context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 8
values | metadata dict | model_outputs stringlengths 1 195k |
|---|---|---|---|---|---|---|
[
{
"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... | To solve this problem, we will use the principle of inclusion-exclusion. Let's denote the four sets as follows:
- \( D \): residents who own a diamond ring,
- \( G \): residents who own golf clubs,
- \( S \): residents who own a garden spade,
- \( C \): residents who own a bag of candy hearts (which everyone owns, so i... |
[
{
"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.... | To solve the problem, we need to find a list of positive integers that satisfies three conditions:
1. The sum of the items is 30.
2. The unique mode is 9.
3. The median is a positive integer that does not appear in the list.
First, since the mode is 9 and it must be unique, 9 must appear more times than any other numb... |
[
{
"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... | To solve the problem, we need to fill a 2x3 grid with digits such that the sum of the two numbers formed by reading left to right (i.e., the first row and the second row) is 999, and the sum of the three numbers formed by reading top to bottom (i.e., the first column, second column, and third column) is 99. Let's break... |
[
{
"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 = \\... | To solve the given system of logarithmic equations, let's start by translating each equation into exponential form. The first equation is:
\[
\log_2\left(\frac{x}{yz}\right) = \frac{1}{2} \implies \frac{x}{yz} = 2^{1/2} = \sqrt{2}.
\]
Similarly, the second equation:
\[
\log_2\left(\frac{y}{xz}\right) = \frac{1}{3} \... |
[
{
"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... | To solve for the side length of the convex equilateral hexagon \(ABCDEF\) where opposite sides are parallel, we start by understanding the structure. Since it's a regular hexagon with opposite sides parallel, we can position it in the coordinate plane for easier calculation.
Let’s denote the side length of the hexagon... |
[
{
"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... | To solve the problem, we need to determine the set \( A \) such that when Bob lists all finite nonempty sets \( B \) where the maximum element of \( B \) is in \( A \), there are exactly 2024 such sets. We need to find the sum of the elements of \( A \).
Let's denote the elements of \( A \) as \( a_1, a_2, \dots, a_k ... |
[
{
"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... | To solve for the greatest four-digit number \( N \) such that changing any digit to 1 results in a number divisible by 7, we start by expressing \( N \) as \( \overline{abcd} \), where \( a, b, c, d \) are its digits. The key condition is that for each digit position, replacing that digit with 1 yields a number divisib... |
[{"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) | "To solve the problem, we need to analyze the geometry of the torus \\( T \\) and the sphere \\( S \(...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) | "To solve this problem, we need to count the number of ways to place 25 white and 25 black chips in (...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) | "To solve for \\( AB \\cdot AC \\) given that the circumradius \\( R = 13 \\), inradius \\( r = 6 \\(...TRUNCATED) |
End of preview. Expand in Data Studio
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mlfoundations-dev/a1_code_primeintellect_stack_exchange_1744623234_eval_1331
Precomputed model outputs for evaluation.
Evaluation Results
Summary
| Metric | AIME24 | AMC23 | MATH500 | GPQADiamond | JEEBench | MMLUPro | LiveCodeBench | CodeElo |
|---|---|---|---|---|---|---|---|---|
| Accuracy | 14.0 | 53.2 | 76.0 | 33.2 | 30.4 | 25.8 | 8.9 | 3.0 |
AIME24
- Average Accuracy: 14.00% ± 1.48%
- Number of Runs: 10
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 13.33% | 4 | 30 |
| 2 | 10.00% | 3 | 30 |
| 3 | 16.67% | 5 | 30 |
| 4 | 13.33% | 4 | 30 |
| 5 | 23.33% | 7 | 30 |
| 6 | 6.67% | 2 | 30 |
| 7 | 13.33% | 4 | 30 |
| 8 | 13.33% | 4 | 30 |
| 9 | 20.00% | 6 | 30 |
| 10 | 10.00% | 3 | 30 |
AMC23
- Average Accuracy: 53.25% ± 1.73%
- Number of Runs: 10
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 40.00% | 16 | 40 |
| 2 | 57.50% | 23 | 40 |
| 3 | 55.00% | 22 | 40 |
| 4 | 52.50% | 21 | 40 |
| 5 | 60.00% | 24 | 40 |
| 6 | 47.50% | 19 | 40 |
| 7 | 57.50% | 23 | 40 |
| 8 | 55.00% | 22 | 40 |
| 9 | 55.00% | 22 | 40 |
| 10 | 52.50% | 21 | 40 |
MATH500
- Accuracy: 76.00%
Accuracy Questions Solved Total Questions 76.00% 380 500
GPQADiamond
- Average Accuracy: 33.16% ± 0.36%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 33.33% | 66 | 198 |
| 2 | 32.32% | 64 | 198 |
| 3 | 33.84% | 67 | 198 |
JEEBench
- Average Accuracy: 30.36% ± 0.37%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 29.66% | 152.75 | 515 |
| 2 | 31.21% | 160.75 | 515 |
| 3 | 30.19% | 155.5 | 515 |
MMLUPro
- Average Accuracy: 25.80% ± 0.00%
- Number of Runs: 1
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 25.80% | 129 | 500 |
LiveCodeBench
- Average Accuracy: 8.94% ± 1.07%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 9.59% | 49 | 511 |
| 2 | 6.85% | 35 | 511 |
| 3 | 10.37% | 53 | 511 |
CodeElo
- Average Accuracy: 2.98% ± 0.31%
- Number of Runs: 3
| Run | Accuracy | Questions Solved | Total Questions |
|---|---|---|---|
| 1 | 2.81% | 11 | 391 |
| 2 | 2.56% | 10 | 391 |
| 3 | 3.58% | 14 | 391 |
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