data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Suppose that $y = \\frac34x$ and $x^y = y^x$. The quantity $x + y$ can be expressed as a rational number $\\frac {r}{s}$, where $r$ and $s$ are relatively prime positive integers. Find $r + s$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "529"
} | {
"split": "train",
"index": 3100,
"solution": "Substitute $y = \\frac34x$ into $x^y = y^x$ and solve. \\[x^{\\frac34x} = \\left(\\frac34x\\right)^x\\] \\[x^{\\frac34x} = \\left(\\frac34\\right)^x \\cdot x^x\\] \\[x^{-\\frac14x} = \\left(\\frac34\\right)^x\\] \\[x^{-\\frac14} = \\frac34\\] \\[x = \\frac{256}{81}\... |
deepscaler | [
{
"role": "user",
"content": "Bill buys a stock that decreases by $20\\%$ on the first day, and then on the second day the stock increases by $30\\%$ of its value at the end of the first day. What was the overall percent increase in Bill's stock over the two days? Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 3101,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\( f(x) = 2^x \\) and \\( g(x) = \\log_{\\sqrt{2}} (8x) \\), find the value of \\( x \\) that satisfies \\( f[g(x)] = g[f(x)] \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1 + \\sqrt{385}}{64}"
} | {
"split": "train",
"index": 3102,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=2 \\sqrt {3}\\tan ( \\frac {x}{2}+ \\frac {π}{4})\\cos ^{2}( \\frac {x}{2}+ \\frac {π}{4})-\\sin (x+π)$.\n(I) Find the domain and the minimum positive period of $f(x)$;\n(II) If the graph of $f(x)$ is shifted to the right by $\\frac {π}{6}$ units to obt... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 3103,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In rectangle $ABCD,$ $P$ is a point on side $\\overline{BC}$ such that $BP = 12$ and $CP = 4.$ If $\\tan \\angle APD = 2,$ then find $AB.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 3104,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "22. Let the function $f : \\mathbb{Z} \\to \\mathbb{Z}$ take only integer inputs and have integer outputs. For any integers $x$ and $y$ , f satisfies $$ f(x) + f(y) = f(x + 1) + f(y - 1) $$ If $f(2016) = 6102$ and $f(6102) = 2016$ , what is $f(1)$ ?\n\n23. Let $d$ ... | math | {
"style": "rule",
"ground_truth": "8117"
} | {
"split": "train",
"index": 3105,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "All positive odd numbers are arranged in the following table (the number of numbers in the next row is twice the number of numbers in the previous row) \nFirst row 1 \nSecond row 3 5 \nThird row 7 9 11 13 \n… \nThen, the third number in the sixth row is ． ... | math | {
"style": "rule",
"ground_truth": "67"
} | {
"split": "train",
"index": 3106,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The product of $\\sqrt[3]{4}$ and $\\sqrt[4]{8}$ equals Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt[12]{32}"
} | {
"split": "train",
"index": 3107,
"solution": "1. **Express the radicals in terms of exponents:**\n - The cube root of 4 can be written as $\\sqrt[3]{4} = 4^{1/3}$. Since $4 = 2^2$, we have $4^{1/3} = (2^2)^{1/3} = 2^{2/3}$.\n - The fourth root of 8 can be written as $\\sqrt[4]{8} = 8^{1/4}$. Since $8 = 2^3$... |
deepscaler | [
{
"role": "user",
"content": "Given:\n$$\n\\begin{array}{l}\nA \\cup B \\cup C=\\{a, b, c, d, e, f\\}, \\\\\nA \\cap B=\\{a, b, c, d\\}, \\\\\nc \\in A \\cap B \\cap C .\n\\end{array}\n$$\n\nHow many sets $\\{A, B, C\\}$ satisfy the given conditions? Let's think step by step and put only the final answer wi... | math | {
"style": "rule",
"ground_truth": "200"
} | {
"split": "train",
"index": 3108,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the distance \\( B_{1} H \\) from point \\( B_{1} \\) to the line \\( D_{1} B \\), given \\( B_{1}(5, 8, -3) \\), \\( D_{1}(-3, 10, -5) \\), and \\( B(3, 4, 1) \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{6}"
} | {
"split": "train",
"index": 3109,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A drawer in a darkened room contains $100$ red socks, $80$ green socks, $60$ blue socks and $40$ black socks. A youngster selects socks one at a time from the drawer but is unable to see the color of the socks drawn. What is the smallest number of socks that must be selected to... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 3110,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(2x+1)=x^{2}-2x$, determine the value of $f(\\sqrt{2})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5-4\\sqrt{2}}{4}"
} | {
"split": "train",
"index": 3111,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given an arithmetic-geometric sequence $\\{a\\_n\\}$ with a sum of the first $n$ terms denoted as $S\\_n$ and a common ratio of $\\frac{3}{2}$.\n(1) If $S\\_4 = \\frac{65}{24}$, find $a\\_1$;\n(2) If $a\\_1=2$, $c\\_n = \\frac{1}{2}a\\_n + bn$, and $c\\_2$, $c\\_4$, $c\\_5$ for... | math | {
"style": "rule",
"ground_truth": "-\\frac{3}{16}"
} | {
"split": "train",
