context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 4 | request_idx int64 0 29 | task_name stringclasses 1
value | metadata dict | model_outputs stringlengths 5.09k 152k |
|---|---|---|---|---|---|---|
[
{
"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... | Alright, let's tackle this problem step by step. It's about set theory, specifically dealing with the principle of inclusion-exclusion. The problem states that there are 900 residents in Aimeville, each owning a bag of candy hearts. Additionally, they own either a diamond ring, a set of golf clubs, or a garden spade. T... |
[
{
"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.... | Alright, let's tackle this problem step by step. So, we have a list of positive integers with three main properties:
1. The sum of all the numbers in the list is 30.
2. The unique mode of the list is 9. That means 9 appears more frequently than any other number, and no other number repeats as much as 9 does.
3. The me... |
[{"content":"Problem: Find the number of ways to place a digit in each cell of a 2x3 grid so that th(...TRUNCATED) | {
"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{(...TRUNCATED) | "Alright, let's tackle this problem step by step. So, we have a 2x3 grid, and each cell must contain(...TRUNCATED) |
[{"content":"Problem: Let $x,y$ and $z$ be positive real numbers that satisfy the following syst(...TRUNCATED) | {
"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 $\\log_2(x) = a$ , $\(...TRUNCATED) | "Alright, let's tackle this problem step by step. It's about solving a system of logarithmic equatio(...TRUNCATED) |
[{"content":"Problem: Let ABCDEF be a convex equilateral hexagon in which all pairs of opposite side(...TRUNCATED) | {
"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(...TRUNCATED) | "Alright, let's tackle this problem step by step. So, we have a convex equilateral hexagon ABCDEF wh(...TRUNCATED) |
[{"content":"Problem: Alice chooses a set $A$ of positive integers. Then Bob lists all finite none(...TRUNCATED) | {
"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 elemen(...TRUNCATED) | "Alright, let's tackle this problem step by step. So, Alice picks a set A of positive integers. Then(...TRUNCATED) |
[{"content":"Problem: Let $N$ be the greatest four-digit positive integer with the property that w(...TRUNCATED) | {
"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 di(...TRUNCATED) | "Alright, let's tackle this problem step by step. So, we need to find the greatest four-digit number(...TRUNCATED) |
[{"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) | "Alright, let's tackle this problem step by step. It's about a torus (which is like a donut shape) i(...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) | "Alright, let's tackle this problem step by step. So, we have a 5x5 grid, and we need to place some (...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) | "Alright, let's tackle this geometry problem step by step. So, we have a triangle ABC with circumrad(...TRUNCATED) |
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