data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)= \\sqrt {6}\\sin \\dfrac {x}{2}\\cos \\dfrac {x}{2}+ \\sqrt {2}\\cos ^{2} \\dfrac {x}{2}$,\n(1) Simplify the function $f(x)$ into the form of $A\\sin (ωx... | math | {
"ground_truth": "\\dfrac {3 \\sqrt {2}}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are $800$ marbles in a bag. Each marble is colored with one of $100$ colors, and there are eight marbles of each color. Anna draws one marble at a time from the bag, wi... | math | {
"ground_truth": "\\frac{99}{101}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Circle $C$ has its center at $C(3, 5)$ and has a radius of 5 units. Circle $D$ has its center at $D(13, 5)$ and has a radius of 5 units. What is the area of the gray region bound... | math | {
"ground_truth": "50 - 12.5\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 growth rate of a certain mold doubles every day. If the mold can cover the entire surface of a tank after 14 days, calculate the number of days it will take to cover half of ... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 harmonic mean of $1$ and $100$ using the formula $\\frac{2ab}{a+b}$.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 $10^{2015}$ planets in an Intergalactic empire. Every two planets are connected by a two-way space line served by one of $2015$ travel companies. The Emperor would ... | math | {
"ground_truth": "1007",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 triangular array of squares has one square in the first row, two in the second, and in general, $k$ squares in the $k$ th row for $1 \\leq k \\leq 11.$ With the exception ... | math | {
"ground_truth": "640",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "With a monthly income of 30,000 rubles, obligatory monthly expenses are as follows: 15,000 rubles for food, 5,000 rubles for utilities, and 2,500 rubles for phone, Internet, and ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"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 inverse of $f(x) = 7 - 3x$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{7 - x}{3}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine all real values of $x$ for which\n\\[\\frac{1}{\\sqrt{x} + \\sqrt{x - 2}} + \\frac{1}{\\sqrt{x} + \\sqrt{x + 2}} = \\frac{1}{4}.\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{257}{16}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 $180\\div \\left(12+15\\cdot 3\\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "3\\frac{9}{19}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Construct the cross-section of a triangular pyramid \\( A B C D \\) with a plane passing through the midpoints \\( M \\) and \\( N \\) of edges \\( A C \\) and \\( B D \\) and th... | math | {
"ground_truth": "1:2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cube of mass $m$ slides down the felt end of a ramp semicircular of radius $h$ , reaching a height $h/2$ at the opposite extreme.\nFind the numerical coefficient of fricti... | math | {
"ground_truth": "\\frac{1}{\\sqrt{1 - \\left(\\frac{1}{2\\pi}\\right)^2}}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 greatest common divisor of $12347$ and $30841$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 positive integers \\( a \\) and \\( b \\), with \\( a > b \\), such that:\n\n\\[ \\frac{2}{7} = \\frac{1}{a} + \\frac{1}{b} \\]",
"role": "user"
}
] | math | {
"ground_truth": "a = 28 \\text{ and } b = 4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a function \\( f: \\mathbf{N} \\rightarrow \\mathbf{N} \\) defined as follows:\n$$\nf(x)=\\left\\{\\begin{array}{ll}\n\\frac{x}{2}, & x \\text{ is even}; \\\\\n\\frac{x+7}{... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $N$ be the second smallest positive integer that is divisible by every positive integer less than $9$. Find the sum of the digits of $N$.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 sequence $a_1, a_2, a_3, \\dots,$ is defined recursively by $a_1 = 2, a_2 = 2,$ and for $k \\ge 3,$\n\\[a_k = \\frac{2}{5} a_{k - 1} + \\frac{1}{6} a_{k - 2}.\\]Evaluate $a_1 +... | math | {
"ground_truth": "\\frac{96}{13}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 geometric sequence $\\{a_n\\}$ with a common ratio $q=-5$, and $S_n$ denotes the sum of the first $n$ terms of the sequence, the value of $\\frac{S_{n+1}}{S_n}=\\boxed{?}... | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 triangle ABC is isosceles with sides AB = AC = 7 and BC = 8, and O is the center of the inscribed circle of this triangle, find the area of the circle passing through ... | math | {
