data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given: $x^{2}-3x+5=\\left(x-2\\right)^{2}+a\\left(x-2\\right)+b$, find $a+b$.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that a quadratic polynomial $q(x)$ has real coefficients and a leading coefficient of $1$, and is termed **unruly** if the equation $q(q(x)) = 1$ is satisfied by exactly th... | math | {
"ground_truth": "\\textbf{(C) } -1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The equation of the tangent line to the curve \\\\(f(x)= \\dfrac {f′(1)}{e}e^{x}-f(0)x+ \\dfrac {1}{2}x^{2}\\\\) at the point \\\\((1,f(1))\\\\) is \\_\\_\\_\\_\\_\\_.",
"rol... | math | {
"ground_truth": "y=ex- \\dfrac {1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all triples $(a, b, c)$ of nonnegative integers that satisfy: $$ (c-1) (ab- b -a) = a + b-2 $$",
"role": "user"
}
] | math | {
"ground_truth": "(2, 1, 0), (1, 2, 0), (3, 4, 2), (4, 3, 2), (1, 0, 2), (0, 1, 2), (2, 4, 3), (4, 2, 3)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the power function $f(x)=x^{m^{2}-2m-3}$, where $m\\in\\mathbb{Z}$. The graph of the function has no points in common with the coordinate axes and is symmetric about the... | math | {
"ground_truth": "m=1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the distribution of grades is A: 6 students, B: 3 students, C: 4 students, D: 2 students, and E: 1 student, while F and G are unsatisfactory with 7 and 2 students resp... | math | {
"ground_truth": "\\frac{16}{25}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two circles touch each other and the sides of triangle \\(ABC\\). The first circle, with radius \\(\\frac{1}{18}\\), touches the sides \\(AB\\) and \\(AC\\) at points \\(L\\) and... | math | {
"ground_truth": "\\frac{15}{22}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Omega and Theta both took part in a three-day problem-solving competition. At the end of the third day, each had attempted questions worth a total of 600 points. Omega scored 200... | math | {
"ground_truth": "\\frac{56}{75}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all functions $f:\\mathbb{N}^* \\rightarrow \\mathbb{N}$ such that\n\n\n\n- $f(x \\cdot y) = f(x) + f(y)$\n- $f(30) = 0$\n- $f(x)=0$ always when the units digit of $x$ ... | math | {
"ground_truth": "f(n) = 0 \\quad \\forall n \\in \\mathbb{N}^*",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "As shown in the diagram, a square is divided into 4 identical rectangles, each of which has a perimeter of 20 centimeters. What is the area of this square?",
"role": "user"
... | math | {
"ground_truth": "64",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $(-3)^7 \\div 3^5 + 5^5 - 8^2$ as an integer.",
"role": "user"
}
] | math | {
"ground_truth": "3052",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that there are $r$ red marbles, and there are $30\\%$ more red marbles than blue marbles, $50\\%$ more green marbles than red marbles, and $20\\%$ more yellow marbles than ... | math | {
"ground_truth": "5.069r",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine if there is a scalar \\(d\\) such that\n\\[\\mathbf{i} \\times (\\mathbf{v} \\times \\mathbf{i}) + \\mathbf{j} \\times (\\mathbf{v} \\times \\mathbf{j}) + \\mathbf{k} \... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A bee starts flying from point $P_0$. She flies $1$ inch due north to point $P_1$. For $j \\ge 1$, once the bee reaches point $P_j$, she turns $45^{\\circ}$ clockwise and then fl... | math | {
"ground_truth": "2016 \\sqrt{2 + \\sqrt{2}}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $P_0P_5Q_5Q_0$ be a rectangular chocolate bar, one half dark chocolate and one half white chocolate, as shown in the diagram below. We randomly select $4$ points on the s... | math | {
"ground_truth": "39",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For which \\( k \\) is the number \\( N = 101 \\cdots 0101 \\) with \\( k \\) ones a prime?",
"role": "user"
}
] | math | {
"ground_truth": "k=2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x) = x^3 - 3x^2$. For what values of $x$ is $f(f(x)) = f(x)$? List all solutions, separated by commas.",
"role": "user"
}
] | math | {
"ground_truth": "0, 3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Ten men sit side by side at a long table, all facing the same direction. Each of them is either a knight (and always tells the truth) or a knave (and always lies). Each of the pe... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "At a women's doubles tennis tournament, there were four teams of two women each. After the tournament, each woman shook hands once with each of the women from the other teams but... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f$ be a random permutation on $\\{1, 2, \\dots, 100\\}$ satisfying $f(1) > f(4)$ and $f(9)>f(16)$ . The probability that $f(1)>f(16)>f(25)$ can be written as $\\fr... | math | {
