data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive angle \\( x \\) for which\n\n\\[ \n2^{\\sin^2 x} \\cdot 4^{\\cos^2 x} \\cdot 2^{\\tan x} = 8 \n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 22849,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The hundreds digit of a three-digit number is $2$ more than the units digit. The digits of the three-digit number are reversed, and the result is subtracted from the original three-digit number. What is the units digit of the result? Let's think step by step and put only the fi... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 22850,
"solution": "1. **Define the digits of the number**: Let the hundreds, tens, and units digits of the original three-digit number be $a$, $b$, and $c$, respectively.\n\n2. **Use the given relationship**: We know that the hundreds digit $a$ is $2$ more than the units digit $c$. T... |
deepscaler | [
{
"role": "user",
"content": "Determine the value of the following product with a short calculation:\n\n$$\n\\frac{6 \\cdot 27^{12}+2 \\cdot 81^{9}}{8000000^{2}} \\cdot \\frac{80 \\cdot 32^{3} \\cdot 125^{4}}{9^{19}-729^{6}}\n$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 22851,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the value of $a^3 - b^3$ given that $a+b=12$ and $ab=20$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "992"
} | {
"split": "train",
"index": 22852,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Using an electric stove with a power of $P=500 \\mathrm{W}$, a certain amount of water is heated. When the electric stove is turned on for $t_{1}=1$ minute, the water temperature increases by $\\Delta T=2^{\\circ} \\mathrm{C}$, and after turning off the heater, the temperature ... | math | {
"style": "rule",
"ground_truth": "2.38"
} | {
"split": "train",
"index": 22853,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A hyperbola is centered at the origin and opens either horizontally or vertically. It passes through the points $(-3, 4),$ $(-2, 0),$ and $(t, 2).$ Find $t^2.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{21}{4}"
} | {
"split": "train",
"index": 22854,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given vectors $\\overrightarrow{m}=(\\cos \\alpha- \\frac{\\sqrt{2}}{3},-1)$ and $\\overrightarrow{n}=(\\sin \\alpha,1)$, vectors $\\overrightarrow{m}$ and $\\overrightarrow{n}$ are collinear, and $\\alpha \\in [-\\frac{\\pi}{2},0]$. \n$(1)$ Find the value of $\\sin \\alpha + ... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{12}"
} | {
"split": "train",
"index": 22855,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $α$ is an acute angle and $\\sin α= \\frac {3}{5}$, find the value of $\\cos α$ and $\\cos (α+ \\frac {π}{6})$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {4\\sqrt {3}-3}{10}"
} | {
"split": "train",
"index": 22856,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the area, in square units, of triangle $ABC$? [asy]\nunitsize(0.15inch);\npath X = (-6.5, 0)--(5.5, 0);\npath Y = (0, -3.5)--(0, 7.5);\ndraw(X); draw(Y);\n\nfor(int n=-6; n <= 5; ++n)\nif( n != 0 )\ndraw( (n,0.25)--(n,-0.25) );\nfor(int n=-3; n <= 7; ++n)\nif( n != 0 )\... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"split": "train",
"index": 22857,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a parallelogram with area $1$ and we will construct lines where this lines connect a vertex with a midpoint of the side no adjacent to this vertex; with the $8$ lines formed we have a octagon inside of the parallelogram. Determine the area of this octagon Let's think... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 22858,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)= \\dfrac {x+3}{x+1}$, let $f(1)+f(2)+f(4)+f(8)+f(16)=m$ and $f( \\dfrac {1}{2})+f( \\dfrac {1}{4})+f( \\dfrac {1}{8})+f( \\dfrac {1}{16})=n$, then $m+n=$ \\_\\_\\_\\_\\_\\_. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 22859,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The bases \\(AB\\) and \\(CD\\) of trapezoid \\(ABCD\\) are 155 and 13 respectively, and its lateral sides are mutually perpendicular. Find the scalar product of the vectors \\(\\overrightarrow{AC}\\) and \\(\\overrightarrow{BD}\\). Let's think step by step and put only the fin... | math | {
"style": "rule",
"ground_truth": "-2015"
} | {
"split": "train",
"index": 22860,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x \\ne 0$ or $4$ and $y \\ne 0$ or $6$, then $\\frac{2}{x} + \\frac{3}{y} = \\frac{1}{2}$ is equivalent to Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4y}{y-6}=x"
} | {
"split": "train",
"index": 22861,
"solution": "1. Start with the given equation:\n \\[\n \\frac{2}{x} + \\frac{3}{y} = \\frac{1}{2}\n \\]\n\n2. To eliminate the fractions, multiply through by $2xy$ (assuming $x \\neq 0$ and $y \\neq 0$):\n \\[\n 2xy \\left(\\frac{2}{x} + \\frac{3}{y}\\right) = 2xy \\c... |
deepscaler | [
{
"role": "user",
"content": "Joe has exactly enough paint to paint the surface of a cube whose side length is 2. It turns out that this is also exactly enough paint to paint the surface of a sphere. If the volume of this sphere is $\\frac{K \\sqrt{6}}{\\sqrt{\\pi}}$, then what is $K$? Let's think step by... | math | {
"style": "rule",
"ground_truth": "K=8"
} | {
"split": "train",
"index": 22862,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x=1$ is a solution of the equation $x^{2} + ax + 1 = 0$, what is the value of $a$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 22863,
"solution": "Since $x=1$ is a solution of the equation $x^{2} + ax + 1 = 0$, then $1^{2} + a(1) + 1 = 0$ or $2 + a = 0$ and so $a = -2$."
