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 879 163k |
|---|---|---|---|---|---|---|
[
{
"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": ""
} | Alright, so I've got this problem: I need to find the sum of all integer bases \( b > 9 \) for which \( 17_b \) is a divisor of \( 97_b \). Hmm, okay. Let me try to unpack this step by step.
First off, I remember that when a number is written in a certain base \( b \), each digit represents a power of \( b \). So, for... |
[
{
"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": ""
} | Alright, let's tackle this problem step by step. It's a bit complex, but I'll try to break it down. So, we have triangle ABC with points A, D, E, B on side AB, and points A, F, G, C on side AC. The lengths are given: AD = 4, DE = 16, EB = 8 on AB, and AF = 13, FG = 52, GC = 26 on AC. Then we have points M and N, which ... |
[
{
"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": ""
} | Alright, so I have this problem where there are 9 baseball team members who each got an ice cream cone. The cones can be chocolate, vanilla, or strawberry. The conditions are that each flavor is chosen by at least one player, and the number of chocolate cones is greater than vanilla, which is greater than strawberry. I... |
[
{
"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": ""
} | Alright, so I have this problem: I need to find the number of ordered pairs (x, y) where both x and y are integers between -100 and 100, inclusive. The condition given is 12x² - xy - 6y² = 0. Hmm, okay. Let's try to figure this out step by step.
First, let me write down the equation clearly:
12x² - xy - 6y² = 0.
Hmm... |
[
{
"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": ""
} | Alright, so I have this problem where I need to find how many eight-digit numbers, made by using each digit from 1 to 8 exactly once, are divisible by 22. Then, I need to find the difference between that number, N, and 2025. Hmm, okay. Let me break this down step by step.
First, I know that a number divisible by 22 mu... |
[
{
"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": ""
} | Alright, so I have this problem about an isosceles trapezoid with an inscribed circle. The radius of the circle is 3, and the area of the trapezoid is 72. I need to find r squared plus s squared, where r and s are the lengths of the two parallel sides, and they're not equal. Hmm, okay.
First off, I remember that for a... |
[
{
"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": ""
} | Alright, so I have this probability problem to solve, and I need to figure it out step by step. Let me read it again and try to understand what it's asking.
We have twelve letters: A, B, C, D, E, F, G, H, I, J, K, and L. These are going to be randomly grouped into six pairs. Each pair is then placed next to each other... |
[
{
"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": ""
} | Alright, so I have this problem here, and I need to find the sum of all possible values of \( k \) such that the system of equations has exactly one complex solution \( z \). The equations are:
1. \( |25 + 20i - z| = 5 \)
2. \( |z - 4 - k| = |z - 3i - k| \)
Hmm, okay. Let me try to understand what each equation repre... |
[{"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": ""
} | "Alright, so I have this problem where I need to find the y-coordinate of the unique intersection po(...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": ""
} | "Alright, so I have this problem about counting the number of ways to fill a 3x9 grid with numbers 1(...TRUNCATED) |
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mlfoundations-dev/test_r1_7b_verifier_model_1743102486_eval_baa0
Precomputed model outputs for evaluation.
Evaluation Results
Summary
| Metric | AIME24 | AIME25 | GPQADiamond | MATH500 |
|---|---|---|---|---|
| Accuracy | 52.0 | 36.7 | 22.2 | 85.0 |
AIME24
- Average Accuracy: 52.00% ± 1.79%
- Number of Runs: 5
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 50.00% | 15 | 30 |
| 2 | 56.67% | 17 | 30 |
| 3 | 46.67% | 14 | 30 |
| 4 | 50.00% | 15 | 30 |
| 5 | 56.67% | 17 | 30 |
AIME25
- Average Accuracy: 36.67% ± 2.49%
- Number of Runs: 5
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 40.00% | 12 | 30 |
| 2 | 43.33% | 13 | 30 |
| 3 | 30.00% | 9 | 30 |
| 4 | 40.00% | 12 | 30 |
| 5 | 30.00% | 9 | 30 |
GPQADiamond
- Average Accuracy: 22.22% ± 1.04%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 21.21% | 42 | 198 |
| 2 | 24.75% | 49 | 198 |
| 3 | 20.71% | 41 | 198 |
MATH500
- Accuracy: 85.00%
Accuracy Questions Solved Total Questions 85.00% 425 500
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