data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "In the rectangular coordinate system $xOy$, the parametric equations of line $l$ are given by $\\begin{cases} x=2t \\\\ y=-2-t \\end{cases}$ (where $t$ is the parameter). In the polar coordinate system (using the same length unit as the rectangular coordinate system and with th... | math | {
"style": "rule",
"ground_truth": "\\frac{12\\sqrt{5}}{5}"
} | {
"split": "train",
"index": 8400,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define $\\phi_n(x)$ to be the number of integers $y$ less than or equal to $n$ such that $\\gcd(x,y)=1$ . Also, define $m=\\text{lcm}(2016,6102)$ . Compute $$ \\frac{\\phi_{m^m}(2016)}{\\phi_{m^m}(6102)}. $$ Let's think step by step and put only the final answer with... | math | {
"style": "rule",
"ground_truth": "339/392"
} | {
"split": "train",
"index": 8401,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Square $EFGH$ is inside the square $ABCD$ so that each side of $EFGH$ can be extended to pass through a vertex of $ABCD$. Square $ABCD$ has side length $\\sqrt {50}$ and $BE = 1$. What is the area of the inner square $EFGH$? Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 8402,
"solution": "1. **Understanding the Problem Setup:**\n - We have two squares, $ABCD$ and $EFGH$, where $EFGH$ is inside $ABCD$.\n - Each side of $EFGH$ can be extended to pass through a vertex of $ABCD$.\n - The side length of $ABCD$ is given as $\\sqrt{50}$.\n - The dis... |
deepscaler | [
{
"role": "user",
"content": "Let $p(x)=x^{2}-x+1$. Let $\\alpha$ be a root of $p(p(p(p(x))))$. Find the value of $(p(\\alpha)-1) p(\\alpha) p(p(\\alpha)) p(p(p(\\alpha)))$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 8403,
"solution": "Since $(x-1) x=p(x)-1$, we can set $$(p(\\alpha)-1) p(\\alpha) p(p(\\alpha)) p(p(p(\\alpha))) =(p(p(\\alpha))-1) p(p(\\alpha)) p(p(p(\\alpha))) =(p(p(p(\\alpha)))-1) p(p(p(\\alpha))) =p(p(p(p(\\alpha))))-1 =-1$$"
} |
deepscaler | [
{
"role": "user",
"content": "Let $x$ and $y$ be positive real numbers. Define $a=1+\\frac{x}{y}$ and $b=1+\\frac{y}{x}$. If $a^{2}+b^{2}=15$, compute $a^{3}+b^{3}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 8404,
"solution": "Note that $a-1=\\frac{x}{y}$ and $b-1=\\frac{y}{x}$ are reciprocals. That is, $$(a-1)(b-1)=1 \\Longrightarrow a b-a-b+1=1 \\Longrightarrow a b=a+b$$ Let $t=a b=a+b$. Then we can write $$a^{2}+b^{2}=(a+b)^{2}-2 a b=t^{2}-2 t$$ so $t^{2}-2 t=15$, which factors as $(t-... |
deepscaler | [
{
"role": "user",
"content": "Find the smallest natural number such that when multiplied by 9, the resulting number consists of the same digits but in some different order. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1089"
} | {
"split": "train",
"index": 8405,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Applied to a bill for $\\$10,000$ the difference between a discount of $40\\%$ and two successive discounts of $36\\%$ and $4\\%$, expressed in dollars, is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "144"
} | {
"split": "train",
"index": 8406,
"solution": "1. **Calculate the single discount of 40% on $\\textdollar{10,000}$:**\n - A 40% discount means the remaining amount to be paid is 100% - 40% = 60% of the original price.\n - Calculation: \n \\[\n 10,000 \\times 0.6 = \\textdollar{6,000}\n \\]\n\n2. ... |
deepscaler | [
{
"role": "user",
"content": "Compute the definite integral:\n\n$$\n\\int_{\\pi / 2}^{\\pi} 2^{4} \\cdot \\sin ^{6} x \\cos ^{2} x \\, dx\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5\\pi}{16}"
} | {
"split": "train",
"index": 8407,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The value $b^n$ has both $b$ and $n$ as positive integers less than or equal to 15. What is the greatest number of positive factors $b^n$ can have? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "496"
} | {
"split": "train",
"index": 8408,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest prime factor of 1821? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 8409,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\\(\\log_{5} x + \\log_{25} x = \\log_{1/5} \\sqrt{3}\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{\\sqrt[3]{3}}"
} | {
"split": "train",
"index": 8410,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An octagon is inscribed in a square so that the vertices of the octagon trisect the sides of the square. The perimeter of the square is 108 centimeters. What is the number of square centimeters in the area of the octagon? Let's think step by step and put only the final answer w... | math | {
"style": "rule",
