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": "Solve the following equations and determine which statement is true for all solutions:\n1. $2x^2 - 4 = 36$\n2. $(3x-2)^2 = (x+2)^2$\n3. $\\sqrt{3x^2 - 10} = \\sqrt{2x + 2}$\nA) A... | math | {
"ground_truth": "\\textbf{(B)}\\ \\text{no root greater than 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": "n points lie in a line. How many ways are there of coloring the points with 5 colors, one of them red, so that every two adjacent points are either the same color or one or more ... | math | {
"ground_truth": "\\frac{3^n + (-1)^n}{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": "Calculate the value of $3^3 \\cdot 5^3 \\cdot 3^5 \\cdot 5^5$.\nA) $15^5$\nB) $8^{15}$\nC) $15^8$\nD) $15^{15}$",
"role": "user"
}
] | math | {
"ground_truth": "15^8",
"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 that the number $2.5252525\\ldots$ can be written as a fraction, when reduced to lowest terms, find the sum of the numerator and denominator of this fraction.",
"role":... | math | {
"ground_truth": "349",
"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": "Given that $f(x)$ is an odd function defined on $\\mathbb{R}$, and for $x \\geq 0,$ $f(x)=5^{x}+m$ (where $m$ is a constant), find the value of $f(-\\log_{5}7)$.",
"role": "u... | math | {
"ground_truth": "-6",
"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": "\"Modulo $6$ graph paper\" consists of a grid of $36$ points, representing all pairs of integer residues $(x,y)$ where $0\\le x, y <6$. To graph a congruence on modulo $6$ graph ... | math | {
"ground_truth": "6",
"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 a complex number $z$ satisfies $z\\left(1-i\\right)=2+i$, solve for $z$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2} + \\frac{3}{2}i",
"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": "Circles \\( A \\) and \\( B \\) each have a radius of 1 and they touch each other at one point. Circle \\( C \\) has a radius of 2 and is tangential to the midpoint of the line s... | math | {
"ground_truth": "B) \\( 3\\pi + 4 \\)",
"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 that \n$$\n\\frac{1}{x}=\\frac{2}{y+z}=\\frac{3}{z+x}=\\frac{x^{2}-y-z}{x+y+z},\n$$\n\nfind the value of $\\frac{z-y}{x}$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "For a set of five distinct lines in a plane, there are exactly $M$ distinct points that lie on two or more of the lines. What is the sum of all possible values of $M$?\nA) 45\nB)... | math | {
"ground_truth": "The correct answer is **C) 55.**",
"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": "Find the Fourier series expansion of the function \\( f(x) = (x - 4)^2 \\) in the interval \\( (0, 4) \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{16}{3} + \\frac{64}{\\pi^2} \\sum_{m=1}^{\\infty} \\frac{1}{m^2} \\cos \\left( \\frac{m \\pi x}{4} \\right)",
"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": "Archimedes planned to count all of the prime numbers between $2$ and $1000$ using the Sieve of Eratosthenes as follows:\n(a) List the integers from $2$ to $1000$ .\n(b) Ci... | math | {
"ground_truth": "331",
"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 lines $a$ and $b$, and a plane $\\alpha$, which of the following propositions is correct? \n① If $a \\parallel b$ and $a \\subset \\alpha$, then $b \\parallel \\alpha$... | math | {
"ground_truth": "\\text{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": "Point \\( M \\) lies on side \\( AC \\) of an equilateral triangle \\( ABC \\) with side length \\( a \\) such that \\( AM:MC = 1:2 \\). Points \\( K \\) and \\( L \\), located o... | math | {
"ground_truth": "a \\sqrt{10}",
"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 $a_1, a_2, \\cdots , a_n$ be real numbers, with $n\\geq 3,$ such that $a_1 + a_2 +\\cdots +a_n = 0$ and $$ 2a_k\\leq a_{k-1} + a_{k+1} \\ \\ \\ \\text{for} \\ \\ ... | math | {
"ground_truth": "\\frac{n+1}{n-1}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $$\\frac{\\cot^{2016}\\theta+2}{\\sin\\theta+1} = 1$$, find the value of $(\\sin\\theta+2)^2(\\cos\\theta+1)$.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"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 fair dice, each with a different number of faces, are rolled. On each face of each die is printed a distinct integer from 1 to the number of faces on that die, inclusive. The... | math | {
