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 a positive integer $c$ , we construct a sequence of fractions $a_1, a_2, a_3,...$ as follows: $\\bullet$ $a_1 =\\frac{c}{c+1} $ $\\bullet$ to get $a_n$ , we take $... | math | {
"ground_truth": "n = 7",
"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(x) = 2x^6 - 5x^4 + 7x^2 + 6 \\). If \\( g(15) = 82 \\), find \\( g(15) + g(-15) \\).",
"role": "user"
}
] | math | {
"ground_truth": "164",
"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 \\( x \\in \\mathbf{R} \\), find the minimum value of the function \\( f(x) = |2x - 1| + |3x - 2| + |4x - 3| + |5x - 4| \\).",
"role": "user"
}
] | math | {
"ground_truth": "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": "Let $A$ be the set of all permutations $a = (a_1, a_2, \\ldots, a_{2003})$ of the 2003 first positive integers such that each permutation satisfies the condition: there is no... | math | {
"ground_truth": "4010006",
"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": "Eight points are selected on the positive $x$-axis,$X^+$, and six points are selected on the positive $y$-axis,$Y^+$. Every point on $X^+$ is connected by a segment to every poin... | math | {
"ground_truth": "The correct answer is C) 420.",
"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": "Armando rolls 8 standard 6-sided dice simultaneously and calculates the product of the 8 numbers he obtains. What is the probability that the product is divisible by 8?\n**A)** $... | math | {
"ground_truth": "\\frac{35}{36}",
"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 $n$ points $A_1, A_2, \\ldots, A_n$ on a circle. How many ways are there if we want to color these points by $p$ colors, so that each two neighbors points are col... | math | {
"ground_truth": "f(C_n, p) = p(p-1)^{n-1} - f(C_{n-1}, p)",
"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": "Petya and 9 other people are playing a game where each person rolls a die. A player wins a prize if they roll a number of points that no one else rolls.\n\na) What is the probabi... | math | {
"ground_truth": "0.919",
"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 the numbers $4^{0.2}$, $3^{0.5}$, $3^{0.4}$, and $\\log_{0.4} 0.5$, arrange the numbers in increasing order.",
"role": "user"
}
] | math | {
"ground_truth": "\\log_{0.4}0.5 < 4^{0.2} < 3^{0.4} < 3^{0.5}",
"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 height of an isosceles triangle, dropped perpendicularly to its lateral side, divides it into segments equal to 2 and 1, counting from the vertex of the triangle. Find the ba... | math | {
"ground_truth": "\\sqrt{6}",
"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 $$f(x)=\\sin\\left( \\frac {1}{2}x+ \\frac {\\pi}{3}\\right)$$ \n(1) Find the smallest positive period and the maximum value of the function $f(x)$, and determine the valu... | math | {
"ground_truth": "\\left[- \\frac {5\\pi}{3}, \\frac {\\pi}{3}\\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 minimum value of\n\\[x^2 + 3xy + y^2\\]\nover all real numbers $x$ and $y$.",
"role": "user"
}
] | 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": "In a certain year, the price of a commodity rose by $15\\%$ during January, fell by $10\\%$ during February, rose by $20\\%$ during March, fell by $15\\%$ during April, and fell ... | math | {
"ground_truth": "\\text{B) 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": "Let's call any natural number \"very prime\" if any number of consecutive digits (in particular, a digit or number itself) is a prime number. For example, $23$ and $37$ are \... | math | {
"ground_truth": "373",
"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": "For each integer \\( n \\geq 2 \\), let \\( S_n \\) be the sum of all products \\( jk \\), where \\( j \\) and \\( k \\) are integers and \\( 1 \\leq j < k \\leq n \\). Find the ... | math | {
"ground_truth": "C) 285",
"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": "Given that the function $f(x)$ defined on $[-2,2]$ is monotonically decreasing on the interval $[0,2]$ and $f(1-m) < f(3m)$.\n(1) If the function $f(x)$ is an odd function on the... | math | {
"ground_truth": "-\\frac{1}{2} \\leq m < \\frac{1}{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": "Consider a regular hexagon with a side length of 4 units. Outside of each vertex of the hexagon, a quarter-circle is drawn with radius equal to the side length of the hexagon. Ca... | math | {