"index": 3112,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At Academic Academy, to pass an algebra test you must score at least $80\\%$. If there are 35 problems on the test, what is the greatest number you can miss and still pass? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 3113,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x,$ $y,$ $z$ be positive real numbers. Find the set of all possible values of\n\\[f(x,y,z) = \\frac{x}{x + y} + \\frac{y}{y + z} + \\frac{z}{z + x}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(1,2)"
} | {
"split": "train",
"index": 3114,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle ABC, $\\sin A = \\frac{4}{5}$, $\\cos B = \\frac{5}{13}$, and $c=56$. Find $\\sin C$ and the circumference of the circumscribed circle of triangle ABC. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "65\\pi"
} | {
"split": "train",
"index": 3115,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve the equations:\n1. $2x^{2}+4x+1=0$ (using the method of completing the square)\n2. $x^{2}+6x=5$ (using the formula method) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3-\\sqrt{14}"
} | {
"split": "train",
"index": 3116,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the positive difference between $\\frac{8^2 - 8^2}{8}$ and $\\frac{8^2 \\times 8^2}{8}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "512"
} | {
"split": "train",
"index": 3117,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The greatest common divisor of 30 and some number between 70 and 80 is 10. What is the number, if the least common multiple of these two numbers is also between 200 and 300? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "80"
} | {
"split": "train",
"index": 3118,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The height of a right-angled triangle, dropped to the hypotenuse, divides this triangle into two triangles. The distance between the centers of the inscribed circles of these triangles is 1. Find the radius of the inscribed circle of the original triangle. Let's think step by s... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 3119,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve for $x$ in the equation $ \\frac35 \\cdot \\frac19 \\cdot x = 6$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"split": "train",
"index": 3120,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a tetrahedron \\( PABC \\), \\(\\angle APB = \\angle BPC = \\angle CPA = 90^\\circ\\). The dihedral angles formed between \\(\\triangle PBC, \\triangle PCA, \\triangle PAB\\), and \\(\\triangle ABC\\) are denoted as \\(\\alpha, \\beta, \\gamma\\), respectively. Consider the ... | math | {
"style": "rule",
"ground_truth": "(2)"
} | {
"split": "train",
"index": 3121,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the smallest positive integer such that, no matter how you rearrange its digits (in base ten), the resulting number is a multiple of 63. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "111888"
} | {
"split": "train",
"index": 3122,
"solution": "First, the number must be a multiple of 9 and 7. The first is easy to check and holds for all permutations. Note that when two adjacent digits $a$ and $b$ are swapped, the number changes by $9(a-b) \\cdot 10^{k}$ (we disregard sign), so $9(a-b)$ must also be a multi... |
deepscaler | [
{
"role": "user",
"content": "What is the constant term in the expansion of $\\left(\\sqrt{x}+\\dfrac5x\\right)^{9}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10500"
} | {
"split": "train",
"index": 3123,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "a) Is the equation \\( A = B \\) true if\n\n\\[ \nA = \\frac{1 + \\frac{1 + \\frac{1 + \\frac{1}{2}}{4}}{2}}{2}, \\quad B = \\frac{1}{1 + \\frac{1}{2 + \\frac{1}{1 + \\frac{1}{2 + \\frac{1}{4}}}}} \n\\]\n\nb) Which is greater between the numbers \\( \\frac{23}{31} \\) and \\( \... | math | {
"style": "rule",
"ground_truth": "0.7433"
} | {
"split": "train",
"index": 3124,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $D$ be the set of divisors of 100. Let $Z$ be the set of integers between 1 and 100, inclusive. Mark chooses an element $d$ of $D$ and an element $z$ of $Z$ uniformly at random. What is the probability that $d$ divides $z$? Let's think step by step and put only the final an... | math | {
"style": "rule",
"ground_truth": "\\frac{217}{900}"
} | {
"split": "train",
"index": 3125,
"solution": "As $100=2^{2} \\cdot 5^{2}$, there are $3 \\cdot 3=9$ divisors of 100, so there are 900 possible pairs of $d$ and $z$ that can be chosen. If $d$ is chosen, then there are $\\frac{100}{d}$ possible values of $z$ such that $d$ divides $z$, so the total number of valid... |
deepscaler | [
{
"role": "user",
"content": "If I have a $5\\times 5$ chess board, in how many ways can I place five distinct pawns on the board such that each column and row of the board contains no more than one pawn? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "14400"
} | {
"split": "train",
"index": 3126,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Point $Q$ is located inside triangle $DEF$ such that angles $QDE, QEF,$ and $QFD$ are all congruent. The sides of the triangle have lengths $DE = 15, EF = 16,$ and $FD = 17.$ Find $\\tan \\angle QDE.$ Let's think step by step and put only the final answer within \\boxed{}."