"ground_truth": "124",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The imaginary part of the complex number $z=1-2i$ (where $i$ is the imaginary unit) is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two numbers have their difference, their sum, and their product corresponding to each other in the ratio 1:8:30. Find the product of the two numbers.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{400}{7}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each face of a regular tetrahedron is painted either red, white, blue, or green. Two colorings are considered indistinguishable if two congruent tetrahedra with those colorings c... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Polina's Pizza has now introduced 8 different toppings. If a customer wants to create a pizza with a combination of 3 different toppings, how many unique combinations are possibl... | math | {
"ground_truth": "56",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "**p1.** In the following $3$ by $3$ grid, $a, b, c$ are numbers such that the sum of each row is listed at the right and the sum of each column is written below it:\n[cente... | math | {
"ground_truth": "\\sqrt{19}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that isosceles $\\triangle ABC$ has $\\overline{AB} = \\overline{BC} = 3$ and $\\overline{AC} = 4$, $M$ is the midpoint of $\\overline{AB}$, and $D$ is a point on $\\overli... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the arithmetic sequence $\\{a_n\\}$, $a_3=7$ and $a_5=a_2+6$. Find the general term formula for $\\{a_n\\}$.",
"role": "user"
}
] | math | {
"ground_truth": "a_n = 2n + 1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$\\sqrt{3 x} \\cdot \\sqrt{2 x^{2}}$\n\n$\\sqrt{3} \\cdot x \\cdot \\sqrt{2} \\cdot x^{2}$\n\n$\\sqrt{\\sqrt{3 x^{2}}+\\sqrt{2 x}} \\cdot \\sqrt{\\sqrt{5 x^{2}}+\\sqrt{4 x}}$",
... | math | {
"ground_truth": "\\sqrt{(\\sqrt{3} + \\sqrt{2}) \\cdot (\\sqrt{5} + 2)} \\cdot x",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a triangle $ABC$ with the sides opposite angles $A$, $B$, and $C$ being $a$, $b$, and $c$ respectively, and $a+2c=2b\\cdot\\cos A$.\n\n$(1)$ Find the magnitude of angle $B$... | math | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A sphere with center O has radius 6. A triangle with sides of length 15, 15, and 24 is situated in space so that each of its sides is tangent to the sphere. Find the distance bet... | math | {
"ground_truth": "2\\sqrt{5}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If Linda picks one letter randomly from the English alphabet, what is the probability that the letter is in the word `MATHEMATICS`?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{4}{13}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose $ A $ is a subset of $ n $ -elements taken from $ 1,2,3,4,...,2009 $ such that the difference of any two numbers in $ A $ is not a prime number. Find the largest ... | math | {
"ground_truth": "n = 503",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x) = Ax^2 - 3B^3$ and $g(x) = Bx^2 + C$, where $B, C \\neq 0$. If $f(g(2)) = 0$, determine $A$ in terms of $B$ and $C$.",
"role": "user"
}
] | math | {
"ground_truth": "A = \\frac{3B^3}{(4B + C)^2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the vectors $\\mathbf{a} = \\begin{pmatrix} 1 \\\\ 1 \\\\ 1 \\end{pmatrix},$ $\\mathbf{b} = \\begin{pmatrix} 2 \\\\ -3 \\\\ 1 \\end{pmatrix},$ and $\\mathbf{c} = \\beg... | math | {
"ground_truth": "\\left(\\frac{5}{3}, \\frac{3}{14}, \\frac{-1}{21}\\right)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x$ is tripled, decreased by $7$, and then divided by $4$, the result is $14$. What is the value of $x$?",
"role": "user"
}
] | math | {
"ground_truth": "21",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $n$ , for which there exists a positive integer $k$ such that for every positive divisor $d$ of $n$ , the number $d - k$ is also a (not necessa... | math | {
"ground_truth": "n = 3, 4, 6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(\\theta\\) and \\(\\phi\\) be angles in radians. Define \\(s = \\sin(\\theta + \\phi)\\) and \\(c = \\cos(\\theta - \\phi)\\). Determine the range of values that \\(s^2 - ... | math | {
"ground_truth": "\\textbf{(D)} \\text{ between -1 and +1, both included}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider seven-digit natural numbers in which each of the digits \\(1, 2, 3, 4, 5, 6, 7\\) appears exactly once.\n\n(a) How many of these numbers have the digits from the first t... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sides of a triangle are $13, 17,$ and $k,$ where $k$ is a positive integer. For how many values of $k$ is the triangle a right triangle?",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all triplets of real numbers $(x,y,z)$ such that the following equations are satisfied simultaneously: \n\\begin{align*} \n x^3+y=z^2 \ny^3+z=x^2 \nz^3+x =y^2 \n\\end{al... | math | {