"ground_truth": "567"
} | {
"split": "train",
"index": 8411,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Grisha has 5000 rubles. Chocolate bunnies are sold in a store at a price of 45 rubles each. To carry the bunnies home, Grisha will have to buy several bags at 30 rubles each. One bag can hold no more than 30 chocolate bunnies. Grisha bought the maximum possible number of bunnie... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 8412,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Samantha leaves her house at 7:15 a.m. to catch the school bus, starts her classes at 8:00 a.m., and has 8 classes that last 45 minutes each, a 40-minute lunch break, and spends an additional 90 minutes in extracurricular activities. If she takes the bus home and arrives back a... | math | {
"style": "rule",
"ground_truth": "110"
} | {
"split": "train",
"index": 8413,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A factory assigns five newly recruited employees, including A and B, to three different workshops. Each workshop must be assigned at least one employee, and A and B must be assigned to the same workshop. The number of different ways to assign the employees is \\_\\_\\_\\_\\_\\_... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 8414,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In how many ways can you rearrange the letters of ‘Alejandro’ such that it contains one of the words ‘ned’ or ‘den’? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "40320"
} | {
"split": "train",
"index": 8415,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the area enclosed by the region defined by the equation $x^2+y^2+10x+24y=0$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "169\\pi"
} | {
"split": "train",
"index": 8416,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A company's capital increases by a factor of two each year compared to the previous year after dividends have been paid, with a fixed dividend of 50 million yuan paid to shareholders at the end of each year. The company's capital after dividends were paid at the end of 2010 was... | math | {
"style": "rule",
"ground_truth": "2017"
} | {
"split": "train",
"index": 8417,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Graphs of several functions are shown below. Which functions have inverses?\n\n[asy]\nunitsize(0.5 cm);\n\npicture[] graf;\nint i, n;\n\nreal funce(real x) {\n return(x^3/40 + x^2/20 - x/2 + 2);\n}\n\nfor (n = 1; n <= 5; ++n) {\n graf[n] = new picture;\n for (i = -5; i <= 5... | math | {
"style": "rule",
"ground_truth": "\\text{B,C}"
} | {
"split": "train",
"index": 8418,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the real numbers \\( x \\) and \\( y \\) satisfy \\( 3x + 2y - 1 \\geqslant 0 \\), then the minimum value of \\( u = x^2 + y^2 + 6x - 2y \\) is _______ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-66/13"
} | {
"split": "train",
"index": 8419,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Moving only south and east along the line segments, how many paths are there from $A$ to $B$? [asy]\nimport olympiad; size(250); defaultpen(linewidth(0.8)); dotfactor=4;\nfor(int i = 0; i <= 9; ++i)\n\nif (i!=4 && i !=5)\n\ndraw((2i,0)--(2i,3));\nfor(int j = 0; j <= 3; ++j)\n\n... | math | {
"style": "rule",
"ground_truth": "160"
} | {
"split": "train",
"index": 8420,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\tan \\alpha$ and $\\frac{1}{\\tan \\alpha}$ are the two real roots of the equation $x^2 - kx + k^2 - 3 = 0$, and $3\\pi < \\alpha < \\frac{7}{2}\\pi$, find $\\cos \\alpha + \\sin \\alpha$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "-\\sqrt{2}"
} | {
"split": "train",
"index": 8421,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the real numbers \\( x \\) and \\( y \\) that satisfy\n\n\\[ x + y = 3 \\]\n\\[ \\frac{1}{x + y^2} + \\frac{1}{x^2 + y} = \\frac{1}{2} \\]\n\nfind the value of \\( x^5 + y^5 \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "123"
} | {
"split": "train",
"index": 8422,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A factory uses radiation to sterilize food and is now planning to build a dormitory for its workers near the factory, with radiation protection measures for the dormitory. The choice of radiation protection materials for the building and the distance of the dormitory from the f... | math | {
"style": "rule",
"ground_truth": "150"
} | {
"split": "train",
"index": 8423,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A strictly increasing sequence of positive integers $a_1$, $a_2$, $a_3$, $\\cdots$ has the property that for every positive integer $k$, the subsequence $a_{2k-1}$, $a_{2k}$, $a_{2k+1}$ is geometric and the subsequence $a_{2k}$, $a_{2k+1}$, $a_{2k+2}$ is arithmetic. Suppose tha... | math | {
