data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "1-2-3+4+5-6-7+8+9-10-11+\\cdots + 1992+1993-1994-1995+1996= Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 8900,
"solution": "1. **Group the terms**: We group the terms in sets of four as follows:\n \\[\n (1-2-3+4) + (5-6-7+8) + (9-10-11+12) + \\cdots + (1993-1994-1995+1996)\n \\]\n\n2. **Calculate the sum of each group**: \n - For the first group: \n \\[\n 1 - 2 - 3 + 4 = ... |
deepscaler | [
{
"role": "user",
"content": "Let $u,$ $v,$ and $w$ be the roots of the equation $x^3 - 18x^2 + 20x - 8 = 0.$ Find the value of $(2+u)(2+v)(2+w).$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "128"
} | {
"split": "train",
"index": 8901,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a regular tetrahedron $S-ABC$ with a base that is an equilateral triangle of side length 1 and side edges of length 2. If a plane passing through line $AB$ divides the tetrahedron's volume into two equal parts, the cosine of the dihedral angle between the plane and the ba... | math | {
"style": "rule",
"ground_truth": "\\frac{2 \\sqrt{15}}{15}"
} | {
"split": "train",
"index": 8902,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\( x, y, z \\) be positive numbers that satisfy the following system of equations:\n\n\\[\n\\begin{cases}\nx^2 + xy + y^2 = 108 \\\\\ny^2 + yz + z^2 = 9 \\\\\nz^2 + xz + x^2 = 117\n\\end{cases}\n\\]\n\nFind the value of the expression \\( xy + yz + xz \\). Let's think step... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 8903,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of integers $n$ greater than 1 such that for any integer $a$, $n$ divides $a^{25} - a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"split": "train",
"index": 8904,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A bag contains 4 blue marbles and 6 green marbles. Three marbles are drawn one after another without replacement. What is the probability that the first marble is blue, the second one is green, and the third one is also green? Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"split": "train",
"index": 8905,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of solutions to the equation $x+y+z=525$ where $x$ is a multiple of 7, $y$ is a multiple of 5, and $z$ is a multiple of 3. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"split": "train",
"index": 8906,
"solution": "First, note that $525=3 \\times 7 \\times 5 \\times 5$. Then, taking the equation modulo 7 gives that $7 \\mid x$; let $x=7 x^{\\prime}$ for some nonnegative integer $x^{\\prime}$. Similarly, we can write $y=5 y^{\\prime}$ and $z=3 z^{\\prime}$ for some nonnegative ... |
deepscaler | [
{
"role": "user",
"content": "A certain item is always sold with a 30% discount, and the profit margin is 47%. During the shopping festival, the item is sold at the original price, and there is a \"buy one get one free\" offer. Calculate the profit margin at this time. (Note: Profit margin = (selling price ... | math | {
"style": "rule",
"ground_truth": "5\\%"
} | {
"split": "train",
"index": 8907,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the value of $1006 \\sin \\frac{\\pi}{1006}$. Approximating directly by $\\pi=3.1415 \\ldots$ is worth only 3 points. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3.1415875473"
} | {
"split": "train",
"index": 8908,
"solution": "The answer is $1006 \\sin \\frac{\\pi}{1006}$. Using the third-degree Taylor polynomial for sin we can approximate $\\sin x \\approx x-\\frac{x^{3}}{6}$. This gives an answer of 3.1415875473 worth full points. If during the calculation we use the approximation $\\pi... |
deepscaler | [
{
"role": "user",
"content": "A piece of iron wire with a length of $80cm$ is randomly cut into three segments. Calculate the probability that each segment has a length of no less than $20cm$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{16}"
} | {
"split": "train",
"index": 8909,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For a $k$-element subset $T$ of the set $\\{1,2,\\cdots,242\\}$, every pair of elements (which may be the same) in $T$ has a sum that is not an integer power of 3. Find the maximum value of $k$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "121"
} | {
"split": "train",
"index": 8910,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In 2000, there were 60,000 cases of a disease reported in a country. By 2020, there were only 300 cases reported. Assume the number of cases decreased exponentially rather than linearly. Determine how many cases would have been reported in 2010. Let's think step by step and put... | math | {
"style": "rule",
"ground_truth": "4243"
} | {
"split": "train",