"ground_truth": "37\\pi",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 different integers can be expressed as the sum of three distinct members of the set $\\{3, 5, 9, 13, 17, 21, 27\\}$?",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 $a,b,c$ be three distinct positive integers such that the sum of any two of them is a perfect square and having minimal sum $a + b + c$ . Find this sum.",
"role": "use... | math | {
"ground_truth": "55",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 \\( g \\) be a function defined by \\( g(x) = bx^3 - \\sqrt{3} \\) for some positive \\( b \\). If \\( g(g(\\sqrt{3})) = -\\sqrt{3} \\), then determine the value of \\( b \\)... | math | {
"ground_truth": "B) \\( \\frac{1}{3} \\)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the line $l: y=kx+1$ intersects the circle $C: x^2+y^2-2x-3=0$ at points $A$ and $B$, then the minimum value of $|AB|$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "2\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For which integers $n \\ge 5$ is it possible to color the vertices of a regular $ n$ -gon using at most $6$ colors in such a way that any $5$ consecutive vertices have diff... | math | {
"ground_truth": "\\{ n \\ge 5 \\mid n \\notin \\{7, 8, 9, 13, 14, 19\\} \\}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many three-digit numbers have digits whose sum is a perfect cube?",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 coefficients of the polynomial\n\\[a_6 x^6 + a_5 x^5 + a_4 x^4 + a_3 x^3 + a_2 x^2 + a_1 x + a_0 = 0\\] are all integers, and its roots $s_1, s_2, \\dots, s_6$ are all intege... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Multiple-choice questions are a type of question in the new college entrance examination. The rules are as follows: if all the selected options are correct, the student gets $5$ ... | math | {
"ground_truth": "\\frac{1}{54}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 the total number of different ways to distribute 5 student volunteers to 4 projects, such that each volunteer is assigned to only 1 project and each project has at leas... | math | {
"ground_truth": "240",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 $a \\gt 0$, $b \\gt 0$, and $a+b=1$, find the maximum value of $\\frac{1}{{a+2b-3ab}}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( \\theta \\) is an acute angle, \\( \\sin 2\\theta = a \\), and \\( \\cos 2\\theta = b \\), find the value of \\( \\sin\\theta + \\cos\\theta \\).\nA) \\( \\sqrt{1 - a} \\)... | math | {
"ground_truth": "\\textbf{(B)}\\ \\sqrt{1 + a}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the positive difference between the two largest prime factors of $171689$?",
"role": "user"
}
] | math | {
"ground_truth": "282",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine how many integers $x$ satisfy the equation $(x^2 - x - 6)^{x+4} = 1$.\nA) 1\nB) 2\nC) 3\nD) 4\nE) 5",
"role": "user"
}
] | math | {
"ground_truth": "C) 3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 players face off in a dice combat game. The attacker will roll three dice and the defender will roll two. The attacker will defeat the defender in a single roll of dice if an... | math | {
"ground_truth": "\\frac{43}{216}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Joseane's calculator is malfunctioning: each digit pressed appears doubled on the screen. The addition, subtraction, multiplication, and division operation keys work normally and... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "**Solve \\( \\arcsin(2x) + \\arcsin(1 - 2x) = \\arccos(2x) \\).**",
"role": "user"
}
] | math | {
"ground_truth": "x = 0, \\pm \\frac{1}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 a real number and $\\lceil x \\rceil = -3,$ how many possible values are there for $\\lceil x^2 \\rceil$?",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 circumcircle $\\omega$ . Let the bisector of $\\angle ABC$ meet segment $AC$ at $D$ and circle $\\omega$ at $M\\ne B$ . The circumcircle ... | math | {
"ground_truth": "40^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify\n\\[\n\\frac{2 + 2\\sin x - 2\\cos x}{2 + 2\\sin x + 2\\cos x}.\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\tan \\frac{x}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 gambler starts with $100. During a series of 4 rounds, they bet each time one-third of the amount they have. They win twice and lose twice, but now the wins are twice the stake... | math | {
"ground_truth": "\\frac{8000}{81}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\cos x,$ $\\sin x,$ $\\cot x$ form a geometric sequence, in this order, then find $\\tan^6 x - \\tan^2 x.$",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 each positive integer $n\\ge2$ , find a polynomial $P_n(x)$ with rational coefficients such that $\\displaystyle P_n(\\sqrt[n]2)=\\frac1{1+\\sqrt[n]2}$ . (Note that $\\s... | math | {