"ground_truth": "(0, 0, 0)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Three parallel lines $L_1, L_2, L_2$ are drawn in the plane such that the perpendicular distance between $L_1$ and $L_2$ is $3$ and the perpendicular distance between lin... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the infinite geometric series $5 - \\frac{10}{3} + \\frac{20}{9} - \\frac{40}{27} + \\dots$. Find the sum $s$ of this series.\nA) 2.5 \nB) 3 \nC) 3.5 \nD) 4",
"r... | math | {
"ground_truth": "B) 3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a geometric sequence with positive terms $\\{a_n\\}$, the sum of the first $n$ terms is denoted as $S_n$. Find the ratio of the 8th term to the 4th term of the arithmetic s... | math | {
"ground_truth": "\\sqrt{5}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $x = -2023$. Find the value of $\\left| \\left| |x| - x \\right| - |x| \\right| - x$.",
"role": "user"
}
] | math | {
"ground_truth": "4046",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Using the 0.618 method to find the optimal addition amount for an experiment, if the current optimal range is $[628, 774]$ and the better point is 718, then the value of the addi... | math | {
"ground_truth": "684",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A beam of light is emitted from point M(4, 5) and reflects off the x-axis at point N(2, 0). Find the equations of the lines for both the incident and reflected beams of light (pl... | math | {
"ground_truth": "5x-2y-10=0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all such three-digit numbers that, when increased by 3, the sum of their digits is reduced to one-third of the original sum.",
"role": "user"
}
] | math | {
"ground_truth": "117, 207, 108",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the range of the function \\( y = \\frac{x^2 + 5x + 6}{x + 2} \\).",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty, 1) \\cup (1, \\infty)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $\\overrightarrow {a}=(1, 2)$ and $\\overrightarrow {b}=(-2, k)$, find the value of the real number $k$ such that $\\overrightarrow {a} \\perp \\overrightarrow {b}$.",
... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ be a positive integer. Find the number of polynomials $P(x)$ with coefficients in $\\{0, 1, 2, 3\\}$ for which $P(2) = n$ .",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the product \\((5x^2 - 3x + 2)(9 - 3x)\\) can be written in the form \\(ax^3 + bx^2 + cx + d\\), where \\(a, b, c, d\\) are real numbers, then find \\(27a + 9b + 3c + d\\).",
... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all positive integers $ n$ such that $ 20^n \\minus{} 13^n \\minus{} 7^n$ is divisible by $ 309$ .",
"role": "user"
}
] | math | {
"ground_truth": "n = 1 + 6k",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest natural number ending in the digit 2 such that it doubles when this digit is moved to the beginning.",
"role": "user"
}
] | math | {
"ground_truth": "105263157894736842",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the product of all integer divisors of $150$ that also divide $30$.",
"role": "user"
}
] | math | {
"ground_truth": "182250000",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a different right triangle, the two legs have lengths of 30 inches and 34 inches. What is the area of this triangle?",
"role": "user"
}
] | math | {
"ground_truth": "510\\text{ square inches}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "At least $ n - 1$ numbers are removed from the set $\\{1, 2, \\ldots, 2n - 1\\}$ according to the following rules:\n(i) If $ a$ is removed, so is $ 2a$ ;\n(ii) If $ a$ a... | math | {
"ground_truth": "n^2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be at triangle with incircle $\\Gamma$ . Let $\\Gamma_1$ , $\\Gamma_2$ , $\\Gamma_3$ be three circles inside $\\triangle ABC$ each of which is tangent to $\\G... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A basketball player has the same free-throw shooting percentage for every attempt, and the probability that they make at most one basket in two attempts is $\\frac{16}{25}$. Find... | math | {
"ground_truth": "\\frac{3}{5}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The first term of the sequence $\\{a_n\\}$ is 3, and $\\{b_n\\}$ is an arithmetic sequence, where $b_1=2$, $b_3=6$, and $b_n=a_{n+1}-a_n$ ($n\\in\\mathbb{N}^*$). Calculate the va... | math | {
"ground_truth": "33",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A *coloring* of the set of integers greater than or equal to $1$ , must be done according to the following rule: Each number is colored blue or red, so that the sum of any two n... | math | {
"ground_truth": "\\text{All colorings have the following form: the first } t \\text{ odd numbers are red, and all other positive integers are blue}, \\forall t=0,1,2,3,...,\\infty",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the positive integer $n$ such that $\\frac12 \\cdot \\frac34 + \\frac56 \\cdot \\frac78 + \\frac{9}{10}\\cdot \\frac{11}{12 }= \\frac{n}{1200}$ .",