"style": "rule",
"ground_truth": "504"
} | {
"split": "train",
"index": 8424,
"solution": "We first create a similar sequence where $a_1=1$ and $a_2=2$. Continuing the sequence,\n\\[1, 2,4,6,9,12,16,20,25,30,36,42,49,\\cdots\\]\n Here we can see a pattern; every second term (starting from the first) is a square, and every second term (starting from the th... |
deepscaler | [
{
"role": "user",
"content": "Let\n\n$$\n2^{x}=\\left(1+\\tan 0.01^{\\circ}\\right)\\left(1+\\tan 0.02^{\\circ}\\right)\\left(1+\\tan 0.03^{\\circ}\\right) \\ldots\\left(1+\\tan 44.99^{\\circ}\\right)\n$$\n\nFind \\( x \\). If necessary, round the answer to the nearest 0.01. Let's think step by step and put... | math | {
"style": "rule",
"ground_truth": "2249.5"
} | {
"split": "train",
"index": 8425,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Circle $A$ has radius $100$. Circle $B$ has an integer radius $r<100$ and remains internally tangent to circle $A$ as it rolls once around the circumference of circle $A$. The two circles have the same points of tangency at the beginning and end of circle $B$'s trip. How many p... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 8426,
"solution": "1. **Calculate the circumference of circle A**: \n The radius of circle A is given as $100$. Therefore, its circumference is:\n \\[\n C_A = 2\\pi \\times 100 = 200\\pi\n \\]\n\n2. **Expression for the circumference of circle B**:\n Circle B has radius $r$,... |
deepscaler | [
{
"role": "user",
"content": "Given that the interior angles \\(A, B, C\\) of triangle \\(\\triangle ABC\\) are opposite to the sides \\(a, b, c\\) respectively, and that \\(A - C = \\frac{\\pi}{2}\\), and \\(a, b, c\\) form an arithmetic sequence, find the value of \\(\\cos B\\). Let's think step by step a... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"split": "train",
"index": 8427,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $21^{-1} \\equiv 15 \\pmod{61}$, find $40^{-1} \\pmod{61}$, as a residue modulo 61. (Provide a number between 0 and 60, inclusive.) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "46"
} | {
"split": "train",
"index": 8428,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From the set $\\{1, 2, \\cdots, 20\\}$, choose 5 numbers such that the difference between any two numbers is at least 4. How many different ways can this be done? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "56"
} | {
"split": "train",
"index": 8429,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( T \\) be the set of positive real numbers. Let \\( g : T \\to \\mathbb{R} \\) be a function such that\n\\[ g(x) g(y) = g(xy) + 2006 \\left( \\frac{1}{x} + \\frac{1}{y} + 2005 \\right) \\] for all \\( x, y > 0 \\).\n\nLet \\( m \\) be the number of possible values of \\(... | math | {
"style": "rule",
"ground_truth": "\\frac{6019}{3}"
} | {
"split": "train",
"index": 8430,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a chess match between players A and B, the probabilities of A winning, B winning, and a tie are $0.5$, $0.3$, and $0.2$, respectively. Find the probability of B winning at least one match against A after two matches. Let's think step by step and put only the final answer wit... | math | {
"style": "rule",
"ground_truth": "0.51"
} | {
"split": "train",
"index": 8431,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $\\mathbf{a}$, $\\mathbf{b}$, $\\mathbf{c}$, and $\\mathbf{d}$ are unit vectors, find the largest possible value of\n\\[\n\\|\\mathbf{a} - \\mathbf{b}\\|^2 + \\|\\mathbf{a} - \\mathbf{c}\\|^2 + \\|\\mathbf{a} - \\mathbf{d}\\|^2 + \\|\\mathbf{b} - \\mathbf{c}\\|^2 + \\|\\math... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 8432,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What would the 25th number be in a numeric system where the base is five? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"split": "train",
"index": 8433,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Louise is designing a custom dress and needs to provide her hip size in millimeters. If there are $12$ inches in a foot and $305$ millimeters in a foot, and Louise's hip size is $42$ inches, what size should she specify in millimeters? Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "1067.5"
} | {
"split": "train",
"index": 8434,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When $1 - i \\sqrt{3}$ is converted to the exponential form $re^{i \\theta}$, what is $\\theta$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5\\pi}{3}"
