of digits of $m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 22185,
"solution": "One can show that if $m>0$, then we must either have $n>3003$ or $n<1001$. If $n<1001$, each term other than $n-1001$ has absolute value at least 1000 , so $m>1000^{5}$, meaning that $m$ has at least 16 digits. However, if $n>3003$, it is clear that the minimal $m$... |
deepscaler | [
{
"role": "user",
"content": "Given that $\\cos 78^{\\circ}$ is approximately $\\frac{1}{5}$, $\\sin 66^{\\circ}$ is approximately: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.92"
} | {
"split": "train",
"index": 22186,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "(In the preliminaries of optimal method and experimental design) When using the 0.618 method to find the optimal amount to add in an experiment, if the current range of excellence is $[628, 774]$ and the good point is 718, then the value of the addition point for the current ex... | math | {
"style": "rule",
"ground_truth": "684"
} | {
"split": "train",
"index": 22187,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An entrepreneur took out a discounted loan of 12 million HUF with a fixed annual interest rate of 8%. What will be the debt after 10 years if they can repay 1.2 million HUF annually? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8523225"
} | {
"split": "train",
"index": 22188,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $g(x) = dx^3 + ex^2 + fx + g$, where $d$, $e$, $f$, and $g$ are integers. Suppose that $g(1) = 0$, $70 < g(5) < 80$, $120 < g(6) < 130$, $10000m < g(50) < 10000(m+1)$ for some integer $m$. What is $m$? Let's think step by step and put only the final answer within \\boxed{}.... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 22189,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a $5 \\times 18$ rectangle, the numbers from 1 to 90 are placed. This results in five rows and eighteen columns. In each column, the median value is chosen, and among the medians, the largest one is selected. What is the minimum possible value that this largest median can ta... | math | {
"style": "rule",
"ground_truth": "54"
} | {
"split": "train",
"index": 22190,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many non-negative real values of $x$ is $\\sqrt{144-\\sqrt[3]{x}}$ an integer? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 22191,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the expression $\\left(b^b - b(b-1)^b\\right)^b$ when $b=4$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "21381376"
} | {
"split": "train",
"index": 22192,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the numbers 2 and 8, find the product of three numbers that form a geometric sequence with these two numbers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 22193,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( 990 \\times 991 \\times 992 \\times 993 = \\overline{966428 A 91 B 40} \\), find the values of \\( \\overline{A B} \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 22194,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABCD$ be a convex quadrilateral with $AB=AD, m\\angle A = 40^{\\circ}, m\\angle C = 130^{\\circ},$ and $m\\angle ADC - m\\angle ABC = 20^{\\circ}.$ Find the measure of the non-reflex angle $\\angle CDB$ in degrees. Let's think step by step and put only the final a... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 22195,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ms. Blackwell gives an exam to two classes. The mean of the scores of the students in the morning class is $84$, and the afternoon class's mean score is $70$. The ratio of the number of students in the morning class to the number of students in the afternoon class is $\\frac{3}... | math | {
"style": "rule",
"ground_truth": "76"
} | {
"split": "train",
"index": 22196,
"solution": "1. **Identify the given information:**\n - Mean score of the morning class, $M = 84$.\n - Mean score of the afternoon class, $A = 70$.\n - Ratio of the number of students in the morning class to the afternoon class, $\\frac{m}{a} = \\frac{3}{4}$.\n\n2. **Expr... |
deepscaler | [
{
"role": "user",
"content": "Calculate $8 \\cdot 9\\frac{2}{5}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "75\\frac{1}{5}"
} | {
"split": "train",
"index": 22197,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a school there are $1200$ students. Each student is part of exactly $k$ clubs. For any $23$ students, they are part of a common club. Finally, there is no club to which all students belong. Find the smallest possible value of $k$ . Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 22198,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Reading material: In general, the equation $\\frac{1}{x}+\\frac{1}{y}=1$ is not valid, but some special real numbers can make it valid. For example, when $x=2$ and $y=2$, $\\frac{1}{2}+\\frac{1}{2}=1$ is valid. We call $(2,2)$ a \"magical number pair\" that makes $\\frac{1}{x}+... | math | {