"ground_truth": "19",
"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": "Find all positive integers $x$ such that the product of all digits of $x$ is given by $x^2 - 10 \\cdot x - 22.$",
"role": "user"
}
] | math | {
"ground_truth": "12",
"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 Mr. Brown's geometry class, 40 of the 50 students took the Chapter 7 test, and their mean score was $85 \\%$. The remaining 10 students took the test the following day and the... | math | {
"ground_truth": "84\\%",
"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 magician has 3 red chips and 3 green chips in a hat. Chips are drawn randomly one at a time without replacement, until all 3 of the red chips are drawn or until all 3 green chi... | 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": "Definition: In the plane rectangular coordinate system $xOy$, for points $P(a,b)$ and $Q(c,d)$, if $c=ka$ and $d=-kb$, where $k$ is a constant and $k\\neq 0$, then point $Q$ is c... | math | {
"ground_truth": "(3,-6) \\text{ or } (-3,6)",
"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 company incurs a fixed daily maintenance fee of $550$, an additional one-time daily setup cost of $200$, and pays each worker $18$ per hour. Each worker now makes 6 widgets per... | math | {
"ground_truth": "32",
"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": "Two positive integers differ by $60$. The sum of their square roots is the square root of an integer that is not a perfect square. What is the maximum possible sum of the two int... | math | {
"ground_truth": "156",
"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": "The diagonals of an inscribed quadrilateral $\\mathrm{ABCD}$ are perpendicular. Perpendiculars dropped from vertices $\\mathrm{B}$ and $\\mathrm{C}$ to side $\\mathrm{AD}$ inters... | math | {
"ground_truth": "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": "Given the operation $a * b=(a-b)^2$, where $a$ and $b$ are real numbers, calculate $(x-y)^2*(y-x)^2$.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"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": "Given that the equation (sinx+cosx)²+cos2x=m has two roots x₁, x₂ in the interval [0, π), and |x₁-x₂|≥π/4, find the range of the real number m.",
"role": "user"
}
] | math | {
"ground_truth": "[0, 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": "The surface area of a sphere with radius $r$ is $4\\pi r^2$. If considering the area of its circular base as well, what is the total surface area of a hemisphere with radius 8 cm... | math | {
"ground_truth": "192\\pi",
"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 the lines \\( y = ax - 4 \\) and \\( y = 8x - b \\) be symmetric with respect to the line \\( y = x \\). Find the values of \\( a \\) and \\( b \\).",
"role": "user"
}
... | math | {
"ground_truth": "a=\\frac{1}{8}, b=-32",
"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 units digit of \\(7^{3^4}\\).",
"role": "user"
}
] | math | {
"ground_truth": "7",
"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": "\"Modulo $m$ graph paper\" consists of a grid of $m^2$ points, representing all pairs of integer residues $(x, y)$ where $0 \\leq x, y < m$. To graph a congruence on modulo $m$ g... | math | {
"ground_truth": "19",
"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 positive term geometric sequence $\\{a\\_n\\}$ satisfies: $(2a\\_5 - 3a\\_4 = 2a\\_3)$, find the common ratio $q =$ $\\_\\_\\_\\_\\_\\_\\_$.",
"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": "A circle with a radius of 6 is perfectly inscribed in a rectangle. The ratio of the length of the rectangle to its width is 3:1. Calculate the area of the rectangle.",
"role"... | math | {
"ground_truth": "432",
"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 a certain tournament bracket, a player must be defeated three times to be eliminated. If 512 contestants enter the tournament, what is the greatest number of games that could ... | math | {
"ground_truth": "1535",
