context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 4 | request_idx int64 0 499 | task_name stringclasses 4
values | metadata dict | model_outputs stringlengths 877 176k |
|---|---|---|---|---|---|---|
[
{
"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\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 0 | AIME25 | {
"expected_answer": "70",
"problem_id": "I-1",
"reference_solution": ""
} | <think>
Okay, I need to solve this problem where I have to find the sum of all integer bases \( b \) greater than 9 such that \( 17_b \) divides \( 97_b \). Hmm, let's break this down.
First, I should understand what \( 17_b \) and \( 97_b \) mean. In base \( b \), the number \( 17_b \) is equal to \( 1 \times b + 7 =... |
[
{
"content": "Problem: On $\\triangle ABC$, points $A$, $D$, $E$, and $B$ lie in that order on side $\\overline{AB}$ with $AD = 4$, $DE = 16$, and $EB = 8$. Points $A$, $F$, $G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF = 13$, $FG = 52$, and $GC = 26$. Let $M$ be the reflection of $D$ through... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 1 | AIME25 | {
"expected_answer": "588",
"problem_id": "I-2",
"reference_solution": ""
} | <think>
Okay, I need to solve this geometry problem. Let's read it carefully.
The problem says that on triangle ABC, points A, D, E, and B lie in that order on side AB with AD=4, DE=16, EB=8. Points A, F, G, and C lie on AC in order with AF=13, FG=52, GC=26. Then, M is the reflection of D through F, and N is the refle... |
[
{
"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 chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 2 | AIME25 | {
"expected_answer": "16",
"problem_id": "I-3",
"reference_solution": ""
} | <think>
Okay, I need to solve this problem where 9 players each choose a single scoop of ice cream from three flavors: chocolate, vanilla, and strawberry. The conditions are that each flavor is chosen by at least one player, and the counts follow chocolate > vanilla > strawberry. I need to find the number of such assig... |
[
{
"content": "Problem: Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between -100 and 100, inclusive, such that $12x^2 - xy - 6y^2 = 0$.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 3 | AIME25 | {
"expected_answer": "117",
"problem_id": "I-4",
"reference_solution": ""
} | <think>
Okay, I need to find the number of ordered pairs (x, y) where both x and y are integers between -100 and 100, inclusive, such that the equation 12x² - xy - 6y² = 0 holds. Hmm, let's see.
First, I think about factoring the equation. The equation is a quadratic in terms of x and y. Maybe I can factor it into two... |
[
{
"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 $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 4 | AIME25 | {
"expected_answer": "279",
"problem_id": "I-5",
"reference_solution": ""
} | <think>
Okay, I need to solve this problem where I have to find the number of 8-digit numbers using each digit from 1 to 8 exactly once that are divisible by 22. Then subtract 2025 from that number and put the result in a box. Let's break this down.
First, I remember that a number is divisible by 22 if it's divisible ... |
[
{
"content": "Problem: 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 of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^2 + s^2$.\nMark your solution with \\boxed\nAns... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 5 | AIME25 | {
"expected_answer": "504",
"problem_id": "I-6",
"reference_solution": ""
} | <think>
Okay, I need to solve this problem where I have an isosceles trapezoid with an inscribed circle. The radius is 3, the area is 72, and I have to find r squared plus s squared, where r and s are the lengths of the parallel sides. Hmm, let's think about this step by step.
First, I remember that a trapezoid with a... |
[{"content":"Problem: The twelve letters $A$, $B$, $C$, $D$, $E$, $F$, $G$, $H$, $I$, $J$, $K$, and (...TRUNCATED) | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 6 | AIME25 | {
"expected_answer": "821",
"problem_id": "I-7",
"reference_solution": ""
} | "<think>\nOkay, I need to solve this problem where twelve letters are grouped into six pairs, each p(...TRUNCATED) |
[{"content":"Problem: Let $k$ be a real number such that the system\n$|25 + 20i - z| = 5$\n$|z - 4 -(...TRUNCATED) | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 7 | AIME25 | {
"expected_answer": "77",
"problem_id": "I-8",
"reference_solution": ""
} | "<think>\nOkay, I need to solve this problem where I have two equations involving a complex number z(...TRUNCATED) |
[{"content":"Problem: The parabola with equation $y = x^2 - 4$ is rotated $60°$ counterclockwise ar(...TRUNCATED) | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 8 | AIME25 | {
"expected_answer": "62",
"problem_id": "I-9",
"reference_solution": ""
} | "<think>\nOkay, I need to solve this problem where I have a parabola y = x² - 4, and it's rotated 6(...TRUNCATED) |
[{"content":"Problem: The 27 cells of a $3 \\times 9$ grid are filled in using the numbers 1 through(...TRUNCATED) | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 9 | AIME25 | {
"expected_answer": "81",
"problem_id": "I-10",
"reference_solution": ""
} | "<think>\nOkay, I need to solve this problem where I have a 3x9 grid, and I have to fill it with num(...TRUNCATED) |
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