"style": "rule",
"ground_truth": "-36"
} | {
"split": "train",
"index": 22199,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest composite number that has no prime factors less than 20. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "529"
} | {
"split": "train",
"index": 22200,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A wooden cube with edge length $n$ units (where $n$ is an integer $>2$) is painted black all over. By slices parallel to its faces, the cube is cut into $n^3$ smaller cubes each of unit length. If the number of smaller cubes with just one face painted black is equal to the numb... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 22201,
"solution": "1. **Understanding the problem**: We have a cube of side length $n$ units, painted black on all sides, and then cut into $n^3$ smaller unit cubes. We need to find $n$ such that the number of smaller cubes with exactly one face painted is equal to the number of smal... |
deepscaler | [
{
"role": "user",
"content": "A rectangular floor that is $12$ feet wide and $19$ feet long is tiled with rectangular tiles that are $1$ foot by $2$ feet. Find the number of tiles a bug visits when walking from one corner to the diagonal opposite corner. Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 22202,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Eight spheres of radius 100 are placed on a flat surface so that each sphere is tangent to two others and their centers are the vertices of a regular octagon. A ninth sphere is placed on the flat surface so that it is tangent to each of the other eight spheres. The radius of th... | math | {
"style": "rule",
"ground_truth": "152"
} | {
"split": "train",
"index": 22203,
"solution": "Isolate a triangle, with base length $200$ (a side of the octagon). This triangle is obviously isoceles. Denote the other side length as $x$. Since the interior angle is $45$ degrees (due to the shape being an octagon), then we can apply Law of Cosines to this tria... |
deepscaler | [
{
"role": "user",
"content": "What is the sum and product of the distinct prime factors of 420? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "210"
} | {
"split": "train",
"index": 22204,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$ , three lines are drawn parallel to side $BC$ dividing the altitude of the triangle into four equal parts. If the area of the second largest part is $35$ , what is the area of the whole $\\triangle ABC$ ?\n\n[asy]\ndefaultpen(linewidth(0.7)); size(120);... | math | {
"style": "rule",
"ground_truth": "560/3"
} | {
"split": "train",
"index": 22205,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( f \\) be a function taking positive integers to positive integers, such that:\n\n(i) \\( f \\) is increasing (\\( f(n + 1) > f(n) \\) for all positive integers \\( n \\))\n(ii) \\( f(mn) = f(m) f(n) \\) for all positive integers \\( m \\) and \\( n \\)\n(iii) if \\( m \... | math | {
"style": "rule",
"ground_truth": "3600"
} | {
"split": "train",
"index": 22206,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of units in the length of diagonal $DA$ of the regular hexagon shown. Express your answer in simplest radical form. [asy]\nsize(120);\ndraw((1,0)--(3,0)--(4,1.732)--(3,3.464)--(1,3.464)--(0,1.732)--cycle);\ndraw((1,0)--(1,3.464));\nlabel(\"10\",(3.5,2.598),NE);\... | math | {
"style": "rule",
"ground_truth": "10\\sqrt{3}"
} | {
"split": "train",
"index": 22207,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many pairs of consecutive integers in $\\{1000,1001,1002,\\ldots,2000\\}$ is no carrying required when the two integers are added?\n Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "156"
} | {
"split": "train",
"index": 22208,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that a point on the terminal side of angle \\(\\alpha\\) has coordinates \\((\\sin \\frac{2\\pi }{3},\\cos \\frac{2\\pi }{3})\\), find the smallest positive angle for \\(\\alpha\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{11\\pi }{6}"
} | {
"split": "train",
"index": 22209,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A car travels due east at $\\frac 23$ mile per minute on a long, straight road. At the same time, a circular storm, whose radius is $51$ miles, moves southeast at $\\frac 12\\sqrt{2}$ mile per minute. At time $t=0$, the center of the storm is $110$ miles due north of the car. A... | math | {
"style": "rule",
"ground_truth": "198"
} | {
"split": "train",
"index": 22210,
"solution": "We set up a coordinate system, with the starting point of the car at the origin. At time $t$, the car is at $\\left(\\frac 23t,0\\right)$ and the center of the storm is at $\\left(\\frac{t}{2}, 110 - \\frac{t}{2}\\right)$. Using the distance formula,\n\\begin{eqnar... |
deepscaler | [
{
"role": "user",
