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 598 147k |
|---|---|---|---|---|---|---|
[
{
"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... | Okay, let me try to figure out this problem step by step. So, we have 900 residents in Aimeville, and each owns a bag of candy hearts, so everyone has at least one item. Then, some people own a diamond ring, some own golf clubs, and some own a garden spade. The numbers given are 195 diamond rings, 367 golf clubs, 562 g... |
[
{
"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.... | Okay, let's tackle this problem step by step. So, we have 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 is a positive integer not in the list itself.
We need to find the sum of the squares of all the items in the list. Hmm, let's break this do... |
[
{
"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... | Okay, let's tackle this problem step by step. So, we need to find the number of ways to place a digit in each cell of a 2x3 grid such that two conditions are satisfied:
1. The sum of the two numbers formed by reading left to right (i.e., the two 3-digit numbers in the rows) is 999.
2. The sum of the three numbers form... |
[
{
"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 = \\... | Okay, so I have this problem where I need to find the value of |log₂(x⁴y³z²)| given that x, y, z are positive real numbers satisfying three logarithmic equations. The answer should be in the form m/n where m and n are coprime, and then find m + n. Alright, let's break this down step by step.
First, the given equations... |
[
{
"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... | Alright, let's tackle this problem step by step. So, we have a convex equilateral hexagon named ABCDEF. All pairs of opposite sides are parallel. Then, there's a triangle formed by extending AB, CD, and EF, and this triangle has side lengths 200, 240, and 300. We need to find the side length of the hexagon. Hmm, okay. ... |
[
{
"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... | Okay, let's try to tackle this problem step by step. So, Alice chooses a set A of positive integers. Then Bob lists all finite nonempty sets B of positive integers where the maximum element of B is in A. Bob's list has 2024 sets. We need to find the sum of the elements of A.
First, let me parse the problem carefully. ... |
[
{
"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... | Alright, let's tackle this problem step by step. So, we need to find the greatest four-digit number N such that changing any single digit to 1 results in a number divisible by 7. Then, once we find N, we divide it by 1000 to get quotient Q and remainder R, and finally compute Q + R.
First, let me parse the problem ca... |
[
{
"content": "Problem: Torus $T$ is the surface produced by revolving a circle with radius $3$ around an axis in the plane of the circle that is a distance $6$ from the center of the circle (so like a donut). Let $S$ be a sphere with a radius $11$ . When $T$ rests on the inside of $S$ , it is intern... | {
"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 section $\\mathcal{P}$ of the solids, along the axis.\nBy some 3D-Geomerty thinking, we can simply know that the axis crosses the sphere center. So, that is saying, the $\\mathcal{P}$ we took crosses one of th... | Okay, let's see. I need to find the difference between the radii of the circles where the torus is tangent to the sphere when resting inside and outside. The problem mentions that the torus T is created by revolving a circle of radius 3 around an axis in its plane, 6 units away from the center. The sphere S has a radiu... |
[{"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) | "Okay, let's tackle this problem step by step. So, we have a 5x5 grid, and we need to place some chi(...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) | "Okay, so I have this geometry problem here. Let me read it again. It says: In triangle ABC, the cir(...TRUNCATED) |
End of preview. Expand in Data Studio
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mlfoundations-dev/Light-R1-32B_1743609585_eval_0981
Precomputed model outputs for evaluation.
Evaluation Results
Summary
| Metric | AIME24 | AIME25 | AMC23 | MATH500 | GPQADiamond | LiveCodeBench |
|---|---|---|---|---|---|---|
| Accuracy | 74.7 | 58.0 | 96.0 | 90.4 | 62.0 | 56.0 |
AIME24
- Average Accuracy: 74.67% ± 1.19%
- Number of Runs: 5
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 80.00% | 24 | 30 |
| 2 | 73.33% | 22 | 30 |
| 3 | 73.33% | 22 | 30 |
| 4 | 73.33% | 22 | 30 |
| 5 | 73.33% | 22 | 30 |
AIME25
- Average Accuracy: 58.00% ± 5.30%
- Number of Runs: 5
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 60.00% | 18 | 30 |
| 2 | 80.00% | 24 | 30 |
| 3 | 50.00% | 15 | 30 |
| 4 | 46.67% | 14 | 30 |
| 5 | 53.33% | 16 | 30 |
AMC23
- Average Accuracy: 96.00% ± 0.55%
- Number of Runs: 5
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 95.00% | 38 | 40 |
| 2 | 95.00% | 38 | 40 |
| 3 | 97.50% | 39 | 40 |
| 4 | 95.00% | 38 | 40 |
| 5 | 97.50% | 39 | 40 |
MATH500
- Accuracy: 90.40%
Accuracy Questions Solved Total Questions 90.40% 452 500
GPQADiamond
- Average Accuracy: 61.95% ± 0.36%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 62.12% | 123 | 198 |
| 2 | 61.11% | 121 | 198 |
| 3 | 62.63% | 124 | 198 |
LiveCodeBench
- Average Accuracy: 56.03% ± 0.62%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 54.79% | 280 | 511 |
| 2 | 56.56% | 289 | 511 |
| 3 | 56.75% | 290 | 511 |
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