} |
deepscaler | [
{
"role": "user",
"content": "Let $T$ be the set of all positive integers that have five digits in base $2$. What is the sum of all the elements in $T$, when expressed in base $10$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "376"
} | {
"split": "train",
"index": 22864,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $$(x+y+z)(xy+xz+yz)=25$$and that $$x^2(y+z)+y^2(x+z)+z^2(x+y)=7$$for real numbers $x$, $y$, and $z$, what is the value of $xyz$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 22865,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four fair coins are tossed once. For every head that appears, two six-sided dice are rolled. What is the probability that the sum of all dice rolled is exactly ten?\nA) $\\frac{1} {48}$\nB) $\\frac{1} {20}$\nC) $\\frac{1} {16}$\nD) $\\frac{1} {30}$ Let's think step by step and ... | math | {
"style": "rule",
"ground_truth": "\\frac{1} {20}"
} | {
"split": "train",
"index": 22866,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The parabolas $y = (x - 2)^2$ and $x + 6 = (y - 2)^2$ intersect at four points $(x_1, y_1), (x_2, y_2), (x_3, y_3), (x_4, y_4)$. Find\n\\[\nx_1 + x_2 + x_3 + x_4 + y_1 + y_2 + y_3 + y_4.\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 22867,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A factory received a task to process 6000 pieces of part P and 2000 pieces of part Q. The factory has 214 workers. Each worker spends the same amount of time processing 5 pieces of part P as they do processing 3 pieces of part Q. The workers are divided into two groups to work ... | math | {
"style": "rule",
"ground_truth": "137"
} | {
"split": "train",
"index": 22868,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two people, A and B, form a team called \"Star Team\" to participate in a guessing idiom activity. In each round, A and B each guess an idiom. It is known that the probability of A guessing correctly in each round is $\\frac{2}{3}$, and the probability of B guessing correctly i... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{3}"
} | {
"split": "train",
"index": 22869,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For any $x \\in (0, +\\infty)$, the inequality $(x-a+\\ln \\frac{x}{a})(-2x^2+ax+10) \\leq 0$ always holds. Then, the range of the real number $a$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{10}"
} | {
"split": "train",
"index": 22870,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Alice celebrated her birthday on Friday, March 15 in the year 2012. Determine the next year when her birthday will next fall on a Monday.\nA) 2021\nB) 2022\nC) 2023\nD) 2024\nE) 2025 Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2025"
} | {
"split": "train",
"index": 22871,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the magnitude of vector $\\overrightarrow {a}$ is 1, the magnitude of vector $\\overrightarrow {b}$ is 2, and the magnitude of $\\overrightarrow {a}+ \\overrightarrow {b}$ is $\\sqrt {7}$, find the angle between $\\overrightarrow {a}$ and $\\overrightarrow {b}$. Let'... | math | {
"style": "rule",
"ground_truth": "\\frac {\\pi}{3}"
} | {
"split": "train",
"index": 22872,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cube has a square pyramid placed on one of its faces. Determine the sum of the combined number of edges, corners, and faces of this new shape. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "34"
} | {
"split": "train",
"index": 22873,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $p=2^{16}+1$ be a prime. A sequence of $2^{16}$ positive integers $\\{a_n\\}$ is *monotonically bounded* if $1\\leq a_i\\leq i$ for all $1\\leq i\\leq 2^{16}$ . We say that a term $a_k$ in the sequence with $2\\leq k\\leq 2^{16}-1$ is a *mountain* if $a_k$ is... | math | {
"style": "rule",
"ground_truth": "49153"
} | {
"split": "train",
"index": 22874,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "From the sequence of natural numbers $1, 2, 3, 4, \\ldots$, erase every multiple of 3 and 4, but keep every multiple of 5 (for example, 15 and 20 are not erased). After removing the specified numbers, write the remaining numbers in a sequence: $A_{1}=1, A_{2}=2, A_{3}=5, A_{4}=... | math | {
"style": "rule",
"ground_truth": "3314"
} | {
"split": "train",
