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": "The equation $y=-4.9t^2 + 5t + 10$ describes the height (in meters) of a ball thrown upward at $5.0$ meters per second from $10$ meters above the ground, where $t$ is the time in... | math | {
"ground_truth": "\\frac{20}{7} \\text{ seconds}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Compute $\\frac{x^6 - 64x^3 + 1024}{x^3 - 16}$ when $x = 8$.",
"role": "user"
}
] | math | {
"ground_truth": "480",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the equation \\( y^{\\prime \\prime} + 4y = -8 \\sin 2x + 32 \\cos 2x + 4 e^{2x} \\).",
"role": "user"
}
] | math | {
"ground_truth": "y = C_1 \\cos 2x + C_2 \\sin 2x + (2 \\cos 2x + 8 \\sin 2x)x + \\frac{1}{2} e^{2x}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the smallest positive integer \\( n \\) such that there exist positive integers \\( x, y, z \\) so that \n\\[\nn^2 = x^2+y^2+z^2+2xy+2yz+2zx+4x+4y+4z-11\n\\]",
"rol... | math | {
"ground_truth": "n = 11",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given an arithmetic-geometric sequence ${a_n}$ with the sum of the first $n$ terms denoted as $S_n$, if $S_6 : S_3 = 3$, find the value of $S_9 : S_6$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{7}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the largest prime $ p $ that makes $ \\sqrt{17p+625} $ an integer?",
"role": "user"
}
] | math | {
"ground_truth": "67",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A tetrahedron with four equilateral triangular faces has a sphere inscribed within it and a sphere circumscribed about it. For each of the four faces, there is a sphere tangent e... | math | {
"ground_truth": "0.1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the real number $\\alpha$ such that the curve $f(x)=e^x$ is tangent to the curve $g(x)=\\alpha x^2$ .",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{e^2}{4}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The equation $$ (x-1)(x-2)\\cdots(x-2016)=(x-1)(x-2)\\cdots (x-2016) $$ is written on the board, with $2016$ linear factors on each side. What is the least possible value of ... | math | {
"ground_truth": "k = 2016",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Equilateral triangle $ABC$ has side length $6$ . Circles with centers at $A$ , $B$ , and $C$ are drawn such that their respective radii $r_A$ , $r_B$ , and $r_C$ form ... | math | {
"ground_truth": "\\frac{29\\pi}{24}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the matrix $M= \\begin{bmatrix} 1 & a \\\\ -1 & b \\end{bmatrix}$ has an eigenvalue $\\lambda=2$ with a corresponding eigenvector $\\alpha= \\begin{bmatrix} 2 \\\\ 1 \\end{... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A non-square rectangle has integer dimensions. The number of square units in its area is numerically equal to twice the number of units in its perimeter. What is the number of un... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the range of \\( g(x) = \\sin^4 x - \\sin x \\cos x + \\cos^4 x + \\sin^2 x \\cos^2 x \\).",
"role": "user"
}
] | math | {
"ground_truth": "\\left[ \\frac{1}{4}, \\frac{5}{4} \\right]",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two rays with common endpoint $O$ form a $45^\\circ$ angle. Point $A$ lies on one ray, point $B$ on the other ray, and $AB = \\sqrt{2}$. What is the maximum possible length of $\... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the image, the plane is covered with hexagons of seven colors such that the centers of hexagons of the same color form the vertices of a grid of identical equilateral triangle... | math | {
"ground_truth": "\\text{a) for squares } n=k^2+l^2 \\text{ and b) for hexagons } n=k^2+k \\cdot l + l^2, \\text{ where } k, l \\text{ are non-negative integers not both zero.}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the value of \\( n \\) for which the following equation holds:\n\n$$\n\\frac{1}{1+\\sqrt{2}}+\\frac{1}{\\sqrt{2}+\\sqrt{3}}+\\frac{1}{\\sqrt{3}+\\sqrt{4}}+\\ldots+\\frac{1}{... | math | {
"ground_truth": "4064255",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A point has rectangular coordinates $(8, 6, -3)$ and spherical coordinates $(\\rho, \\theta, \\phi)$. Find the rectangular coordinates of the point with spherical coordinates $(\... | math | {