"ground_truth": "**\\( A) 48\\sqrt{3} - 24\\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": "Solve for the roots of the equation \\( 4x^{1/4} + 4x^{-1/4} = 9 \\).\n**A)** \\( \\left( \\frac{9 + \\sqrt{17}}{8} \\right)^4, \\left( \\frac{9 - \\sqrt{17}}{8} \\right)^4 \\)\n... | math | {
"ground_truth": "**A)** \\( \\left( \\frac{9 + \\sqrt{17}}{8} \\right)^4, \\left( \\frac{9 - \\sqrt{17}}{8} \\right)^4 \\)",
"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 set of positive real numbers $x$ that satisfy $2 | \fx^2 - 9\f | \\le 9 | x | $ is an interval $[m, M]$ . Find $10m + M$ .",
"role": "user"
}
] | math | {
"ground_truth": "21",
"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": "Two distinct integers, $x$ and $y$, are randomly chosen from the set $\\{1,2,3,4,5,6,7,8,9,10,11,12\\}$. What is the probability that $xy-x-y+2$ is even?",
"role": "user"
}... | math | {
"ground_truth": "\\frac{5}{22}",
"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 real numbers $a$ for which the following equation has a unique real solution: $$ |x-1|+|x-2|+\\ldots+|x-99|=a. $$",
"role": "user"
}
] | math | {
"ground_truth": "2450",
"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 tenth and twelfth terms of an arithmetic sequence are 3 and 9, respectively. What is the fifth term?",
"role": "user"
}
] | math | {
"ground_truth": "-12",
"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 pairs of nonnegative integers $(x, y)$ for which $(xy + 2)^2 = x^2 + y^2 $ .",
"role": "user"
}
] | math | {
"ground_truth": "(0, 2) \\text{ and } (2, 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 right-angled triangle has sides of lengths 6 cm, 8 cm, and 10 cm. The height to the hypotenuse is \\_\\_\\_\\_\\_\\_ cm.",
"role": "user"
}
] | math | {
"ground_truth": "4.8 \\text{ cm}",
"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 \\[f(x) =\n\\begin{cases}\n3x^2 + 5 & \\text{if } x \\leq 3, \\\\\nbx + 6 & \\text{if } x > 3.\n\\end{cases}\n\\]\nFind \\( b \\) to ensure that the graph of \\( y = f(x) \\)... | math | {
"ground_truth": "\\frac{26}{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 a line $l$ passes through the focus $F$ of the parabola $y^{2}=4x$, and intersects the parabola at points $A$ and $B$.\n$(1)$ If $|AF|=4$, find the coordinates of point $A$... | 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": "If \\( \\mathrm{f}(x) = x^{4} + x^{3} + x^{2} + x + 1 \\), determine the remainder \\( a \\) of \\( \\mathrm{f}(x^{5}) \\) divided by \\( \\mathrm{f}(x) \\).",
"role": "user"... | math | {
"ground_truth": "5",
"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 school club sells $200$ concert tickets for a total of $2688$ dollars. Some tickets are sold at full price, while others are sold at a discounted rate of one-third of the full ... | math | {
"ground_truth": "\\textbf{(B) } \\textdollar 2128",
"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": "Given that \\( x + y - 2 \\) is a factor of the polynomial \\( x^{2} + axy + by^{2} - 5x + y + 6 \\) in terms of \\( x \\) and \\( y \\), determine the value of \\( a - b \\).",
... | math | {
"ground_truth": "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": "Given that the complex conjugate of a complex number $z$ is $\\overline{z}$, and $z + \\overline{z}(2 - 3i) = -3 - 5i$, determine the value of $z$.",
"role": "user"
}
] | math | {
"ground_truth": "1 + 2i",
"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": "Triangle $A_0B_0C_0$ is given in the plane. Consider all triangles $ABC$ such that:\n(i) The lines $AB,BC,CA$ pass through $C_0,A_0,B_0$ , respectvely,\n(ii) The triangles... | math | {
"ground_truth": "\\text{The circumcenter of } \\triangle ABC \\text{ is the image of the circumcenter of } \\triangle A_0B_0C_0 \\text{ under the homothety.}",
"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 pairs of real numbers $(a,b)$ such that the biggest of the numbers $x=b^2-\\frac{a-1}{2}$ and $y=a^2+\\frac{b+1}{2}$ is less than or equal to $\\frac{7}{16}$",
... | math | {
"ground_truth": "(a, b) = \\left(\\frac{1}{4}, -\\frac{1}{4}\\right)",
"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 $B = \\{1, 2, 3, 4, 5, 6, 7, 8\\}$, and let $M$ be the number of functions $g$ from set $B$ to set $B$ such that $g(g(g(x)))$ is a constant function. Find the remainder when ... | math | {
"ground_truth": "1600",