"index": 8911,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nCalculate the degree of ionization using the formula:\n\n$$\n\\alpha=\\sqrt{ } K_{\\mathrm{HCN}} \\mathrm{C}\n$$\n\nGiven values:\n\n$$\n\\alpha_{\\text {ion }}=\\sqrt{ }\\left(7,2 \\cdot 10^{-10}\\right) / 0,1=\\sqrt{ } 7,2 \\cdot 10^{-9}=8,5 \\cdot 10^{-5}, \\text{ or } 8,5... | math | {
"style": "rule",
"ground_truth": "0.0085"
} | {
"split": "train",
"index": 8912,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The distance from the point $(3,0)$ to one of the asymptotes of the hyperbola $\\frac{{x}^{2}}{16}-\\frac{{y}^{2}}{9}=1$ is $\\frac{9}{5}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9}{5}"
} | {
"split": "train",
"index": 8913,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a triangle $\\triangle ABC$ with sides $a$, $b$, $c$ opposite to angles $A$, $B$, $C$ respectively. If $a=2$, $A= \\frac{\\pi}{3}$, and $\\frac{\\sqrt{3}}{2} - \\sin(B-C) = \\sin 2B$, find the area of $\\triangle ABC$. Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{3}}{3}"
} | {
"split": "train",
"index": 8914,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Alice places a coin, heads up, on a table then turns off the light and leaves the room. Bill enters the room with 2 coins and flips them onto the table and leaves. Carl enters the room, in the dark, and removes a coin at random. Alice reenters the room, turns on the light and n... | math | {
"style": "rule",
"ground_truth": "3/5"
} | {
"split": "train",
"index": 8915,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a unique polynomial $P(x)$ of degree $4$ with rational coefficients and leading coefficient $1$ which has $\\sqrt{2}+\\sqrt{5}$ as a root. What is $P(1)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-4"
} | {
"split": "train",
"index": 8916,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\sin x= \\frac {3}{5}$, and $x\\in( \\frac {\\pi}{2},\\pi)$, find the values of $\\cos 2x$ and $\\tan (x+ \\frac {\\pi}{4})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {1}{7}"
} | {
"split": "train",
"index": 8917,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=2\\sin (\\pi-x)\\cos x$.\n- (I) Find the smallest positive period of $f(x)$;\n- (II) Find the maximum and minimum values of $f(x)$ in the interval $\\left[- \\frac {\\pi}{6}, \\frac {\\pi}{2}\\right]$. Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "- \\frac{ \\sqrt{3}}{2}"
} | {
"split": "train",
"index": 8918,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A child builds towers using identically shaped cubes of different colors. Determine the number of different towers with a height of 6 cubes that can be built with 3 yellow cubes, 3 purple cubes, and 2 orange cubes (Two cubes will be left out). Let's think step by step and put o... | math | {
"style": "rule",
"ground_truth": "350"
} | {
"split": "train",
"index": 8919,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the largest integer $n$ for which $12^n$ evenly divides $20!$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 8920,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If the surface area of a cone is $3\\pi$, and its lateral surface unfolds into a semicircle, then the diameter of the base of the cone is ___. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{6}"
} | {
"split": "train",
"index": 8921,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In how many ways can 10 fillér and 50 fillér coins be placed side by side (with all centers on a straight line) to cover a $1 \\mathrm{~m}$ long segment (not more), using at least 50 coins, and considering the order of the two types of coins? (Coins of the same value are not di... | math | {
"style": "rule",
"ground_truth": "270725"
} | {
"split": "train",
"index": 8922,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In acute triangle $ABC$, let $H$ be the orthocenter and $D$ the foot of the altitude from $A$. The circumcircle of triangle $BHC$ intersects $AC$ at $E \\neq C$, and $AB$ at $F \\neq B$. If $BD=3, CD=7$, and $\\frac{AH}{HD}=\\frac{5}{7}$, the area of triangle $AEF$ can be expre... | math | {
"style": "rule",
"ground_truth": "12017"
} | {
"split": "train",
"index": 8923,
"solution": "Let $AH$ intersect the circumcircle of $\\triangle ABC$ again at $P$, and the circumcircle of $\\triangle BHC$ again at Q. Because $\\angle BHC=180-\\angle A=\\angle BPC, P$ is the reflection of $H$ over $D$. Thus, we know that $PD=HD$. From power of a point and $AD... |
deepscaler | [
{
"role": "user",
"content": "Evaluate the sum $$\\lceil\\sqrt{10}\\rceil + \\lceil\\sqrt{11}\\rceil + \\lceil\\sqrt{12}\\rceil + \\cdots + \\lceil\\sqrt{40}\\rceil$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "170"
} | {
"split": "train",
"index": 8924,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the tower function $T(n)$ defined by $T(1) = 3$ and $T(n + 1) = 3^{T(n)}$ for $n \\geq 1$, calculate the largest integer $k$ for which $\\underbrace{\\log_3\\log_3\\log_3\\ldots\\log_3B}_{k\\text{ times}}$ is defined, where $B = (T(2005))^A$ and $A = (T(2005))^{T(2005)}$.... | math | {
