data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "If $\\overrightarrow{a} = (2, 3)$, $\\overrightarrow{b} = (-4, 7)$, and $\\overrightarrow{a} + \\overrightarrow{c} = 0$, then the projection of $\\overrightarrow{c}$ in the direction of $\\overrightarrow{b}$ is \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final... | math | {
"style": "rule",
"ground_truth": "-\\frac{\\sqrt{65}}{5}"
} | {
"split": "train",
"index": 37749,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "John believes that the amount of sleep he gets the night before a test and his score on that test are inversely related. On his first exam, he got eight hours of sleep and scored 70 on the exam. To the nearest tenth, how many hours does John believe he must sleep the night be... | math | {
"style": "rule",
"ground_truth": "6.2"
} | {
"split": "train",
"index": 37750,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( O \\) is the circumcenter of \\(\\triangle ABC\\), where \\(|AB|=2\\), \\(|AC|=1\\), and \\(\\angle BAC = \\frac{2}{3} \\pi\\). Let \\(\\overrightarrow{AB} = \\mathbf{a}\\) and \\(\\overrightarrow{AC} = \\mathbf{b}\\). If \\(\\overrightarrow{AO} = \\lambda_1 \\ma... | math | {
"style": "rule",
"ground_truth": "\\frac{13}{6}"
} | {
"split": "train",
"index": 37751,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Five cards have the numbers 101, 102, 103, 104, and 105 on their fronts. On the reverse, each card has one of five different positive integers: \\(a, b, c, d,\\) and \\(e\\) respectively. We know that \\(a + 2 = b - 2 = 2c = \\frac{d}{2} = e^2\\).\n\nGina picks up the card whic... | math | {
"style": "rule",
"ground_truth": "105"
} | {
"split": "train",
"index": 37752,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sides $x$ and $y$ of a scalene triangle satisfy $x + \\frac{2\\Delta }{x}=y+ \\frac{2\\Delta }{y}$ , where $\\Delta$ is the area of the triangle. If $x = 60, y = 63$ , what is the length of the largest side of the triangle? Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "87"
} | {
"split": "train",
"index": 37753,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the angle of inclination of the tangent line to the curve $y= \\frac {1}{2}x^{2}-2x$ at the point $(1,- \\frac {3}{2})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3\\pi}{4}"
} | {
"split": "train",
"index": 37754,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Unit squares $A B C D$ and $E F G H$ have centers $O_{1}$ and $O_{2}$ respectively, and are originally situated such that $B$ and $E$ are at the same position and $C$ and $H$ are at the same position. The squares then rotate clockwise about their centers at the rate of one revo... | math | {
"style": "rule",
"ground_truth": "\\frac{2-\\sqrt{3}}{4}"
} | {
"split": "train",
"index": 37755,
"solution": "Note that $A E=B F=C G=D H=1$ at all times. Suppose that the squares have rotated $\\theta$ radians. Then $\\angle O_{1} O_{2} H=\\frac{\\pi}{4}-\\theta=\\angle O_{1} D H$, so $\\angle H D C=\\frac{\\pi}{4}-\\angle O_{1} D H=\\theta$. Let $P$ be the intersection of... |
deepscaler | [
{
"role": "user",
"content": "Find the number of real solutions of the equation\n\\[\\frac{x}{100} = \\sin x.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "63"
} | {
"split": "train",
"index": 37756,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest composite number that has no prime factors less than 10. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "121"
} | {
"split": "train",
"index": 37757,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $n \\geq 2$ be a natural. Define \n$$X = \\{ (a_1,a_2,\\cdots,a_n) | a_k \\in \\{0,1,2,\\cdots,k\\}, k = 1,2,\\cdots,n \\}$$.\nFor any two elements $s = (s_1,s_2,\\cdots,s_n) \\in X, t = (t_1,t_2,\\cdots,t_n) \\in X$, define \n$$s \\vee t = (\\max \\{s_1,t_1\\},\\max \\{s_2... | math | {
"style": "rule",
"ground_truth": "(n + 1)! - (n - 1)!"