"content": "The numbers from 1 to 150, inclusive, are placed in a bag and a number is randomly selected from the bag. What is the probability it is neither a perfect square nor a perfect cube? Express your answer as a common fraction. Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{10}"
} | {
"split": "train",
"index": 22211,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the circumradius of cyclic hexagon $A B C D E F$, which has side lengths $A B=B C=$ $2, C D=D E=9$, and $E F=F A=12$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 22212,
"solution": "Construct point $E^{\\prime}$ on the circumcircle of $A B C D E F$ such that $D E^{\\prime}=E F=12$ and $E^{\\prime} F=D E=9$; then $\\overline{B E^{\\prime}}$ is a diameter. Let $B E^{\\prime}=d$. Then $C E^{\\prime}=\\sqrt{B E^{\\prime 2}-B C^{2}}=\\sqrt{d^{2}-4}... |
deepscaler | [
{
"role": "user",
"content": "A school has eight identical copies of a particular book. At any given time, some of these copies are in the school library and some are with students. How many different ways are there for some of the books to be in the library and the rest to be with students if at least one ... | math | {
"style": "rule",
"ground_truth": "254"
} | {
"split": "train",
"index": 22213,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number of integer solutions for the inequality \\( |x| < 3 \\pi \\) is ( ). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 22214,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest integer less than or equal to \\[\\frac{5^{80} + 3^{80}}{5^{75} + 3^{75}}?\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3124"
} | {
"split": "train",
"index": 22215,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a regular quadrilateral pyramid \\(P-ABCD\\) with a volume of 1, points \\(E\\), \\(F\\), \\(G\\), and \\(H\\) are the midpoints of segments \\(AB\\), \\(CD\\), \\(PB\\), and \\(PC\\), respectively. Find the volume of the polyhedron \\(BEG-CFH\\). Let's think step by step an... | math | {
"style": "rule",
"ground_truth": "5/16"
} | {
"split": "train",
"index": 22216,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a local election based on proportional representation, each voter is given a ballot with 10 candidate names. The voter must mark No. 1 against the candidate for whom they cast their first vote, and they may optionally fill out No. 2 through No. 10 for their subsequent prefer... | math | {
"style": "rule",
"ground_truth": "3628800"
} | {
"split": "train",
"index": 22217,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $A=\\{x|x^{3}+3x^{2}+2x > 0\\}$, $B=\\{x|x^{2}+ax+b\\leqslant 0\\}$ and $A\\cap B=\\{x|0 < x\\leqslant 2\\}$, $A\\cup B=\\{x|x > -2\\}$, then $a+b=$ ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 22218,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Sasha wrote down numbers from one to one hundred, and Misha erased some of them. Among the remaining numbers, 20 contain the digit one, 19 contain the digit two, and 30 contain neither one nor two. How many numbers did Misha erase? Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "33"
} | {
"split": "train",
"index": 22219,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nThe numerical sequence \\(a_{0}, a_{1}, a_{2}, \\ldots \\) is such that for all non-negative \\(m\\) and \\(n\\) (where \\(m \\geq n\\)), the following relation holds:\n\n\\[a_{m+n} + a_{m-n} = \\frac{1}{2} (a_{2m} + a_{2n})\\]\n\nFind \\(a_{1995}\\) if \\(a_{1} = 1\\). Let's... | math | {
"style": "rule",
"ground_truth": "1995^2"
} | {
"split": "train",
"index": 22220,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of $7$-tuples of positive integers $(a,b,c,d,e,f,g)$ that satisfy the following systems of equations: \\begin{align*} abc&=70,\\\\ cde&=71,\\\\ efg&=72. \\end{align*} Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "96"
} | {
"split": "train",
"index": 22221,
"solution": "We know that any two consecutive numbers are coprime. Using this, we can figure out that $c=1$ and $e=1$. $d$ then has to be $71$. Now we have two equations left. $ab=70$ and $fg=72$. To solve these we just need to figure out all of the factors. Doing the prime fac... |
deepscaler | [
{
"role": "user",
"content": "A list of $2018$ positive integers has a unique mode, which occurs exactly $10$ times. What is the least number of distinct values that can occur in the list? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "225"
} | {
"split": "train",
"index": 22222,
"solution": "To find the least number of distinct values in the list, we need to consider how the integers are distributed among these values. Given that the mode occurs exactly 10 times, we want to minimize the number of distinct values while ensuring that no other number appe... |
deepscaler | [
{
"role": "user",
