context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 4 | request_idx int64 0 510 | task_name stringclasses 6
values | metadata dict | model_outputs stringlengths 1.47k 149k |
|---|---|---|---|---|---|---|
[
{
"content": "Problem: 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 residents owns a bag of candy hearts. There are 437 residents who own exactly two of these things, and 234 residents wh... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 0 | AIME24 | {
"expected_answer": "73",
"problem_id": "aime24-0",
"reference_solution": "Let $w,x,y,z$ denote the number of residents who own 1,2,3 and 4 of these items, respectively. We know $w+x+y+z=900$ , since there are 900 residents in total. This simplifies to $w+z=229$ , since we know $x=437$ and $y=234$ . Now, w... | <|begin_of_thought|>
Okay, let's try to tackle this problem step by step. So, we have 900 residents in Aimeville, and we need to find out how many own all four items: a diamond ring, a set of golf clubs, a garden spade, and a bag of candy hearts.
First, let me note down all the given information to organize my thoug... |
[
{
"content": "Problem: A list of positive integers has the following properties: $\\bullet$ The sum of the items in the list is $30$ . $\\bullet$ The unique mode of the list is $9$ . $\\bullet$ The median of the list is a positive integer that does not appear in the list itself. Find the sum of the squares... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 1 | AIME24 | {
"expected_answer": "236",
"problem_id": "aime24-1",
"reference_solution": "The third condition implies that the list's size must be an even number, as if it were an odd number, the median of the list would surely appear in the list itself. Therefore, we can casework on what even numbers work. Say the size is 2.... | <|begin_of_thought|>
Okay, let's try to tackle this problem step by step. The problem states that there's a list of positive integers with three properties:
1. The sum of the items is 30.
2. The unique mode is 9.
3. The median of the list is a positive integer that does not appear in the list itself.
We need to find... |
[
{
"content": "Problem: 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 formed by reading top to bottom is $99$ . The grid below is an example of such an arrangement because $8+99... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 2 | AIME24 | {
"expected_answer": "45",
"problem_id": "aime24-2",
"reference_solution": "Consider this table: $\\begin{array}{|c|c|c|} \\hline a & b & c \\\\ \\hline d & e & f\\\\ \\hline \\end{array}$ We note that $c+f = 9$ , because $c+f \\leq 18$ , meaning it never achieves a unit's digit sum of $9$ otherwise. Since no... | <|begin_of_thought|>
Okay, let's try to tackle this problem step by step. The problem is about placing digits in a 2x3 grid such that two conditions are satisfied: the sum of the two 3-digit numbers formed by reading left to right in each row is 999, and the sum of the three 2-digit numbers formed by reading top to bo... |
[
{
"content": "Problem: 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}\\right) = {1 \\over 3}\\] \\[\\log_2\\left({z \\over xy}\\right) = {1 \\over 4}\\] \nThen the value of... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 3 | AIME24 | {
"expected_answer": "33",
"problem_id": "aime24-3",
"reference_solution": "Denote $\\log_2(x) = a$ , $\\log_2(y) = b$ , and $\\log_2(z) = c$ . Then, we have:\n $a-b-c = \\frac{1}{2}$ \n $-a+b-c = \\frac{1}{3}$ \n $-a-b+c = \\frac{1}{4}$ Now, we can solve to get $a = \\frac{-7}{24}, b = \\frac{-9}{24}, c = \\... | <|begin_of_thought|>
Okay, let's try to solve this problem step by step. So, we have three variables x, y, z, all positive real numbers, and they satisfy three logarithmic equations. The goal is to find the absolute value of log base 2 of (x^4 y^3 z^2), expressed as a reduced fraction m/n, and then find m + n. Alright... |
[
{
"content": "Problem: 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 200, 240, and 300. Find the side length of the hexagon.\nMark your solution with \\boxed\nAnswer:",
"role":... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 4 | AIME24 | {
"expected_answer": "80",
"problem_id": "aime24-4",
"reference_solution": "Draw a good diagram!\nLet $AF \\cap BC$ , $BC \\cap DE$ , and $AF \\cap DE$ be K, L, and M, respectively. Let $KL=200, KM=300, ML=240$ . Notice that all smaller triangles formed are all similar to the larger $(200,240,300)$ triangl... | <|begin_of_thought|>
Okay, let's try to tackle this problem step by step. So, we have a convex equilateral hexagon ABCDEF where all pairs of opposite sides are parallel. The triangle formed by extending the segments AB, CD, and EF has side lengths 200, 240, and 300. We need to find the side length of the hexagon.