} | {
"split": "train",
"index": 37758,
"solution": "\nLet \\( n \\geq 2 \\) be a natural number. Define \n\\[\nX = \\{ (a_1, a_2, \\cdots, a_n) \\mid a_k \\in \\{0, 1, 2, \\cdots, k\\}, k = 1, 2, \\cdots, n \\}.\n\\]\nFor any two elements \\( s = (s_1, s_2, \\cdots, s_n) \\in X \\) and \\( t = (t_1, t_2, \\cdots, t_... |
deepscaler | [
{
"role": "user",
"content": "The base of a prism is an equilateral triangle $ABC$. The lateral edges of the prism $AA_1$, $BB_1$, and $CC_1$ are perpendicular to the base. A sphere, whose radius is equal to the edge of the base of the prism, touches the plane $A_1B_1C_1$ and the extensions of the segments ... | math | {
"style": "rule",
"ground_truth": "\\sqrt{44} - 6"
} | {
"split": "train",
"index": 37759,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Through the vertices \\( A \\) and \\( C \\) of triangle \\( ABC \\), lines are drawn perpendicular to the bisector of angle \\( ABC \\), intersecting lines \\( CB \\) and \\( BA \\) at points \\( K \\) and \\( M \\) respectively. Find \\( AB \\) if \\( BM = 10 \\) and \\( KC =... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 37760,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Dean scored a total of 252 points in 28 basketball games. Ruth played 10 fewer games than Dean. Her scoring average was 0.5 points per game higher than Dean's scoring average. How many points, in total, did Ruth score? Let's think step by step and put only the final answer with... | math | {
"style": "rule",
"ground_truth": "171"
} | {
"split": "train",
"index": 37761,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose \\(x\\) and \\(y\\) are positive real numbers such that \\(x+\\frac{1}{y}=y+\\frac{2}{x}=3\\). Compute the maximum possible value of \\(xy\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3+\\sqrt{7}"
} | {
"split": "train",
"index": 37762,
"solution": "Rewrite the equations as \\(xy+1=3y\\) and \\(xy+2=3x\\). Let \\(xy=C\\), so \\(x=\\frac{C+2}{3}\\) and \\(y=\\frac{C+1}{3}\\). Then \\(\\left(\\frac{C+2}{3}\\right)\\left(\\frac{C+1}{3}\\right)=C \\Longrightarrow C^{2}-6C+2=0\\). The larger of its two roots is \\(... |
deepscaler | [
{
"role": "user",
"content": "In triangle $\\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. It is known that $\\cos A \\cos B = \\sin A \\sin B - \\frac{\\sqrt{2}}{2}$. \n$(1)$ Find the measure of angle $C$. \n$(2)$ Given $b=4$ and the area of $\\triangle AB... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{10}"
} | {
"split": "train",
"index": 37763,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all natural numbers \\( x \\) that satisfy the following conditions: the product of the digits of \\( x \\) is equal to \\( 44x - 86868 \\), and the sum of the digits is a cube of a natural number. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "1989"
} | {
"split": "train",
"index": 37764,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\sin (\\omega x+\\varphi)$ with $\\omega > 0$ and $|\\varphi| < \\frac {\\pi}{2}$, the function has a minimum period of $4\\pi$ and, after being shifted to the right by $\\frac {2\\pi}{3}$ units, becomes symmetric about the $y$-axis. Determine the valu... | math | {
"style": "rule",
"ground_truth": "-\\frac{\\pi}{6}"
} | {
"split": "train",
"index": 37765,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The new individual income tax law has been implemented since January 1, 2019. According to the \"Individual Income Tax Law of the People's Republic of China,\" it is known that the part of the actual wages and salaries (after deducting special, additional special, and other leg... | math | {
"style": "rule",
"ground_truth": "9720"
} | {
"split": "train",
"index": 37766,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $\\sin(\\alpha - \\beta) = \\frac{1}{3}$ and $\\cos \\alpha \\sin \\beta = \\frac{1}{6}$, calculate the value of $\\cos(2\\alpha + 2\\beta)$. 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": 37767,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let the odd function $f(x)$ defined on $\\mathbb{R}$ satisfy $f(2-x) = f(x)$, and it is monotonically decreasing on the interval $[0, 1)$. If the equation $f(x) = -1$ has real roots in the interval $[0, 1)$, then the sum of all real roots of the equation $f(x) = 1$ in the inter... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 37768,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a parallelogram \\\\(ABCD\\\\) where \\\\(AD=2\\\\), \\\\(∠BAD=120^{\\\\circ}\\\\), and point \\\\(E\\\\) is the midpoint of \\\\(CD\\\\), if \\\\( \\overrightarrow{AE} \\cdot \\overrightarrow{BD}=1\\\\), then \\\\( \\overrightarrow{BD} \\cdot \\overrightarrow{BE}=\\\\) \... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 37769,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $(1+\\sin t)(1+\\cos t)=5/4$ and\n$(1-\\sin t)(1-\\cos t)=\\frac mn-\\sqrt{k},$\nwhere $k, m,$ and $n$ are positive integers with $m$ and $n$ relatively prime, find $k+m+n.$\n Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "27"
} | {
"split": "train",
"index": 37770,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The radius of Earth at the equator is approximately 4000 miles. Suppose a jet flies once around Earth at a speed of 500 miles per hour relative to Earth. If the flight path is a neglibile height above the equator, then, among the following choices, the best estimate of the numb... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 37771,
"solution": "1. **Calculate the circumference of the Earth at the equator:** \n The formula for the circumference, $C$, of a circle is given by:\n \\[\n C = 2\\pi r\n \\]\n where $r$ is the radius of the circle. Given that the radius of the Earth at the equator is ap... |
deepscaler | [
{
"role": "user",
"content": "What is the perimeter of the figure shown if $x=3$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 37772,
"solution": "Since $x=3$, the side lengths of the figure are $4,3,6$, and 10. Thus, the perimeter of the figure is $4+3+6+10=23$. (Alternatively, the perimeter is $x+6+10+(x+1)=2x+17$. When $x=3$, this equals $2(3)+17$ or 23.)"