"index": 22875,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A convex polyhedron has 32 faces, each of which is either a triangle or a pentagon. For the \\( V \\) vertices, each vertex has \\( T \\) triangular faces and \\( P \\) pentagonal faces intersecting. Find the value of \\( P + T + V \\). Let's think step by step and put only the... | math | {
"style": "rule",
"ground_truth": "34"
} | {
"split": "train",
"index": 22876,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The fifth term of an arithmetic sequence is $11$. If the difference between two consecutive terms is $1$, what is the product of the first two terms? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "56"
} | {
"split": "train",
"index": 22877,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A car is braking to a complete stop. It is known that its speed at the midpoint of the distance was 100 km/h. Determine its initial speed. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "141.4"
} | {
"split": "train",
"index": 22878,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all positive integers $a$ and $b$ such that $\\frac{a^{2}+b}{b^{2}-a}$ and $\\frac{b^{2}+a}{a^{2}-b}$ are both integers. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "(2,2),(3,3),(1,2),(2,3),(2,1),(3,2)"
} | {
"split": "train",
"index": 22879,
"solution": "By the symmetry of the problem, we may suppose that $a \\leq b$. Notice that $b^{2}-a \\geq 0$, so that if $\\frac{a^{2}+b}{b^{2}-a}$ is a positive integer, then $a^{2}+b \\geq b^{2}-a$. Rearranging this inequality and factorizing, we find that $(a+b)(a-b+1) \\geq ... |
deepscaler | [
{
"role": "user",
"content": "Given the functions $f(x)=x^{2}-2x+2$ and $g(x)=-x^{2}+ax+b- \\frac {1}{2}$, one of their intersection points is $P$. The tangent lines $l_{1}$ and $l_{2}$ to the functions $f(x)$ and $g(x)$ at point $P$ are perpendicular. Find the maximum value of $ab$. Let's think step by ste... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{4}"
} | {
"split": "train",
"index": 22880,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "\nFind the length of the shortest path on the surface of a unit cube between its opposite vertices. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{5}"
} | {
"split": "train",
"index": 22881,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Sophie has written three tests. Her marks were $73\\%$, $82\\%$, and $85\\%$. She still has two tests to write. All tests are equally weighted. Her goal is an average of $80\\%$ or higher. With which of the following pairs of marks on the remaining tests will Sophie not reach h... | math | {
"style": "rule",
"ground_truth": "73\\% and 83\\%"
} | {
"split": "train",
"index": 22882,
"solution": "For Sophie's average over 5 tests to be $80\\%$, the sum of her marks on the 5 tests must be $5 \\times 80\\% = 400\\%$. After the first 3 tests, the sum of her marks is $73\\% + 82\\% + 85\\% = 240\\%$. Therefore, she will reach her goal as long as the sum of her ... |
deepscaler | [
{
"role": "user",
"content": "There are twenty-four $4$-digit numbers that use each of the four digits $2$, $4$, $5$, and $7$ exactly once. Listed in numerical order from smallest to largest, the number in the $17\\text{th}$ position in the list is Let's think step by step and put only the final answer wit... | math | {
"style": "rule",
"ground_truth": "5724"
} | {
"split": "train",
"index": 22883,
"solution": "1. **Identify the total number of permutations**: We are given four distinct digits: $2$, $4$, $5$, and $7$. The total number of $4$-digit numbers that can be formed using each digit exactly once is calculated by finding the number of permutations of $4$ distinct d... |
deepscaler | [
{
"role": "user",
"content": "Given that the terminal side of angle $\\alpha$ passes through the fixed point $P$ on the function $y=\\log _{a}(x-3)+2$, find the value of $\\sin 2\\alpha+\\cos 2\\alpha$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{5}"
} | {
"split": "train",
"index": 22884,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the expression where the digit 2 appears 2013 times. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2013}{2014}"
} | {
"split": "train",
"index": 22885,
"solution": "Let $f(n)$ denote the corresponding expression with the digit 2 appearing exactly $n$ times. Then $f(1)=\\frac{1}{2}$ and for $n>1, f(n)=\\frac{1}{2-f(n-1)}$. By induction using the identity $\\frac{1}{2-\\frac{N-1}{N}}=\\frac{N}{N+1}$, $f(n)=\\frac{n}{n+1}$ for al... |
