context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 4 | request_idx int64 0 499 | task_name stringclasses 2
values | metadata dict | model_outputs stringlengths 1.7k 98k |
|---|---|---|---|---|---|---|
[
{
"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": ""
} | <|begin_of_thought|>
Okay, let's try to solve this problem. The question is asking for the sum of all integer bases \( b > 9 \) such that \( 17_b \) is a divisor of \( 97_b \). Hmm, bases can be a bit tricky, so I need to recall how numbers are represented in different bases.
First, let me convert the numbers \( 17_... |
[
{
"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": ""
} | <|begin_of_thought|>
Okay, let's try to tackle this geometry problem step by step. First, I need to understand the problem statement clearly.
We have triangle ABC. Points A, D, E, B are on side AB in that order. The lengths are given: AD = 4, DE = 16, EB = 8. Similarly, points A, F, G, C are on side AC in that order... |
[
{
"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": ""
} | <|begin_of_thought|>
Okay, let's try to tackle this problem step by step. So, we have 9 baseball players, each choosing a single scoop of chocolate, vanilla, or strawberry ice cream. The conditions are:
1. At least one player chose each flavor.
2. The number of chocolate scoops (let's call this C) is greater than the... |
[
{
"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": ""
} | <|begin_of_thought|>
Okay, so I need to find the number of ordered pairs (x, y) where both x and y are integers between -100 and 100 inclusive, and they satisfy the equation 12x² - xy - 6y² = 0. Hmm, let's start by understanding the equation and figuring out how to approach this.
First, the equation is a quadratic in... |
[
{
"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": ""
} | <|begin_of_thought|>
Okay, let's try to figure out this problem. So, we need to find how many 8-digit numbers using each digit from 1 to 8 exactly once are divisible by 22. Then, subtract 2025 from that number and put the answer in a box. Hmm, okay. Let's start by understanding the problem step by step.
First, 8-digi... |
[
{
"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": ""
} | <|begin_of_thought|>
Okay, let's try to solve this problem step by step. So, we have an isosceles trapezoid with an inscribed circle. The radius of the circle is 3, and the area is 72. We need to find \( r^2 + s^2 \) where \( r \) and \( s \) are the lengths of the parallel sides.
First, let me recall some propertie... |
[
{
"content": "Problem: 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 in alphabetical order to form six two-letter words, and then those six words are listed alphabetical... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 6 | AIME25 | {
"expected_answer": "821",
"problem_id": "I-7",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's try to tackle this probability problem. So, we have twelve letters: A, B, C, D, E, F, G, H, I, J, K, L. They are randomly grouped into six pairs. Each pair is then arranged in alphabetical order to form two-letter words. Then these six words are listed alphabetically. We need to find t... |
[
{
"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 complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$. Here $i ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 7 | AIME25 | {
"expected_answer": "77",
"problem_id": "I-8",
"reference_solution": ""
} | <|begin_of_thought|>
Okay, let's try to tackle this problem step by step. The problem says that we need to find all real numbers k such that the system of equations:
1. |25 + 20i - z| = 5
2. |z - 4 - k| = |z - 3i - k|
has exactly one complex solution z. Then, we need to find the sum of all possible values of k and e... |
[{"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": ""
} | "<|begin_of_thought|>\n\nOkay, so I need to find the y-coordinate of the unique intersection point i(...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": ""
} | "<|begin_of_thought|>\n\nOkay, let's try to figure out this problem. So, we have a 3x9 grid where ea(...TRUNCATED) |
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mlfoundations-dev/OpenThinker-7B_1743026501_eval_71e5
Precomputed model outputs for evaluation.
Evaluation Results
Summary
| Metric | AIME25 | MATH500 |
|---|---|---|
| Accuracy | 23.3 | 84.0 |
AIME25
- Average Accuracy: 23.33% ± 1.63%
- Number of Runs: 5
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 20.00% | 6 | 30 |
| 2 | 20.00% | 6 | 30 |
| 3 | 23.33% | 7 | 30 |
| 4 | 23.33% | 7 | 30 |
| 5 | 30.00% | 9 | 30 |
MATH500
- Accuracy: 84.00%
Accuracy Questions Solved Total Questions 84.00% 420 500
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