} |
deepscaler | [
{
"role": "user",
"content": "The solution of $\\sqrt{5x-1}+\\sqrt{x-1}=2$ is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x=1"
} | {
"split": "train",
"index": 37773,
"solution": "1. **Start by squaring both sides of the equation**:\n \\[\n \\left(\\sqrt{5x-1} + \\sqrt{x-1}\\right)^2 = 2^2\n \\]\n Expanding the left side using the identity $(a+b)^2 = a^2 + 2ab + b^2$, we get:\n \\[\n \\sqrt{5x-1}^2 + 2\\sqrt{5x-1}\\sqrt{x-1} + \\... |
deepscaler | [
{
"role": "user",
"content": "Bertha has 6 daughters and no sons. Some of her daughters have 6 daughters, and the rest have none. Bertha has a total of 30 daughters and granddaughters, and no great-granddaughters. How many of Bertha's daughters and granddaughters have no daughters? Let's think step by step ... | math | {
"style": "rule",
"ground_truth": "26"
} | {
"split": "train",
"index": 37774,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Eugene swam on Sunday, Monday, and Tuesday. On Monday, he swam for 30 minutes. On Tuesday, he swam for 45 minutes. His average swim time over the three days was 34 minutes. For how many minutes did he swim on Sunday? Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "27"
} | {
"split": "train",
"index": 37775,
"solution": "Since Eugene swam three times and had an average swim time of 34 minutes, he swam for \\( 3 \\times 34 = 102 \\) minutes in total. Since he swam for 30 minutes and 45 minutes on Monday and Tuesday, then on Sunday, he swam for \\( 102 - 30 - 45 = 27 \\) minutes."
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( \\mathrm{a}, \\mathrm{b}, \\mathrm{c} \\) are three natural numbers, and the least common multiple (LCM) of \\( \\mathrm{a} \\) and \\( \\mathrm{b} \\) is 60, and the LCM of \\( \\mathrm{a} \\) and \\( \\mathrm{c} \\) is 270, find the LCM of \\( \\mathrm{b} \\) a... | math | {
"style": "rule",
"ground_truth": "540"
} | {
"split": "train",
"index": 37776,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC,$ point $D$ is on $\\overline{BC}$ with $CD = 2$ and $DB = 5,$ point $E$ is on $\\overline{AC}$ with $CE = 1$ and $EA = 3,$ $AB = 8,$ and $\\overline{AD}$ and $\\overline{BE}$ intersect at $P.$ Points $Q$ and $R$ lie on $\\overline{AB}$ so that $\\overline{PQ}$... | math | {
"style": "rule",
"ground_truth": "901"
} | {
"split": "train",
"index": 37777,
"solution": "[asy] size(10cm); pair A,B,C,D,E,P,Q,R; A=(0,0); B=(8,0); C=(1.9375,3.4994); D=(3.6696,2.4996); E=(1.4531,2.6246); P=(2.9639,2.0189); Q=(1.8462,0); R=(6.4615,0); dot(A); dot(B); dot(C); dot(D); dot(E); dot(P); dot(Q); dot(R); label(\"$A$\",A,WSW); label(\"$B$\",B,E... |
deepscaler | [
{
"role": "user",
"content": "Seventy percent of a train's passengers are women, and fifteen percent of those women are in the luxury compartment. What is the number of women in the luxury compartment if the train is carrying 300 passengers? Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 37778,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Rationalize the denominator of $\\frac{3}{2\\sqrt[3]{5}}$. The answer can be written in the form of $\\frac{A\\sqrt[3]{B}}{C}$, where $A$, $B$, and $C$ are integers, $C$ is positive, and $B$ is not divisible by the cube of any prime. Find $A+B+C$. Let's think step by step and p... | math | {
"style": "rule",
"ground_truth": "38"
} | {
"split": "train",
"index": 37779,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ice-cream-o-rama is eager to advertise how many flavors it has. But it really only has three basic flavors: chocolate, vanilla, and strawberry. However, they can make \"new\" flavors by taking four scoops of ice cream of those basic flavors and blending them together. Different... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 37780,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a large box of ribbons, $\\frac{1}{4}$ are yellow, $\\frac{1}{3}$ are purple, $\\frac{1}{6}$ are orange, and the remaining 40 are black. How many of the ribbons are orange? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "27"
} | {
"split": "train",
"index": 37781,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A large batch of tires contains $1.5\\%$ defects. What should be the sample size for the probability of finding at least one defective tire in the sample to be more than $0.92 ?$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "168"
} | {
"split": "train",
"index": 37782,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the arithmetic sequence $\\{a\\_n\\}$, the common difference $d=\\frac{1}{2}$, and the sum of the first $100$ terms $S\\_{100}=45$. Find the value of $a\\_1+a\\_3+a\\_5+...+a\\_{99}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-69"
} | {
"split": "train",
"index": 37783,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate $\\sqrt{\\sqrt[3]{0.000064}}$. Express your answer as a decimal to the nearest tenth. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.2"