deepscaler | [
{
"role": "user",
"content": "Let $ABCD$ be a trapezium with $AB// DC, AB = b, AD = a ,a<b$ and $O$ the intersection point of the diagonals. Let $S$ be the area of the trapezium $ABCD$ . Suppose the area of $\\vartriangle DOC$ is $2S/9$ . Find the value of $a/b$ . Let's think step by step and p... | math | {
"style": "rule",
"ground_truth": "\\frac{2 + 3\\sqrt{2}}{7}"
} | {
"split": "train",
"index": 22886,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the letters $A$, $B$, $C$, $D$, and $E$, calculate the total number of different arrangements of these letters in a row with the constraints that $A$ and $E$ are not placed at the two ends. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 22887,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A 5-digit natural number \\(abcde\\) is called a \"\\(\\pi_1\\)\" number if and only if it satisfies \\(a < b < c\\) and \\(c > d > e\\). Determine the total number of \"\\(\\pi_1\\)\" numbers among all 5-digit numbers. Let's think step by step and put only the final answer wit... | math | {
"style": "rule",
"ground_truth": "2142"
} | {
"split": "train",
"index": 22888,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Indecisive Andy starts out at the midpoint of the 1-unit-long segment $\\overline{H T}$. He flips 2010 coins. On each flip, if the coin is heads, he moves halfway towards endpoint $H$, and if the coin is tails, he moves halfway towards endpoint $T$. After his 2010 moves, what i... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 22889,
"solution": "Let Andy's position be $x$ units from the H end after 2009 flips. If Any moves towards the $H$ end, he ends up at $\\frac{x}{2}$, a distance of $\\frac{1-x}{2}$ from the midpoint. If Andy moves towards the $T$ end, he ends up at $\\frac{1+x}{2}$, a distance of $\\f... |
deepscaler | [
{
"role": "user",
"content": "In the animal kingdom, tigers always tell the truth, foxes always lie, and monkeys sometimes tell the truth and sometimes lie. There are 100 of each of these three types of animals, divided into 100 groups. Each group has exactly 3 animals, with exactly 2 animals of one type an... | math | {
"style": "rule",
"ground_truth": "76"
} | {
"split": "train",
"index": 22890,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\{b_k\\}$ be a sequence of integers such that $b_1=2$ and $b_{m+n}=b_m+b_n+mn^2,$ for all positive integers $m$ and $n.$ Find $b_{12}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "98"
} | {
"split": "train",
"index": 22891,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABCD$ be a rectangle. We consider the points $E\\in CA,F\\in AB,G\\in BC$ such that $DC\\perp CA,EF\\perp AB$ and $EG\\perp BC$ . Solve in the set of rational numbers the equation $AC^x=EF^x+EG^x$ . Let's think step by step and put only the final answer within \\bo... | math | {
"style": "rule",
"ground_truth": "2/3"
} | {
"split": "train",
"index": 22892,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Seven cards numbered $1$ through $7$ are to be lined up in a row. Find the number of arrangements of these seven cards where one of the cards can be removed leaving the remaining six cards in either ascending or descending order. Let's think step by step and put only the final ... | math | {
"style": "rule",
"ground_truth": "74"
} | {
"split": "train",
"index": 22893,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x + y = 16$ and $x-y = 2$, what is the value of $x^2 - y^2$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 22894,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 22895,
"solution": "1. **Understanding the Clock's Degree System**: A clock face is a full circle, which contains 360 degrees. Since there are 12 hours marked on the clock, the angle between each hour is calculated by dividing the total degrees by the number of hours:\n \\[\n \\fr... |
deepscaler | [
{
"role": "user",
"content": "In a rectangular array of points, with 5 rows and $N$ columns, the points are numbered consecutively from left to right beginning with the top row. Thus the top row is numbered 1 through $N,$ the second row is numbered $N + 1$ through $2N,$ and so forth. Five points, $P_1, P_2,... | math | {
