context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 4 | request_idx int64 0 499 | task_name stringclasses 3
values | metadata dict | model_outputs stringlengths 695 192k |
|---|---|---|---|---|---|---|
[
{
"content": "You are a math expert. You will be given a math problem. Please solve it step by step and provide your final answer as an integer. Your response MUST contain the final answer inside '\\boxed{}', like '\\boxed{82}', otherwise it will be considered incorrect automatically. \n\n Question: Among the 9... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.6,
"top_p": 0.95
} | 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... | Alright, let's tackle this problem step by step. It's about using set theory, specifically the principle of inclusion-exclusion, to find the number of residents who own all four items. Let me break it down.
First, let's list out the given information:
- Total residents (U) = 900
- Own diamond ring (D) = 195
- Own gol... |
[
{
"content": "You are a math expert. You will be given a math problem. Please solve it step by step and provide your final answer as an integer. Your response MUST contain the final answer inside '\\boxed{}', like '\\boxed{82}', otherwise it will be considered incorrect automatically. \n\n Question: A list of p... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.6,
"top_p": 0.95
} | 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.... | Alright, so I have this math 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.
"A list of positive integers has the following properties:
- The sum of the items in the list is 30.
- The unique mode of the list is 9.
- The median of the list is a p... |
[
{
"content": "You are a math expert. You will be given a math problem. Please solve it step by step and provide your final answer as an integer. Your response MUST contain the final answer inside '\\boxed{}', like '\\boxed{82}', otherwise it will be considered incorrect automatically. \n\n Question: Find the nu... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.6,
"top_p": 0.95
} | 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... | Alright, so I have this problem where I need to figure out how many ways there are to place a digit in each cell of a 2x3 grid. The conditions are that the sum of the two numbers formed by reading left to right in each row should be 999, and the sum of the three numbers formed by reading top to bottom in each column sh... |
[
{
"content": "You are a math expert. You will be given a math problem. Please solve it step by step and provide your final answer as an integer. Your response MUST contain the final answer inside '\\boxed{}', like '\\boxed{82}', otherwise it will be considered incorrect automatically. \n\n Question: Let $x,y$ ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.6,
"top_p": 0.95
} | 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 = \\... | Alright, so I have this problem where I need to find the value of |log₂(x⁴y³z²)| given a system of logarithmic equations. The answer needs to be in the form m/n where m and n are coprime, and then find m + n. Let me try to figure this out step by step.
First, let me write down the given equations:
1. log₂(x / (y z)) ... |
[
{
"content": "You are a math expert. You will be given a math problem. Please solve it step by step and provide your final answer as an integer. Your response MUST contain the final answer inside '\\boxed{}', like '\\boxed{82}', otherwise it will be considered incorrect automatically. \n\n Question: Let ABCDEF ... | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.6,
"top_p": 0.95
} | 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, so I have this problem about a convex equilateral hexagon where all pairs of opposite sides are parallel. The extensions of sides AB, CD, and EF form a triangle with side lengths 200, 240, and 300. I need to find the side length of the hexagon.
First, let me try to visualize the hexagon. It's convex and equil... |
[{"content":"You are a math expert. You will be given a math problem. Please solve it step by step a(...TRUNCATED) | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.6,
"top_p": 0.95
} | 0 | 5 | AIME24 | {"expected_answer":"55","problem_id":"aime24-5","reference_solution":"Let $k$ be one of the elemen(...TRUNCATED) | "Alright, so I have this problem where Alice picks a set A of positive integers. Then Bob makes a li(...TRUNCATED) |
[{"content":"You are a math expert. You will be given a math problem. Please solve it step by step a(...TRUNCATED) | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.6,
"top_p": 0.95
} | 0 | 6 | AIME24 | {"expected_answer":"699","problem_id":"aime24-6","reference_solution":"We note that by changing a di(...TRUNCATED) | "Alright, so I have this problem where I need to find the greatest four-digit number N. The conditio(...TRUNCATED) |
[{"content":"You are a math expert. You will be given a math problem. Please solve it step by step a(...TRUNCATED) | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.6,
"top_p": 0.95
} | 0 | 7 | AIME24 | {"expected_answer":"127","problem_id":"aime24-7","reference_solution":"First, let's consider a secti(...TRUNCATED) | "Alright, so I have this problem about a torus and a sphere. Let me try to visualize it first. A tor(...TRUNCATED) |
[{"content":"You are a math expert. You will be given a math problem. Please solve it step by step a(...TRUNCATED) | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.6,
"top_p": 0.95
} | 0 | 8 | AIME24 | {"expected_answer":"902","problem_id":"aime24-8","reference_solution":"The problem says \"some\", so(...TRUNCATED) | "Alright, so I have this problem about placing chips on a 5x5 grid. There are 25 white chips and 25 (...TRUNCATED) |
[{"content":"You are a math expert. You will be given a math problem. Please solve it step by step a(...TRUNCATED) | {
"do_sample": true,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.6,
"top_p": 0.95
} | 0 | 9 | AIME24 | {"expected_answer":"468","problem_id":"aime24-9","reference_solution":"By Euler's formula $OI^{2}=R(...TRUNCATED) | "Alright, so I have this geometry problem here about triangle ABC. It says that the circumradius is (...TRUNCATED) |
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