context listlengths 2 2 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 29 | task_name stringclasses 1
value | metadata dict |
|---|---|---|---|---|---|
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Find the sum of all integer bases $b > 9$ for which $17_b$ is a divisor of $97_b$.\nMark your solution with \\boxed\nA... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 0 | AIME25 | {
"expected_answer": "70",
"problem_id": "I-1",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: On $\\triangle ABC$, points $A$, $D$, $E$, and $B$ lie in that order on side $\\overline{AB}$ with $AD = 4$, $DE = 16$... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 1 | AIME25 | {
"expected_answer": "588",
"problem_id": "I-2",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The 9 members of a baseball team went to an ice-cream parlor after their game. Each player had a singlescoop cone of c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 2 | AIME25 | {
"expected_answer": "16",
"problem_id": "I-3",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between -100 and 100, inclusive, such th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 3 | AIME25 | {
"expected_answer": "117",
"problem_id": "I-4",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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 $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 4 | AIME25 | {
"expected_answer": "279",
"problem_id": "I-5",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 5 | AIME25 | {
"expected_answer": "504",
"problem_id": "I-6",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The twelve letters $A$, $B$, $C$, $D$, $E$, $F$, $G$, $H$, $I$, $J$, $K$, and $L$ are randomly grouped into six pairs ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 6 | AIME25 | {
"expected_answer": "821",
"problem_id": "I-7",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $k$ be a real number such that the system\n$|25 + 20i - z| = 5$\n$|z - 4 - k| = |z - 3i - k|$\nhas exactly one com... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 7 | AIME25 | {
"expected_answer": "77",
"problem_id": "I-8",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The parabola with equation $y = x^2 - 4$ is rotated $60°$ counterclockwise around the origin. The unique point in the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 8 | AIME25 | {
"expected_answer": "62",
"problem_id": "I-9",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 9 | AIME25 | {
"expected_answer": "81",
"problem_id": "I-10",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: A piecewise linear periodic function is defined by\n$f(x)=\\begin{cases} x & \\text{if } x \\in [-1,1) \\\\ 2-x & \\te... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 10 | AIME25 | {
"expected_answer": "259",
"problem_id": "I-11",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The set of points in 3-dimensional coordinate space that lie in the plane $x + y + z = 75$ whose coordinates satisfy t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 11 | AIME25 | {
"expected_answer": "510",
"problem_id": "I-12",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He dr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 12 | AIME25 | {
"expected_answer": "204",
"problem_id": "I-13",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $ABCDE$ be a convex pentagon with $AB = 14$, $BC = 7$, $CD = 24$, $DE = 13$, $EA = 26$, and $\\angle ZBA = 60°$. F... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 13 | AIME25 | {
"expected_answer": "60",
"problem_id": "I-14",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 14 | AIME25 | {
"expected_answer": "735",
"problem_id": "I-15",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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 ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 15 | AIME25 | {
"expected_answer": "468",
"problem_id": "II-1",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Find the sum of all positive integers $n$ such that $n+2$ divides the product $3(n+3)(n^2+9)$.\nMark your solution wit... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 16 | AIME25 | {
"expected_answer": "49",
"problem_id": "II-2",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Four unit squares form a $2 \\times 2$ grid. Each of the $12$ unit line segments forming the sides of the squares is c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 17 | AIME25 | {
"expected_answer": "82",
"problem_id": "II-3",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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})}... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 18 | AIME25 | {
"expected_answer": "106",
"problem_id": "II-4",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Suppose $\\triangle ABC$ has angles $\\angle BAC = 84^\\circ, \\angle ABC=60^\\circ,$ and $\\angle ACB = 36^\\circ.$ L... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 19 | AIME25 | {
"expected_answer": "336",
"problem_id": "II-5",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Circle $\\omega_1$ with radius $6$ centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 20 | AIME25 | {
"expected_answer": "293",
"problem_id": "II-6",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $A$ be the set of positive integer divisors of $2025$. Let $B$ be a randomly selected subset of $A$. The probabili... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 21 | AIME25 | {
"expected_answer": "237",
"problem_id": "II-7",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 22 | AIME25 | {
"expected_answer": "610",
"problem_id": "II-8",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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 $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 23 | AIME25 | {
"expected_answer": "149",
"problem_id": "II-9",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 24 | AIME25 | {
"expected_answer": "907",
"problem_id": "II-10",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $S$ be the set of vertices of a regular $24$-gon. Find the number of ways to draw $12$ segments of equal lengths s... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 25 | AIME25 | {