} | {
"split": "train",
"index": 8435,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sequence $y_1,y_2,\\dots,y_k$ of real numbers is called \\emph{zigzag} if $k=1$, or if $y_2-y_1, y_3-y_2, \\dots, y_k-y_{k-1}$ are nonzero and alternate in sign. Let $X_1,X_2,\\dots,X_n$ be chosen independently from the uniform distribution on $[0,1]$. Let $a(X_1,X_2,\\dots,X... | math | {
"style": "rule",
"ground_truth": "\\frac{2n+2}{3}"
} | {
"split": "train",
"index": 8436,
"solution": "The expected value is $\\frac{2n+2}{3}$. Divide the sequence $X_1,\\dots,X_n$ into alternating increasing and decreasing segments, with $N$ segments in all. Note that removing one term cannot increase $N$: if the removed term is interior to some segment then the num... |
deepscaler | [
{
"role": "user",
"content": "Find the smallest positive integer $n$ with the property that the polynomial $x^4 - nx + 63$ can be written as a product of two nonconstant polynomials with integer coefficients. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 8437,
"solution": "You can factor the polynomial into two quadratic factors or a linear and a cubic factor.\n For two quadratic factors, let $x^2+ax+b$ and $x^2+cx+d$ be the two quadratics, so that\n\\[(x^2 + ax + b )(x^2 + cx + d) = x^4 + (a + c)x^3 + (b + d + ac)x^2 + (ad + bc)x + b... |
deepscaler | [
{
"role": "user",
"content": "For positive real numbers $x,$ $y,$ and $z,$ compute the maximum value of\n\\[\\frac{xyz(x + y + z)}{(x + y)^2 (y + z)^2}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 8438,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A positive real number $x$ is such that \\[\n\\sqrt[3]{1-x^3} + \\sqrt[3]{1+x^3} = 1.\n\\]Find $x^6.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{28}{27}"
} | {
"split": "train",
"index": 8439,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a set of data $(1)$, $(a)$, $(3)$, $(6)$, $(7)$, its average is $4$, what is its variance? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{24}{5}"
} | {
"split": "train",
"index": 8440,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Using one each of the coins and bills of 1 jiao, 2 jiao, 5 jiao, 1 yuan, 2 yuan, and 5 yuan, how many different monetary values can be formed? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "63"
} | {
"split": "train",
"index": 8441,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two lines with slopes $\\dfrac{1}{3}$ and $3$ intersect at $(3,3)$. Find the area of the triangle enclosed by these two lines and the line $x+y=12$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8.625"
} | {
"split": "train",
"index": 8442,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all the integers $n>1$ with the following property: the numbers $1,2, \\ldots, n$ can be arranged in a line so that, of any two adjacent numbers, one is divisible by the other. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2, 3, 4, 6"
} | {
"split": "train",
"index": 8443,
"solution": "$2,3,4,6$ The values $n=2,3,4,6$ work, as shown by respective examples 1,$2 ; 2,1,3 ; 2,4,1,3 ; 3,6,2,4,1,5$. We shall show that there are no other possibilities. If $n=2 k+1$ is odd, then none of the numbers $k+1, k+2, \\ldots, 2 k+1$ can divide any other, so no tw... |
deepscaler | [
{
"role": "user",
"content": "Consider the set of 5-tuples of positive integers at most 5. We say the tuple $\\left(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\\right)$ is perfect if for any distinct indices $i, j, k$, the three numbers $a_{i}, a_{j}, a_{k}$ do not form an arithmetic progression (in any order). Find ... | math | {
"style": "rule",
"ground_truth": "780"
} | {
"split": "train",
"index": 8444,
"solution": "There are two situations. 1. The multiset is aabbc; the only condition here is $c \\neq \\frac{1}{2}(a+b)$, for $\\left(\\binom{5}{3}-|S|\\right) \\cdot\\binom{3}{1}=18$ such triples, where $S$ is the set of unordered triples $(a, b, c)$ which do not satisfy the con... |
deepscaler | [
{
"role": "user",
"content": "Plane M is parallel to plane N. There are 3 different points on plane M and 4 different points on plane N. The maximum number of tetrahedrons with different volumes that can be determined by these 7 points is ____. Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "34"
} | {
"split": "train",
"index": 8445,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The knights in a certain kingdom come in two colors. $\\frac{2}{7}$ of them are red, and the rest are blue. Furthermore, $\\frac{1}{6}$ of the knights are magical, and the fraction of red knights who are magical is $2$ times the fraction of blue knights who are magical. What fr... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{27}"