"ground_truth": "(8, -6, -3)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The negation of the proposition \"$\\exists x \\in \\mathbb{R}$, $x^2 \\geqslant x$\" is ______.",
"role": "user"
}
] | math | {
"ground_truth": "\\forall x \\in \\mathbb{R}, x^2 < x",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The graph of $y = ax^2 + bx + c$, where $a$, $b$, and $c$ are integers, is given. The vertex of the parabola is at $(2, 3)$ and another point on the graph is $(1, 5)$. Find the v... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(\\{ x \\}\\) denote the nearest integer to \\(x\\), so that \\(x - \\frac{1}{2} \\leq \\{ x \\} < x + \\frac{1}{2}\\). Define the sequence \\(u_1, u_2, u_3, \\ldots\\) by ... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "$A$ and $B$ travel around a circular track at uniform speeds in opposite directions, starting from diametrically opposite points. If they start at the same time, meet first after... | math | {
"ground_truth": "The correct choice is D) 720 yards.",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A convex \\( n \\)-gon (\\( n \\geq 4 \\)) is drawn on a board. Each of its vertices must be colored either black or white. A diagonal is called multicolored if its endpoints are... | math | {
"ground_truth": "n^2 - n",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the Blue Bird High School chess team consists of two boys and three girls, determine the number of arrangements for the team to sit in a row with a boy at each end and the ... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two students, A and B, start jogging in opposite directions from the same point on a 400-meter circular track, with speeds of 2 meters per second and 3 meters per second, respect... | math | {
"ground_truth": "444",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Convert the parametric equations \\(\\left\\{\\begin{array}{l}x=\\frac{\\cos \\theta}{1+\\cos \\theta} \\\\ y=\\frac{\\sin \\theta}{1+\\cos \\theta}\\end{array}\\right.\\) to the... | math | {
"ground_truth": "y^2 = -2 \\left(x - \\frac{1}{2} \\right)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The graph of the equation $y = 5x + 24$ intersects the graph of the equation $y = x^2$ at two points. The two points are a distance $\\sqrt{N}$ apart. Find $N$ .",
"r... | math | {
"ground_truth": "3146",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A positive integer \\( n \\) is considered \"loose\" if it has six positive divisors and satisfies the property that any two positive divisors \\( a < b \\) of \\( n \\) satisfy ... | math | {
"ground_truth": "462",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A rectangle has dimensions $4 \\times 5$. A semicircle with a diameter of $2$ is removed from one end of the rectangle. Find the whole number closest to the area of the remaining... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Functions $f$ and $g$ are defined so that $f(1) = 4$ , $g(1) = 9$ , and for each integer $n \\ge 1$ , $f(n+1) = 2f(n) + 3g(n) + 2n $ and $g(n+1) = 2g(n) + 3 f(n) + 5$ .... | math | {
"ground_truth": "1004",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ be a positive integer. From the set $A=\\{1,2,3,...,n\\}$ an element is eliminated. What's the smallest possible cardinal of $A$ and the eliminated element, since ... | math | {
"ground_truth": "n = 68",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the positive difference between the solutions of the equation $\\dfrac{r^2 - 5r - 22}{r + 4} = 3r + 8$?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Positive integers \\(a, b\\), and \\(c\\) are all powers of \\(k\\) for some positive integer \\(k\\). It is known that the equation \\(a x^{2}-b x+c=0\\) has exactly one real so... | math | {
"ground_truth": "64",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a lawn with a rectangular shape of $120$ feet by $200$ feet, a mower with a $32$-inch swath width, and a $6$-inch overlap between each cut, and a walking speed of $4000$ fe... | math | {
"ground_truth": "2.8",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(n)$ be the sum of all the divisors of a positive integer $n$. Define $n$ as superabundant if $f(f(n)) = n+3$. Determine all superabundant positive integers.",