} | {
"split": "train",
"index": 37784,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=3\\sin ( \\frac {1}{2}x+ \\frac {π}{4})-1$, where $x\\in R$, find:\n1) The minimum value of the function $f(x)$ and the set of values of the independent variable $x$ at this time;\n2) How is the graph of the function $y=\\sin x$ transformed to obtain th... | math | {
"style": "rule",
"ground_truth": "(4)"
} | {
"split": "train",
"index": 37785,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the last two digits of base- $3$ representation of $2005^{2003^{2004}+3}$ ? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 37786,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For all $x \\in (0, +\\infty)$, the inequality $(2x - 2a + \\ln \\frac{x}{a})(-2x^{2} + ax + 5) \\leq 0$ always holds. Determine the range of values for the real number $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\left\\{ \\sqrt{5} \\right\\}"
} | {
"split": "train",
"index": 37787,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A spider is making a web between $n>1$ distinct leaves which are equally spaced around a circle. He chooses a leaf to start at, and to make the base layer he travels to each leaf one at a time, making a straight line of silk between each consecutive pair of leaves, such that no... | math | {
"style": "rule",
"ground_truth": "n 2^{n-2}"
} | {
"split": "train",
"index": 37788,
"solution": "There are $n$ ways to choose a starting vertex, and at each vertex he has only two choices for where to go next: the nearest untouched leaf in the clockwise direction, and the nearest untouched leaf in the counterclockwise direction. For, if the spider visited a le... |
deepscaler | [
{
"role": "user",
"content": "Start with an angle of \\(60^\\circ\\) and bisect it, then bisect the lower \\(30^\\circ\\) angle, then the upper \\(15^\\circ\\) angle, and so on, always alternating between the upper and lower of the previous two angles constructed. This process approaches a limiting line tha... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 37789,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the sets \\( A = \\{(x, y) \\mid |x| + |y| = a, a > 0\\} \\) and \\( B = \\{(x, y) \\mid |xy| + 1 = |x| + |y| \\} \\), if the intersection \\( A \\cap B \\) is the set of vertices of a regular octagon in the plane, determine the value of \\( a \\). Let's think step by ste... | math | {
"style": "rule",
"ground_truth": "2 + \\sqrt{2}"
} | {
"split": "train",
"index": 37790,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number $a=\\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers, has the property that the sum of all real numbers $x$ satisfying\n\\[\\lfloor x \\rfloor \\cdot \\{x\\} = a \\cdot x^2\\]is $420$, where $\\lfloor x \\rfloor$ denotes the greatest integer les... | math | {
"style": "rule",
"ground_truth": "929"
} | {
"split": "train",
"index": 37791,
"solution": "1. **Define Variables**:\n Let $w = \\lfloor x \\rfloor$ and $f = \\{x\\}$ denote the whole part and the fractional part of $x$, respectively. Thus, $x = w + f$ where $0 \\leq f < 1$.\n\n2. **Rewrite the Equation**:\n The given equation is:\n \\[\n \\lfloor... |
deepscaler | [
{
"role": "user",
"content": "Find all real numbers $k$ for which there exists a nonzero, 2-dimensional vector $\\mathbf{v}$ such that\n\\[\\begin{pmatrix} 1 & 8 \\\\ 2 & 1 \\end{pmatrix} \\mathbf{v} = k \\mathbf{v}.\\]Enter all the solutions, separated by commas. Let's think step by step and put only the f... | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 37792,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A math teacher requires Noelle to do one homework assignment for each of the first five homework points she wants to earn; for each of the next five homework points, she needs to do two homework assignments; and so on, so that to earn the $n^{\\text{th}}$ homework point, she ha... | math | {
"style": "rule",
"ground_truth": "75"
} | {
"split": "train",
"index": 37793,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Chewbacca has 25 pieces of orange gum and 35 pieces of apple gum. Some of the pieces are in complete packs, while others are loose. Each complete pack has exactly $y$ pieces of gum. If Chewbacca loses two packs of orange gum, then the ratio of the number of pieces of orange gum... | math | {
"style": "rule",
"ground_truth": "\\frac{15}{4}"
} | {
"split": "train",
"index": 37794,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Kenton watched 2000 adult men and women board a cruise ship. Half of the adults were women. If 20$\\%$ of the women and 9$\\%$ of the men were wearing sunglasses, what was the total number of men and women wearing sunglasses? Let's think step by step and put only the final answ... | math | {
"style": "rule",
"ground_truth": "290"
} | {
"split": "train",