} | {
"split": "train",
"index": 8446,
"solution": "1. **Define the total number of knights**: Let the total number of knights be $42$. This choice is made because the least common multiple (LCM) of the denominators from the fractions given in the problem ($7$ and $6$) is $42$.\n\n2. **Calculate the number of red and... |
deepscaler | [
{
"role": "user",
"content": "Find the range of $f(x) = \\sin^4 x - \\sin x \\cos x +\\cos^4 x.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\left[ 0, \\frac{9}{8} \\right]"
} | {
"split": "train",
"index": 8447,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a, b, c$ be positive real numbers such that $a + b + c = 2.$ Find the maximum value of $a^2 b^3 c^2.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{128}{2187}"
} | {
"split": "train",
"index": 8448,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A square 10cm on each side has four quarter circles drawn with centers at the four corners. How many square centimeters are in the area of the shaded region? Express your answer in terms of $\\pi$.\n\n[asy]\nunitsize (1.5 cm);\n\ndraw((-1,-1)--(1,-1)--(1,1)--(-1,1)--cycle);\nfi... | math | {
"style": "rule",
"ground_truth": "100-25\\pi"
} | {
"split": "train",
"index": 8449,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Express the given value of $22$ nanometers in scientific notation. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2.2\\times 10^{-8}"
} | {
"split": "train",
"index": 8450,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that the graph of \\[2x^2 + y^2 + 8x - 10y + c = 0\\]consists of a single point. (In this case, we call the graph a degenerate ellipse.) Find $c.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "33"
} | {
"split": "train",
"index": 8451,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Inside triangle \\(ABC\\), a random point \\(M\\) is chosen. What is the probability that the area of one of the triangles \\(ABM\\), \\(BCM\\), and \\(CAM\\) will be greater than the sum of the areas of the other two? Let's think step by step and put only the final answer with... | math | {
"style": "rule",
"ground_truth": "0.75"
} | {
"split": "train",
"index": 8452,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Twelve standard 6-sided dice are rolled. What is the probability that exactly two of the dice show a 1? Express your answer as a decimal rounded to the nearest thousandth. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.138"
} | {
"split": "train",
"index": 8453,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In how many ways can you select two letters from the word \"УЧЕБНИК\" such that one of the letters is a consonant and the other is a vowel? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 8454,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two sectors of a circle of radius $12$ are placed side by side, as shown. Determine the $\\textit{area}$ of figure $ABCD.$ [asy]\ndraw((0,0)--(12,0)..(10.3923,6)..(6,10.3923)--(-6,10.3923)..(-4.3923,4.3923)..(0,0),black+linewidth(1));\ndraw((0,0)--(6,10.3923),black+linewidth(1)... | math | {
"style": "rule",
"ground_truth": "48\\pi"
} | {
"split": "train",
"index": 8455,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( a_0 = -3 \\), \\( b_0 = 2 \\), and for \\( n \\geq 0 \\), let:\n\\[\n\\begin{align*}\na_{n+1} &= 2a_n + 2b_n + 2\\sqrt{a_n^2 + b_n^2}, \\\\\nb_{n+1} &= 2a_n + 2b_n - 2\\sqrt{a_n^2 + b_n^2}.\n\\end{align*}\n\\]\nFind \\( \\frac{1}{a_{2023}} + \\frac{1}{b_{2023}} \\). Let... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 8456,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The GDP of a certain city last year was 84,300,000 ten thousand yuan. Represent this number in scientific notation. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8.43 \\times 10^7"
} | {
"split": "train",
"index": 8457,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = |x^2 + bx|$ ($b \\in \\mathbb{R}$), when $x \\in [0, 1]$, find the minimum value of the maximum value of $f(x)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3-2\\sqrt{2}"
} | {
"split": "train",
"index": 8458,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x y=5$ and $x^{2}+y^{2}=21$, compute $x^{4}+y^{4}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "391"
} | {
"split": "train",
"index": 8459,
"solution": "We have $441=\\left(x^{2}+y^{2}\\right)^{2}=x^{4}+y^{4}+2(x y)^{2}=x^{4}+y^{4}+50$, yielding $x^{4}+y^{4}=391$."