"style": "rule",
"ground_truth": "2005"
} | {
"split": "train",
"index": 8925,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the length of the common chord of the circle $x^{2}+y^{2}=50$ and $x^{2}+y^{2}-12x-6y+40=0$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{5}"
} | {
"split": "train",
"index": 8926,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cylinder has a radius of 5 cm and a height of 12 cm. What is the longest segment, in centimeters, that would fit inside this cylinder? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2\\sqrt{61}"
} | {
"split": "train",
"index": 8927,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The distance between two parallel lines $l_1: 3x + 4y - 2 = 0$ and $l_2: ax + 6y = 5$ is _______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{15}"
} | {
"split": "train",
"index": 8928,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the polynomial of minimal degree, in $x,$ which has rational coefficients, leading coefficient $1$, and roots $1+\\sqrt{2}$ and $1+\\sqrt{3}.$ (Write the terms in decreasing order of degree.) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x^4-4x^3+x^2+6x+2"
} | {
"split": "train",
"index": 8929,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest possible sum of two consecutive integers whose product is greater than 420? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "43"
} | {
"split": "train",
"index": 8930,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In right $\\triangle ABC$ with hypotenuse $\\overline{AB}$, $AC = 12$, $BC = 35$, and $\\overline{CD}$ is the altitude to $\\overline{AB}$. Let $\\omega$ be the circle having $\\overline{CD}$ as a diameter. Let $I$ be a point outside $\\triangle ABC$ such that $\\overline{AI}$ ... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 8931,
"solution": "This solution is not a real solution and is solving the problem with a ruler and compass.\n Draw $AC = 4.8, BC = 14, AB = 14.8$. Then, drawing the tangents and intersecting them, we get that $IA$ is around $6.55$ and $IB$ is around $18.1$. We then find the ratio to ... |
deepscaler | [
{
"role": "user",
"content": "A point moving in the positive direction of the $OX$ axis has its horizontal coordinate given by $x(t) = 5(t + 1)^2 + \\frac{a}{(t + 1)^5}$, where $a$ is a positive constant. Find the minimum value of $a$ such that $x(t) \\geqslant 24$ for all $t \\geqslant 0$. Let's think step... | math | {
"style": "rule",
"ground_truth": "2 \\sqrt{\\left( \\frac{24}{7} \\right)^{7}}"
} | {
"split": "train",
"index": 8932,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate $\\lfloor 3.998 \\rfloor + \\lceil 7.002 \\rceil$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 8933,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$ the medians $AM$ and $CN$ to sides $BC$ and $AB$, respectively, intersect in point $O$. $P$ is the midpoint of side $AC$, and $MP$ intersects $CN$ in $Q$. If the area of triangle $OMQ$ is $n$, then the area of triangle $ABC$ is: Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "24n"
} | {
"split": "train",
"index": 8934,
"solution": "1. **Construct the Triangle and Medians**: Begin by constructing triangle $\\triangle ABC$. Let $M$, $N$, and $P$ be the midpoints of sides $\\overline{BC}$, $\\overline{AB}$, and $\\overline{AC}$ respectively. Draw the medians $\\overline{AM}$, $\\overline{BP}$, an... |
deepscaler | [
{
"role": "user",
"content": "A green point and a purple point are chosen at random on the number line between 0 and 1. What is the probability that the purple point is greater than the green point but less than three times the green point? Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 8935,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A triangle has a base of 20 inches. Two lines are drawn parallel to the base, intersecting the other two sides and dividing the triangle into four regions of equal area. Determine the length of the parallel line closer to the base. Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 8936,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For which values of the parameter \\(a\\) does the equation \\(x^{3} + 16x^{2} + ax + 64 = 0\\) have three distinct real roots that form a geometric progression? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 8937,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $b$ be a number such that $(2b+5)(b-1)=6b.$ What is the largest possible value of $b$? Express your answer as a common fraction. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{2}"
} | {
"split": "train",