"expected_answer": "113",
"problem_id": "II-11",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $A_1A_2\\dots A_{11}$ be a non-convex $11$-gon such that \n- The area of $A_iA_1A_{i+1}$ is $1$ for each $2 \\le i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 26 | AIME25 | {
"expected_answer": "19",
"problem_id": "II-12",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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}\\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 27 | AIME25 | {
"expected_answer": "248",
"problem_id": "II-13",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let ${\\triangle ABC}$ be a right triangle with $\\angle A = 90^\\circ$ and $BC = 38.$ There exist points $K$ and $L$ ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 28 | AIME25 | {
"expected_answer": "104",
"problem_id": "II-14",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let \\[f(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x}.\\]There exist exactly three positive real values of $k$ such that $f$ ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 29 | AIME25 | {
"expected_answer": "240",
"problem_id": "II-15",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Find the sum of all integer bases $b > 9$ for which $17_b$ is a divisor of $97_b$.\nMark your solution with \\boxed\nA... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 0 | AIME25 | {
"expected_answer": "70",
"problem_id": "I-1",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: On $\\triangle ABC$, points $A$, $D$, $E$, and $B$ lie in that order on side $\\overline{AB}$ with $AD = 4$, $DE = 16$... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 1 | AIME25 | {
"expected_answer": "588",
"problem_id": "I-2",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The 9 members of a baseball team went to an ice-cream parlor after their game. Each player had a singlescoop cone of c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 2 | AIME25 | {
"expected_answer": "16",
"problem_id": "I-3",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between -100 and 100, inclusive, such th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 3 | AIME25 | {
"expected_answer": "117",
"problem_id": "I-4",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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 $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 4 | AIME25 | {
"expected_answer": "279",
"problem_id": "I-5",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 5 | AIME25 | {
"expected_answer": "504",
"problem_id": "I-6",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The twelve letters $A$, $B$, $C$, $D$, $E$, $F$, $G$, $H$, $I$, $J$, $K$, and $L$ are randomly grouped into six pairs ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 6 | AIME25 | {
"expected_answer": "821",
"problem_id": "I-7",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $k$ be a real number such that the system\n$|25 + 20i - z| = 5$\n$|z - 4 - k| = |z - 3i - k|$\nhas exactly one com... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 7 | AIME25 | {
"expected_answer": "77",
"problem_id": "I-8",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The parabola with equation $y = x^2 - 4$ is rotated $60°$ counterclockwise around the origin. The unique point in the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 8 | AIME25 | {
"expected_answer": "62",
"problem_id": "I-9",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 9 | AIME25 | {
"expected_answer": "81",
"problem_id": "I-10",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: A piecewise linear periodic function is defined by\n$f(x)=\\begin{cases} x & \\text{if } x \\in [-1,1) \\\\ 2-x & \\te... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 10 | AIME25 | {
"expected_answer": "259",
"problem_id": "I-11",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The set of points in 3-dimensional coordinate space that lie in the plane $x + y + z = 75$ whose coordinates satisfy t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 11 | AIME25 | {
"expected_answer": "510",
"problem_id": "I-12",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He dr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 12 | AIME25 | {
"expected_answer": "204",
"problem_id": "I-13",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $ABCDE$ be a convex pentagon with $AB = 14$, $BC = 7$, $CD = 24$, $DE = 13$, $EA = 26$, and $\\angle ZBA = 60°$. F... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 13 | AIME25 | {
"expected_answer": "60",
"problem_id": "I-14",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 14 | AIME25 | {
"expected_answer": "735",
"problem_id": "I-15",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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 ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 15 | AIME25 | {
"expected_answer": "468",
"problem_id": "II-1",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Find the sum of all positive integers $n$ such that $n+2$ divides the product $3(n+3)(n^2+9)$.\nMark your solution wit... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 16 | AIME25 | {
"expected_answer": "49",
"problem_id": "II-2",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Four unit squares form a $2 \\times 2$ grid. Each of the $12$ unit line segments forming the sides of the squares is c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 17 | AIME25 | {
"expected_answer": "82",
"problem_id": "II-3",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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})}... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 18 | AIME25 | {
"expected_answer": "106",
"problem_id": "II-4",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Suppose $\\triangle ABC$ has angles $\\angle BAC = 84^\\circ, \\angle ABC=60^\\circ,$ and $\\angle ACB = 36^\\circ.$ L... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 19 | AIME25 | {
"expected_answer": "336",