"style": "rule",
"ground_truth": "149"
} | {
"split": "train",
"index": 22896,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the Cartesian coordinate system $xOy$, the parametric equations of curve $C$ are $\\left\\{\\begin{array}{l}{x=2+\\sqrt{5}\\cos\\theta,}\\\\{y=\\sqrt{5}\\sin\\theta}\\end{array}\\right.$ ($\\theta$ is the parameter). Line $l$ passes through point $P(1,-1)$ with a slope of $6... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{16+2\\sqrt{3}}}{3}"
} | {
"split": "train",
"index": 22897,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the following powers to 4 decimal places:\na) \\(1.02^{30}\\)\nb) \\(0.996^{13}\\) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.9492"
} | {
"split": "train",
"index": 22898,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x + \\frac{1}{x} = 3$, what is $x^6 + \\frac{1}{x^6}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "322"
} | {
"split": "train",
"index": 22899,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=x^{3}-x^{2}+1$. \n$(1)$ Find the equation of the tangent line to the function $f(x)$ at the point $(1,f(1))$; \n$(2)$ Find the extreme values of the function $f(x)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac {23}{27}"
} | {
"split": "train",
"index": 22900,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Solve the following equations using appropriate methods: \n$(1)\\left(3x-1\\right)^{2}=9$. \n$(2)x\\left(2x-4\\right)=\\left(2-x\\right)^{2}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 22901,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There is a unique positive integer $n$ such that $\\log_2{(\\log_{16}{n})} = \\log_4{(\\log_4{n})}.$ 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": "13"
} | {
"split": "train",
"index": 22902,
"solution": "1. **Rewrite the equation using logarithmic identities:**\n Given the equation \\(\\log_2{(\\log_{16}{n})} = \\log_4{(\\log_4{n})}\\), we use the identity \\(\\log_{a^b} c = \\frac{1}{b} \\log_a c\\) to simplify the bases:\n \\[\n \\log_2{(\\log_{2^4}{n})} = ... |
deepscaler | [
{
"role": "user",
"content": "If $\\log_9 (x-2)=\\frac{1}{2}$, find $\\log_{625} x$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac14"
} | {
"split": "train",
"index": 22903,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given any set $A = \\{a_1, a_2, a_3, a_4\\}$ of four distinct positive integers, we denote the sum $a_1 +a_2 +a_3 +a_4$ by $s_A$. Let $n_A$ denote the number of pairs $(i, j)$ with $1 \\leq i < j \\leq 4$ for which $a_i +a_j$ divides $s_A$. Find all sets $A$ of four distinct p... | math | {
"style": "rule",
"ground_truth": "\\{k, 5k, 7k, 11k\\} \\text{ and } \\{k, 11k, 19k, 29k\\}"
} | {
"split": "train",
"index": 22904,
"solution": "\nLet \\( A = \\{ a_1, a_2, a_3, a_4 \\} \\) be a set of four distinct positive integers. We define \\( s_A = a_1 + a_2 + a_3 + a_4 \\) as the sum of these integers. We also define \\( n_A \\) as the number of pairs \\( (i, j) \\) with \\( 1 \\leq i < j \\leq 4 \\)... |
deepscaler | [
{
"role": "user",
"content": "Add 75.892 to 34.5167 and then multiply the sum by 2. Round the final result to the nearest thousandth. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "220.817"
} | {
"split": "train",
"index": 22905,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The sum of the interior numbers in the sixth row of Pascal's Triangle is 30. What is the sum of the interior numbers of the eighth row? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "126"
} | {
"split": "train",
"index": 22906,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the area of triangle ABC, whose vertices have coordinates A(0,0), B(1424233,2848467), C(1424234,2848469). Round the answer to two decimal places. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.50"
} | {
"split": "train",
"index": 22907,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 16 students who form a $4 \\times 4$ square matrix. In an examination, their scores are all different. After the scores are published, each student compares their score with the scores of their adjacent classmates (adjacent refers to those directly in front, behind, l... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 22908,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$ , find the smallest possible value of $$ |(\\cot A + \\cot B)(\\cot B +\\cot C)(\\cot C + \\cot A)| $$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{8\\sqrt{3}}{9}"