}... | math | {
"style": "rule",
"ground_truth": "\\frac{272}{385}"
} | {
"split": "train",
"index": 3127,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A painting $20$\" X $30$\" is to be framed where the frame border at the top and bottom is three times as wide as the frame on the sides. If the total area of the frame (not including the painting) equals twice the area of the painting itself, find the ratio of the smaller dime... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 3128,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many possible sequences of the experiment are there, given that 6 procedures need to be implemented in sequence, procedure A can only appear in the first or last step, and procedures B and C must be adjacent when implemented? Let's think step by step and put only the final ... | math | {
"style": "rule",
"ground_truth": "96"
} | {
"split": "train",
"index": 3129,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "As shown in the diagram, the area of parallelogram \\(ABCD\\) is 60. The ratio of the areas of \\(\\triangle ADE\\) and \\(\\triangle AEB\\) is 2:3. Find the area of \\(\\triangle BEF\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 3130,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a regular tetrahedron \\( P-ABCD \\) with lateral and base edge lengths both equal to 4, find the total length of all curve segments formed by a moving point on the surface at a distance of 3 from vertex \\( P \\). Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "6\\pi"
} | {
"split": "train",
"index": 3131,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\cos x\\cdot \\sin \\left(x+\\frac{\\pi }{3}\\right)-\\sqrt{3}\\cos ^{2}x+\\frac{\\sqrt{3}}{4}$, where $x\\in R$.\n\n(1) Find the smallest positive period of $f(x)$;\n\n(2) Find the maximum and minimum values of $f(x)$ on the closed interval $\\left[-\... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{2}"
} | {
"split": "train",
"index": 3132,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of the first four terms of an arithmetic progression, as well as the sum of the first seven terms, are natural numbers. Furthermore, its first term \\(a_1\\) satisfies the inequality \\(a_1 \\leq \\frac{2}{3}\\). What is the greatest value that \\(a_1\\) can take? Let's... | math | {
"style": "rule",
"ground_truth": "9/14"
} | {
"split": "train",
"index": 3133,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a certain school, there are $3$ times as many boys as girls and $9$ times as many girls as teachers. Using the letters $b, g, t$ to represent the number of boys, girls, and teachers, respectively, then the total number of boys, girls, and teachers can be represented by the e... | math | {
"style": "rule",
"ground_truth": "\\frac{37b}{27}"
} | {
"split": "train",
"index": 3134,
"solution": "1. **Identify relationships**: \n Given that there are $3$ times as many boys as girls, we can write:\n \\[\n b = 3g\n \\]\n Also, there are $9$ times as many girls as teachers, so:\n \\[\n g = 9t \\quad \\text{or equivalently} \\quad t = \\frac{g}{9}\... |
deepscaler | [
{
"role": "user",
"content": "In the diagram below, we have $AB = 24$ and $\\angle ADB =90^\\circ$. If $\\sin A = \\frac23$ and $\\sin C = \\frac13$, then what is $DC$?\n\n\n[asy]\npair A,B,C,D;\nA = (0,0);\nB = (8*sqrt(5),16);\nD = (8*sqrt(5),0);\nC = (8*sqrt(5) + 32*sqrt(2),0);\ndraw(D--B--A--C--B);\nlab... | math | {
"style": "rule",
"ground_truth": "32\\sqrt{2}"
} | {
"split": "train",
"index": 3135,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Cubes. As is known, the whole space can be filled with equal cubes. At each vertex, eight cubes will converge. Therefore, by appropriately truncating the vertices of the cubes and joining the adjacent truncated parts into a single body, it is possible to fill the space with reg... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"split": "train",
"index": 3136,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of $102^{4} - 4 \\cdot 102^{3} + 6 \\cdot 102^2 - 4 \\cdot 102 + 1$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "104060401"
} | {
"split": "train",
"index": 3137,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A_1A_2A_3\\ldots A_{12}$ be a dodecagon ($12$-gon). Three frogs initially sit at $A_4,A_8,$ and $A_{12}$. At the end of each minute, simultaneously, each of the three frogs jumps to one of the two vertices adjacent to its current position, chosen randomly and independently... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 3138,