"content": "Given that $m$ is a positive integer, and given that $\\mathop{\\text{lcm}}[40,m]=120$ and $\\mathop{\\text{lcm}}[m,45]=180$, what is $m$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 22223,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $[ABCD]$ be a convex quadrilateral with area $2014$ , and let $P$ be a point on $[AB]$ and $Q$ a point on $[AD]$ such that triangles $[ABQ]$ and $[ADP]$ have area $1$ . Let $R$ be the intersection of $[AC]$ and $[PQ]$ . Determine $\\frac{\\overline{RC}... | math | {
"style": "rule",
"ground_truth": "2013"
} | {
"split": "train",
"index": 22224,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\angle XOY = \\frac{\\pi}{2}$; $P$ is a point inside $\\angle XOY$ and we have $OP = 1; \\angle XOP = \\frac{\\pi}{6}.$ A line passes $P$ intersects the Rays $OX$ and $OY$ at $M$ and $N$. Find the maximum value of $OM + ON - MN.$ Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 22225,
"solution": "\nGiven that \\(\\angle XOY = \\frac{\\pi}{2}\\), \\(P\\) is a point inside \\(\\angle XOY\\) with \\(OP = 1\\) and \\(\\angle XOP = \\frac{\\pi}{6}\\). We need to find the maximum value of \\(OM + ON - MN\\) where a line passing through \\(P\\) intersects the rays... |
deepscaler | [
{
"role": "user",
"content": "Let $a,$ $b,$ $c$ be distinct, nonzero real numbers such that\n\\[a + \\frac{1}{b} = b + \\frac{1}{c} = c + \\frac{1}{a}.\\]Find $|abc|.$\n\nNote: Intermediate Algebra writing problem, week 12. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 22226,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $(a+b)(\\sin A - \\sin B) = (c-b)\\sin C.$ \n(1) Determine the measure of angle $A$. \n(2) If $2c=3b$ and the area of $\\triangle ABC$ is $6 \\sqrt{3}$, find the value of $a... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{21}}{3}"
} | {
"split": "train",
"index": 22227,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( f(x) \\) be a function from \\( \\mathbf{R} \\) to \\( \\mathbf{R} \\), and for any real numbers, it holds that\n$$\nf(x^{2}+x) + 2 f(x^{2}-3x+2) = 9x^{2} - 15x,\n$$\nthen the value of \\( f(50) \\) is ( ). Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "146"
} | {
"split": "train",
"index": 22228,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the digit in the thousandths place of the decimal equivalent of $\\frac{3}{16}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 22229,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a unique two-digit positive integer $t$ for which the last two digits of $11\\cdot t$ are $36$.\n\nWhat is $t$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "76"
} | {
"split": "train",
"index": 22230,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the constant term in the expansion of \\\\((x+ \\frac {2}{x}+1)^{6}\\\\) (Answer with a numerical value) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "581"
} | {
"split": "train",
"index": 22231,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of all positive integers $m$ such that $\\frac{13!}{m}$ is a perfect square can be written as $2^a3^b5^c7^d11^e13^f,$ where $a,b,c,d,e,$ and $f$ are positive integers. Find $a+b+c+d+e+f.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "012"
} | {
"split": "train",
"index": 22232,
"solution": "We first rewrite $13!$ as a prime factorization, which is $2^{10}\\cdot3^5\\cdot5^2\\cdot7\\cdot11\\cdot13.$\n For the fraction to be a square, it needs each prime to be an even power. This means $m$ must contain $7\\cdot11\\cdot13$. Also, $m$ can contain any even ... |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\sin (2x+ \\frac {\\pi}{3})$. \n$(1)$ If $x\\in(- \\frac {\\pi}{6},0]$, find the minimum value of $4f(x)+ \\frac {1}{f(x)}$ and determine the value of $x$ at this point; \n$(2)$ If $(a\\in(- \\frac {\\pi}{2},0),f( \\frac {a}{2}+ \\frac {\\pi}{3})= \\... | math | {
"style": "rule",
"ground_truth": "\\frac {3 \\sqrt {3}-4}{10}"
} | {
"split": "train",
"index": 22233,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $n\\ge 2$ be a given integer. Find the greatest value of $N$, for which the following is true: there are infinitely many ways to find $N$ consecutive integers such that none of them has a divisor greater than $1$ that is a perfect $n^{\\mathrm{th}}$ power. Let's think step ... | math | {
"style": "rule",
"ground_truth": "2^n - 1"
} | {
"split": "train",
"index": 22234,
"solution": "\nLet \\( n \\geq 2 \\) be a given integer. We are tasked with finding the greatest value of \\( N \\) such that there are infinitely many ways to select \\( N \\) consecutive integers where none of them has a divisor greater than 1 that is a perfect \\( n^{\\text{... |
deepscaler | [
{
"role": "user",
