data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 8
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Each vertex of a regular octagon is independently colored either red or blue with equal probability. The probability that the octagon can then be rotated so that all of the blue ... | math | {
"ground_truth": "371",
"style": "rule"
} | {
"id": "aime24-62",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Define $f(x)=|| x|-\\tfrac{1}{2}|$ and $g(x)=|| x|-\\tfrac{1}{4}|$. Find the number of intersections of the graphs of \\[y=4 g(f(\\sin (2 \\pi x))) \\quad\\text{ and }\\quad x=4 ... | math | {
"ground_truth": "385",
"style": "rule"
} | {
"id": "aime24-63",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $p$ be the least prime number for which there exists a positive integer $n$ such that $n^{4}+1$ is divisible by $p^{2}$. Find the least positive integer $m$ such that $m^{4}+... | math | {
"ground_truth": "110",
"style": "rule"
} | {
"id": "aime24-64",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABCD$ be a tetrahedron such that $AB=CD= \\sqrt{41}$, $AC=BD= \\sqrt{80}$, and $BC=AD= \\sqrt{89}$. There exists a point $I$ inside the tetrahedron such that the distances f... | math | {
"ground_truth": "104",
"style": "rule"
} | {
"id": "aime24-65",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\mathcal{B}$ be the set of rectangular boxes with surface area $54$ and volume $23$. Let $r$ be the radius of the smallest sphere that can contain each of the rectangular b... | math | {
"ground_truth": "721",
"style": "rule"
} | {
"id": "aime24-66",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There exist real numbers $x$ and $y$, both greater than 1, such that $\\log_x\\left(y^x\\right)=\\log_y\\left(x^{4y}\\right)=10$. Find $xy$.",
"role": "user"
}
] | math | {
"ground_truth": "25",
"style": "rule"
} | {
"id": "aime24-67",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice and Bob play the following game. A stack of $n$ tokens lies before them. The players take turns with Alice going first. On each turn, the player removes either $1$ token or... | math | {
"ground_truth": "809",
"style": "rule"
} | {
"id": "aime24-68",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Jen enters a lottery by picking $4$ distinct numbers from $S=\\{1,2,3,\\cdots,9,10\\}.$ $4$ numbers are randomly chosen from $S.$ She wins a prize if at least two of her numbers ... | math | {
"ground_truth": "116",
"style": "rule"
} | {
"id": "aime24-69",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Rectangles $ABCD$ and $EFGH$ are drawn such that $D,E,C,F$ are collinear. Also, $A,D,H,G$ all lie on a circle. If $BC=16$,$AB=107$,$FG=17$, and $EF=184$, what is the length of $C... | math | {
"ground_truth": "104",
"style": "rule"
} | {
"id": "aime24-70",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Consider the paths of length $16$ that follow the lines from the lower left corner to the upper right corner on an $8\\times 8$ grid. Find the number of such paths that change di... | math | {
"ground_truth": "294",
"style": "rule"
} | {
"id": "aime24-71",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the largest possible real part of \\[(75+117i)z+\\frac{96+144i}{z}\\]where $z$ is a complex number with $|z|=4$.",
"role": "user"
}
] | math | {
"ground_truth": "540",
"style": "rule"
} | {
"id": "aime24-72",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Eight circles of radius $34$ are sequentially tangent, and two of the circles are tangent to $AB$ and $BC$ of triangle $ABC$, respectively. $2024$ circles of radius $1$ can be ar... | math | {
"ground_truth": "197",
"style": "rule"
} | {
"id": "aime24-73",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $A$, $B$, $C$, and $D$ be point on the hyperbola $\\frac{x^2}{20}- \\frac{y^2}{24} = 1$ such that $ABCD$ is a rhombus whose diagonals intersect at the origin. Find the greate... | math | {
"ground_truth": "480",
"style": "rule"
} | {
"id": "aime24-74",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Among the 900 residents of Aimeville, there are 195 who own a diamond ring, 367 who own a set of golf clubs, and 562 who own a garden spade. In addition, each of the 900 resident... | math | {