"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 sum of the (decimal) digits of a natural number $n$ equals $100$ , and the sum of digits of $44n$ equals $800$ . Determine the sum of digits of $3n$ .",
"role": "... | math | {
"ground_truth": "300",
"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 $n\\ge 3$ . consider a sequence $a_1,a_2,...,a_n$ , if $(a_i,a_j,a_k)$ with i+k=2j (i<j<k) and $a_i+a_k\\ne 2a_j$ , we call such a triple a $NOT-AP$ triple. If a seq... | math | {
"ground_truth": "\\left \\lfloor \\frac{n-1}{2} \\right \\rfloor",
"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 cubical die has faces marked with the numbers $1$, $2$, $3$, $3$, $4$, and $4$. Another die has faces marked with the numbers $1$, $2$, $5$, $6$, $7$, and $9$. Calculate the pr... | math | {
"ground_truth": "\\frac{11}{36}",
"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": "Define a \"digitized number\" as a ten-digit number $a_0a_1\\ldots a_9$ such that for $k=0,1,\\ldots, 9$ , $a_k$ is equal to the number of times the digit $k$ occurs in th... | math | {
"ground_truth": "6210001000",
"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 the differences between the first hundred positive even integers and the preceding odd integers for those pairs where the even integer is divisible by 5.",
... | math | {
"ground_truth": "10",
"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 \\( x \\) and \\( y \\) be positive real numbers such that \\( x^{2}+y^{2}=1 \\) and \\( \\left(3 x-4 x^{3}\\right)\\left(3 y-4 y^{3}\\right)=-\\frac{1}{2} \\). Compute \\( x... | math | {
"ground_truth": "\\frac{\\sqrt{6}}{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": "Circles centered at $A$ and $B$ each have radius 3. Point $O$ is the midpoint of $\\overline{AB}$, and $OA = 3\\sqrt{2}$. Segments $OC$ and $OD$ are tangent to the circles center... | math | {
"ground_truth": "18\\sqrt{2} - 9 - \\frac{9\\pi}{4}",
"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": "Calculate: ${(-1)}^{2023}+|2\\sqrt{2}-3|+\\sqrt[3]{8}$.",
"role": "user"
}
] | math | {
"ground_truth": "4 - 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": "Find a quadratic equation with rational coefficients and the quadratic term $x^2$ that has $\\sqrt{5}-3$ as a root.",
"role": "user"
}
] | math | {
"ground_truth": "x^2 - 6x - 4",
"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": "Real numbers \\( r \\) and \\( s \\) are roots of \\( p(x)=x^3+cx+d \\), and \\( r+5 \\) and \\( s-4 \\) are roots of \\( q(x)=x^3+cx+d+210 \\). Determine all possible values of ... | math | {
"ground_truth": "240, 420",
"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 that $A$ and $B$ are non-empty sets, define the operation $A-B=\\{x|x\\in A \\text{ and } x\\notin B\\}$. If $M=\\{x|y= \\sqrt{1-x}\\}$, $N=\\{y|y=x^2\\}$, $-1\\leq x\\leq ... | math | {
"ground_truth": "\\{x|x<0\\}",
"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": "In triangle $ABC$, point $D$ is on side $BC$ such that $BD:DC = 1:2$. A line through $A$ and $D$ intersects $BC$ at $E$. If the area of triangle $ABE$ is $30$, find the total are... | math | {
"ground_truth": "90",
"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 $2021$ points on a circle. Kostya marks a point, then marks the adjacent point to the right, then he marks the point two to its right, then three to the next point's ... | math | {
"ground_truth": "66",
"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": "In a class of 25 students, it is known that the number of boy friends for any two girls in the class does not match. What is the maximum number of girls that can be in this class... | 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": "How many three-digit integers are exactly 17 more than a two-digit integer?",
"role": "user"
}
] | math | {
"ground_truth": "17",
"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 the standard equation of a hyperbola with asymptotes forming an acute angle of $60^{\\circ}$ and passing through the point $(\\sqrt{2}, \\sqrt{3})$.",
"role": "user"
}... | math | {
"ground_truth": "\\frac{x^2}{7}-\\frac{y^2}{\\frac{7}{3}}=1",
"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": "A point is randomly thrown onto the segment [12, 17] and let \\( k \\) be the resulting value. Find the probability that the roots of the equation \\((k^{2} + k - 90)x^{2} + (3k ... | math | {
"ground_truth": "\\frac{2}{3}",