"role": ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The coordinates of point A′, which is symmetric to point A(2,3) with respect to the line $x+y=0$, are \\_\\_\\_\\_\\_\\_.",
"role": "user"
}
] | math | {
"ground_truth": "(-3, -2)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the equation of the line that passes through the center of the circle $C: x^2 + y^2 + 2x = 0$ and is perpendicular to the line $3x + y - 2 = 0$.",
"role": "user"
}
] | math | {
"ground_truth": "x - 3y + 1 = 0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "With the digits $1, 2, 3,. . . . . . , 9$ three-digit numbers are written such that the sum of the three digits is $17$ . How many numbers can be written?",
"role": "user"... | math | {
"ground_truth": "57",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Heather and Kyle need to mow a lawn and paint a room. If Heather does both jobs by herself, it will take her a total of nine hours. If Heather mows the lawn and, after she finish... | math | {
"ground_truth": "41",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the fractions $\\frac{1}{5}$ and $\\frac{1}{3}$, find the fraction that lies exactly halfway between them on the number line.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{4}{15}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the positive integer $n$ so that $n^2$ is the perfect square closest to $8 + 16 + 24 + \\cdots + 8040.$",
"role": "user"
}
] | math | {
"ground_truth": "2011",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In an isosceles right triangle $PQR$, with $PQ=PR=10$ and angle $QPR$ being a right angle, a circle is inscribed. Find the radius of this circle.",
"role": "user"
}
] | math | {
"ground_truth": "10 - 5\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the number of solution-pairs in the positive integers for the equation $4x + 7y = 975$.",
"role": "user"
}
] | math | {
"ground_truth": "35",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For what values of the parameter \\(a\\) does the equation \\(x^{3} + ax^{2} + 13x - 6 = 0\\) have a unique solution?",
"role": "user"
}
] | math | {
"ground_truth": "(-\\infty,-8) \\cup(-20/3,61/8)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find which positive integers \\( x \\) and \\( y \\) satisfy the equation \\( x^{4} = y^{2} + 71 \\).",
"role": "user"
}
] | math | {
"ground_truth": "(x, y) = (6, 35)",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Round to the nearest hundredth: -23.4985",
"role": "user"
}
] | math | {
"ground_truth": "-23.50",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f\\in C^1[a,b]$ , $f(a)=0$ and suppose that $\\lambda\\in\\mathbb R$ , $\\lambda >0$ , is such that $$ |f'(x)|\\leq \\lambda |f(x)| $$ for all $x\\in [a,b]$ . Is it ... | math | {
"ground_truth": "f(x) = 0",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many diagonals does a convex polygon with 24 sides have?",
"role": "user"
}
] | math | {
"ground_truth": "126",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the radius of the circle circumscribed around a triangle, given its sides.",
"role": "user"
}
] | math | {
"ground_truth": "R = \\frac{a \\cdot b \\cdot c}{4 \\sqrt{s(s-a)(s-b)(s-c)}}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A cube with $4$-inch edges is to be constructed from $64$ smaller cubes with $1$-inch edges. Forty-four of these cubes are colored green and $20$ are colored blue. If the $4$-inc... | math | {
"ground_truth": "\\textbf{(C) } \\frac{1}{8}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $f$ is a polynomial, and $f(-2)=3$ , $f(-1)=-3=f(1)$ , $f(2)=6$ , and $f(3)=5$ , then what is the minimum possible degree of $f$ ?",
"role": "user"
}
] | math | {
"ground_truth": "4",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A positive integer $n$ is called *good* if for all positive integers $a$ which can be written as $a=n^2 \\sum_{i=1}^n {x_i}^2$ where $x_1, x_2, \\ldots ,x_n$ are integers... | math | {