"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 triangle ABC has vertices at points $A = (0,2)$, $B = (0,0)$, and $C = (10,0)$. A vertical line $x = a$ divides the triangle into two regions. Find the value of $a$ such that t... | math | {
"ground_truth": "\\frac{10}{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": "Solve the following equations using appropriate methods:<br/>\n$(1)\\left(x-1\\right)^{2}-5=0$;<br/>\n$(2)x\\left(x+4\\right)=-3\\left(x+4\\right)$;<br/>\n$(3)2y^{2}-5y+2=0$;<br/... | math | {
"ground_truth": "m_{1}=\\frac{7+\\sqrt{73}}{4}, m_{2}=\\frac{7-\\sqrt{73}}{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": "Calculate: \n(1) $$\\sqrt{18} - \\sqrt{8} + \\sqrt{2}$$; \n(2) ($$\\sqrt{48} - \\sqrt{12}$$) ÷ $$\\sqrt{3}$$.",
"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": "Let n be a non-negative integer. Define the *decimal digit product* \\(D(n)\\) inductively as follows:\n\n- If \\(n\\) has a single decimal digit, then let \\(D(n) = n\\).\n\n- O... | math | {
"ground_truth": "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": "The greatest common divisor of 360 and 504 is what value?",
"role": "user"
}
] | math | {
"ground_truth": "72",
"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": "At least how many moves must a knight make to get from one corner of a chessboard to the opposite corner?",
"role": "user"
}
] | math | {
"ground_truth": "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": "Both roots of the quadratic equation $x^2 - 76x + k = 0$ are prime numbers. Find the number of possible values of $k$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"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": "The vertices of a rectangle inscribed in a circle divide the circle into four arcs. Find the distances from the midpoint of one of the larger arcs to the vertices of the rectangl... | math | {
"ground_truth": "15 \\text{ cm} \\text{ and } 20 \\text{ cm}",
"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": "Compute $\\frac{x^{10} + 20x^5 + 100}{x^5 + 10}$ when $x=2$.",
"role": "user"
}
] | math | {
"ground_truth": "42",
"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 $\\frac{8}{12} + \\frac{7}{15}$. Express your answer as a fraction in simplest form.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{17}{15}",
"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 $a$ and $b$ are positive integers, and $a$ and $b$ leave remainders of 2 and 5, respectively, when divided by 6, find the remainder when $b^2 - 3a$ is divided by 6.",
... | 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": "In triangle $\\triangle ABC$, $\\cos A= \\frac {3}{5}$, and $\\cos B= \\frac {5}{13}$. The value of $\\cos C$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac {33}{65}",
"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 the sum of the squares of all real numbers satisfying the equation $x^{256}-256^{32}=0$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "What is the smallest integer value of $y$ for which $3 - 5y < 23$?",
"role": "user"
}
] | 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": "The fraction $\\frac1{10}$ can be expressed as the sum of two unit fraction in many ways, for example, $\\frac1{30}+\\frac1{15}$ and $\\frac1{60}+\\frac1{12}$ .\n\nFind the ... | math | {
"ground_truth": "7",
"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 \\( a^{4} b^{3} c^{5} = 18 \\) and \\( a^{3} b^{5} c^{4} = 8 \\), find the value of \\( a^{5} b c^{6} \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{81}{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": "How many real numbers \\( x \\) are solutions to the following equation? \\[ |x-1| = |x-2| + |x-3| + |x-4| \\]",
"role": "user"
}
] | math | {
"ground_truth": "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": "Points $A$ , $B$ , $C$ , and $D$ lie on a circle such that chords $\\overline{AC}$ and $\\overline{BD}$ intersect at a point $E$ inside the circle. Suppose that $\\a... | math | {
"ground_truth": "115",
"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": "Can the numbers 1 and 0 be the indices of a root?",
"role": "user"
}
] | math | {
"ground_truth": "\\text{Yes, 1 and 0 can be indicators of roots.}",
"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": "Consider the sum\n\\[\n S_n = \\sum_{k = 1}^n \\frac{1}{\\sqrt{2k-1}} \\, .\n\\]\nDetermine $\\lfloor S_{4901} \\rfloor$ . Recall that if $x$ is a real number, then $\\lflo... | math | {