"index": 8938,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all functions $ f: \\mathbb{R}^{ \\plus{} }\\to\\mathbb{R}^{ \\plus{} }$ satisfying $ f\\left(x \\plus{} f\\left(y\\right)\\right) \\equal{} f\\left(x \\plus{} y\\right) \\plus{} f\\left(y\\right)$ for all pairs of positive reals $ x$ and $ y$. Here, $ \\mathbb{R}^{ \\plus... | math | {
"style": "rule",
"ground_truth": "f(x) = 2x"
} | {
"split": "train",
"index": 8939,
"solution": "\nTo find all functions \\( f: \\mathbb{R}^{+} \\to \\mathbb{R}^{+} \\) satisfying the given functional equation:\n\n\\[\nf(x + f(y)) = f(x + y) + f(y)\n\\]\n\nfor all positive real numbers \\( x \\) and \\( y \\), we will proceed as follows.\n\n### Step 1: Explorin... |
deepscaler | [
{
"role": "user",
"content": "What is the number of centimeters in the length of $EF$ if $AB\\parallel CD\\parallel EF$?\n\n[asy]\n\nsize(4cm,4cm);\npair A,B,C,D,E,F,X;\n\nA=(0,1);\nB=(1,1);\nC=(1,0);\nX=(0,0);\nD=(1/3)*C+(2/3)*X;\n\ndraw (A--B--C--D);\ndraw(D--B);\ndraw(A--C);\n\nE=(0.6,0.4);\nF=(1,0.4);\n... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 8940,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the polynomials $P(x) = x^{6} - x^{5} - x^{3} - x^{2} - x$ and $Q(x) = x^{4} - x^{3} - x^{2} - 1.$ Given that $z_{1},z_{2},z_{3},$ and $z_{4}$ are the roots of $Q(x) = 0,$ find $P(z_{1}) + P(z_{2}) + P(z_{3}) + P(z_{4}).$ Let's think step by step and put only the final... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 8941,
"solution": "Let $S_k=z_1^k+z_2^k+z_3^k+z_4^k$ then by Vieta's Formula we have \\[S_{-1}=\\frac{z_1z_2z_3+z_1z_3z_4+z_1z_2z_4+z_1z_2z_3}{z_1z_2z_3z_4}=0\\] \\[S_0=4\\] \\[S_1=1\\] \\[S_2=3\\] By Newton's Sums we have \\[a_4S_k+a_3S_{k-1}+a_2S_{k-2}+a_1S_{k-1}+a_0S_{k-4}=0\\]\n A... |
deepscaler | [
{
"role": "user",
"content": "An unfair coin has the property that when flipped four times, it has the same probability of turning up 2 heads and 2 tails (in any order) as 3 heads and 1 tail (in any order). What is the probability of getting a head in any one flip? Let's think step by step and put only the ... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"split": "train",
"index": 8942,
"solution": "Let $p$ be the probability of getting a head in one flip. There are 6 ways to get 2 heads and 2 tails, each with probability $p^{2}(1-p)^{2}$, and 4 ways to get 3 heads and 1 tail, each with probability $p^{3}(1-p)$. We are given that $6 p^{2}(1-p)^{2}=4 p^{3}(1-p)$... |
deepscaler | [
{
"role": "user",
"content": "In the year 2001, the United States will host the International Mathematical Olympiad. Let $I$, $M$, and $O$ be distinct positive integers such that the product $I\\cdot M\\cdot O=2001$. What is the largest possible value of the sum $I+M+O$? Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "671"
} | {
"split": "train",
"index": 8943,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is $8^{15} \\div 64^3$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8^9"
} | {
"split": "train",
"index": 8944,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the lines $l_{1}$: $ax+y+3=0$ and $l_{2}$: $2x+\\left(a-1\\right)y+a+1=0$ are parallel, find the value of $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 8945,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $a$, $b$, and $c$ are positive numbers such that $ab = 24\\sqrt{3}$, $ac = 30\\sqrt{3}$, and $bc = 40\\sqrt{3}$, find the value of $abc$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "120\\sqrt{6}"
} | {
"split": "train",
"index": 8946,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Call a string of letters $S$ an almost palindrome if $S$ and the reverse of $S$ differ in exactly two places. Find the number of ways to order the letters in $H M M T T H E M E T E A M$ to get an almost palindrome. Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "2160"
} | {
"split": "train",
"index": 8947,
"solution": "Note that $T, E, A$ are used an odd number of times. Therefore, one must go in the middle spot and the other pair must match up. There are are $3 \\cdot 2\\left(\\frac{6!}{2!}\\right)=2160$ ways to fill in the first six spots with the letters $T, H, E, M, M$ and a p... |
deepscaler | [
{
"role": "user",
"content": "In the diagram, $P$ is on $RS$ so that $QP$ bisects $\\angle SQR$. Also, $PQ=PR$, $\\angle RSQ=2y^\\circ$, and $\\angle RPQ=3y^\\circ$. What is the measure, in degrees, of $\\angle RPQ$? [asy]\n// C14\nimport olympiad;\nsize(7cm);\n\nreal x = 50; real y = 20;\n\npair q = (1, ... | math | {
"style": "rule",
"ground_truth": "108"
} | {
"split": "train",
"index": 8948,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian plane let $A = (1,0)$ and $B = \\left( 2, 2\\sqrt{3} \\right)$. Equilateral triangle $ABC$ is constructed so that $C$ lies in the first quadrant. Let $P=(x,y)$ be the center of $\\triangle ABC$. Then $x \\cdot y$ can be written as $\\tfrac{p\\sqrt{q}}{r}$, wher... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 8949,