} | {
"split": "train",
"index": 22909,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A tetrahedron of spheres is formed with thirteen layers and each sphere has a number written on it. The top sphere has a 1 written on it and each of the other spheres has written on it the number equal to the sum of the numbers on the spheres in the layer above with which it is... | math | {
"style": "rule",
"ground_truth": "772626"
} | {
"split": "train",
"index": 22910,
"solution": "First, we fill in the numbers on the top four layers. The top layer consists of only one sphere, labelled 1. In the second layer, each sphere touches only one sphere in the layer above. This sphere is labelled 1, so each sphere in the second layer is labelled 1. In... |
deepscaler | [
{
"role": "user",
"content": "On the sides \\(A B, B C, C D\\) and \\(A D\\) of the convex quadrilateral \\(A B C D\\) are points \\(M, N, K\\) and \\(L\\) respectively, such that \\(A M: M B = 3: 2\\), \\(C N: N B = 2: 3\\), \\(C K = K D\\) and \\(A L: L D = 1: 2\\). Find the ratio of the area of the hexag... | math | {
"style": "rule",
"ground_truth": "4/5"
} | {
"split": "train",
"index": 22911,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many distinct pairs of integers \\(x, y\\) are there between 1 and 1000 such that \\(x^{2} + y^{2}\\) is divisible by 49? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10153"
} | {
"split": "train",
"index": 22912,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Chandler wants to buy a $500$ dollar mountain bike. For his birthday, his grandparents send him $50$ dollars, his aunt sends him $35$ dollars and his cousin gives him $15$ dollars. He earns $16$ dollars per week for his paper route. He will use all of his birthday money and all... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"split": "train",
"index": 22913,
"solution": "1. **Identify the total amount of money Chandler needs:** Chandler wants to buy a mountain bike that costs $500.\n\n2. **Calculate the total amount of birthday money Chandler received:**\n - From his grandparents: $50$\n - From his aunt: $35$\n - From his cou... |
deepscaler | [
{
"role": "user",
"content": "When \\( \\frac{1}{2222} \\) is expressed as a decimal, what is the sum of the first 50 digits after the decimal point? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "90"
} | {
"split": "train",
"index": 22914,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let the hyperbola $\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1(a>b>0)$ have its right focus at $F$ and eccentricity $e$. A line passing through $F$ with a slope of 1 intersects the asymptotes of the hyperbola at points $A$ and $B$. If the midpoint of $A$ and $B$ is $M$ and $|FM... | math | {
"style": "rule",
"ground_truth": "\\sqrt[4]{2}"
} | {
"split": "train",
"index": 22915,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle \\(ABC\\), the side lengths are 4, 5, and \\(\\sqrt{17}\\). Find the area of the region consisting of those and only those points \\(X\\) inside triangle \\(ABC\\) for which the condition \\(XA^{2} + XB^{2} + XC^{2} \\leq 21\\) is satisfied. Let's think step by step... | math | {
"style": "rule",
"ground_truth": "\\frac{5 \\pi}{9}"
} | {
"split": "train",
"index": 22916,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABCDE$ be a convex pentagon such that $AB=AE=CD=1$ , $\\angle ABC=\\angle DEA=90^\\circ$ and $BC+DE=1$ . Compute the area of the pentagon. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 22917,
"solution": "Solution 1\nLet $BC = a, ED = 1 - a$ \nLet $\\angle DAC = X$ \nApplying cosine rule to $\\triangle DAC$ we get:\n$\\cos X = \\frac{AC ^ {2} + AD ^ {2} - DC ^ {2}}{ 2 \\cdot AC \\cdot AD }$ \nSubstituting $AC^{2} = 1^{2} + a^{2}, AD ^ {2} = 1^{2} + (1-a)^{2}, DC = 1... |
deepscaler | [
{
"role": "user",
"content": "There are 2019 bags, each bag containing 2019 beads with a total weight of 1 kilogram. The beads in each bag are numbered \\(1, 2, \\cdots, 2019\\). A selection is considered proper if and only if beads with different numbers are selected from different bags (at most one bead f... | math | {
"style": "rule",
"ground_truth": "2018!"