"solution": "We can solve the problem by removing $1$ frog, and calculate the expected time for the remaining $2$ frogs. In the original problem, when the movement stops, $2$ of the $3$ frogs meet. Because the $3$ frogs cannot meet at one vertex, the probability that those two s... |
deepscaler | [
{
"role": "user",
"content": "Given two groups of numerical sequences, each containing 15 arithmetic progressions with 10 terms each. The first terms of the progressions in the first group are $1, 2, 3, \\ldots, 15$, and their differences are respectively $2, 4, 6, \\ldots, 30$. The second group of progress... | math | {
"style": "rule",
"ground_truth": "160/151"
} | {
"split": "train",
"index": 3139,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A, B, and C are three people passing a ball to each other. The first pass is made by A, who has an equal chance of passing the ball to either of the other two people. After three passes, the probability that the ball is still with A is _______. Let's think step by step and put ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 3140,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $ABC$ is an isosceles right triangle with the measure of angle $A$ equal to 90 degrees. The length of segment $AC$ is 6 cm. What is the area of triangle $ABC$, in square centimeters? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 3141,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $n\\geq 2$ be a positive integer and let $a_1,a_2,...,a_n\\in[0,1]$ be real numbers. Find the maximum value of the smallest of the numbers: \\[a_1-a_1a_2, \\ a_2-a_2a_3,...,a_n-a_na_1.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1/4"
} | {
"split": "train",
"index": 3142,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the parametric equation of line $l$ as $$\\begin{cases} \\left.\\begin{matrix}x= \\frac {1}{2}t \\\\ y=1+ \\frac { \\sqrt {3}}{2}t\\end{matrix}\\right.\\end{cases}$$ (where $t$ is the parameter), and the polar equation of curve $C$ as $\\rho=2 \\sqrt {2}\\sin(\\theta+ \\f... | math | {
"style": "rule",
"ground_truth": "\\sqrt {5}"
} | {
"split": "train",
"index": 3143,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A numerical value is assigned to each letter of the alphabet. The value of a word is determined by adding up the numerical values of each of its letters. The value of SET is 2, the value of HAT is 7, the value of TASTE is 3, and the value of MAT is 4. What is the value of the w... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 3144,
"solution": "From the given information, we know that $S+E+T=2$, $H+A+T=7$, $T+A+S+T+E=3$, and $M+A+T=4$. Since $T+A+S+T+E=3$ and $S+E+T=2$, then $T+A=3-2=1$. Since $H+A+T=7$ and $T+A=1$, then $H=7-1=6$. Since $M+A+T=4$ and $H=7$, then $M+(A+T)+H=4+6=10$. Therefore, the value of... |
deepscaler | [
{
"role": "user",
"content": "Given that Ms. Demeanor's class consists of 50 students, more than half of her students bought crayons from the school bookstore, each buying the same number of crayons, with each crayon costing more than the number of crayons bought by each student, and the total cost for all ... | math | {
"style": "rule",
"ground_truth": "37"
} | {
"split": "train",
"index": 3145,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The coefficient of the $x$ term in the expansion of $(x^{2}-x-2)^{3}$ is what value? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-12"
} | {
"split": "train",
"index": 3146,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Give an example of an expression consisting of ones, parentheses, the symbols \"+\", and \"×\" such that:\n\n- Its value is equal to 11\n- If in this expression all \"+\" signs are replaced with \"×\" signs, and all \"×\" signs are replaced with \"+\" signs, it will still resul... | math | {
"style": "rule",
"ground_truth": "1+1+1+1+1+1+1+1+1+1+1"
} | {
"split": "train",
"index": 3147,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Lead used to make twelve solid lead balls, each with a radius of 2 cm, is reused to form a single larger solid lead sphere. What is the radius of this larger sphere? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt[3]{96}"
} | {
"split": "train",
"index": 3148,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given two circles that intersect at two points $(2,3)$ and $(m,2)$, and both circle centers lie on the line $x+y+n=0$. Find the value of $m+n$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 3149,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If \\(x\\) and \\(y\\) are positive real numbers such that \\(6x^2 + 12xy + 6y^2 = x^3 + 3x^2 y + 3xy^2\\), find the value of \\(x\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{24}{7}"
} | {
"split": "train",