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest number that uses only the digits 2 and 3 in equal quantity and is divisible by both 2 and 3. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "223332"
} | {
"split": "train",
"index": 8460,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number of solutions to the equation $\\sin |x| = |\\cos x|$ in the closed interval $[-10\\pi, 10\\pi]$ is __. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 8461,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the area of quadrilateral $EFGH$, given that $m\\angle F = m \\angle G = 135^{\\circ}$, $EF=4$, $FG=6$, and $GH=8$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18\\sqrt{2}"
} | {
"split": "train",
"index": 8462,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many integers from 1 through 9999, inclusive, do not contain any of the digits 2, 3, 4 or 5? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1295"
} | {
"split": "train",
"index": 8463,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a sequence $a_1, a_2, . . . , a_{1000}$ consisting of $1000$ distinct numbers a pair $(a_i, a_j )$ with $i < j$ is called *ascending* if $a_i < a_j$ and *descending* if $a_i > a_j$ . Determine the largest positive integer $k$ with the property that every sequen... | math | {
"style": "rule",
"ground_truth": "333"
} | {
"split": "train",
"index": 8464,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( a_{1}, a_{2}, \\ldots, a_{9} \\) be nine real numbers, not necessarily distinct, with average \\( m \\). Let \\( A \\) denote the number of triples \\( 1 \\leq i<j<k \\leq 9 \\) for which \\( a_{i}+a_{j}+a_{k} \\geq 3m \\). What is the minimum possible value of \\( A \\... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 8465,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The lottery in our state consists of two drawings. First, a MegaBall is picked from among 27 numbered balls. Second, five WinnerBalls are picked from among 44 numbered balls. To win the lottery, you must pick the MegaBall number correctly and also pick the numbers on the five... | math | {
"style": "rule",
"ground_truth": "\\dfrac{1}{29,\\!322,\\!216}"
} | {
"split": "train",
"index": 8466,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the base-ten number represented by the base-eight number 31? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 8467,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of the $x$-coordinates of the vertices of a triangle in the Cartesian plane equals $10$. Find the sum of the $x$-coordinates of the midpoints of the sides of the triangle. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 8468,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\{a_n\\}$ is a geometric sequence with a common ratio of $q$, and $a_m$, $a_{m+2}$, $a_{m+1}$ form an arithmetic sequence.\n\n(Ⅰ) Find the value of $q$; \n(Ⅱ) Let the sum of the first $n$ terms of the sequence $\\{a_n\\}$ be $S_n$. Determine whether $S_m$, $S_{m+2... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{2}"
} | {
"split": "train",
"index": 8469,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The area of rectangle PRTV is divided into four rectangles, PQXW, QRSX, XSTU, and WXUV. Given that the area of PQXW is 9, the area of QRSX is 10, and the area of XSTU is 15, find the area of rectangle WXUV. Let's think step by step and put only the final answer within \\boxed{}... | math | {
"style": "rule",
"ground_truth": "\\frac{27}{2}"
} | {
"split": "train",
"index": 8470,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two cars, $A$ and $B$, depart from one city to another. In the first 5 minutes, they traveled the same distance. Then, due to an engine failure, $B$ had to reduce its speed to 2/5 of its original speed, and thus arrived at the destination 15 minutes after car $A$, which continu... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 8471,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ have an angle of $45^\\circ$ between them, and $|\\overrightarrow{a}|=1$, $|2\\overrightarrow{a}-\\overrightarrow{b}|=\\sqrt{10}$, find the magnitude of vector $\\overrightarrow{b}$. Let's think step by step and put ... | math | {
"style": "rule",
"ground_truth": "3\\sqrt{2}"
} | {
"split": "train",
"index": 8472,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "1. Given that $α$ and $β$ are acute angles, and $\\cos α= \\frac{4}{5}$, $\\cos (α+β)=- \\frac{16}{65}$, find the value of $\\cos β$.\n2. Given that $0 < β < \\frac{π}{4} < α < \\frac{3}{4}π$, $\\cos ( \\frac{π}{4}-α)= \\frac{3}{5}$, $\\sin ( \\frac{3π}{4}+β)= \\frac{5}{13}$, f... | math | {
"style": "rule",
"ground_truth": "\\frac{56}{65}"
} | {
"split": "train",
"index": 8473,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a function $f(x) = (m^2 - m - 1)x^{m^2 - 2m - 1}$ which is a power function and is increasing on the interval $(0, \\infty)$, find the value of the real number $m$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 8474,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $N$ be the number of ordered triples $(A,B,C)$ of integers satisfying the conditions (a) $0\\le A<B<C\\le99$, (b) there exist integers $a$, $b$, and $c$, and prime $p$ where $0\\le b<a<c<p$, (c) $p$ divides $A-a$, $B-b$, and $C-c$, and (d) each ordered triple $(A,B,C)$ and ... | math | {