} | {
"split": "train",
"index": 22918,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $x$ and $y$ are distinct nonzero real numbers such that $x - \\tfrac{2}{x} = y - \\tfrac{2}{y}$, determine the product $xy$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 22919,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the least common multiple of 220 and 504? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "27720"
} | {
"split": "train",
"index": 22920,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A and B are playing a series of Go games, with the first to win 3 games declared the winner. Assuming in a single game, the probability of A winning is 0.6 and the probability of B winning is 0.4, with the results of each game being independent. It is known that in the first tw... | math | {
"style": "rule",
"ground_truth": "2.48"
} | {
"split": "train",
"index": 22921,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a certain competition, the rules are as follows: among the 5 questions preset by the organizer, if a contestant can answer two consecutive questions correctly, they will stop answering and advance to the next round. Assuming the probability of a contestant correctly answerin... | math | {
"style": "rule",
"ground_truth": "0.128"
} | {
"split": "train",
"index": 22922,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The graph shows the constant rate at which Suzanna rides her bike. If she rides a total of a half an hour at the same speed, how many miles would she have ridden? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 22923,
"solution": "1. **Interpreting the Graph**: The problem states that Suzanna rides her bike at a constant rate, and the graph shows that every 5 minutes, her distance increases by 1 mile.\n\n2. **Total Riding Time**: Suzanna rides for a total of half an hour. Half an hour is equ... |
deepscaler | [
{
"role": "user",
"content": "One hundred people are in line to see a movie. Each person wants to sit in the front row, which contains one hundred seats, and each has a favorite seat, chosen randomly and independently. They enter the row one at a time from the far right. As they walk, if they reach their fa... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 22924,
"solution": "Let $S(i)$ be the favorite seat of the $i$ th person, counting from the right. Let $P(n)$ be the probability that at least $n$ people get to sit. At least $n$ people sit if and only if $S(1) \\geq n, S(2) \\geq n-1, \\ldots, S(n) \\geq 1$. This has probability: $$P... |
deepscaler | [
{
"role": "user",
"content": "In a magical swamp there are two species of talking amphibians: toads, whose statements are always true, and frogs, whose statements are always false. Four amphibians, Brian, Chris, LeRoy, and Mike live together in this swamp, and they make the following statements.\nBrian: \"M... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 22925,
"solution": "1. **Analyzing Chris and LeRoy's Statements:**\n - Chris says, \"LeRoy is a frog.\"\n - LeRoy says, \"Chris is a frog.\"\n\n Since one of them must be lying (as one is a frog and the other a toad), we can conclude:\n - If Chris is a frog (and thus lying), t... |
deepscaler | [
{
"role": "user",
"content": "In the expansion of $\\left(a - \\dfrac{1}{\\sqrt{a}}\\right)^7$ the coefficient of $a^{-\\frac{1}{2}}$ is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-21"
} | {
"split": "train",
"index": 22926,
"solution": "1. **Identify the general term in the binomial expansion**: \n The binomial expansion of $\\left(a-\\dfrac{1}{\\sqrt{a}}\\right)^7$ can be expressed using the Binomial Theorem, which states that:\n \\[\n (x+y)^n = \\sum_{k=0}^n \\binom{n}{k} x^{n-k} y^k\n ... |
deepscaler | [
{
"role": "user",
"content": "If the graph of the linear function $y=(7-m)x-9$ does not pass through the second quadrant, and the fractional equation about $y$ $\\frac{{2y+3}}{{y-1}}+\\frac{{m+1}}{{1-y}}=m$ has a non-negative solution, calculate the sum of all integer values of $m$ that satisfy the conditio... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 22927,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the limit of the function:\n\n\\[\n\\lim _{x \\rightarrow 1}\\left(\\frac{x+1}{2 x}\\right)^{\\frac{\\ln (x+2)}{\\ln (2-x)}}\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 22928,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all integers $n \\geq 3$ such that the following property holds: if we list the divisors of $n!$ in increasing order as $1 = d_1 < d_2 < \\dots < d_k = n!$, then we have\n\\[ d_2 - d_1 \\leq d_3 - d_2 \\leq \\dots \\leq d_k - d_{k-1}. \\] Let's think step by step and put o... | math | {
"style": "rule",
"ground_truth": "3 \\text{ and } 4"
} | {
"split": "train",
"index": 22929,
"solution": "\nConsider the property that for integers \\( n \\geq 3 \\), the divisors of \\( n! \\), listed in increasing order as \\( 1 = d_1 < d_2 < \\dots < d_k = n! \\), satisfy:\n\n\\[\nd_2 - d_1 \\leq d_3 - d_2 \\leq \\dots \\leq d_k - d_{k-1}.\n\\]\n\nTo solve this prob... |
deepscaler | [
{
"role": "user",
"content": "Let $a, b, c, d$ be the four roots of $X^{4}-X^{3}-X^{2}-1$. Calculate $P(a)+P(b)+P(c)+P(d)$, where $P(X) = X^{6}-X^{5}-X^{4}-X^{3}-X$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 22930,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A 4-inch by 6-inch picture is enlarged for framing by tripling its dimensions. A 2-inch-wide border is then placed around each side of the enlarged picture, as shown. Thin metal framing is sold only in increments of one foot. What is the minimum number of linear feet of... | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 22931,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "An integer $n$ is decreased by 2 and then multiplied by 5. If the result is 85, 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": "19"
} | {
"split": "train",
"index": 22932,
"solution": "We undo each of the operations in reverse order. The final result, 85, was obtained by multiplying a number by 5. This number was $85 \\div 5=17$. The number 17 was obtained by decreasing $n$ by 2. Thus, $n=17+2=19$."