"ground_truth": "73",
"style": "rule"
} | {
"id": "aime24-75",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\triangle ABC$ have circumcenter $O$ and incenter $I$ with $\\overline{IA}\\perp\\overline{OI}$, circumradius $13$, and inradius $6$. Find $AB\\cdot AC$.",
"role": "use... | math | {
"ground_truth": "468",
"style": "rule"
} | {
"id": "aime24-76",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of triples of nonnegative integers \\((a,b,c)\\) satisfying \\(a + b + c = 300\\) and\n\\begin{equation*}\na^2b + a^2c + b^2a + b^2c + c^2a + c^2b = 6,000,000.\n\... | math | {
"ground_truth": "601",
"style": "rule"
} | {
"id": "aime24-77",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(O=(0,0)\\), \\(A=\\left(\\tfrac{1}{2},0\\right)\\), and \\(B=\\left(0,\\tfrac{\\sqrt{3}}{2}\\right)\\) be points in the coordinate plane. Let \\(\\mathcal{F}\\) be the fam... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"id": "aime24-78",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $\\omega\\neq 1$ be a 13th root of unity. Find the remainder when\n\\[\\prod_{k=0}^{12}(2-2\\omega^k+\\omega^{2k})\\]\nis divided by 1000.",
"role": "user"
}
] | math | {
"ground_truth": "321",
"style": "rule"
} | {
"id": "aime24-79",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(b\\ge 2\\) be an integer. Call a positive integer \\(n\\) \\(b\\text-\\textit{eautiful}\\) if it has exactly two digits when expressed in base \\(b\\) and these two digit... | math | {
"ground_truth": "211",
"style": "rule"
} | {
"id": "aime24-80",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of rectangles that can be formed inside a fixed regular dodecagon ($12$-gon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon... | math | {
"ground_truth": "315",
"style": "rule"
} | {
"id": "aime24-81",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A list of positive integers has the following properties:\n$\\bullet$ The sum of the items in the list is $30$.\n$\\bullet$ The unique mode of the list is $9$.\n$\\bullet$ The me... | math | {
"ground_truth": "236",
"style": "rule"
} | {
"id": "aime24-82",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of ways to place a digit in each cell of a 2x3 grid so that the sum of the two numbers formed by reading left to right is $999$, and the sum of the three numbers ... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"id": "aime24-83",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $x,y$ and $z$ be positive real numbers that satisfy the following system of equations:\n\\[\\log_2\\left({x \\over yz}\\right) = {1 \\over 2}\\]\\[\\log_2\\left({y \\over xz}... | math | {
"ground_truth": "33",
"style": "rule"
} | {
"id": "aime24-84",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let ABCDEF be a convex equilateral hexagon in which all pairs of opposite sides are parallel. The triangle whose sides are extensions of segments AB, CD, and EF has side lengths ... | math | {
"ground_truth": "80",
"style": "rule"
} | {
"id": "aime24-85",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alice chooses a set $A$ of positive integers. Then Bob lists all finite nonempty sets $B$ of positive integers with the property that the maximum element of $B$ belongs to $A$. B... | math | {
"ground_truth": "55",
"style": "rule"
} | {
"id": "aime24-86",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $N$ be the greatest four-digit positive integer with the property that whenever one of its digits is changed to $1$, the resulting number is divisible by $7$. Let $Q$ and $R$... | math | {
"ground_truth": "699",
"style": "rule"
} | {
"id": "aime24-87",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Torus $T$ is the surface produced by revolving a circle with radius $3$ around an axis in the plane of the circle that is a distance $6$ from the center of the circle (so like a ... | math | {
"ground_truth": "127",
"style": "rule"
} | {
"id": "aime24-88",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There is a collection of $25$ indistinguishable white chips and $25$ indistinguishable black chips. Find the number of ways to place some of these chips in the $25$ unit cells of... | math | {
"ground_truth": "902",