"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": "If $x=\\frac{a}{b}$, $a\\neq b$ and $b\\neq 0$, then $\\frac{2a+b}{a-2b}=$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2x + 1}{x - 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": "A circle of radius 3 is centered at point $A$. An equilateral triangle with side 6 has a vertex at $A$. Calculate the difference between the area of the region that lies inside t... | math | {
"ground_truth": "9(\\pi - \\sqrt{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": "A mathematics competition committee is composed of 9 professors. The finalized exam questions are stored in a safe that requires at least 6 professors to be present to open it. H... | math | {
"ground_truth": "504",
"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": "For how many values of the digit $A$ is it true that $120$ is divisible by $A$ and $451{,}2A8$ is divisible by $8$?",
"role": "user"
}
] | math | {
"ground_truth": "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 projection takes $\\begin{pmatrix} 3 \\\\ -1 \\end{pmatrix}$ to $\\begin{pmatrix} 6 \\\\ -2 \\end{pmatrix}.$ Which vector does the projection take $\\begin{pmatrix} 2 \\\\ -6 \... | math | {
"ground_truth": "\\begin{pmatrix} 3.6 \\\\ -1.2 \\end{pmatrix}",
"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": "An $m\\times n\\times p$ rectangular box has half the volume of an $(m + 2)\\times(n + 2)\\times(p + 2)$ rectangular box, where $m, n,$ and $p$ are integers, and $m\\le n\\le p.$... | math | {
"ground_truth": "130",
"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": "Let $z$ be a complex number with a positive real part, satisfying $|z|=2\\sqrt{5}$, and the complex number $\\left(1+2i\\right)z$ is purely imaginary. \n$(1)$ Find the complex n... | math | {
"ground_truth": "20",
"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 ${{\\left( {{a}_{n}} \\right)}_{n\\ge 1}}$ an increasing sequence and bounded.Calculate $\\underset{n\\to \\infty }{\\mathop{\\lim }}\\,\\left( 2{{a}_{n}}-{{a}_{1}}-{{a}_{... | math | {
"ground_truth": "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": "The area of isosceles $\\triangle ABC$ is $120$ and its base is $30$, find the length of one of the congruent sides.",
"role": "user"
}
] | math | {
"ground_truth": "17",
"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": "Compute the product of the matrices:\n\\[\n\\begin{pmatrix} \n2 & 0 & -1 \\\\\n1 & 3 & -2 \\\\\n0 & 5 & 4 \\\\\n-2 & 2 & 3 \n\\end{pmatrix} \n\\begin{pmatrix} \n3 & -1 & 0 & 4\\\... | math | {
"ground_truth": "\\begin{pmatrix}\n5 & -2 & 0 & 6 \\\\\n7 & -1 & -9 & -3 \\\\\n14 & 0 & -15 & 3 \\\\\n1 & 2 & -6 & -4\n\\end{pmatrix}",
"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 zoo has five pairs of different animals, each consisting of one male and one female. To maintain harmony, the zookeeper decides to feed them in a way such that each time he fee... | math | {
"ground_truth": "2880",
"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": "Consider the equation: $\\left(x-\\frac{4}{5}\\right)^2 + \\left(x-\\frac{4}{5}\\right)\\left(x-\\frac{2}{5}\\right) + \\left(x-\\frac{1}{2}\\right)^2 = 0$, solve for x.",
"r... | math | {
"ground_truth": "\\frac{14}{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": "The number of solutions to the equation $3x^4 - 4x^3 - 12x^2 + 12 = 0$ is to be calculated.",
"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": "A set of marbles can be divided in equal shares among $3$, $4$, $5$, $6$, $7$, or $8$ children with no marbles left over. What is the least number of marbles that the set could h... | math | {
"ground_truth": "830",
"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 square table of 49 cells is filled with numbers from 1 to 7 such that each column and each row contains all these numbers. If the table is symmetric with respect to the diagona... | math | {
"ground_truth": "\\text{On the main diagonal, all numbers from 1 to 7 appear exactly once.}",
"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": "Triangle ABC, which is isosceles with AB=AC, triangle XYZ is inscribed, and triangle XYZ is equilateral. Determine the relationship amongst the measures of angles BXZ, AXY, and C... | math | {
"ground_truth": "d = \\frac{e + f}{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": "Place point \\( C \\) at the origin of the Cartesian coordinate system and point \\( B \\) on the x-axis, as shown in the diagram. Then the coordinates of points \\( C, B, A \\) ... | math | {