"style": "rule",
"ground_truth": "272"
} | {
"split": "train",
"index": 8475,
"solution": "From condition (d), we have $(A,B,C)=(B-D,B,B+D)$ and $(b,a,c)=(a-d,a,a+d)$. Condition $\\text{(c)}$ states that $p\\mid B-D-a$, $p | B-a+d$, and $p\\mid B+D-a-d$. We subtract the first two to get $p\\mid-d-D$, and we do the same for the last two to get $p\\mid 2d-D... |
deepscaler | [
{
"role": "user",
"content": "At the beginning of the school year, Lisa's goal was to earn an $A$ on at least $80\\%$ of her $50$ quizzes for the year. She earned an $A$ on $22$ of the first $30$ quizzes. If she is to achieve her goal, on at most how many of the remaining quizzes can she earn a grade lowe... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 8476,
"solution": "1. **Determine the total number of quizzes Lisa needs to score an A on to meet her goal**: Lisa's goal is to earn an A on at least 80% of her 50 quizzes. Therefore, the total number of quizzes she needs to score an A on is:\n \\[\n 0.80 \\times 50 = 40\n \\]\n... |
deepscaler | [
{
"role": "user",
"content": "Suppose that point $D$ lies on side $B C$ of triangle $A B C$ such that $A D$ bisects $\\angle B A C$, and let $\\ell$ denote the line through $A$ perpendicular to $A D$. If the distances from $B$ and $C$ to $\\ell$ are 5 and 6 , respectively, compute $A D$. Let's think step by... | math | {
"style": "rule",
"ground_truth": "\\frac{60}{11}"
} | {
"split": "train",
"index": 8477,
"solution": "Let $\\ell$, the external angle bisector, intersect $B C$ at $X$. By the external angle bisector theorem, $A B$ : $A C=X B: X C=5: 6$, so $B D: D C=5: 6$ by the angle bisector theorem. Then $A D$ is a weighted average of the distances from $B$ and $C$ to $\\ell$, na... |
deepscaler | [
{
"role": "user",
"content": "Find the sum of all positive integers such that their expression in base $5$ digits is the reverse of their expression in base $11$ digits. Express your answer in base $10$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 8478,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of functions of the form \\( f(x) = ax^3 + bx^2 + cx + d \\) such that\n\\[ f(x)f(-x) = f(x^3). \\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 8479,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Cagney can frost a cupcake every 25 seconds and Lacey can frost a cupcake every 35 seconds. If Lacey spends the first minute exclusively preparing frosting and then both work together to frost, determine the number of cupcakes they can frost in 10 minutes. Let's think step by s... | math | {
"style": "rule",
"ground_truth": "37"
} | {
"split": "train",
"index": 8480,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the value of $\\text{rem} \\left(\\frac{5}{7}, \\frac{3}{4}\\right)$ and then multiply the result by $-2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{10}{7}"
} | {
"split": "train",
"index": 8481,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the perimeter of a rectangle is $p$ and its diagonal is $d$, the difference between the length and width of the rectangle is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {\\sqrt {8d^2 - p^2}}{2}"
} | {
"split": "train",
"index": 8482,
"solution": "1. Let the sides of the rectangle be $x$ and $y$. Without loss of generality, assume $x > y$. The perimeter of the rectangle is given by $2x + 2y = p$, which simplifies to:\n \\[\n x + y = \\frac{p}{2}.\n \\]\n\n2. By the Pythagorean theorem, the square of the... |
deepscaler | [
{
"role": "user",
"content": "Which of the following multiplication expressions has a product that is a multiple of 54? (Fill in the serial number). \n$261 \\times 345$ \n$234 \\times 345$ \n$256 \\times 345$ \n$562 \\times 345$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "234 \\times 345"
} | {
"split": "train",
"index": 8483,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jim wrote a sequence of symbols a total of 50 times. How many more of one symbol than another did he write? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "150"
} | {
"split": "train",
"index": 8484,
"solution": "The sequence of symbols includes 5 of one symbol and 2 of another. This means that, each time the sequence is written, there are 3 more of one symbol written than the other. When the sequence is written 50 times, in total there are \\( 50 \\times 3 = 150 \\) more of... |
deepscaler | [
{
"role": "user",
"content": "A cube has side length $6$. Its vertices are alternately colored black and purple, as shown below. What is the volume of the tetrahedron whose corners are the purple vertices of the cube? (A tetrahedron is a pyramid with a triangular base.)\n\n[asy]\nimport three;\nreal t=-0.05... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 8485,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify first, then evaluate: $3a^{2}+\\left[a^{2}+\\left(5a^{2}-2a\\right)-3\\left(a^{2}-3a\\right)\\right]$, where $a=-2$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 8486,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each segment with endpoints at the vertices of a regular 100-gon is painted red if there is an even number of vertices between its endpoints, and blue otherwise (in particular, all sides of the 100-gon are red). Numbers are placed at the vertices such that the sum of their squa... | math | {