"ground_truth": "98",
"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": "By removing certain terms from the sum, \\(\\frac{1}{2}+\\frac{1}{4}+\\frac{1}{6}+\\frac{1}{8}+\\frac{1}{10}+\\frac{1}{12}\\), we can get 1. What is the product of the removed te... | math | {
"ground_truth": "\\frac{1}{80}",
"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": "Math teacher wrote in a table a polynomial $P(x)$ with integer coefficients and he said:\n\"Today my daughter have a birthday.If in polynomial $P(x)$ we have $x=a$ where $... | 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": "Define\n\\[ d_k = k + \\cfrac{1}{3k + \\cfrac{1}{3k + \\cfrac{1}{3k + \\dotsb}}}. \\]\nCalculate $\\sum_{k = 1}^{20} d_k^2.$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{20 \\cdot 21 \\cdot 41}{6} + 21 \\cdot 20 (\\sqrt{5} - 2) + 20 (\\sqrt{5} - 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": "What is $111111111_2 + 110110_2$? Write your answer in base $10$.",
"role": "user"
}
] | math | {
"ground_truth": "571",
"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 $\\triangle PQR$, side $\\overline{PQ}$ has length $12$. The bisector of angle $P$ meets $\\overline{QR}$ at $S$, and $RS = 5$. Determine the set of all possible values of $PR... | math | {
"ground_truth": "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": "Let $ABCD$ be a square of side length $1$ , and let $P$ be a variable point on $\\overline{CD}$ . Denote by $Q$ the intersection point of the angle bisector of $\\angle... | math | {
"ground_truth": "3 - 2\\sqrt{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": "If the odd function $f(x)$ has a domain of $\\mathbb{R}$, and $f(x+2) = -f(x)$, and $f(-1) = 6$, then $f(2017) = $ ?",
"role": "user"
}
] | math | {
"ground_truth": "-6",
"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": "Calculate the definite integral:\n\n$$\n\\int_{0}^{\\operatorname{arctg} \\frac{1}{3}} \\frac{8+\\operatorname{tg} x}{18 \\sin ^{2} x+2 \\cos ^{2} x} \\, dx\n$$",
"role": "us... | math | {
"ground_truth": "\\frac{\\pi}{3} + \\frac{\\ln 2}{36}",
"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 computer screen shows a $98 \\times 98$ chessboard, colored in the usual way. One can select with a mouse any rectangle with sides on the lines of the chessboard and click the ... | math | {
"ground_truth": "98",
"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 set $S$ consists of triangles whose sides have integer lengths less than 7, and no two elements of $S$ are congruent or similar. Furthermore, no triangle in $S$ is a right tria... | math | {
"ground_truth": "14",
"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 line $y=kx-2$ intersects the parabola $y^2=8x$ at points A and B. If the x-coordinate of the midpoint of AB is 2, calculate the length of $|AB|$.",
"role": "user"
}
] | math | {
"ground_truth": "2\\sqrt{15}",
"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 the number of ordered pairs of integers \\( (a, b) \\) with \\( 1 \\leq a \\leq 150 \\) and \\( b \\geq 0 \\) such that the polynomial \\( x^2 - ax + b \\) can be factored i... | math | {
"ground_truth": "5851",
"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": "Eight points on a circle are given. Five of the chords joining pairs of the eight points are selected at random. What is the probability that the five chords form a convex pentag... | math | {
"ground_truth": "\\frac{1}{1755}",
"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 ratio of the perimeter of a rhombus to the sum of its diagonals is equal to $k$. Find the angles of the rhombus and the permissible values of $k$.",
"role": "user"
}
] | math | {
"ground_truth": "\\arcsin \\left( \\frac{4 - k^2}{k^2} \\right), \\pi - \\arcsin \\left( \\frac{4 - k^2}{k^2} \\right) \\,; \\, \\sqrt{2} \\leq 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": "What is the largest four-digit number that is divisible by $33$?",
"role": "user"
}
] | math | {
"ground_truth": "9999",
"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 certain school club has 10 members, and two of them are put on duty each day from Monday to Friday. Given that members A and B must be scheduled on the same day, and members C ... | math | {