"ground_truth": "\\frac{93 + 9 \\sqrt{409}}{40}",
"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 Stromquist Comet is visible every 61 years. If the comet is visible in 2017, what is the next leap year when the comet will be visible?",
"role": "user"
}
] | math | {
"ground_truth": "2444",
"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 two equiangular polygons \\(P\\) and \\(Q\\) with different numbers of sides; each angle of \\(P\\) is \\(p\\) degrees, and each angle of \\(Q\\) is \\(q\\) degrees, determ... | 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": "Three real numbers $a, b,$ and $c$ satisfy the equations $a+b+c=3$, $ab+ac+bc=-8$, and $abc=-20$. What is the largest of the three numbers? Express your answer in simplest radica... | math | {
"ground_truth": "\\frac{1 + \\sqrt{41}}{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": "Given that \\( \\text{rem} \\left(\\frac{5}{7}, \\frac{3}{4}\\right) \\) must be calculated, determine the value of the remainder.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{5}{7}",
"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 the diagram, a regular octagon has a square inside it, sharing one side with the octagon. Determine the degree measure of $\\angle XYZ$ in the configuration where $X, Y, Z$ ar... | math | {
"ground_truth": "90^\\circ",
"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 \\( n \\geq 3 \\) be an integer. A frog is to jump along the real axis, starting at the point 0 and making \\( n \\) jumps: one of length 1, one of length 2, \\ldots, one of ... | math | {
"ground_truth": "\\left\\lfloor \\frac{n-1}{2} \\right\\rfloor",
"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 an integer $n\\ge\\ 3$ , find the least positive integer $k$ , such that there exists a set $A$ with $k$ elements, and $n$ distinct reals $x_{1},x_{2},\\ldots,x_{n... | math | {
"ground_truth": "k = 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": "The base of a triangle is 36. A line parallel to the base divides the area of the triangle into two equal parts. Find the length of the segment of this line that lies between the... | math | {
"ground_truth": "18\\sqrt{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": "Triangle $ABC$ has a right angle at $C$ , and $D$ is the foot of the altitude from $C$ to $AB$ . Points $L, M,$ and $N$ are the midpoints of segments $AD, DC,$ and ... | math | {
"ground_truth": "193",
"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": "Solve for $x$: $5x - 3x = 420 - 10(x + 2)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{100}{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": "Find the point on the line\n\\[ y = -2x + 3 \\]\nthat is closest to the point $(3,1)$.",
"role": "user"
}
] | math | {
"ground_truth": "\\left(\\frac{7}{5}, \\frac{1}{5}\\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 a positive geometric sequence $\\{a_n\\}$, if $a_5a_4a_2a_1 = 16$, calculate the minimum value of $a_1 + a_5$.",
"role": "user"
}
] | 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": "Let $\\overrightarrow{a}=\\left(1,2\\right)$, $\\overrightarrow{b}=\\left(-1,x\\right)$. If $\\overrightarrow{a}\\bot \\overrightarrow{b}$, then $x=\\_\\_\\_\\_\\_\\_$.",
"ro... | math | {
"ground_truth": "x = \\frac{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": "Given that the angle between vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ is $30^{\\circ}$, and $|\\overrightarrow{a}|=1$, $|2\\overrightarrow{a}-\\overrightarrow{b}|=... | math | {
"ground_truth": "\\sqrt{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": "John dines at a restaurant where the sales tax on meals is 9%. He leaves an 18% tip on the price of his meal before the sales tax is added, and the tax is calculated only on the ... | math | {
"ground_truth": "29",
"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": "Color the numbers $2, 3, \\cdots, 9$ with one of three colors - red, green, or blue - such that each number is colored differently from its factors. Calculate the number of diffe... | math | {
"ground_truth": "432",
"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 $x$ be the number of juniors and $y$ be the number of seniors in the class. It is given that $\\frac{x}{x+y}=0.2$ and $\\frac{y}{x+y}=0.8$. The sum of the scores of the junio... | math | {