"problem_id": "II-5",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Circle $\\omega_1$ with radius $6$ centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 20 | AIME25 | {
"expected_answer": "293",
"problem_id": "II-6",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $A$ be the set of positive integer divisors of $2025$. Let $B$ be a randomly selected subset of $A$. The probabili... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 21 | AIME25 | {
"expected_answer": "237",
"problem_id": "II-7",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 22 | AIME25 | {
"expected_answer": "610",
"problem_id": "II-8",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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 $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 23 | AIME25 | {
"expected_answer": "149",
"problem_id": "II-9",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 24 | AIME25 | {
"expected_answer": "907",
"problem_id": "II-10",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $S$ be the set of vertices of a regular $24$-gon. Find the number of ways to draw $12$ segments of equal lengths s... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 25 | AIME25 | {
"expected_answer": "113",
"problem_id": "II-11",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $A_1A_2\\dots A_{11}$ be a non-convex $11$-gon such that \n- The area of $A_iA_1A_{i+1}$ is $1$ for each $2 \\le i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 26 | AIME25 | {
"expected_answer": "19",
"problem_id": "II-12",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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}\\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 27 | AIME25 | {
"expected_answer": "248",
"problem_id": "II-13",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let ${\\triangle ABC}$ be a right triangle with $\\angle A = 90^\\circ$ and $BC = 38.$ There exist points $K$ and $L$ ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 28 | AIME25 | {
"expected_answer": "104",
"problem_id": "II-14",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let \\[f(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x}.\\]There exist exactly three positive real values of $k$ such that $f$ ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 29 | AIME25 | {
"expected_answer": "240",
"problem_id": "II-15",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Find the sum of all integer bases $b > 9$ for which $17_b$ is a divisor of $97_b$.\nMark your solution with \\boxed\nA... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 0 | AIME25 | {
"expected_answer": "70",
"problem_id": "I-1",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: On $\\triangle ABC$, points $A$, $D$, $E$, and $B$ lie in that order on side $\\overline{AB}$ with $AD = 4$, $DE = 16$... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 1 | AIME25 | {
"expected_answer": "588",
"problem_id": "I-2",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The 9 members of a baseball team went to an ice-cream parlor after their game. Each player had a singlescoop cone of c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 2 | AIME25 | {
"expected_answer": "16",
"problem_id": "I-3",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between -100 and 100, inclusive, such th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 3 | AIME25 | {
"expected_answer": "117",
"problem_id": "I-4",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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 $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 4 | AIME25 | {
"expected_answer": "279",
"problem_id": "I-5",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 5 | AIME25 | {
"expected_answer": "504",
"problem_id": "I-6",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The twelve letters $A$, $B$, $C$, $D$, $E$, $F$, $G$, $H$, $I$, $J$, $K$, and $L$ are randomly grouped into six pairs ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 6 | AIME25 | {
"expected_answer": "821",
"problem_id": "I-7",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $k$ be a real number such that the system\n$|25 + 20i - z| = 5$\n$|z - 4 - k| = |z - 3i - k|$\nhas exactly one com... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 7 | AIME25 | {
"expected_answer": "77",
"problem_id": "I-8",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The parabola with equation $y = x^2 - 4$ is rotated $60°$ counterclockwise around the origin. The unique point in the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 8 | AIME25 | {
"expected_answer": "62",
"problem_id": "I-9",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 9 | AIME25 | {
"expected_answer": "81",
"problem_id": "I-10",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: A piecewise linear periodic function is defined by\n$f(x)=\\begin{cases} x & \\text{if } x \\in [-1,1) \\\\ 2-x & \\te... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 10 | AIME25 | {
"expected_answer": "259",
"problem_id": "I-11",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The set of points in 3-dimensional coordinate space that lie in the plane $x + y + z = 75$ whose coordinates satisfy t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 11 | AIME25 | {
"expected_answer": "510",
"problem_id": "I-12",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He dr... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 12 | AIME25 | {
"expected_answer": "204",
"problem_id": "I-13",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $ABCDE$ be a convex pentagon with $AB = 14$, $BC = 7$, $CD = 24$, $DE = 13$, $EA = 26$, and $\\angle ZBA = 60°$. F... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 13 | AIME25 | {
"expected_answer": "60",
"problem_id": "I-14",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 14 | AIME25 | {
"expected_answer": "735",
"problem_id": "I-15",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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 ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 15 | AIME25 | {
"expected_answer": "468",