"ground_truth": "n = 1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "(1) In $\\triangle ABC$, if $2\\lg \\tan B=\\lg \\tan A+\\lg \\tan C$, then the range of values for $B$ is ______. \n(2) Find the maximum value of the function $y=7-4\\sin x\\co... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the equation $4 \\cdot f(x) + 5 \\cdot g(x) = h(x)$ where $f(x),$ $g(x),$ and $h(x)$ are polynomials in $x$. If the degree of $f(x)$ is $10$ and the degree of $h(x)$ is $12... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two swimmers, at opposite ends of a 90-foot pool, start to swim the length of the pool, one at the rate of 3 feet per second, the other at 2 feet per second. They swim back and f... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An isosceles triangle has one angle equal to 40°. The other two angles are .",
"role": "user"
}
] | math | {
"ground_truth": "70°, 70° \\text{ or } 40°, 100°",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In an acute triangle, two of the altitudes divide the triangle’s sides into segments of lengths $7$, $3$, $6$, and $y$ units. Find the value of $y$.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For integers $a$ and $b$ with $0 \\leq a,b < {2010}^{18}$ let $S$ be the set of all polynomials in the form of $P(x)=ax^2+bx.$ For a polynomial $P$ in $S,$ if for a... | math | {
"ground_truth": "2^8 \\cdot 3^2 \\cdot 11^2 \\cdot 2010^9",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A fast train is moving at a speed of \\(c = 60 \\, \\frac{\\text{km}}{\\text{hour}}\\) past a person standing by a straight railway track. When the train is stationary, its whist... | math | {
"ground_truth": "2153 \\ \\text{Hz} \\ \\text{(approaching)} \\quad \\text{and} \\quad 1952 \\ \\text{Hz} \\ \\text{(receding)}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Emily runs parallel to a riverbank, overtaking a train moving at a constant but slower speed. She counts **300** steps running from the back of the train to the front and then, w... | math | {
"ground_truth": "\\textbf{(C) }200",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the smallest integer \\( x \\) for which \\( x + 5 < 3x - 9 \\)?",
"role": "user"
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the below diagram, if the area of $\\triangle ABC$ is 36, find the value of $p$. [asy]\nsize(5cm);defaultpen(fontsize(9));\npair o = (0, 0); pair q = (0, 15); pair b = (15, 0)... | math | {
"ground_truth": "12.75",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Ivan Ivanovich approached a water source with two empty canisters, one with a capacity of 10 liters and the other with a capacity of 8 liters. Water flowed from the source in two... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Does there exist a non-constant polynomial with integer coefficients $Q(x)$ such that for every positive integer $n > 2$, the values $Q(0), Q(1), \\cdots, Q(n-1)$ taken modulo $n... | math | {
"ground_truth": "Q(x) = 420 (x^2 - 1)^2",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of zeros of the function $f(x) = \\ln x + 2x - 1$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate \\( t(0) - t(\\pi / 5) + t(2 \\pi / 5) - t(3 \\pi / 5) + \\ldots + t(8 \\pi / 5) - t(9 \\pi / 5) \\), where \\( t(x) = \\cos 5x + *\\cos 4x + *\\cos 3x + *\\cos 2x + \\... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the area of the region described by $x \\ge 0,$ $y \\ge 0,$ and\n\\[50 \\{y\\} \\ge \\lfloor x \\rfloor + \\lfloor y \\rfloor.\\]",
"role": "user"
}
] | math | {
"ground_truth": "25.48",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The domain of the function $y=\\sqrt{\\log_{2}x}$ is $\\boxed{(0,+\\infty )}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\left[1,+\\infty \\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Before the World Cup, the coach of country \\( F \\) plans to evaluate seven players \\( A_{1}, A_{2}, \\cdots, A_{7} \\) by letting them all play in three training matches (each... | math | {
"ground_truth": "315160",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A dilation of the plane—that is, a size transformation with a positive scale factor—sends the circle of radius $2$ centered at $A(2,2)$ to the circle of radius $3$ centered at $A... | math | {
"ground_truth": "\\sqrt{13}",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "test",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the sum of digits of all the even numbers in the sequence $1,2,3,4,\\cdots, 5000$.\nA) 49215\nB) 49325\nC) 45000\nD) 48025",
"role": "user"
}
] | math | {
"ground_truth": "B) 49325",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a real number $x$, simplify the expression $\\sqrt{x^4 - x^2}$.",