"ground_truth": "P_n(x) = \\sum_{i=0}^{n-1} x^i - \\frac{2}{3} x^{2i}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We know that $201$ and $9$ give the same remainder when divided by $24$ . What is the smallest positive integer $k$ such that $201+k$ and $9+k$ give the same remainder... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 2-digit integers from 31 to 68 are written consecutively to form the integer $N=313233\\cdots6768$. Suppose that $3^k$ is the highest power of 3 that is a factor of $N$. What... | math | {
"ground_truth": "\\text{B) } 1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 conference room, each row can seat either 9 or 10 people. Fifty-four people need seating with every seat filled. How many rows must seat exactly 10 people?",
"role": "us... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 sum of $231_5 + 414_5 + 123_5$. Express your answer in base $5$.",
"role": "user"
}
] | math | {
"ground_truth": "1323_5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 a $5 \\times 5$ grid we randomly place two \\emph{cars}, which each occupy a single cell and randomly face in one of the four cardinal directions. It is given that the two c... | math | {
"ground_truth": "1148",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 integral $$ \\int_{-1}^1 x^nf(x) \\; dx $$ for every $n$ -th degree polynomial $f$ with integer coefficients. Let $\\alpha_n$ denote the smallest positive ... | math | {
"ground_truth": "-\\log 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 a triangle and a trapezoid share the same altitude, and they are equal in area, the base of the triangle is 24 inches, and the smaller base of the trapezoid is half th... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 natural numbers \\(n\\) are there such that\n\n\\[ 100 < \\sqrt{n} < 101 ? \\]",
"role": "user"
}
] | math | {
"ground_truth": "200",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the Cartesian coordinate system, with the origin \\\\(O\\\\) as the pole and the non-negative half-axis of the \\\\(x\\\\)-axis as the polar axis, a polar coordinate system is... | math | {
"ground_truth": "[ \\sqrt {13}-2, \\sqrt {13}+2]",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 $A,B,C,D$ denote four points in space such that at most one of the distances $AB,AC,AD,BC,BD,CD$ is greater than $1$. Determine the maximum value of the sum of the six distan... | math | {
"ground_truth": "6 + \\sqrt{2}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest positive number $\\lambda $ , such that for any complex numbers ${z_1},{z_2},{z_3}\\in\\{z\\in C\\big| |z|<1\\}$ ,if $z_1+z_2+z_3=0$ , then $$ \\left|z_... | math | {
"ground_truth": "\\lambda = 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Factor the polynomial \\(a^{3}+b^{3}+c^{3}-3abc\\) into three linear factors.",
"role": "user"
}
] | math | {
"ground_truth": "(a + b + c)\\left(a + \\omega b + \\omega^2 c\\right)\\left(a + \\omega^2 b + \\omega c\\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all natural numbers that cannot be represented as the difference of squares of any natural numbers.",
"role": "user"
}
] | math | {
"ground_truth": "1, 4 \\text{ and all numbers of the form } 4k+2.",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The Euler's totient function $\\varphi(n)$ is defined as the number of integers from 1 to $n$ that are relatively prime to $n$. Find\n\na) $\\varphi(17)$; b) $\\varphi(p)$; c) $\... | math | {
"ground_truth": "p^{\\alpha - 1}(p-1)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "List all two-digit numbers that can be formed using the digits 1, 2, and 3, without repeating any digit in the number.",
"role": "user"
}
] | math | {
"ground_truth": "10, 12, 13, 20, 21, 23, 30, 31, 32",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The four roots of the equation \\[ax^4 + bx^3 + cx^2 + dx + e = 0\\] are $1,$ $2,$ $3$, and $5$. Compute $\\frac{d}{e}$.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{61}{30}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Pinocchio buried two ingots in the Field of Wonders: one gold and one silver. On days when the weather is good, the gold ingot increases by 30%, and the silver ingot increases by... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of the numerical coefficients in the binomial $(2a+2b)^7$ is $\\boxed{32768}$.",
"role": "user"
}
] | math | {
"ground_truth": "16384",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 area of a circle whose circumference is $36\\pi$ is $k\\pi$. What is the value of $k$?\nA) 288 \nB) 324 \nC) 162 \nD) 648",
"role": "user"
}
] | math | {