Fir... |
[
{
"content": "Problem: 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 $A$ . Bob's list has 2024 sets. Find the sum of the elements of A.\nMark your solution with \\boxed\nAnswer:",... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 5 | AIME24 | {
"expected_answer": "55",
"problem_id": "aime24-5",
"reference_solution": "Let $k$ be one of the elements in Alices set $A$ of positive integers. The number of sets that Bob lists with the property that their maximum element is k is $2^{k-1}$ , since every positive integer less than k can be in the set or o... | <|begin_of_thought|>
Okay, let's try to tackle this problem step by step. The problem says that Alice chooses a set A of positive integers. Then Bob lists all finite nonempty sets B of positive integers such that the maximum element of B is in A. The total number of such sets B is 2024. We need to find the sum of the ... |
[
{
"content": "Problem: 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 $R$ be the quotient and remainder, respectively, when $N$ is divided by $1000$ . Find $Q+R$ .\nMark ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 6 | AIME24 | {
"expected_answer": "699",
"problem_id": "aime24-6",
"reference_solution": "We note that by changing a digit to $1$ for the number $\\overline{abcd}$ , we are subtracting the number by either $1000(a-1)$ , $100(b-1)$ , $10(c-1)$ , or $d-1$ . Thus, $1000a + 100b + 10c + d \\equiv 1000(a-1) \\equiv 100(b-1... | <|begin_of_thought|>
Okay, let's try to tackle this problem step by step. The problem says:
"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 be the quotient and remainder, respectively, when N is d... |
[{"content":"Problem: Torus $T$ is the surface produced by revolving a circle with radius $3$ ar(...TRUNCATED) | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 7 | AIME24 | {"expected_answer":"127","problem_id":"aime24-7","reference_solution":"First, let's consider a secti(...TRUNCATED) | "<|begin_of_thought|>\n\nOkay, let's try to tackle this problem step by step. So, we have a torus T (...TRUNCATED) |
[{"content":"Problem: There is a collection of $25$ indistinguishable white chips and $25$ indis(...TRUNCATED) | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 8 | AIME24 | {"expected_answer":"902","problem_id":"aime24-8","reference_solution":"The problem says \"some\", so(...TRUNCATED) | "<|begin_of_thought|>\n\nOkay, let's try to tackle this problem step by step. The problem is about p(...TRUNCATED) |
[{"content":"Problem: Let $\\triangle ABC$ have circumcenter $O$ and incenter $I$ with $\\ove(...TRUNCATED) | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 9 | AIME24 | {"expected_answer":"468","problem_id":"aime24-9","reference_solution":"By Euler's formula $OI^{2}=R(...TRUNCATED) | "<|begin_of_thought|>\n\nOkay, let's try to tackle this geometry problem. So, we have triangle ABC w(...TRUNCATED) |
End of preview. Expand in Data Studio
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Check out the documentation for more information.
mlfoundations-dev/OpenThinker-32B_1743609016_eval_0981
Precomputed model outputs for evaluation.
Evaluation Results
Summary
| Metric | AIME24 | AIME25 | AMC23 | MATH500 | GPQADiamond | LiveCodeBench |
|---|---|---|---|---|---|---|
| Accuracy | 68.0 | 49.3 | 95.5 | 90.6 | 63.5 | 68.6 |
AIME24
- Average Accuracy: 68.00% ± 2.42%
- Number of Runs: 5
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 63.33% | 19 | 30 |
| 2 | 60.00% | 18 | 30 |
| 3 | 73.33% | 22 | 30 |
| 4 | 73.33% | 22 | 30 |
| 5 | 70.00% | 21 | 30 |
AIME25
- Average Accuracy: 49.33% ± 4.75%
- Number of Runs: 5
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 46.67% | 14 | 30 |
| 2 | 56.67% | 17 | 30 |
| 3 | 53.33% | 16 | 30 |
| 4 | 60.00% | 18 | 30 |
| 5 | 30.00% | 9 | 30 |
AMC23
- Average Accuracy: 95.50% ± 0.84%
- Number of Runs: 5
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 92.50% | 37 | 40 |
| 2 | 97.50% | 39 | 40 |
| 3 | 97.50% | 39 | 40 |
| 4 | 95.00% | 38 | 40 |
| 5 | 95.00% | 38 | 40 |
MATH500
- Accuracy: 90.60%
Accuracy Questions Solved Total Questions 90.60% 453 500
GPQADiamond
- Average Accuracy: 63.47% ± 1.79%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 59.09% | 117 | 198 |
| 2 | 65.66% | 130 | 198 |
| 3 | 65.66% | 130 | 198 |
LiveCodeBench
- Average Accuracy: 68.62% ± 1.03%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 67.91% | 347 | 511 |
| 2 | 70.65% | 361 | 511 |
| 3 | 67.32% | 344 | 511 |
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