"content": "Two of the altitudes of the scalene triangle $ABC$ have length $4$ and $12$. If the length of the third altitude is also an integer, what is the biggest it can be?\n$\\textbf{(A)}\\ 4\\qquad \\textbf{(B)}\\ 5\\qquad \\textbf{(C)}\\ 6\\qquad \\textbf{(D)}\\ 7\\qquad \\textbf{(E)... | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 22235,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Insert a digit in the middle of a two-digit number to form a three-digit number. For some two-digit numbers, the resulting three-digit number can be $k$ times the original two-digit number (where $k$ is a positive integer). What is the maximum value of $k$? Let's think step by ... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 22236,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 2008 red cards and 2008 white cards. 2008 players sit down in circular toward the inside of the circle in situation that 2 red cards and 2 white cards from each card are delivered to each person. Each person conducts the following procedure in one turn as follows.\r\... | math | {
"style": "rule",
"ground_truth": "1004"
} | {
"split": "train",
"index": 22237,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On December 8, 2022, the Joint Prevention and Control Mechanism of the State Council held a press conference to introduce further optimization of the implementation of epidemic prevention and control measures. It was emphasized that individuals are responsible for their own hea... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{6}"
} | {
"split": "train",
"index": 22238,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $n$ be a positive integer. In how many ways can a $4 \\times 4n$ grid be tiled with the following tetromino?\n[asy]\nsize(4cm);\ndraw((1,0)--(3,0)--(3,1)--(0,1)--(0,0)--(1,0)--(1,2)--(2,2)--(2,0));\n[/asy] Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "2^{n+1} - 2"
} | {
"split": "train",
"index": 22239,
"solution": "\nWe are tasked with determining the number of ways to tile a \\(4 \\times 4n\\) grid using the \\(L\\)-shaped tetromino described in the problem. The shape of the \\(L\\)-shaped tetromino can cover precisely 4 unit squares.\n\n### Step-by-step Analysis\n\n1. **Und... |
deepscaler | [
{
"role": "user",
"content": "Find all positive integers $ k$ with the following property: There exists an integer $ a$ so that $ (a\\plus{}k)^{3}\\minus{}a^{3}$ is a multiple of $ 2007$ . Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "669"
} | {
"split": "train",
"index": 22240,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The digits 1, 2, 3, 4 and 9 are each used once to form the smallest possible even five-digit number. The digit in the tens place is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 22241,
"solution": "1. **Identify the requirement for the number to be even**: The number must end in an even digit. The available even digits are 2 and 4.\n\n2. **Determine the smallest possible even digit for the units place**: To form the smallest number, we prefer the smallest dig... |
deepscaler | [
{
"role": "user",
"content": "On a computer keyboard, the key for the digit 1 is not working. For example, if you try to type the number 1231234, only the number 23234 will actually print.\n\nSasha tried to type an 8-digit number, but only 202020 was printed. How many 8-digit numbers satisfy this condition?... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 22242,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate: $|1-\\sqrt{2}|+(\\frac{1}{2})^{-2}-\\left(\\pi -2023\\right)^{0}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{2} + 2"
} | {
"split": "train",
"index": 22243,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $t$ be a parameter that varies over all real numbers. Any parabola of the form\n\\[y = 3x^2 + tx - 2t\\]passes through a fixed point. Find this fixed point. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(2,12)"
} | {
"split": "train",
"index": 22244,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the parabola $y=\\frac{1}{4}x^2$ and the circle $C: (x-1)^2+(y-2)^2=r^2$ $(r > 0)$ share a common point $P$. If the tangent line to the parabola at point $P$ also touches circle $C$, find the value of $r$. Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "r = \\sqrt{2}"
} | {
"split": "train",
"index": 22245,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Uri buys two burgers and a soda for $\\$2.10$, and Gen buys a burger and two sodas for $\\$2.40$. How many cents does a soda cost? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"split": "train",
"index": 22246,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the numbers from 100 to 999, calculate how many numbers have digits in strictly increasing or strictly decreasing order. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "204"
} | {
"split": "train",
"index": 22247,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the largest integer less than 80 that leaves a remainder of 3 when divided by 5. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "78"
} | {
"split": "train",
"index": 22248,
"solution": ""
} |
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