"role": "user"
... | math | {
"ground_truth": "2315",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given two vectors in the plane $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfying $|\\overrightarrow{a}|=1$, $|\\overrightarrow{b}|=2$, and $|\\overrightarrow{a}+ \\overr... | math | {
"ground_truth": "-\\dfrac{1}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Positive integers $a$, $b$, $c$, and $d$ are such that $a<b<c<d$, and the system of equations \n\\[ 2x + y = 2007 \\quad\\text{and}\\quad y = |x-a| + |x-b| + |x-c| + |x-d| \\]\nh... | math | {
"ground_truth": "504",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the maximum value of $\\lambda ,$ such that for $\\forall x,y\\in\\mathbb R_+$ satisfying $2x-y=2x^3+y^3,x^2+\\lambda y^2\\leqslant 1.$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\sqrt{5} + 1}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose $a$ and $b$ are nonzero real numbers, and the equation $x^2 + 2ax + b = 0$ has solutions $a$ and $b$. Find the ordered pair $(a, b)$.",
"role": "user"
}
] | math | {
"ground_truth": "(1, -3)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A digital wristwatch displays time in a 24-hour format along with minutes and seconds. Calculate the largest possible sum of the digits in the display.",
"role": "user"
}
] | math | {
"ground_truth": "37",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many five-digit numbers can be formed using the digits 0, 1, 3, 5, and 7 without repeating any digits and ensuring that 5 is not in the tens place?",
"role": "user"
}
] | math | {
"ground_truth": "78",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Read the following material and answer the questions below. \nMaterial: From the meaning of exponentiation, we have $10^{2}\\times 10^{3}=10\\times 10\\times 10\\times 10\\times... | math | {
"ground_truth": "2016",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $$\\overrightarrow{a} = (1, \\cos x)$$ and $$\\overrightarrow{b} = \\left(\\frac{1}{3}, \\sin x\\right)$$, where \\(x \\in (0, \\pi)\\):\n\n1. If $$\\overrightarrow{a} \\pa... | math | {
"ground_truth": "\\sin x - \\cos x = \\frac{\\sqrt{15}}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A school has \\( 120 \\) students and \\( 6 \\) teachers. In the first period, each student is attending one class, and each teacher is conducting one class. The enrollments in t... | math | {
"ground_truth": "\\text{(B)}\\ -6.67",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose that $S$ is a finite set of positive integers. If the greatest integer in $S$ is removed from $S$, then the average value (arithmetic mean) of the integers remaining is $... | math | {
"ground_truth": "36.8",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A total of $2010$ coins are distributed in $5$ boxes. At the beginning the quantities of coins in the boxes are consecutive natural numbers. Martha should choose and take one... | math | {
"ground_truth": "2004",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the school library, there are 140 comic books and 100 storybooks. If 4 of each type of book are borrowed every day, after how many days will the number of comic books be three... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "a) \\(\\frac{3 \\log_{a} x + 6}{\\log_{a}^{2} x + 2} > 1\\)\n\nb) \\(\\log_{2} \\log_{4} x + \\log_{4} \\log_{2} x \\leq -4\\)",
"role": "user"
}
] | math | {
"ground_truth": "x \\in (1, \\sqrt[4]{2})",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In circle $Q$ with center $O$, diameters $AB$ and $CD$ are perpendicular. If point $P$ lies on diameter $CD$ with $\\measuredangle APB = 45^\\circ$, calculate the ratio of the le... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle{ADE}$ points $B$ and $C$ are on side $AD$ and points $F$ and $G$ are on side $AE$ so that $BG \\parallel CF \\parallel DE$ , as shown. The area of ... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$ABC$ is triangle. $l_1$ - line passes through $A$ and parallel to $BC$ , $l_2$ - line passes through $C$ and parallel to $AB$ . Bisector of $\\angle B$ intersect $... | math | {
"ground_truth": "60^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Assume every 7-digit whole number can be a telephone number except those that begin with $0$, $1$, or $2$. What is the fraction of telephone numbers that begin with $9$ and end w... | math | {
"ground_truth": "\\frac{1}{70}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle with $AB = 7, BC = 5,$ and $CA = 6$ . Let $D$ be a variable point on segment $BC$ , and let the perpendicular bisector of $AD$ meet segments $A... | math | {
"ground_truth": "240124",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice needs to replace a light bulb located 10 centimeters below the ceiling in her kitchen. The ceiling is 2.4 meters above the floor. Alice is 1.5 meters tall and can reach 46 ... | math | {
