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 751 308k |
|---|---|---|---|---|---|---|
[
{
"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... | <think>
Okay, so I need to figure out how many residents in Aimeville own all four things: a diamond ring, a set of golf clubs, a garden spade, and a bag of candy hearts. Let me start by jotting down the given numbers to organize my thoughts.
First, the total number of residents is 900. Each resident owns at least one... |
[
{
"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.... | <think>
Okay, so I need to solve this problem where there's a list of positive integers with certain properties. Let me try to break it down step by step. The problem states:
1. The sum of the items in the list is 30.
2. The unique mode of the list is 9.
3. The median of the list is a positive integer that does not ap... |
[
{
"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... | <think>
Okay, so I need to figure out how many ways there are to place digits in a 2x3 grid such that the sum of the two numbers read left to right is 999, and the sum of the three numbers read top to bottom is 99. The example given is:
\[
\begin{array}{|c|c|c|} \hline
0 & 0 & 8 \\ \hline
9 & 9 & 1 \\ \hline
\end{a... |
[
{
"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 = \\... | <think>
Okay, so I have this problem where I need to find the value of |log₂(x⁴y³z²)|, and express it as a fraction m/n where m and n are coprime. Then, find m + n. The variables x, y, z are positive real numbers that satisfy the following system of logarithmic equations:
1. log₂(x/(yz)) = 1/2
2. log₂(y/(xz)) = 1/3
3.... |
[{"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) | "<think>\nOkay, so I have this problem about a convex equilateral hexagon where all pairs of opposit(...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) | "<think>\nOkay, so let's try to figure out this problem. Alice picks a set A of positive integers. T(...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) | "<think>\nOkay, so I need to find the greatest four-digit number N such that if you change any one o(...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) | "<think>\nOkay, so I need to solve this problem about a torus and a sphere. Let me first try to visu(...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) | "<think>\nOkay, so I need to figure out how many ways there are to place some chips on a 5x5 grid fo(...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) | "<think>\nOkay, so I have this geometry problem here. Let me read it again and make sure I understan(...TRUNCATED) |
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