"role": "user"
}
] | math | {
"ground_truth": "|x|\\sqrt{x^2-1}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given two equiangular polygons \\( P_1 \\) and \\( P_2 \\) with \\( n \\) and \\( m \\) sides respectively such that \\( m = n + k \\) where \\( k \\) is a positive integer, and ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $O$ is the coordinate origin, the focus of the parabola $C:y^{2}=2px\\left(p \\gt 0\\right)$ is $F$, $P$ is a point on $C$, $PF$ is perpendicular to the $x$-axis, $Q$ ... | math | {
"ground_truth": "x=-\\frac{3}{2}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the largest positive integer $n$ for which there exists a unique integer $k$ such that $\\frac{9}{17} < \\frac{n}{n + k} < \\frac{8}{15}$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Six standard six-sided dice are rolled. We are told there is no three-of-a-kind, but there are two pairs of dice that show the same number (but different from each other). These ... | math | {
"ground_truth": "\\frac{17}{18}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the force of water pressure on a vertical wall that has the shape of a semicircle with a radius of $R=6$ meters, with its diameter located at the water surface.",
"... | math | {
"ground_truth": "14.13 \\, \\text{bar}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Schoolchildren are eating chocolate from their New Year's gifts. Each chocolate bar consists of 12 pieces. It was found that if each girl eats 7 pieces and each boy eats 2 pieces... | math | {
"ground_truth": "1 \\text{ boy and } 5 \\text{ girls}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let sequence $\\{a_n\\}$ be such that $a_1 = 1$, $a_2 = 2$, and for integer $n > 1$, $S_{n+1} + S_{n-1} = 2(S_n + S_1)$. Then find the value of $S_{15}$.",
"role": "user"
}... | math | {
"ground_truth": "S_{15} = 1 - 2^{15}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The work was done together by team $C$ and team $D$. How many days did they take to complete it, given that team $C$ alone would have finished the work $c$ days later, and team $... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "test",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the area of a triangle with vertices at $(0, 3, 6)$, $(-2, 2, 2)$, and $(-5, 5, 2)$.",
"role": "user"
}
] | math | {
"ground_truth": "4.5",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( p \\) and \\( q \\) be the real roots of \n\\[ x^4 - 6x - 2 = 0. \\] Find \\( pq + p + q. \\)",
"role": "user"
}
] | math | {
"ground_truth": "1 - 2\\sqrt{2}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $f(x) = x^2 + 6x + c$ for all real number s $x$ , where $c$ is some real number. For what values of $c$ does $f(f(x))$ have exactly $3$ distinct real roots?",
... | math | {
"ground_truth": "c = \\frac{11 - \\sqrt{13}}{2}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Two dice are rolled where the first die has faces showing numbers $1$, $1$, $3$, $3$, $5$, and $6$, and the second die has faces showing numbers $1$, $2$, $4$, $5$, $7$, and $9$.... | math | {
"ground_truth": "\\frac{7}{18}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A woman leaves her office shortly after 5:00 PM and notices that the angle between the hands of her watch is 120 degrees. Later, she arrives at a café before 6:00 PM and again fi... | math | {
"ground_truth": "43.64\\text{ minutes}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given three vectors in the plane: \\\\( \\overrightarrow{a}=(1,-1)\\\\), \\\\( \\overrightarrow{b}=(x,2)\\\\), and \\\\( \\overrightarrow{c}=(2,1)\\\\), such that \\\\( \\overrig... | math | {
"ground_truth": "\\frac{3 \\sqrt {5}}{5}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Rectangle $ABCD$ has area $48$ square units. Point $E$ divides side $AD$ into a ratio $2:1$ (with $DE$ being twice as long as $AE$), and point $F$ divides side $BC$ similarly. Wh... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A train travels for three consecutive segments: the first segment for \\(x\\) miles at 50 mph, a second segment for \\(2x\\) miles at 75 mph, and after a 10-minute stop, it trave... | math | {