"ground_truth": "90",
"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 roots of the polynomial $3x^4 + 16x^3 - 36x^2 + 8x$.",
"role": "user"
}
] | math | {
"ground_truth": "0, \\frac{1}{3}, -3 + 2\\sqrt{17}, -3 - 2\\sqrt{17}",
"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 \\( f(x) = x^{5} - 10x^{3} + ax^{2} + bx + c \\). If all the roots of the equation \\( f(x) = 0 \\) are real numbers and \\( m \\) is the largest of these five real roots, ... | 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": "Given $y=f(x)$ is an even function on $\\mathbb{R}$, and for any $x \\in \\mathbb{R}$, it holds that $f(x)=f(2-x)$. When $x \\in [0,1]$, $f(x)=(x-1)^2$. Find the sum of all zeros... | math | {
"ground_truth": "2016",
"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 rectangles have integer dimensions, and both have a perimeter of 160 cm. What is the greatest possible difference between the areas of two such rectangles, and what are the d... | math | {
"ground_truth": "1 \\times 79",
"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 the arithmetic sequence \\(\\left(a_{n}\\right)\\), we have \\(a_{1000} = 75\\) and \\(d = 0.25\\).\n\nCalculate: \\(99 \\cdot 100 \\cdot\\left(\\frac{1}{a_{1580} \\cdot a_{15... | math | {
"ground_truth": "60",
"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 natural numbers \\( m \\) and \\( n \\) where \\( n > m > 1 \\), the last three digits of the decimal representation of \\( 1978^m \\) and \\( 1978^n \\) are the same. Find... | math | {
"ground_truth": "106",
"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": "Nathaniel and Obediah play a game in which they take turns rolling a fair six-sided die and keep a\nrunning tally of the sum of the results of all rolls made. A player wins if, a... | math | {
"ground_truth": "\\frac{5}{11}",
"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 sum of all four-digit numbers composed of four distinct non-zero digits, with no repeating digits, is 106656. What is the largest and smallest of these four-digit numbers?",
... | math | {
"ground_truth": "1249",
"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 \\( c > 0 \\) be a given positive real number and \\(\\mathbb{R}_{>0}\\) be the set of all positive real numbers. Find all functions \\( f: \\mathbb{R}_{>0} \\rightarrow \\ma... | math | {
"ground_truth": "f(x) = 2x \\quad \\text{for all } x > 0",
"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": "Consider a city grid with intersections labeled A, B, C, and D. Assume a student walks from intersection A to intersection B every morning, always walking along the designated pa... | math | {
"ground_truth": "\\frac{15}{77}",
"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": "Given $\\tan \\alpha=2$, find \n(1) The value of $\\tan (\\alpha+ \\frac {\\pi}{4})$ \n(2) The value of $\\frac {6\\sin \\alpha+\\cos \\alpha}{3\\sin \\alpha-\\cos \\alpha}$.",... | math | {
"ground_truth": "\\frac {13}{5}",
"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 soda is sold in packs of 6, 12, 24, and 30 cans, find the minimum number of packs needed to buy exactly 120 cans of soda.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"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 mythical creature has 10 legs, and for each leg, it has one sock and one shoe. In how many different orders can the creature put on its socks and shoes, assuming that, on each ... | math | {
"ground_truth": "\\frac{20!}{2^{10}}",
"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": "Given points $A(m+1,-2)$ and $B(3,n-1)$, if $AB$ is parallel to the $x$-axis and $AB=4$, then the value of $m+n$ is ____.",
"role": "user"
}
] | math | {
"ground_truth": "5 \\text{ or } -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": "Let $k$ be a natural number.Find all the couples of natural numbers $(n,m)$ such that : $(2^k)!=2^n*m$",
"role": "user"
}
] | math | {
"ground_truth": "(n, m) = \\left(2^k - 1 - t, \\frac{(2^k)!}{2^{2^k - 1 - t}}\\right) \\text{ for some } t \\in \\mathbb{Z}_{\\geq 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": "On the door, BIOLOGY is spelled out with 7 magnets, one letter per magnet. Two vowels and two consonants fall off and are put away in a bag. If the O's are indistinguishable, how... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
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