"solution": "Rather than considering the Cartesian plane, we use complex numbers. Thus A is 1 and B is $2 + 2\\sqrt{3}i$.\n Recall that a rotation of $\\theta$ radians counterclockwise is equivalent to multiplying a complex number by $e^{i\\theta}$, but here we require a clockwi... |
deepscaler | [
{
"role": "user",
"content": "Let $x,$ $y,$ $z$ be real numbers such that\n\\begin{align*}\nx + y + z &= 4, \\\\\nx^2 + y^2 + z^2 &= 6.\n\\end{align*}Let $m$ and $M$ be the smallest and largest possible values of $x,$ respectively. Find $m + M.$ Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "\\frac{8}{3}"
} | {
"split": "train",
"index": 8950,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain operation is performed on a positive integer: if it is even, divide it by 2; if it is odd, add 1. This process continues until the number becomes 1. How many integers become 1 after exactly 10 operations? Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "55"
} | {
"split": "train",
"index": 8951,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let \\(X_{0}\\) be the interior of a triangle with side lengths 3, 4, and 5. For all positive integers \\(n\\), define \\(X_{n}\\) to be the set of points within 1 unit of some point in \\(X_{n-1}\\). The area of the region outside \\(X_{20}\\) but inside \\(X_{21}\\) can be wr... | math | {
"style": "rule",
"ground_truth": "4112"
} | {
"split": "train",
"index": 8952,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The six faces of a three-inch wooden cube are each painted red. The cube is then cut into one-inch cubes along the lines shown in the diagram. How many of the one-inch cubes have red paint on at least two faces? [asy]\n\npair A,B,C,D,E,F,G;\n\npair a,c,d,f,g,i,j,l,m,o,p,r,s,u,v... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 8953,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABCD$ be a convex quadrilateral with $AB = AD$ and $CB = CD$. The bisector of $\\angle BDC$ intersects $BC$ at $L$, and $AL$ intersects $BD$ at $M$, and it is known that $BL = BM$. Determine the value of $2\\angle BAD + 3\\angle BCD$. Let's think step by step and put only ... | math | {
"style": "rule",
"ground_truth": "540^\\circ"
} | {
"split": "train",
"index": 8954,
"solution": "\nLet \\(ABCD\\) be a convex quadrilateral where \\(AB = AD\\) and \\(CB = CD\\). Given that the bisector of \\(\\angle BDC\\) intersects \\(BC\\) at \\(L\\), and \\(AL\\) intersects \\(BD\\) at \\(M\\), we are informed that \\(BL = BM\\). We are to determine the va... |
deepscaler | [
{
"role": "user",
"content": "A conference center is setting up chairs in rows for a seminar. Each row can seat $13$ chairs, and currently, there are $169$ chairs set up. They want as few empty seats as possible but need to maintain complete rows. If $95$ attendees are expected, how many chairs should be re... | math | {
"style": "rule",
"ground_truth": "65"
} | {
"split": "train",
"index": 8955,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of solutions to the equation\n\\[\\tan (3 \\pi \\cos \\theta) = \\cot (3 \\pi \\sin \\theta)\\]\nwhere $\\theta \\in (0, 3\\pi)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 8956,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A fair die is rolled six times. The probability of rolling at least a five at least five times is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{13}{729}"
} | {
"split": "train",
"index": 8957,
"solution": "1. **Determine the probability of rolling at least a five on a single roll**: \n A fair die has six faces, and rolling at least a five corresponds to rolling either a five or a six. There are 2 favorable outcomes (5 and 6) out of 6 possible outcomes. Thus, the pro... |
deepscaler | [
{
"role": "user",
"content": "Consider the operation \"minus the reciprocal of,\" defined by $a \\diamond b = a - \\frac{1}{b}$. What is $((1 \\diamond 2) \\diamond 3) - (1 \\diamond (2 \\diamond 3))$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{7}{30}"
} | {
"split": "train",
"index": 8958,
"solution": "1. **Calculate \\(1 \\diamond 2\\):**\n \\[\n 1 \\diamond 2 = 1 - \\frac{1}{2} = \\frac{2}{2} - \\frac{1}{2} = \\frac{1}{2}\n \\]\n\n2. **Calculate \\((1 \\diamond 2) \\diamond 3\\):**\n \\[\n \\left(\\frac{1}{2}\\right) \\diamond 3 = \\frac{1}{2} - \\frac... |
deepscaler | [
{
"role": "user",
"content": "In a table containing $A$ columns and 100 rows, natural numbers from 1 to $100 \\cdot A$ are written by rows in ascending order, starting from the first row. The number 31 is in the fifth row. In which row is the number 100? Let's think step by step and put only the final answe... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 8959,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given \\( a=\\underset{2016 \\uparrow}{55 \\cdots 5} \\), what is the remainder when \\( a \\) is divided by 84? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "63"