"ground_truth": "C) \\(\\frac{14x + 3y + 50}{300}\\) hours",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A store prices an item so that when 5% sales tax is added to the price in cents, the total cost rounds naturally to the nearest multiple of 5 dollars. What is the smallest possib... | math | {
"ground_truth": "55",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A biologist placed some lotus plants in a lake on New Year's Day. The lotus plants spread faster and faster in the lake. At the end of February, the area covered by the lotus pla... | math | {
"ground_truth": "6 \\text{ months}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "test",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice and Bob are each secretly given a real number between 0 and 1 uniformly at random. Alice states, “My number is probably greater than yours.” Bob repudiates, saying, “No, my... | math | {
"ground_truth": "\\frac{11}{12}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A real number $b$ is chosen randomly and uniformly from the interval $[-15, 15]$. Determine the probability that all the roots of the polynomial\n\\[x^4 + bx^3 + (3b - 4)x^2 + (6... | math | {
"ground_truth": "\\frac{5}{6}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "When the base of a triangle is increased by $10\\%$ and the altitude to this base is decreased by $10\\%$, calculate the change in area.",
"role": "user"
}
] | math | {
"ground_truth": "1\\% \\text{ decrease}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( M = 18 \\cdot 18 \\cdot 125 \\cdot 210 \\). What is the ratio of the sum of the odd divisors of \\( M \\) to the sum of the even divisors of \\( M \\)?\nA) 1 : 16\nB) 1 :... | math | {
"ground_truth": "\\textbf{(C)} ~1 : 14",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $H$ be a regular hexagon with area 360. Three distinct vertices $X$ , $Y$ , and $Z$ are picked randomly, with all possible triples of distinct vertices equally likely.... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the least positive integer, which may not be represented as ${2^a-2^b\\over 2^c-2^d}$ , where $a,\\,b,\\,c,\\,d$ are positive integers.",
"role": "user"
}
] | math | {
"ground_truth": "11",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify $\\left(\\sqrt[3]{125} - \\sqrt{12 \\frac{1}{2} }\\right)^2$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{75 - 50\\sqrt{2}}{2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "While Lucy and Ron are fishing 3 miles from shore, their boat springs a leak, and water starts flooding in at a rate of 8 gallons per minute. After rowing halfway to the shore, a... | math | {
"ground_truth": "B) 12 gallons/minute",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A fenced, rectangular field measures 24 meters by 52 meters. An agricultural researcher has 1994 meters of fence that can be used for internal fencing to partition the field int... | math | {
"ground_truth": "78",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "test",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $x = -2$ and $y = 4$, what is the value of $5x - 2y + 7$?",
"role": "user"
}
] | math | {
"ground_truth": "-11",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many positive integers, including $1,$ are divisors of both $60$ and $108?$",
"role": "user"
}
] | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "test",
"sub_source": "synthetic_math"
} | synthetic_math |
End of preview. Expand in Data Studio
rl-value-eval-math
Math-domain evaluation set (~5K) for confidence / correctness estimation, sampled from the
numina portion of PRIME-RL/Eurus-2-RL-Data.
Pairs with YangyiYY/rl-value-eval-math
(confidence-train) and a 50K RL-training split from the same pool (disjoint).
Sampled ~uniformly across the 6 numina sub-sources (cn_k12, synthetic_math, olympiads, synthetic_amc, aops_forum, amc_aime), deduplicated by problem text, and disjoint from the RL-train and eval splits (0 problem-text overlap).
Schema (our recipe)
data_source="math_box" · prompt=[{system: "Please reason step by step, and put your final answer within \boxed{}."}, {user: <problem>}] · ability="math" · reward_model.ground_truth (numina
answer) · sub_source (numina origin: cn_k12/synthetic_math/olympiads/synthetic_amc/aops_forum/amc_aime)
· extra_info (id, sub_source, split).
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