"ground_truth": "5400",
"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": "In triangle $ABC$, side $AB = 40$. The incenter $I$ of the inscribed circle divides the angle bisector $AL$ in the ratio $5:3$ from the vertex $A$. Find the radius of the circumc... | math | {
"ground_truth": "42.5",
"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": "Given the system of equations:\n1. \\( y \\cdot x^{\\log_{y} x} = x^{2.5} \\)\n2. \\( \\log_{3} y \\cdot \\log_{y}(y - 2x) = 1 \\)\n\nSolve for \\( x \\) and \\( y \\).",
"ro... | math | {
"ground_truth": "(3, 9)",
"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": "What is the greatest prime factor of $15! + 18!$?",
"role": "user"
}
] | math | {
"ground_truth": "17",
"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 the Cartesian coordinate system $xOy$, with the origin as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. The polar equ... | math | {
"ground_truth": "(0,2)",
"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": "A tournament is held among $n$ teams, following such rules:\na) every team plays all others once at home and once away.(i.e. double round-robin schedule)\nb) each team may part... | math | {
"ground_truth": "n = 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": "Given the system of equations:\n\\[\n\\begin{cases}\n\\sin x \\cos y = 0.25 \\\\\n\\sin y \\cos x = 0.75\n\\end{cases}\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "x_1 = \\frac{\\pi}{6} + \\pi (m - n), \\quad y_1 = \\frac{\\pi}{3} + \\pi (m + n) \\\\ \nx_2 = -\\frac{\\pi}{6} + \\pi (m - n), \\quad y_2 = \\frac{2\\pi}{3} + \\pi (m + n)",
"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 area of the region of the \\( xy \\)-plane defined by the inequality \\( |x|+|y|+|x+y| \\leq 1 \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{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": "The equation of the circle with the smallest area that passes through points A(-3,0) and B(3,0) is _____________.",
"role": "user"
}
] | math | {
"ground_truth": "x^2 + y^2 = 9",
"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_0, a_1, \\ldots, a_{100}$ and $b_1, b_2,\\ldots, b_{100}$ are sequences of real numbers, for which the property holds: for all $n=0, 1, \\ldots, 99$ , either $$ a_{n+1}=\... | math | {
"ground_truth": "50",
"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": "Points \\(E\\) and \\(F\\) are positioned on line segment \\(\\overline{GH}\\). The length of \\(\\overline{GE}\\) is \\(3\\) times the length of \\(\\overline{EH}\\), and the le... | math | {
"ground_truth": "D) \\(\\frac{5}{36}\\)",
"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 that $\\tan \\beta= \\frac{4}{3}$, $\\sin (\\alpha+\\beta)= \\frac{5}{13}$, and both $\\alpha$ and $\\beta$ are within $(0, \\pi)$, find the value of $\\sin \\alpha$.",
... | math | {
"ground_truth": "\\frac{63}{65}",
"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 roots of\n\\[ z^7 = -\\frac{i}{\\sqrt{2}} - \\frac{1}{\\sqrt{2}} \\]\nare $\\text{cis } \\phi_1$, $\\text{cis } \\phi_2$, $\\dots$, $\\text{cis } \\phi_7$, where $0^\\circ \\... | math | {
"ground_truth": "1305^\\circ",
"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": "Two tangents are drawn to a circle from an exterior point $A$; they touch the circle at points $B$ and $C$ respectively. A third tangent intersects segment $AB$ in $P$—a point ha... | math | {
"ground_truth": "48",
"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": "$\\lim _{x \\rightarrow 0^{+}} \\frac{[x]}{\\tan x}$ where $[x]$ is the greatest integer function\n[list=1]\n[*] -1\n[*] 0\n[*] 1\n[*] Does not exists\n[/list]",
"role": "... | math | {
"ground_truth": "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": "What is the least possible value of\n\\[(x+2)(x+3)(x+4)(x+5) + 2024\\] where \\( x \\) is a real number?\nA) 2022\nB) 2023\nC) 2024\nD) 2025\nE) 2026",
"role": "user"
}
] | math | {
"ground_truth": "2023",
"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 the functions $f$ that satisfy $f(x+5) + f(x-5) = f(x)$ for all real $x$, determine the smallest positive period $p$ for all such functions.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{ Consider the functions } f \\text{ that satisfy } f(x+5) + f(x-5) = f(x) \\text{ for all real } x. \\text{ Determine the smallest positive period } p \\text{ for all such functions.}",