"style": "rule",
"ground_truth": "1/2"
} | {
"split": "train",
"index": 8487,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $P(x)$ be a nonzero polynomial such that $(x-1)P(x+1)=(x+2)P(x)$ for every real $x$, and $\\left(P(2)\\right)^2 = P(3)$. Then $P(\\tfrac72)=\\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$. Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "109"
} | {
"split": "train",
"index": 8488,
"solution": "Substituting $x=2$ into the given equation, we find that $P(3)=4P(2)=P(2)^2$. Therefore, either $P(2)=0$ or $P(2)=4$. Now for integers $n\\ge 2$, we know that \\[P(n+1)=\\frac{n+2}{n-1}P(n).\\] Applying this repeatedly, we find that \\[P(n+1)=\\frac{(n+2)!/3!}{(n-1)... |
deepscaler | [
{
"role": "user",
"content": "Sequence $(a_n)$ is defined as $a_{n+1}-2a_n+a_{n-1}=7$ for every $n\\geq 2$ , where $a_1 = 1, a_2=5$ . What is $a_{17}$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "905"
} | {
"split": "train",
"index": 8489,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Among the first 1500 positive integers, there are n whose hexadecimal representation contains only numeric digits. What is the sum of the digits of n? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 8490,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are six unmarked envelopes on a table, each containing a letter for a different person. If the mail is randomly distributed among these six people, with each person getting one letter, what is the probability that exactly three people get the right letter? Let's think ste... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{18}"
} | {
"split": "train",
"index": 8491,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The lengths of two sides of a triangle are 33 units and 42 units. The third side also has an integral length. What is the least possible number of units in the perimeter of the triangle? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "85"
} | {
"split": "train",
"index": 8492,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that P is a point on the hyperbola $\\frac{x^2}{4} - \\frac{y^2}{3} = 1$, and $F_1$, $F_2$ are the two foci of the hyperbola. If $\\angle F_1PF_2 = 60^\\circ$, calculate the area of $\\triangle PF_1F_2$. Let's think step by step and put only the final answer within \\boxe... | math | {
"style": "rule",
"ground_truth": "3\\sqrt{3}"
} | {
"split": "train",
"index": 8493,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Points $A$, $B$, $C$, $D$ are on the same sphere, with $AB=BC=\\sqrt{2}$, $AC=2$. If the circumscribed sphere of tetrahedron $ABCD$ has its center exactly on edge $DA$, and $DC=2\\sqrt{3}$, then the surface area of this sphere equals \\_\\_\\_\\_\\_\\_\\_\\_\\_\\_ Let's think s... | math | {
"style": "rule",
"ground_truth": "16\\pi"
} | {
"split": "train",
"index": 8494,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest natural number with the following properties:\na) It ends in digit 6 in decimal notation;\nb) If you remove the last digit 6 and place this digit 6 at the beginning of the remaining number, the result is four times the original number. Let's think step by step... | math | {
"style": "rule",
"ground_truth": "153846"
} | {
"split": "train",
"index": 8495,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A circle of radius 1 is internally tangent to two circles of radius 2 at points $A$ and $B$, where $AB$ is a diameter of the smaller circle. What is the area of the region, shaded in the figure, that is outside the smaller circle and inside each of the two larger circles? Ex... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{3}\\pi - 2\\sqrt{3}"
} | {
"split": "train",
"index": 8496,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The product of two 2-digit numbers is $3774$. What is the smaller of the two numbers? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "51"
} | {
"split": "train",
"index": 8497,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "4 12-sided dice are rolled. What is the probability that the number of dice showing a two digit number is equal to the number of dice showing a one digit number? Express your answer as a common fraction. (Assume that the numbers on the 12 sides are the numbers from 1 to 12 expr... | math | {
"style": "rule",
"ground_truth": "\\dfrac{27}{128}"
} | {
"split": "train",
"index": 8498,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Sasha has $\\$3.20$ in U.S. coins. She has the same number of quarters and nickels. What is the greatest number of quarters she could have? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 8499,
"solution": ""
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.