"style": "rule"
} | {
"id": "aime24-89",
"rating": null,
"split": "test",
"sub_source": "aime24"
} | aime24 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the sum of all integer bases $b>9$ for which $17_b$ is a divisor of $97_b.$",
"role": "user"
}
] | math | {
"ground_truth": "70",
"style": "rule"
} | {
"id": "aime25-0",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In $\\triangle ABC$ points $D$ and $E$ lie on $\\overline{AB}$ so that $AD < AE < AB$, while points $F$ and $G$ lie on $\\overline{AC}$ so that $AF < AG < AC$. Suppose $AD = 4$, ... | math | {
"ground_truth": "588",
"style": "rule"
} | {
"id": "aime25-1",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The $9$ members of a baseball team went to an ice-cream parlor after their game. Each player had a single scoop cone of chocolate, vanilla, or strawberry ice cream. At least one ... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"id": "aime25-2",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$ inclusive, such that $12x^2-xy-6y^2=0$.",
"role": "user"
}
] | math | {
"ground_truth": "117",
"style": "rule"
} | {
"id": "aime25-3",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are $8!= 40320$ eight-digit positive integers that use each of the digits $1, 2, 3, 4, 5, 6, 7, 8$ exactly once. Let $N$ be the number of these integers that are divisible ... | math | {
"ground_truth": "279",
"style": "rule"
} | {
"id": "aime25-4",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is $3$, and the area of the trapezoid is $72$. Let the parallel sides o... | math | {
"ground_truth": "504",
"style": "rule"
} | {
"id": "aime25-5",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The twelve letters $A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,$I$,$J$,$K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other... | math | {
"ground_truth": "821",
"style": "rule"
} | {
"id": "aime25-6",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $k$ be a real number such that the system \\begin{align*} &|25 + 20i - z| = 5 \\ &|z - 4 - k| = |z - 3i - k| \\end{align*} has exactly one complex solution $z$. The sum of al... | math | {
"ground_truth": "77",
"style": "rule"
} | {
"id": "aime25-7",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The parabola with equation $y = x^2 - 4$ is rotated $60^\\circ$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its im... | math | {
"ground_truth": "62",
"style": "rule"
} | {
"id": "aime25-8",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The $27$ cells of a $3 \\times 9$ grid are filled in using the numbers $1$ through $9$ so that each row contains $9$ different numbers, and each of the three $3 \\times 3$ blocks... | math | {
"ground_truth": "81",
"style": "rule"
} | {
"id": "aime25-9",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A piecewise linear function is defined by\\[f(x) = \\begin{cases} x & \\operatorname{if} ~ -1 \\leq x < 1 \\ 2 - x & \\operatorname{if} ~ 1 \\leq x < 3\\end{cases}\\]and $f(x + 4... | math | {
"ground_truth": "259",
"style": "rule"
} | {
"id": "aime25-10",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The set of points in $3$-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities\\[x-yz<y-zx<z-xy\\]forms three disjoint convex r... | math | {
"ground_truth": "510",
"style": "rule"
} | {
"id": "aime25-11",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws $25$ more lines segments through the disk, drawing each ... | math | {
"ground_truth": "204",
"style": "rule"
} | {
"id": "aime25-12",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABCDE$ be a convex pentagon with $AB=14,$ $BC=7,$ $CD=24,$ $DE=13,$ $EA=26,$ and $\\angle B=\\angle E=60^{\\circ}.$ For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"id": "aime25-13",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $N$ denote the number of ordered triples of positive integers $(a, b, c)$ such that $a, b, c \\leq 3^6$ and $a^3 + b^3 + c^3$ is a multiple of $3^7$. Find the remainder when ... | math | {
"ground_truth": "735",
"style": "rule"
} | {
"id": "aime25-14",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Six points $A, B, C, D, E,$ and $F$ lie in a straight line in that order. Suppose that $G$ is a point not on the line and that $AC=26, BD=22, CE=31, DF=33, AF=73, CG=40,$ and $DG... | math | {