"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 circumference of a circle $D$ is 72 feet. Calculate the length of arc $\\widehat{EF}$ where $\\angle EDF = 90^\\circ$. The diagram shows angle $EDF$ marked as $90^\\circ$ wit... | math | {
"ground_truth": "18 \\text{ feet}",
"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 $a>0$, $b>0$, and $\\frac {1}{a}$+ $\\frac {1}{b}$$=1$, find the minimum value of $3a+2b+ $$\\frac {b}{a}$.",
"role": "user"
}
] | math | {
"ground_truth": "11",
"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": "What is the value of $$\\frac{1}{4}\\times8\\times\\frac{1}{16}\\times32\\times\\frac{1}{64}\\times128\\times\\frac{1}{256}\\times512\\times\\frac{1}{1024}\\times2048?$$",
"r... | math | {
"ground_truth": "32",
"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": "Islandland consists of ten islands, some of which are connected by two-way air routes. If you select any 9 islands, it is possible to fly around them one by one and return to the... | 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": "Every positive integer can be represented as a sum of one or more consecutive positive integers. For each $n$ , find the number of such represententation of $n$ .",
"role... | math | {
"ground_truth": "\\tau(2l+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": "Consider a chessboard that is infinite in all directions. Alex the T-rex wishes to place a positive integer in each square in such a way that:\n\n\n- No two numbers are equal.\n-... | math | {
"ground_truth": "k = 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": "In an $8 \\times 12$ table, some $N$ cells are black, while the rest are white. In one operation, it is allowed to paint three cells that form a three-cell corner to white (some ... | math | {
"ground_truth": "27",
"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": "Liam takes a long drive in his car, which has a speed of $60$ miles per hour, and he drives for a whole number of hours. At the start of Liam's trip, the odometer reads $abc$ mil... | math | {
"ground_truth": "The correct answer is **B) 29**.",
"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": "A flag consists of three horizontal strips of fabric, each a solid color, chosen from red, white, blue, green, or yellow. No two adjacent strips can have the same color. How many... | math | {
"ground_truth": "80",
"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 points A(3, 1, 3) and B(1, 5, 0), find:\n1. The coordinates of the midpoint of segment AB and its length.\n2. The conditions that the coordinates x, y, z of point P(x, y, z... | math | {
"ground_truth": "4x - 8y + 6z + 7 = 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": "A container with a height of $3$ centimeters, a width of $4$ centimeters, and a length of $6$ centimeters can hold 72 grams of sand. What is the volume of a second container with... | math | {
"ground_truth": "432",
"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": "Find all non-negative integers \\( x \\) and \\( y \\) such that \\( 33^x + 31 = 2^y \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\{(0, 5), (1, 6)\\}",
"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": "If the line that passes through point A$(1-t, 1+t)$ and point B$(3, 2t)$ has an obtuse angle of inclination, then the range of the real number $t$ is _______.",
"role": "user... | math | {
"ground_truth": "-2 < t < 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": "Jerry has nine cards with digits from 1 to 9. He arranges them in a row to form a nine-digit number. Tom writes on the board all 8 two-digit numbers formed by consecutive digits ... | math | {
"ground_truth": "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": "Is there a real number $a$ such that the function $f(x) = \\log_a(ax^2 - x)$ is increasing on the interval $[2, 4]$? If it exists, explain which values $a$ can take; if it does n... | math | {
"ground_truth": "a > 1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
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