"index": 37795,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the minimum number of participants that could have been in the school drama club if fifth-graders constituted more than $25\\%$, but less than $35\\%$; sixth-graders more than $30\\%$, but less than $40\\%$; and seventh-graders more than $35\\%$, but less than $45\\%$ (... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 37796,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the value of $-1 + 2 + 3 + 4 - 5 - 6 - 7 - 8 - 9 + \\dots + 10000$, where the signs change after each perfect square. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1000000"
} | {
"split": "train",
"index": 37797,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nGiven a triangle with side lengths \\( l, m, n \\), where \\( l > m > n \\) are integers, and it is known that:\n\\[\n\\left\\{\\frac{3^{l}}{10^{4}}\\right\\} = \\left\\{\\frac{3^{m}}{10^{4}}\\right\\} = \\left\\{\\frac{3^{n}}{10^{4}}\\right\\}\n\\]\nwhere \\( \\{x\\} = x - \... | math | {
"style": "rule",
"ground_truth": "3003"
} | {
"split": "train",
"index": 37798,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the positive sequence $\\{a_n\\}$, where $a_1=2$, $a_2=1$, and $\\frac {a_{n-1}-a_{n}}{a_{n}a_{n-1}}= \\frac {a_{n}-a_{n+1}}{a_{n}a_{n+1}}(n\\geqslant 2)$, find the value of the 2016th term of this sequence. Let's think step by step and put only the final answer within \\... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{1008}"
} | {
"split": "train",
"index": 37799,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a hyperbola $C_{1}$ defined by $2x^{2}-y^{2}=1$, find the area of the triangle formed by a line parallel to one of the asymptotes of $C_{1}$, the other asymptote, and the x-axis. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{8}"
} | {
"split": "train",
"index": 37800,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the repeating decimal 0.2017, if the sum of all digits from the $m$-th digit to the $n$-th digit after the decimal point is 2017, find the value of $n$ when $m$ takes the minimum value. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "808"
} | {
"split": "train",
"index": 37801,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Place parentheses and operation signs in the sequence 22222 so that the result is 24. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(2+2+2) \\times (2+2)"
} | {
"split": "train",
"index": 37802,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "$(4^{-1} - 3^{-1})^{-1} = $ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-12"
} | {
"split": "train",
"index": 37803,
"solution": "1. **Rewrite the expression using the properties of exponents and reciprocals:**\n \\[\n (4^{-1} - 3^{-1})^{-1} = \\left(\\frac{1}{4} - \\frac{1}{3}\\right)^{-1}\n \\]\n\n2. **Find a common denominator for the fractions inside the parentheses:**\n \\[\n \... |
deepscaler | [
{
"role": "user",
"content": "Two sectors of a circle of radius $12$ overlap as shown, with $P$ and $R$ as the centers of the respective circles. Determine the area of the shaded region.\n\n[asy]\ndraw((0,0)--(10.3923,-6)--(20.7846,0)--(10.3923,6)--cycle,black+linewidth(1));\nfilldraw((10.3923,6)..(12,0)..(... | math | {
"style": "rule",
"ground_truth": "48\\pi-72\\sqrt{3}"
} | {
"split": "train",
"index": 37804,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many ordered pairs of positive integers $(x, y)$ with $x < y$ is the harmonic mean of $x$ and $y$ equal to $4^{15}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "29"
} | {
"split": "train",
"index": 37805,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the number of square units in the area of trapezoid ABCD with vertices A(0,0), B(0,-2), C(4,0), and D(4,6)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 37806,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The line passing through the point $(0,-2)$ intersects the parabola $y^{2}=16x$ at two points $A(x_1,y_1)$ and $B(x_2,y_2)$, with $y_1^2-y_2^2=1$. Calculate the area of the triangle $\\triangle OAB$, where $O$ is the origin. Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{16}"
} | {
"split": "train",
"index": 37807,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and they satisfy the equation $2acosC + ccosA = b$.\n(I) Find the measure of angle $C$;\n(II) Find the maximum value of $sinAcosB + sinB$. Let's think step by ... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{4}"
} | {
"split": "train",
"index": 37808,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $B = (20, 14)$ and $C = (18, 0)$ be two points in the plane. For every line $\\ell$ passing through $B$ , we color red the foot of the perpendicular from $C$ to $\\ell$ . The set of red points enclose a bounded region of area $\\mathcal{A}$ . Find $\\lfloor \\m... | math | {
"style": "rule",
"ground_truth": "157"
} | {
"split": "train",