"problem_id": "II-1",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Find the sum of all positive integers $n$ such that $n+2$ divides the product $3(n+3)(n^2+9)$.\nMark your solution wit... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 16 | AIME25 | {
"expected_answer": "49",
"problem_id": "II-2",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Four unit squares form a $2 \\times 2$ grid. Each of the $12$ unit line segments forming the sides of the squares is c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 17 | AIME25 | {
"expected_answer": "82",
"problem_id": "II-3",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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})}... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 18 | AIME25 | {
"expected_answer": "106",
"problem_id": "II-4",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Suppose $\\triangle ABC$ has angles $\\angle BAC = 84^\\circ, \\angle ABC=60^\\circ,$ and $\\angle ACB = 36^\\circ.$ L... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 19 | AIME25 | {
"expected_answer": "336",
"problem_id": "II-5",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Circle $\\omega_1$ with radius $6$ centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 20 | AIME25 | {
"expected_answer": "293",
"problem_id": "II-6",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $A$ be the set of positive integer divisors of $2025$. Let $B$ be a randomly selected subset of $A$. The probabili... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 21 | AIME25 | {
"expected_answer": "237",
"problem_id": "II-7",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 22 | AIME25 | {
"expected_answer": "610",
"problem_id": "II-8",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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 $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 23 | AIME25 | {
"expected_answer": "149",
"problem_id": "II-9",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 24 | AIME25 | {
"expected_answer": "907",
"problem_id": "II-10",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $S$ be the set of vertices of a regular $24$-gon. Find the number of ways to draw $12$ segments of equal lengths s... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 25 | AIME25 | {
"expected_answer": "113",
"problem_id": "II-11",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $A_1A_2\\dots A_{11}$ be a non-convex $11$-gon such that \n- The area of $A_iA_1A_{i+1}$ is $1$ for each $2 \\le i... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 26 | AIME25 | {
"expected_answer": "19",
"problem_id": "II-12",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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}\\... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 27 | AIME25 | {
"expected_answer": "248",
"problem_id": "II-13",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let ${\\triangle ABC}$ be a right triangle with $\\angle A = 90^\\circ$ and $BC = 38.$ There exist points $K$ and $L$ ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 28 | AIME25 | {
"expected_answer": "104",
"problem_id": "II-14",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let \\[f(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x}.\\]There exist exactly three positive real values of $k$ such that $f$ ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 29 | AIME25 | {
"expected_answer": "240",
"problem_id": "II-15",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Find the sum of all integer bases $b > 9$ for which $17_b$ is a divisor of $97_b$.\nMark your solution with \\boxed\nA... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 0 | AIME25 | {
"expected_answer": "70",
"problem_id": "I-1",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: On $\\triangle ABC$, points $A$, $D$, $E$, and $B$ lie in that order on side $\\overline{AB}$ with $AD = 4$, $DE = 16$... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 1 | AIME25 | {
"expected_answer": "588",
"problem_id": "I-2",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The 9 members of a baseball team went to an ice-cream parlor after their game. Each player had a singlescoop cone of c... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 2 | AIME25 | {
"expected_answer": "16",
"problem_id": "I-3",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between -100 and 100, inclusive, such th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 3 | AIME25 | {
"expected_answer": "117",
"problem_id": "I-4",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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 $... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 4 | AIME25 | {
"expected_answer": "279",
"problem_id": "I-5",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 5 | AIME25 | {
"expected_answer": "504",
"problem_id": "I-6",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The twelve letters $A$, $B$, $C$, $D$, $E$, $F$, $G$, $H$, $I$, $J$, $K$, and $L$ are randomly grouped into six pairs ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 6 | AIME25 | {
"expected_answer": "821",
"problem_id": "I-7",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: Let $k$ be a real number such that the system\n$|25 + 20i - z| = 5$\n$|z - 4 - k| = |z - 3i - k|$\nhas exactly one com... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 7 | AIME25 | {
"expected_answer": "77",
"problem_id": "I-8",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: The parabola with equation $y = x^2 - 4$ is rotated $60°$ counterclockwise around the origin. The unique point in the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 8 | AIME25 | {
"expected_answer": "62",
"problem_id": "I-9",
"reference_solution": ""
} |
[
{
"content": "You are a helpful assistant skilled at solving math problems. Think step-by-step and show your reasoning.\nReasoning: high",
"role": "system"
},
{
"content": "Problem: 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... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 3,
"temperature": 0.7
} | 3 | 9 | AIME25 | {
"expected_answer": "81",
"problem_id": "I-10",
"reference_solution": ""
} |
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