"index": 3150,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The adjacent map is part of a city: the small rectangles are blocks, and the paths in between are streets. \nEach morning, a student walks from intersection $A$ to intersection $B$, always walking along streets shown, \nand always going east or south. For variety, at each inter... | math | {
"style": "rule",
"ground_truth": "\\frac{21}{32}"
} | {
"split": "train",
"index": 3151,
"solution": "To solve this problem, we need to calculate the probability that the student passes through intersection $C$ on his way from $A$ to $B$. We will use combinatorial methods to count the number of valid paths and probability theory to determine the likelihood of each p... |
deepscaler | [
{
"role": "user",
"content": "Bob knows that Alice has 2021 secret positive integers $x_{1}, \\ldots, x_{2021}$ that are pairwise relatively prime. Bob would like to figure out Alice's integers. He is allowed to choose a set $S \\subseteq\\{1,2, \\ldots, 2021\\}$ and ask her for the product of $x_{i}$ over ... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 3152,
"solution": "In general, Bob can find the values of all $n$ integers asking only $\\left\\lfloor\\log _{2} n\\right\\rfloor+1$ queries. For each of Alice's numbers $x_{i}$, let $Q_{i}$ be the set of queries $S$ such that $i \\in S$. Notice that all $Q_{i}$ must be nonempty and d... |
deepscaler | [
{
"role": "user",
"content": "Two cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is a $\\diamondsuit$ and the second card is an ace? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{1}{52}"
} | {
"split": "train",
"index": 3153,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Dr. Fu Manchu has a bank account that has an annual interest rate of 6 percent, but it compounds monthly. If this is equivalent to a bank account that compounds annually at a rate of $r$ percent, then what is $r$? (Give your answer to the nearest hundredth.) Let's think step ... | math | {
"style": "rule",
"ground_truth": "6.17"
} | {
"split": "train",
"index": 3154,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find $7463_{8} - 3254_{8}$. Express your answer first in base $8$, then convert it to base $10$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2183_{10}"
} | {
"split": "train",
"index": 3155,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all real numbers \\( p \\) such that the cubic equation \\( 5x^3 - 5(p+1)x^2 + (71p-1)x + 1 = 66p \\) has two roots that are natural numbers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "76"
} | {
"split": "train",
"index": 3156,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The bases \\( AB \\) and \\( CD \\) of trapezoid \\( ABCD \\) are 65 and 31, respectively, and its diagonals are mutually perpendicular. Find the dot product of vectors \\( \\overrightarrow{AD} \\) and \\( \\overrightarrow{BC} \\). Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "2015"
} | {
"split": "train",
"index": 3157,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Construct a square \\(A B C D\\) with side length \\(6 \\text{ cm}\\). Construct a line \\(p\\) parallel to the diagonal \\(A C\\) passing through point \\(D\\). Construct a rectangle \\(A C E F\\) such that vertices \\(E\\) and \\(F\\) lie on the line \\(p\\).\n\nUsing the giv... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 3158,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An urn contains $4$ green balls and $6$ blue balls. A second urn contains $16$ green balls and $N$ blue balls. A single ball is drawn at random from each urn. The probability that both balls are of the same color is $0.58$. Find $N$.\n Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 3159,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $y = f(x) + x^2$ is an odd function, and $f(1) = 1$, determine the value of $g(x) = f(x) + 2$ when $x = -1$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 3160,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Assuming that the new demand is given by \\( \\frac{1}{1+ep} \\), where \\( p = 0.20 \\) and \\( e = 1.5 \\), calculate the proportionate decrease in demand. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.23077"
} | {
"split": "train",
"index": 3161,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The poetry lecture lasted 2 hours and $m$ minutes. The positions of the hour and minute hands on the clock at the end of the lecture are exactly swapped from their positions at the beginning of the lecture. If $[x]$ denotes the integer part of the decimal number $x$, find $[m]=... | math | {
"style": "rule",
"ground_truth": "46"
} | {
"split": "train",
