context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 4 | request_idx int64 0 510 | task_name stringclasses 8
values | metadata dict | model_outputs stringlengths 1.16k 188k |
|---|---|---|---|---|---|---|
[
{
"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 solve this problem step by step. So, we have 900 residents in Aimeville, and each owns a bag of candy hearts. Additionally, they might own a diamond ring, a set of golf clubs, or a garden spade. The problem gives us the numbers of residents who own each of these items individual... |
[
{
"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. So, we have a list of positive integers with three main properties: the sum is 30, the unique mode is 9, and the median is a positive integer not in the list. We need to find the sum of the squares of all the items. Hmm, let's break this down.
... |
[
{
"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 figure out this problem. So, we have a 2x3 grid where each cell is a digit. We need to place digits in each cell such that two conditions are satisfied:
1. The sum of the two numbers formed by reading left to right is 999.
2. The sum of the three numbers formed by reading top t... |
[
{
"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 which are positive real numbers. They satisfy three logarithmic equations:
1. log₂(x / (y z)) = 1/2
2. log₂(y / (x z)) = 1/3
3. log₂(z / (x y)) = 1/4
And we need to find the absolute value of log₂(x⁴ y³ z²), ... |
[{"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) | "<|begin_of_thought|>\n\nOkay, let's try to tackle this geometry problem. So, we have a convex equil(...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) | "<|begin_of_thought|>\n\nOkay, let's try to tackle this problem step by step. So, Alice chooses a se(...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) | "<|begin_of_thought|>\n\nOkay, let's try to tackle this problem step by step. The problem says: Find(...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) | "<|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. So, we have 25 white c(...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) |
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