} | {
"split": "train",
"index": 8960,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nOleg drew an empty 50×50 table and wrote a number above each column and next to each row.\n\nIt turned out that all 100 written numbers are different, with 50 of them being rational and the remaining 50 being irrational. Then, in each cell of the table, he wrote the sum of th... | math | {
"style": "rule",
"ground_truth": "1250"
} | {
"split": "train",
"index": 8961,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On the board, there are \\( n \\) different integers, each pair of which differs by at least 10. The sum of the squares of the three largest among them is less than three million. The sum of the squares of the three smallest among them is also less than three million. What is t... | math | {
"style": "rule",
"ground_truth": "202"
} | {
"split": "train",
"index": 8962,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given are $100$ positive integers whose sum equals their product. Determine the minimum number of $1$ s that may occur among the $100$ numbers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "95"
} | {
"split": "train",
"index": 8963,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that \\( p \\) is a prime number and \\( r \\) is the remainder when \\( p \\) is divided by 210, if \\( r \\) is a composite number that can be expressed as the sum of two perfect squares, find \\( r \\). Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "169"
} | {
"split": "train",
"index": 8964,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For which $x$ and $y$ is the number $x x y y$ a square of a natural number? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7744"
} | {
"split": "train",
"index": 8965,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a biased coin with probabilities of $\\frac{3}{4}$ for heads and $\\frac{1}{4}$ for tails, determine the difference between the probability of winning Game A, which involves 4 coin tosses and at least three heads, and the probability of winning Game B, which involves 5 co... | math | {
"style": "rule",
"ground_truth": "\\frac{89}{256}"
} | {
"split": "train",
"index": 8966,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nIn the \"Triangle\" cinema, the seats are arranged in the shape of a triangle: the first row has one seat numbered 1, the second row has seats numbered 2 and 3, the third row has seats numbered 4, 5, 6, and so on. We define the best seat in the cinema hall as the one located ... | math | {
"style": "rule",
"ground_truth": "1035"
} | {
"split": "train",
"index": 8967,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $S = \\{1, 2, 3, 4\\}$. Let $a_{1}, a_{2}, \\cdots, a_{k}$ be a sequence composed of numbers from $S$, which includes all permutations of $(1, 2, 3, 4)$ that do not end with 1. That is, if $\\left(b_{1}, b_{2}, b_{3}, b_{4}\\right)$ is a permutation of $(1, 2, 3, 4)$ and ... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 8968,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=\\sin x+\\lambda\\cos x (\\lambda\\in\\mathbb{R})$ is symmetric about $x=-\\frac{\\pi}{4}$, find the equation of one of the axes of symmetry of function $g(x)$ obtained by expanding the horizontal coordinate of each point of the graph of $f(x)$ by a fac... | math | {
"style": "rule",
"ground_truth": "\\frac{11\\pi}{6}"
} | {
"split": "train",
"index": 8969,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a card game called \"Twelve Months\" that is played only during the Chinese New Year. The rules are as follows:\n\nStep 1: Take a brand new deck of playing cards, remove the two jokers and the four Kings, leaving 48 cards. Shuffle the remaining cards.\n\nStep 2: Lay ou... | math | {
"style": "rule",
"ground_truth": "1/12"
} | {
"split": "train",
"index": 8970,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 10 steps, and one can take 1, 2, or 3 steps at a time to complete them in 7 moves. Calculate the total number of different ways to do this. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "77"
} | {
"split": "train",
"index": 8971,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the sum of the squares of cosine for the angles progressing by 10 degrees starting from 0 degrees up to 180 degrees:\n\\[\\cos^2 0^\\circ + \\cos^2 10^\\circ + \\cos^2 20^\\circ + \\dots + \\cos^2 180^\\circ.\\] Let's think step by step and put only the final answer wit... | math | {
"style": "rule",
"ground_truth": "\\frac{19}{2}"
} | {
"split": "train",
"index": 8972,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve $x=\\sqrt{x-\\frac{1}{x}}+\\sqrt{1-\\frac{1}{x}}$ for $x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1+\\sqrt{5}}{2}"
} | {
"split": "train",
"index": 8973,
"solution": "$\\frac{1+\\sqrt{5}}{2}$."