"ground_truth": "468",
"style": "rule"
} | {
"id": "aime25-15",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the sum of all positive integers $n$ such that $n + 2$ divides the product $3(n + 3)(n^2 + 9)$.",
"role": "user"
}
] | math | {
"ground_truth": "49",
"style": "rule"
} | {
"id": "aime25-16",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Four unit squares form a $2 \\times 2$ grid. Each of the $12$ unit line segments forming the sides of the squares is colored either red or blue in such a say that each unit squar... | math | {
"ground_truth": "82",
"style": "rule"
} | {
"id": "aime25-17",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The product\\[\\prod^{63}_{k=4} \frac{\\log_k (5^{k^2 - 1})}{\\log_{k + 1} (5^{k^2 - 4})} = \frac{\\log_4 (5^{15})}{\\log_5 (5^{12})} \\cdot \frac{\\log_5 (5^{24})}{\\log_6 (5^{2... | math | {
"ground_truth": "106",
"style": "rule"
} | {
"id": "aime25-18",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose $\\triangle ABC$ has angles $\\angle BAC = 84^\\circ, \\angle ABC=60^\\circ,$ and $\\angle ACB = 36^\\circ.$ Let $D, E,$ and $F$ be the midpoints of sides $\\overline{BC}... | math | {
"ground_truth": "336",
"style": "rule"
} | {
"id": "aime25-19",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Circle $\\omega_1$ with radius $6$ centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius $15$. Points $C$ and $D$ lie on $\\omega_2$ such tha... | math | {
"ground_truth": "293",
"style": "rule"
} | {
"id": "aime25-20",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $A$ be the set of positive integer divisors of $2025$. Let $B$ be a randomly selected subset of $A$. The probability that $B$ is a nonempty set with the property that the lea... | math | {
"ground_truth": "237",
"style": "rule"
} | {
"id": "aime25-21",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $N$ cents, where $N$ is a positive... | math | {
"ground_truth": "610",
"style": "rule"
} | {
"id": "aime25-22",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are $n$ values of $x$ in the interval $0<x<2\\pi$ where $f(x)=\\sin(7\\pi\\cdot\\sin(5x))=0$. For $t$ of these $n$ values of $x$, the graph of $y=f(x)$ is tangent to the $x... | math | {
"ground_truth": "149",
"style": "rule"
} | {
"id": "aime25-23",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $N$ be the number of subsets of $16$ c... | math | {
"ground_truth": "907",
"style": "rule"
} | {
"id": "aime25-24",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $S$ be the set of vertices of a regular $24$-gon. Find the number of ways to draw $12$ segments of equal lengths so that each vertex in $S$ is an endpoint of exactly one of t... | math | {
"ground_truth": "113",
"style": "rule"
} | {
"id": "aime25-25",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $A_1A_2\\dots A_{11}$ be a non-convex $11$-gon such that The area of $A_iA_1A_{i+1}$ is $1$ for each $2 \\le i \\le 10$, $\\cos(\\angle A_iA_1A_{i+1})=\\frac{12}{13}$ for eac... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"id": "aime25-26",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the sequence of rationals $x_1,x_2,\\dots$ be defined such that $x_1=\\frac{25}{11}$ and\\[x_{k+1}=\\frac{1}{3}\\left(x_k+\\frac{1}{x_k}-1\\right).\\]$x_{2025}$ can be expres... | math | {
"ground_truth": "248",
"style": "rule"
} | {
"id": "aime25-27",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let ${\\triangle ABC}$ be a right triangle with $\\angle A = 90^\\circ$ and $BC = 38.$ There exist points $K$ and $L$ inside the triangle such\\[AK = AL = BK = CL = KL = 14.\\]Th... | math | {
"ground_truth": "104",
"style": "rule"
} | {
"id": "aime25-28",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let\\[f(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x}.\\]There exist exactly three positive real values of $k$ such that $f$ has a minimum at exactly two real values of $x$. Find the sum... | math | {
"ground_truth": "240",
"style": "rule"
} | {
"id": "aime25-29",
"rating": null,
"split": "test",
"sub_source": "aime25"
} | aime25 |
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