"index": 37809,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( A \\) be a 4-digit integer. When both the first digit (left-most) and the third digit are increased by \\( n \\), and the second digit and the fourth digit are decreased by \\( n \\), the new number is \\( n \\) times \\( A \\). Find the value of \\( A \\). Let's think ... | math | {
"style": "rule",
"ground_truth": "1818"
} | {
"split": "train",
"index": 37810,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The quadratic polynomial \\( f(x) = a x^{2} + b x + c \\) has exactly one root, and the quadratic polynomial \\( f(3x + 2) - 2f(2x - 1) \\) also has exactly one root. Find the root of the polynomial \\( f(x) \\). Let's think step by step and put only the final answer within \\b... | math | {
"style": "rule",
"ground_truth": "-7"
} | {
"split": "train",
"index": 37811,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A test has ten questions. Points are awarded as follows:\n\n- Each correct answer is worth 3 points.\n- Each unanswered question is worth 1 point.\n- Each incorrect answer is worth 0 points.\n\nA total score that is not possible is: Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "29"
} | {
"split": "train",
"index": 37812,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(p\\), \\(q\\), \\(r\\), \\(s\\), and \\(t\\) be positive integers such that \\(p+q+r+s+t=3015\\) and let \\(N\\) be the largest of the sums \\(p+q\\), \\(q+r\\), \\(r+s\\), and \\(s+t\\). What is the smallest possible value of \\(N\\)? Let's think step by step and put on... | math | {
"style": "rule",
"ground_truth": "1508"
} | {
"split": "train",
"index": 37813,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Wei decides to modify the design of his logo by using a larger square and three tangent circles instead. Each circle remains tangent to two sides of the square and to one adjacent circle. If each side of the square is now 24 inches, calculate the number of square inches that wi... | math | {
"style": "rule",
"ground_truth": "576 - 108\\pi"
} | {
"split": "train",
"index": 37814,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For two real values of $n$, the equation $4x^2+nx+25=0$ has exactly one solution in $x$. What is the positive value of $n$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 37815,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A company plans to advertise on TV stations A and B for a total time of no more than 300 minutes in 2011, with an advertising budget of no more than 90,000 yuan. The advertising rates for TV stations A and B are 500 yuan/minute and 200 yuan/minute, respectively. Assuming that f... | math | {
"style": "rule",
"ground_truth": "70"
} | {
"split": "train",
"index": 37816,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many ordered triplets $(a, b, c)$ of positive integers less than 10 is the product $a \\times b \\times c$ divisible by 20? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "102"
} | {
"split": "train",
"index": 37817,
"solution": "One number must be 5. The other two must have a product divisible by 4. Either both are even, or one is divisible by 4 and the other is odd. In the former case, there are $48=3 \\times 4 \\times 4$ possibilities: 3 positions for the 5, and any of 4 even numbers to ... |
deepscaler | [
{
"role": "user",
"content": "Find the smallest number composed exclusively of ones that is divisible by 333...33 (where there are 100 threes in the number). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "300"
} | {
"split": "train",
"index": 37818,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Five brothers divided their father's inheritance equally. The inheritance included three houses. Since it was not possible to split the houses, the three older brothers took the houses, and the younger brothers were given money: each of the three older brothers paid $2,000. How... | math | {
"style": "rule",
"ground_truth": "3000"
} | {
"split": "train",
"index": 37819,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Using the same relationships between ball weights, how many blue balls are needed to balance $5$ green, $3$ yellow, and $3$ white balls? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"split": "train",
"index": 37820,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given vectors $\\overrightarrow{a}, \\overrightarrow{b}$ satisfy $\\overrightarrow{a}=(1, \\sqrt {3}), |\\overrightarrow{b}|=1, |\\overrightarrow{a}+ \\overrightarrow{b}|= \\sqrt {3}$, then the angle between $\\overrightarrow{a}$ and $\\overrightarrow{b}$ is ______. Let's think... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\pi}{3}"
} | {
"split": "train",
"index": 37821,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The cost of two pencils and three pens is $4.10, and the cost of three pencils and one pen is $2.95. What is the cost of one pencil and four pens? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4.34"