} |
deepscaler | [
{
"role": "user",
"content": "If $2x+7$ is a factor of $6x^3+19x^2+cx+35$, find $c$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 8974,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the greatest multiple of 3 that is less than 500 and is also a multiple of 4? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "492"
} | {
"split": "train",
"index": 8975,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 8 participants in a performance, with a total of $m$ shows. In each show, 4 people perform on stage. It is required that any two of the 8 people perform together the same number of times. Find the minimum value of $m$. Let's think step by step and put only the final a... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 8976,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many integers \\( n \\) between 1 and 15 (inclusive) is \\(\\frac{n}{18}\\) a repeating decimal? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 8977,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A bullet with a mass of \\( m = 10 \\) g, flying horizontally with a speed of \\( v_{1} = 400 \\) m/s, passes through a massive board and emerges from it with a speed of \\( v_{2} = 100 \\) m/s. Find the amount of work done on the bullet by the resistive force of the board. Let... | math | {
"style": "rule",
"ground_truth": "750"
} | {
"split": "train",
"index": 8978,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the expression: $\\left(2\\left(3\\left(2\\left(3\\left(2\\left(3 \\times (2+1) \\times 2\\right)+2\\right)\\times 2\\right)+2\\right)\\times 2\\right)+2\\right)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "5498"
} | {
"split": "train",
"index": 8979,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABCD$ be a rhombus of sides $AB = BC = CD= DA = 13$ . On the side $AB$ construct the rhombus $BAFC$ outside $ABCD$ and such that the side $AF$ is parallel to the diagonal $BD$ of $ABCD$ . If the area of $BAFE$ is equal to $65$ , calculate the area of $A... | math | {
"style": "rule",
"ground_truth": "120"
} | {
"split": "train",
"index": 8980,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the diagram, $\\triangle XYZ$ is right-angled at $X,$ with $YX=60$ and $XZ=80.$ The point $W$ is on $YZ$ so that $WX$ is perpendicular to $YZ.$ Determine the length of $WZ.$ [asy]\npair X, Y, Z, W;\nY=(0,0);\nX=(36,48);\nZ=(100,0);\nW=(36,0);\ndraw(X--Y--Z--X--W);\nlabel(\"Y... | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 8981,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Knights, who always tell the truth, and liars, who always lie, live on an island. One day, 65 islanders gathered for a meeting. Each of them made the following statement in turn: \"Among the statements made earlier, the true ones are exactly 20 less than the false ones.\" How m... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 8982,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\\spadesuit$, $\\heartsuit$, $\\diamondsuit$, and $\\clubsuit$), such that there is exactly one card for any given rank and suit. Two of the suits ($\\spadesuit$ and $\\... | math | {
"style": "rule",
"ground_truth": "\\dfrac{13}{51}"
} | {
"split": "train",
"index": 8983,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of the expression $(37 + 12)^2 - (37^2 +12^2)$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "888"
} | {
"split": "train",
"index": 8984,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve the equation \\(3 \\cdot 4^{\\log_{x} 2} - 46 \\cdot 2^{\\log_{x} 2 - 1} = 8\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt[3]{2}"
} | {
"split": "train",
"index": 8985,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the sum of all the odd integers between $200$ and $600$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "80000"
} | {
"split": "train",
"index": 8986,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a certain hyperbola, the center is at $(2,0),$ one focus is at $(2,6),$ and one vertex is at $(2,-3).$ The equation of this hyperbola can be written as\n\\[\\frac{(y - k)^2}{a^2} - \\frac{(x - h)^2}{b^2} = 1.\\]Find $h + k + a + b.$ Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "3 \\sqrt{3} + 5"
} | {
"split": "train",
"index": 8987,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the rectangular coordinate system, a pole coordinate system is established with the origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. Given the curve $C$: ${p}^{2}=\\frac{12}{2+{\\mathrm{cos}}^{}θ}$ and the line $l$: $2p\\mathrm{cos}\\left(θ-\\... | math | {