"index": 3162,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate $\\cfrac{\\left\\lceil\\cfrac{17}{7}-\\left\\lceil\\cfrac{27}{17}\\right\\rceil\\right\\rceil}{\\left\\lceil\\cfrac{27}{7}+\\left\\lceil\\cfrac{7\\cdot17}{27}\\right\\rceil\\right\\rceil}$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{9}"
} | {
"split": "train",
"index": 3163,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nFind the root of the following equation to three significant digits:\n\n$$\n(\\sqrt{5}-\\sqrt{2})(1+x)=(\\sqrt{6}-\\sqrt{3})(1-x)\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-0.068"
} | {
"split": "train",
"index": 3164,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In polar coordinates, the point $\\left( -2, \\frac{3 \\pi}{8} \\right)$ is equivalent to what other point, in the standard polar coordinate representation? Enter your answer in the form $(r,\\theta),$ where $r > 0$ and $0 \\le \\theta < 2 \\pi.$ Let's think step by step and p... | math | {
"style": "rule",
"ground_truth": "\\left( 2, \\frac{11 \\pi}{8} \\right)"
} | {
"split": "train",
"index": 3165,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Name the greatest whole number less than $100$ that has an odd number of positive factors. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "81"
} | {
"split": "train",
"index": 3166,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Seven thousand twenty-two can be expressed as the sum of a two-digit number and a four-digit number. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7022"
} | {
"split": "train",
"index": 3167,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The value of $\\frac{x}{2}$ is less than the value of $x^{2}$. The value of $x^{2}$ is less than the value of $x$. Which of the following could be a value of $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 3168,
"solution": "Since $x^{2}<x$ and $x^{2} \\geq 0$, then $x>0$ and so it cannot be the case that $x$ is negative. Thus, neither (D) nor (E) is the answer. Since $x^{2}<x$, then we cannot have $x>1$. This is because when $x>1$, we have $x^{2}>x$. Thus, (A) is not the answer and so ... |
deepscaler | [
{
"role": "user",
"content": "Compute\n\\[\\sin^2 6^\\circ + \\sin^2 12^\\circ + \\sin^2 18^\\circ + \\dots + \\sin^2 174^\\circ.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15.5"
} | {
"split": "train",
"index": 3169,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\frac{\\cos 2x}{\\sin(x+\\frac{π}{4})}$.\n(I) Find the domain of the function $f(x)$;\n(II) If $f(x)=\\frac{4}{3}$, find the value of $\\sin 2x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{9}"
} | {
"split": "train",
"index": 3170,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An Englishman owns a plot of land in Russia. He knows that, in the units familiar to him, the size of his plot is three acres. The cost of the land is 250,000 rubles per hectare. It is known that 1 acre = 4840 square yards, 1 yard = 0.9144 meters, and 1 hectare = 10,000 square ... | math | {
"style": "rule",
"ground_truth": "303514"
} | {
"split": "train",
"index": 3171,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest positive number $\\lambda $ , such that for any complex numbers ${z_1},{z_2},{z_3}\\in\\{z\\in C\\big| |z|<1\\}$ ,if $z_1+z_2+z_3=0$, then $$\\left|z_1z_2 +z_2z_3+z_3z_1\\right|^2+\\left|z_1z_2z_3\\right|^2 <\\lambda .$$ Let's think step by step and put only ... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 3172,
"solution": "\nWe aim to find the smallest positive number \\(\\lambda\\) such that for any complex numbers \\(z_1, z_2, z_3 \\in \\{z \\in \\mathbb{C} \\mid |z| < 1\\}\\) with \\(z_1 + z_2 + z_3 = 0\\), the following inequality holds:\n\\[\n\\left|z_1z_2 + z_2z_3 + z_3z_1\\righ... |
deepscaler | [
{
"role": "user",
"content": "Through a point $P$ inside the $\\triangle ABC$, a line is drawn parallel to the base $AB$, dividing the triangle into two regions where the area of the region containing the vertex $C$ is three times the area of the region adjacent to $AB$. If the altitude to $AB$ has a length... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 3173,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the equation $\\frac{1}{j} + \\frac{1}{k} = \\frac{1}{3}$, both $j$ and $k$ are positive integers. What is the sum of all possible values for $k$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 3174,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From 125 sugar cubes, a $5 \\times 5 \\times 5$ cube was made. Ponchik picked all the cubes that have an odd number of neighbors and ate them (neighbors are those cubes that share a face). How many cubes did Ponchik eat in total? Let's think step by step and put only the final ... | math | {
"style": "rule",