"ground_truth": "B) \\ 324",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If non-zero real numbers $a$ and $b$ ($a\\neq b$) satisfy $a^{2}+a-2007=0$ and $b^{2}+b-2007=0$, then the value of $\\frac{1}{a}+\\frac{1}{b}$ is ______.",
"role": "user"
}... | math | {
"ground_truth": "\\frac{1}{2007}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\frac{3}{4} = \\frac{y}{215+x}$, find the smallest value of $x$, if $x$ and $y$ are positive integers.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Charlyn walks completely around the boundary of a rectangle whose sides are 8 km and 6 km long. From any point on her path, she can see exactly 1.5 km horizontally in all directi... | math | {
"ground_truth": "77",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Positive real numbers \\( x, y, z \\) satisfy\n\\[\n\\left\\{\n\\begin{array}{l}\n\\frac{2}{5} \\leqslant z \\leqslant \\min \\{x, y\\}, \\\\\nxz \\geqslant \\frac{4}{15}, \\\\\n... | math | {
"ground_truth": "13",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given \\(5^a + 5^b = 2^c + 2^d + 17\\), determine the number of integers \\(a, b, c, d\\) which can possibly be negative.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 the equation \\(\\frac{18}{x^2 - 9} - \\frac{3}{x - 3} = 2\\). Find the root(s) of this equation.\nA) 3 only\nB) -4.5 only\nC) 3 and -4.5\nD) No real roots",
"role":... | math | {
"ground_truth": "C)$ 3 and -4.5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 all even numbers $n$ , $n \\in \\mathbb N$ such that \\[{ \\frac{1}{d_{1}}+\\frac{1}{d_{2}}+ \\cdots +\\frac{1}{d_{k}}=\\frac{1620}{1003}}, \\] \r\nwhere $d_1, d_2,... | math | {
"ground_truth": "n = 2006k",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 actual lighthouse's cylindrical base is 60 meters high, and the spherical top's volume is approximately 150,000 liters, and the miniature model's top holds around 0.15 ... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 solutions $x$ of the inequality $$\\frac{3}{20} + \\left|x-\\frac{7}{40}\\right| < \\frac{1}{4}.$$ Express your answer in interval notation, simplifying all fractions in... | math | {
"ground_truth": "\\left(\\frac{3}{40}, \\frac{11}{40}\\right)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 an isosceles triangle \\( ABC \\), where \\( AB = BC \\) and angle \\( B \\) is \\( \\frac{\\pi}{4} \\), a perpendicular \\( AD \\) is dropped onto side \\( BC \\). Semicircle... | math | {
"ground_truth": "\\left(\\tan \\frac{3\\pi}{16}\\right)^2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Estimate the year in which the population of Isla will be approximately 10,000, given that the population doubles every 20 years, starting from a population of 250 in the year 20... | math | {
"ground_truth": "2110",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Below is a portion of the graph of an invertible function, \\( y = g(x) \\):\n\n[asy]\nimport graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps)... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 sets $A=\\{-1,0,1,2\\}$ and $B=\\{x|0 < x < 3\\}$, find $A\\cap B$.",
"role": "user"
}
] | math | {
"ground_truth": "\\{1, 2\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 sum of the areas of the four smaller rectangles is equal to the area of the large rectangle. Given that the areas of three of the smaller rectangles are 6, 15, and 25, find t... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute the only element of the set \\[\\{1, 2, 3, 4, \\ldots\\} \\cap \\left\\{\\frac{404}{r^2-4} \\;\\bigg| \\; r \\in \\mathbb{Q} \\backslash \\{-2, 2\\}\\right\\}.\\]\n\n*Pro... | math | {
"ground_truth": "2500",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the sum of $5.256$, $2.89$, and $3.75$ as a decimal.",
"role": "user"
}
] | math | {
"ground_truth": "11.96",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 monotonic functions $f: \\mathbb{R} \\rightarrow \\mathbb{R}$ satisfying\n\\[f(f(x) - y) + f(x+y) = 0,\\]\nfor every real $x, y$ .\n(Note that monotonic means that fu... | math | {
"ground_truth": "f(x) = 0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 merchant buys notebooks at a discount of $15\\%$ from the list price. He plans to set a marked price that allows him to offer a discount of $10\\%$ on the marked price and stil... | math | {
"ground_truth": "\\textbf{(C) } 126\\%",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$a$ , $b$ , $c$ are real. What is the highest value of $a+b+c$ if $a^2+4b^2+9c^2-2a-12b+6c+2=0$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{17}{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Shift the graph of the function $y=2\\cos(2x+\\frac{\\pi}{3})$ to the right by $\\phi$ ($0 < \\phi < \\frac{\\pi}{2}$) units. If the resulting function is an odd function, then $... | math | {