"style": "rule",
"ground_truth": "\\frac{4\\sqrt{10}}{3}"
} | {
"split": "train",
"index": 8988,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, angle $ACB$ is 50 degrees, and angle $CBA$ is 70 degrees. Let $D$ be the foot of the perpendicular from $A$ to $BC$, $O$ the center of the circle circumscribed about triangle $ABC$, and $E$ the other end of the diameter which goes through $A$. Find the angl... | math | {
"style": "rule",
"ground_truth": "20^\\circ"
} | {
"split": "train",
"index": 8989,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A traffic light runs repeatedly through the following cycle: green for 45 seconds, then yellow for 5 seconds, and then red for 50 seconds. Mark picks a random five-second time interval to watch the light. What is the probability that the color changes while he is watching? Let'... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{20}"
} | {
"split": "train",
"index": 8990,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a unique two-digit positive integer $u$ for which the last two digits of $15\\cdot u$ are $45$, and $u$ leaves a remainder of $7$ when divided by $17$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "43"
} | {
"split": "train",
"index": 8991,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the sum of all integers $1 \\leq a \\leq 10$ with the following property: there exist integers $p$ and $q$ such that $p, q, p^{2}+a$ and $q^{2}+a$ are all distinct prime numbers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 8992,
"solution": "Odd $a$ fail for parity reasons and $a \\equiv 2(\\bmod 3)$ fail for $\\bmod 3$ reasons. This leaves $a \\in\\{4,6,10\\}$. It is easy to construct $p$ and $q$ for each of these, take $(p, q)=(3,5),(5,11),(3,7)$, respectively."
} |
deepscaler | [
{
"role": "user",
"content": "Find the fraction \\(\\frac{p}{q}\\) with the smallest possible natural denominator for which \\(\\frac{1}{2014} < \\frac{p}{q} < \\frac{1}{2013}\\). Enter the denominator of this fraction in the provided field. Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "4027"
} | {
"split": "train",
"index": 8993,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two teachers and 4 students need to be divided into 2 groups, each consisting of 1 teacher and 2 students. Calculate the number of different arrangements. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 8994,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $x$ and $y$ are positive integers, and $x^2 - y^2 = 53$, find the value of $x^3 - y^3 - 2(x + y) + 10$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2011"
} | {
"split": "train",
"index": 8995,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider a square flag with a red cross of uniform width and a blue triangular central region on a white background. The cross is symmetric with respect to each of the diagonals of the square. Let's say the entire cross, including the blue triangle, occupies 45% of the area of ... | math | {
"style": "rule",
"ground_truth": "1.08\\%"
} | {
"split": "train",
"index": 8996,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the trapezoid \\(ABCD\\), the bases \\(AD\\) and \\(BC\\) are 8 and 18 respectively. It is known that the circumcircle of triangle \\(ABD\\) is tangent to the lines \\(BC\\) and \\(CD\\). Find the perimeter of the trapezoid. Let's think step by step and put only the final an... | math | {
"style": "rule",
"ground_truth": "56"
} | {
"split": "train",
"index": 8997,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A wooden cube $n$ units on a side is painted red on all six faces and then cut into $n^3$ unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is $n$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 8998,
"solution": "1. **Understanding the problem**: We start with a cube of side length $n$, which is painted on all six faces. This cube is then cut into $n^3$ smaller unit cubes. Each unit cube has 6 faces. We need to find $n$ such that exactly one-fourth of the total number of fac... |
deepscaler | [
{
"role": "user",
"content": "In a vertical vessel with straight walls closed by a piston, there is water. Its height is $h=2$ mm. There is no air in the vessel. To what height must the piston be raised for all the water to evaporate? The density of water is $\\rho=1000$ kg / $\\mathrm{m}^{3}$, the molar ma... | math | {
"style": "rule",
"ground_truth": "24.258"
} | {
"split": "train",
"index": 8999,
"solution": ""
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.