"ground_truth": "34",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cylindrical oil tank, lying horizontally, has an interior length of 12 feet and an interior diameter of 8 feet. Calculate the depth of the oil, given that the rectangular surfa... | math | {
"ground_truth": "4 \\pm \\frac{\\sqrt{39}}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are 207 different cards with numbers $1, 2, 3, 2^{2}, 3^{2}, \\ldots, 2^{103}, 3^{103}$ (each card has one number, and each number appears exactly once). How many ways can ... | math | {
"ground_truth": "267903",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given lily pads numbered from $0$ to $14$, predators on lily pads $4$ and $9$, and food on lily pad $13$, calculate the probability that Fiona the frog reaches pad $13$ without l... | math | {
"ground_truth": "\\frac{3}{2048}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Julianne has 15 boxes. Eight of the boxes contain markers, four contain crayons, and three contain both markers and crayons. How many boxes contain neither markers nor crayons?",... | math | {
"ground_truth": "6\\text{ boxes}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For how many values of $d$ is $2.d05 > 2.005$?",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute $2 - 3 + 4 - 5 + \\dots + 98 - 99 + 100$.",
"role": "user"
}
] | math | {
"ground_truth": "51",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all triples of pairwise distinct positive integers $(a,b,c)$ , which satisfy the following conditions: $2a-1$ is divisible by $b$ , $2b-1$ is divisible $c$ and $2c-... | math | {
"ground_truth": "(7, 13, 25)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The number $15!$ ($15$ in base $10$), when written in the base $16$ system, ends with exactly $k$ zeros. Determine the value of $k$.",
"role": "user"
}
] | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the difference between the sum of the first 1500 even natural numbers, each reduced by 3, and the sum of the first 1500 odd natural numbers.",
"role": "user"
}
] | math | {
"ground_truth": "-2250",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $$\\sin \\frac{4}{3}\\pi \\cdot \\cos \\frac{5}{6}\\pi \\cdot \\tan \\left(-\\frac{4}{3}\\pi\\right)$$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{3\\sqrt{3}}{4}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cone is formed from a 270-degree sector of a circle of radius 20 by aligning the two straight sides. What is the result when the total surface area of the cone (including the b... | math | {
"ground_truth": "525",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the inequality\n\n\\[ \\frac{(\\sqrt{x+6}-1)(\\sqrt{x+6}-3)\\left(\\log _{2}(x+1)-\\log _{2} 1\\right)}{\\left(2^{x}-1\\right)\\left(2^{x}-2\\right)\\left(\\log _{5}(5-x)-\... | math | {
"ground_truth": "x \\in (-1, 0) \\cup (0, 1) \\cup [3, 4)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate \\(\\sin \\frac{13 \\pi}{4}.\\)",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{\\sqrt{2}}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABC$ be a triangle with sides $51, 52, 53$ . Let $\\Omega$ denote the incircle of $\\bigtriangleup ABC$ . Draw tangents to $\\Omega$ which are parallel to the sides ... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the points \\( A(3, 2), B(-1, 5), C(0, 3) \\). Find the coordinates of the vectors \\( \\overrightarrow{AB}, \\overrightarrow{BC}, \\overrightarrow{AC} \\).",
"role": "... | math | {
"ground_truth": "\\overrightarrow{A B} = (-4, 3), \\ \\overrightarrow{B C} = (1, -2), \\ \\overrightarrow{A C} = (-3, 1)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify $(18 \\times 10^9) \\div (6 \\times 10^4)$. (Your answer should be a single number, with no products or quotients.)",
"role": "user"
}
] | math | {
"ground_truth": "300,\\!000",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all triples $(a,b,c)$ of positive integers such that\n(i) $a \\leq b \\leq c$ ;\n(ii) $\\text{gcd}(a,b,c)=1$ ; and\n(iii) $a^3+b^3+c^3$ is divisible by each of the num... | math | {
"ground_truth": "(1, 1, 1)",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all complex numbers \\(z\\) such that\n\\[z^2 = -100 - 64i.\\]",
"role": "user"
}
] | math | {
"ground_truth": "4 - 8i, -4 + 8i",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On Monday, Misha has five classes, and on Tuesday, he has six. To determine in which of these classes unpredictable teachers will ask him for his homework, Misha flips a coin 11 ... | math | {
"ground_truth": "\\frac{5}{11}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A fifth number, $m$, is added to the set $\\{2, 5, 8, 11\\}$ so that the mean of the resulting set of five numbers equals its median. Determine the number of possible values for ... | math | {
"ground_truth": "C) 3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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