"ground_truth": "\\frac{5\\pi}{12}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 measures, in degrees, of the angles , $\\alpha, \\beta$ and $\\theta$ are greater than $0$ less than $60$ . Find the value of $\\theta$ knowing, also, that $\\alpha... | math | {
"ground_truth": "30^\\circ",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 an isosceles triangle $ABC$ with a perimeter of $24$ cm and equal sides $a$, find the maximum area of triangle $ABC$.",
"role": "user"
}
] | math | {
"ground_truth": "16\\sqrt{3} \\text{ cm}^2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 point in the plane $2x - 3y + 4z = 40$ that is closest to the point $(1, 0, 2).$",
"role": "user"
}
] | math | {
"ground_truth": "\\left(\\frac{89}{29}, -\\frac{90}{29}, \\frac{176}{29}\\right)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine which digit is in the 1000th position after the decimal point in the decimal expansion of the number $\\frac{9}{28}$.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The value range of the function $f(x) = x^2 + ax + b$ ($a, b \\in \\mathbb{R}$) is $[0, +\\infty)$, and the solution set of the inequality $f(x) < c$ with respect to $x$ is $(m, ... | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 degree of the polynomial $(x^3 + x + 1)^5 (x^4 - 1)^2 (x-1)^3$ as a polynomial in $x$?\nA) 15\nB) 23\nC) 26\nD) 34\nE) 40",
"role": "user"
}
] | math | {
"ground_truth": "C) 26",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"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 prime factorization of 8820 is $2^2 \\times 3^2 \\times 5 \\times 7^2$. How many of its positive integer factors are perfect squares?",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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(x) \\) be the product of all the digits of a decimal integer \\( x \\). Find all positive integers \\( x \\) such that \\( p(x) = x^{2} - 10x - 22 \\).",
"role": "u... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $$-\\frac{\\pi}{2} \\leq \\alpha < \\beta \\leq \\frac{\\pi}{2}$$, the range of $$\\frac{\\alpha-\\beta}{2}$$ is \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "\\left[- \\frac{\\pi}{2}, 0\\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 interval of decrease for the function $f(x) = \\ln x - x^2 + x$.",
"role": "user"
}
] | math | {
"ground_truth": "(1/2, +\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"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 walls and the ceiling of a room meet at right angles at point \\(P\\). A fly is in the air three meters from one wall, four meters from the other wall, and seven meters from ... | math | {
"ground_truth": "\\textbf{(D)} 2\\sqrt{6}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If an arc length and the area of a sector are numerically equal to 5, calculate the degree measure of the central angle of this sector.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each square in a $3 \\times 10$ grid is colored black or white. Let $N$ be the number of ways this can be done in such a way that no five squares in an ' $\\mathrm{X}$ ' configur... | math | {
"ground_truth": "25636",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The ratio of the numbers is $2: 1 \\frac{1}{2}$, and the sum of their squares is 400. Find these numbers.",
"role": "user"
}
] | math | {
"ground_truth": "16 \\text{ and } 12",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Twenty kilograms of cheese are on sale in a grocery store. Several customers are lined up to buy this cheese. After a while, having sold the demanded portion of cheese to the nex... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"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 rational numbers $-3^2$, $(-1)^{2006}$, $0$, $|-2|$, $-\\left(-2\\right)$, $-3 \\times 2^2$, determine the number of negative numbers among them.",
"role": "user"
... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Pebbles are placed on the squares of a $2021\\times 2021$ board in such a way that each square contains at most one pebble. The pebble set of a square of the board is the colle... | math | {
"ground_truth": "2021 + \\left\\lfloor \\frac{2021}{2} \\right\\rfloor = 3031",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of $[-2.8]$ using the definition of the floor function.",
"role": "user"
}
] | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"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 3:20 o'clock, calculate the angle formed by the hour and minute hands of a clock.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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