} |
deepscaler | [
{
"role": "user",
"content": "The minimum value of the polynomial $x^2 + y^2 - 6x + 8y + 7$ is ______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-18"
} | {
"split": "train",
"index": 22933,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The diagram shows three triangles which are formed by the five line segments \\(A C D F, B C G, G D E, A B\\), and \\(E F\\) so that \\(A C = B C = C D = G D = D F = E F\\). Also, \\(\\angle C A B = \\angle E F D\\). What is the size, in degrees, of \\(\\angle C A B\\)? Let's t... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 22934,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The probability that three friends, Al, Bob, and Carol, will be assigned to the same lunch group is approximately what fraction. 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": 22935,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the percentage of people with a grade of \"excellent\" among the selected individuals. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "20\\%"
} | {
"split": "train",
"index": 22936,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a taxi, a passenger can sit in the front and three passengers can sit in the back. In how many ways can four passengers sit in a taxi if one of these passengers wants to sit by the window? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"split": "train",
"index": 22937,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Jori has 2 gallons of distilled water and uses 7/6 gallon in a science experiment. What fraction of a gallon does she have left? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{6}"
} | {
"split": "train",
"index": 22938,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the maximum possible value of the greatest common divisor of two consecutive terms of the sequence $a_n = n! + n$, where $n \\ge 0$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 22939,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For what real values of $a$ is the expression $\\frac{a+3}{a^2-4}$ undefined? List your answers in increasing order separated by commas. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2, 2"
} | {
"split": "train",
"index": 22940,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate $\\lfloor\\sqrt{63}\\rfloor$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 22941,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The 5 a.m. temperatures for seven consecutive days were $-7^{\\circ}$, $-4^{\\circ}$, $-4^{\\circ}$, $-5^{\\circ}$, $1^{\\circ}$, $3^{\\circ}$ and $2^{\\circ}$ Celsius. What is the mean 5 a.m. temperature for the week in degrees Celsius? Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 22942,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Points $A$, $B$, $C$, $D$, and $E$ are located in 3-dimensional space with $AB= BC= CD= DE= EA= 2$ and $\\angle ABC = \\angle CDE = \\angle\nDEA = 90^\\circ$. The plane of triangle $ABC$ is parallel to $\\overline{DE}$. What is the area of triangle $BDE$? Let's think step by s... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 22943,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a right triangle, one of the acute angles $\\beta$ satisfies \\[\\tan \\frac{\\beta}{2} = \\frac{1}{\\sqrt[3]{3}}.\\] Let $\\phi$ be the angle between the median and the angle bisector drawn from this acute angle $\\beta$. Calculate $\\tan \\phi.$ Let's think step by step an... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 22944,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Emily's quiz scores so far are: 92, 95, 87, 89 and 100. What score does she need to get on the sixth quiz to make the arithmetic mean of the six scores equal 93? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "95"
} | {
"split": "train",
"index": 22945,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose $50x$ is divisible by 100 and $kx$ is not divisible by 100 for all $k=1,2,\\cdots, 49$ Find number of solutions for $x$ when $x$ takes values $1,2,\\cdots 100$ .\n[list=1]\n[*] 20\n[*] 25\n[*] 15\n[*] 50\n[/list] Let's think step by step and put only the fina... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 22946,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The year 2000 is a leap year. The year 2100 is not a leap year. The following are the complete rules for determining a leap year:\n\n(i) Year \\(Y\\) is not a leap year if \\(Y\\) is not divisible by 4.\n\n(ii) Year \\(Y\\) is a leap year if \\(Y\\) is divisible by 4 but not by... | math | {
"style": "rule",
"ground_truth": "244"
} | {
"split": "train",
"index": 22947,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Each twin from the first 4 sets shakes hands with all twins except his/her sibling and with one-third of the triplets; the remaining 8 sets of twins shake hands with all twins except his/her sibling but does not shake hands with any triplet; and each triplet shakes hands with a... | math | {
"style": "rule",
"ground_truth": "394"
} | {
"split": "train",
"index": 22948,
"solution": ""
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.