} | {
"split": "train",
"index": 37822,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given four points O, A, B, C on a plane satisfying OA=4, OB=3, OC=2, and $\\overrightarrow{OB} \\cdot \\overrightarrow{OC} = 3$, find the maximum area of $\\triangle ABC$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{7} + \\frac{3\\sqrt{3}}{2}"
} | {
"split": "train",
"index": 37823,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find a number \\( N \\) with five digits, all different and none zero, which equals the sum of all distinct three-digit numbers whose digits are all different and are all digits of \\( N \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "35964"
} | {
"split": "train",
"index": 37824,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Anton has two species of ants, Species A and Species B, in his ant farm. The two species are identical in appearance, but Anton knows that every day, there are twice as many ants of Species A than before, while there are three times as many ants of Species B. On Day 0, Anton co... | math | {
"style": "rule",
"ground_truth": "608"
} | {
"split": "train",
"index": 37825,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "After expanding and combining like terms in the expression \\((x+y+z)^{2028} + (x-y-z)^{2028}\\), how many monomials of the form \\(x^{a} y^{b} z^{c}\\) have a non-zero coefficient? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1030225"
} | {
"split": "train",
"index": 37826,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "At a large gathering hosted by Benjamin Franklin, each man shakes hands with every other attendee except their own spouse and except Benjamin Franklin, who is also present. No handshakes take place between women, and Franklin only shakes hands with the women. If 15 married coup... | math | {
"style": "rule",
"ground_truth": "225"
} | {
"split": "train",
"index": 37827,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest possible positive integer value of $x$ if $\\displaystyle\\frac{x^4}{x^2} < 10$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 37828,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify first, then evaluate: $(1-\\frac{a}{a+1})\\div \\frac{{a}^{2}-1}{{a}^{2}+2a+1}$, where $a=\\sqrt{2}+1$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 37829,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a positive integer $n$ such that $(n+1)! + (n+2)! = n! \\cdot 440$. 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": "10"
} | {
"split": "train",
"index": 37830,
"solution": "\nWe start with the given equation:\n\\[\n(n+1)! + (n+2)! = n! \\cdot 440\n\\]\n\nFirst, we express the factorials in terms of \\(n!\\):\n\\[\n(n+1)! = (n+1)n!\n\\]\n\\[\n(n+2)! = (n+2)(n+1)n!\n\\]\n\nSubstituting these into the equation, we get:\n\\[\n(n+1)n! + (n... |
deepscaler | [
{
"role": "user",
"content": "Given that the terminal side of angle $\\alpha$ passes through point $P(-4a, 3a) (a \\neq 0)$, find the value of $\\sin \\alpha + \\cos \\alpha - \\tan \\alpha$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{19}{20}"
} | {
"split": "train",
"index": 37831,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find $n$ such that $2^8 \\cdot 3^4 \\cdot 5^1 \\cdot n = 10!$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 37832,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A crew of workers was tasked with pouring ice rinks on a large and a small field, where the area of the large field is twice the area of the small field. The part of the crew working on the large field had 4 more workers than the part of the crew working on the small field. Whe... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 37833,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An ellipse has foci at $(9,20)$ and $(49,55)$ in the $xy$-plane and is tangent to the $x$-axis. What is the length of its major axis? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "85"
} | {
"split": "train",
"index": 37834,
"solution": "An ellipse is defined as the set of points where the sum of the distances from the foci to the point is fixed. The length of major axis is equal to the sum of these distances $(2a)$. Thus if we find the sum of the distances, we get the answer. Let k be this fixed s... |
deepscaler | [
{
"role": "user",
"content": "What is the largest integer that must divide $n^5-5n^3+4n$ for all integers $n$ ?\n\n*2016 CCA Math Bonanza Lightning #2.4* Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "120"
} | {
"split": "train",
"index": 37835,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $10^n = 1000^{20}$, what is the value of $n$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 37836,
"solution": "Using exponent laws, $1000^{20}=\\left(10^{3}\\right)^{20}=10^{60}$ and so $n=60$."