"ground_truth": "62"
} | {
"split": "train",
"index": 3175,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the sequence $\\{a_n\\}$ with the sum of the first $n$ terms $S_n=1-5+9-13+17-21+......+{(-1)}^{n-1}(4n-3)$, calculate the value of $S_{15}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "29"
} | {
"split": "train",
"index": 3176,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the radius of a sphere is 24cm, and the height of a cone is equal to the diameter of this sphere, and the surface area of the sphere is equal to the surface area of the cone, then the volume of this cone is \\_\\_\\_\\_\\_\\_ cm<sup>3</sup>. Let's think step by step ... | math | {
"style": "rule",
"ground_truth": "12288\\pi"
} | {
"split": "train",
"index": 3177,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The perimeter of a rectangle is 56 meters. The ratio of its length to its width is 4:3. What is the length in meters of a diagonal of the rectangle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 3178,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, the lengths of sides $a$, $b$, and $c$ correspond to angles $A$, $B$, and $C$ respectively. Given that $(2b - \\sqrt{3}c)\\cos A = \\sqrt{3}a\\cos C$.\n\n1. Find the measure of angle $A$.\n2. If angle $B = \\frac{\\pi}{6}$ and the length of the median $AM$ on... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 3179,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "a) Calculate the number of triangles whose three vertices are vertices of the cube.\n\nb) How many of these triangles are not contained in a face of the cube? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 3180,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Pat Peano has plenty of 0's, 1's, 3's, 4's, 5's, 6's, 7's, 8's and 9's, but he has only twenty-two 2's. How far can he number the pages of his scrapbook with these digits? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "119"
} | {
"split": "train",
"index": 3181,
"solution": "To determine how far Pat Peano can number the pages of his scrapbook using only twenty-two 2's, we need to count how many times the digit '2' appears in each number from 1 onwards.\n\n1. **Counting the '2's in one-digit numbers (1-9):**\n - The only one-digit numb... |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system $xOy$, triangle $\\triangle ABC$ has vertices $A(-6, 0)$ and $C(6, 0)$. Vertex $B$ lies on the left branch of the hyperbola $\\frac{x^2}{25} - \\frac{y^2}{11} = 1$. Find the value of $\\frac{\\sin A - \\sin C}{\\sin B}$. Let's think step by st... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{6}"
} | {
"split": "train",
"index": 3182,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jo and Blair take turns counting. Jo starts by saying 1, and each time Blair follows by saying the last number Jo said plus 2, while Jo says the last number Blair said plus 3. Determine the 20th number said. Let's think step by step and put only the final answer within \\boxed{... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 3183,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many two-digit numbers have digits whose sum is a prime number? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 3184,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The product of three consecutive positive integers is $8$ times their sum. What is the sum of their squares? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "77"
} | {
"split": "train",
"index": 3185,
"solution": "1. **Define the integers**: Let the three consecutive positive integers be $a-1$, $a$, and $a+1$. \n\n2. **Express the sum and product**: \n - The sum of these integers is $(a-1) + a + (a+1) = 3a$.\n - The product of these integers is $(a-1)a(a+1)$.\n\n3. **Set ... |
deepscaler | [
{
"role": "user",
"content": "A container with a capacity of 100 liters is filled with pure alcohol. After pouring out a portion of the alcohol, the container is filled with water. The mixture is then stirred thoroughly, and an amount of liquid equal to the first portion poured out is poured out again. The ... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 3186,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC, AB = 10, BC = 8, CA = 7$ and side $BC$ is extended to a point $P$ such that $\\triangle PAB$ is similar to $\\triangle PCA$. Calculate the length of $PC$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{56}{3}"
} | {
"split": "train",
"index": 3187,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that point $P$ is an intersection point of the ellipse $\\frac{x^{2}}{a_{1}^{2}} + \\frac{y^{2}}{b_{1}^{2}} = 1 (a_{1} > b_{1} > 0)$ and the hyperbola $\\frac{x^{2}}{a_{2}^{2}} - \\frac{y^{2}}{b_{2}^{2}} = 1 (a_{2} > 0, b_{2} > 0)$, $F_{1}$, $F_{2}$ are the common foci of... | math | {