} |
deepscaler | [
{
"role": "user",
"content": "Three shepherds met on a large road, each driving their respective herds. Jack says to Jim:\n\n- If I give you 6 pigs for one horse, your herd will have twice as many heads as mine.\n\nAnd Dan remarks to Jack:\n\n- If I give you 14 sheep for one horse, your herd will have three... | math | {
"style": "rule",
"ground_truth": "39"
} | {
"split": "train",
"index": 37837,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Points $( \\sqrt{\\pi} , a)$ and $( \\sqrt{\\pi} , b)$ are distinct points on the graph of $y^2 + x^4 = 2x^2 y + 1$. What is $|a-b|$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 37838,
"solution": "1. **Substitute \\( x = \\sqrt{\\pi} \\) into the equation**: Given the equation of the curve \\( y^2 + x^4 = 2x^2 y + 1 \\), we substitute \\( x = \\sqrt{\\pi} \\):\n \\[\n y^2 + (\\sqrt{\\pi})^4 = 2(\\sqrt{\\pi})^2 y + 1\n \\]\n Simplifying, we get:\n \... |
deepscaler | [
{
"role": "user",
"content": "In triangle $PQR,$ $PQ = 25$ and $QR = 10.$ Find the largest possible value of $\\tan B.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{\\sqrt{21}}"
} | {
"split": "train",
"index": 37839,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What value of $x$ satisfies the equation $$3x + 6 = |{-10 + 5x}|$$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 37840,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The denominator of the fraction $15 \\cdot 18$ in simplest form is 30. Find the sum of all such positive rational numbers less than 10. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "400"
} | {
"split": "train",
"index": 37841,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "We have an $n$-gon, and each of its vertices is labeled with a number from the set $\\{1, \\ldots, 10\\}$. We know that for any pair of distinct numbers from this set there is at least one side of the polygon whose endpoints have these two numbers. Find the smallest possible va... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 37842,
"solution": "Each number be paired with each of the 9 other numbers, but each vertex can be used in at most 2 different pairs, so each number must occur on at least $\\lceil 9 / 2\\rceil=5$ different vertices. Thus, we need at least $10 \\cdot 5=50$ vertices, so $n \\geq 50$. T... |
deepscaler | [
{
"role": "user",
"content": "Compute the exact value of the expression $\\left|\\pi - | \\pi - 7 | \\right|$. Write your answer using only integers and $\\pi$, without any absolute value signs. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7-2\\pi"
} | {
"split": "train",
"index": 37843,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a parabola with vertex V and a focus F. There exists a point B on the parabola such that BF = 25 and BV = 24. Determine the sum of all possible values of the length FV. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{50}{3}"
} | {
"split": "train",
"index": 37844,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A nine-digit integer is formed by repeating a positive three-digit integer three times. For example, 123,123,123 or 307,307,307 are integers of this form. What is the greatest common divisor of all nine-digit integers of this form? Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "1001001"
} | {
"split": "train",
"index": 37845,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Point $P$ is located inside a square $ABCD$ of side length $10$ . Let $O_1$ , $O_2$ , $O_3$ , $O_4$ be the circumcenters of $P AB$ , $P BC$ , $P CD$ , and $P DA$ , respectively. Given that $P A+P B +P C +P D = 23\\sqrt2$ and the area of $O_1O_2O_3O_4$ is $50$... | math | {
"style": "rule",
"ground_truth": "5001"
} | {
"split": "train",
"index": 37846,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n$$\n\\lim_{x \\rightarrow 1} (2-x)^{\\sin \\left(\\frac{\\pi x}{2}\\right) / \\ln (2-x)}\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "e"
} | {
"split": "train",
"index": 37847,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a country, there are 110 cities. Between each pair of cities, there is either a road or no road.\n\nA driver starts in a city with exactly one road leading out of it. After traveling along this road, he arrives at a second city, which has exactly two roads leading out of it.... | math | {
"style": "rule",
"ground_truth": "107"
} | {
"split": "train",
"index": 37848,
"solution": ""
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.