"style": "rule",
"ground_truth": "\\frac{4 \\sqrt{3}}{3}"
} | {
"split": "train",
"index": 3188,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $k$ be a positive integer. Suppose that the integers $1, 2, 3, \\dots, 3k+1$ are written down in random order. What is the probability that at no time during this process, the sum of the integers that have been written up to that time is a positive integer divisible by 3? Y... | math | {
"style": "rule",
"ground_truth": "\\frac{k!(k+1)!}{(3k+1)(2k)!}"
} | {
"split": "train",
"index": 3189,
"solution": "Assume that we have an ordering of $1,2,\\dots,3k+1$ such that no initial subsequence sums to $0$ mod $3$. If we omit the multiples of $3$ from this ordering, then the remaining sequence mod $3$ must look like $1,1,-1,1,-1,\\ldots$ or $-1,-1,1,-1,1,\\ldots$.\nSince ... |
deepscaler | [
{
"role": "user",
"content": "Find a nonzero polynomial $P(x,y)$ such that $P(\\lfloor a \\rfloor, \\lfloor 2a \\rfloor) = 0$ for all real numbers $a$. (Note: $\\lfloor \\nu \\rfloor$ is the greatest integer less than or equal to $\\nu$.) Let's think step by step and put only the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "(y-2x)(y-2x-1)"
} | {
"split": "train",
"index": 3190,
"solution": "Take $P(x,y) = (y-2x)(y-2x-1)$. To see that this works, first note that if $m = \\lfloor a \\rfloor$, then $2m$ is an integer less than or equal to $2a$, so $2m \\leq \\lfloor 2a \\rfloor$. On the other hand, $m+1$ is an integer strictly greater than $a$, so $2m+2$ ... |
deepscaler | [
{
"role": "user",
"content": "Given a sequence $\\{a_n\\}$ that satisfies $a_{n+1} = a_n - a_{n-1}$ ($n \\in N^*, n \\geqslant 2$), with $a_1 = 2018$ and $a_2 = 2017$. Let $S_n$ be the sum of the first $n$ terms of the sequence $\\{a_n\\}$. The value of $S_{100}$ is ______. Let's think step by step and put ... | math | {
"style": "rule",
"ground_truth": "2016"
} | {
"split": "train",
"index": 3191,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $m$ is a root of the equation $4^{x+ \\frac {1}{2}}-9\\cdot2^{x}+4=0$, then the eccentricity of the conic section $x^{2}+ \\frac {y^{2}}{m}=1$ is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt {2}"
} | {
"split": "train",
"index": 3192,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A white cylindrical silo has a diameter of 30 feet and a height of 80 feet. A red stripe with a horizontal width of 3 feet is painted on the silo, as shown, making two complete revolutions around it. What is the area of the stripe in square feet?\n\n[asy]\nsize(250);defaultpe... | math | {
"style": "rule",
"ground_truth": "240"
} | {
"split": "train",
"index": 3193,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many even integers between 4000 and 7000 have four different digits?\n Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "728"
} | {
"split": "train",
"index": 3194,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all real $x$ such that \\[\\left\\lfloor x \\lfloor x \\rfloor\\right \\rfloor = 29.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "[5.8,6)"
} | {
"split": "train",
"index": 3195,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, altitudes $AD$, $BE$, and $CF$ intersect at the orthocenter $H$. If $\\angle ABC = 49^\\circ$ and $\\angle ACB = 12^\\circ$, then find the measure of $\\angle BHC$, in degrees. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "61^\\circ"
} | {
"split": "train",
"index": 3196,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A natural number \\( A \\) is written twice consecutively (for example, writing 12 as 1212) to obtain a new number \\( B \\). If \\( B \\) is a multiple of 2016, then the smallest value of \\( A \\) is ______. Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "288"
} | {
"split": "train",
"index": 3197,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A line parallel to the side $AC$ of a triangle $ABC$ with $\\angle C = 90$ intersects side $AB$ at $M$ and side $BC$ at $N$ , so that $CN/BN = AC/BC = 2/1$ . The segments $CM$ and $AN$ meet at $O$ . Let $K$ be a point on the segment $ON$ such that $MO+OK... | math | {
"style": "rule",
"ground_truth": "90"
} | {
"split": "train",
"index": 3198,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of 2's in the factorization of the number $2011 \\cdot 2012 \\cdot 2013 \\cdot \\ldots \\cdot 4020$. Provide the answer in the given field. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2010"
} | {
"split": "train",
"index": 3199,
"solution": ""
} |
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