aimo-validation-amc

# Dataset Card for AIMO Validation AMC

All 83 come from AMC12 2022, AMC12 2023, and have been extracted from the AOPS wiki page https://artofproblemsolving.com/wiki/index.php/AMC_12_Problems_and_Solutions

This dataset serves as an internal validation set during our participation in the AIMO progress prize competition. Using data after 2021 is to avoid potential overlap with the MATH training set.

Here are the different columns in the dataset:
problem: the *modified* problem statement
answer: the adapted integer answer
url: url to the problem page in the website

## Dataset creation process
The original AMC12 problems are MCQ with 4 choices. In order to be closer to the AIMO progress prize condition, we modified the problem statement to have an integer output. Those problems whose statement can not be modified are rejected.

Example:

### Original problem:
```
Flora the frog starts at 0 on the number line and makes a sequence of jumps to the right. In any one jump, independent of previous jumps, Flora leaps a positive integer distance $m$ with probability $\frac{1}{2^m}$.
What is the probability that Flora will eventually land at 10?
$\textbf{(A)}~\frac{5}{512}\qquad\textbf{(B)}~\frac{45}{1024}\qquad\textbf{(C)}~\frac{127}{1024}\qquad\textbf{(D)}~\frac{511}{1024}\qquad\textbf{(E)}~\frac{1}{2}$
```

### Modified problem:
```
Flora the frog starts at 0 on the number line and makes a sequence of jumps to the right. In any one jump, independent of previous jumps, Flora leaps a positive integer distance $m$ with probability $\frac{1}{2^m}$.
What is the probability that Flora will eventually land at 10? Write the answer as a simplified fraction $\frac{m}{n}$, find $m+n$
```

# AIMO验证AMC数据集卡片

本数据集共收录83道试题，全部取材自2022年、2023年美国数学竞赛12年级组（AMC12），素材提取自AOPS（问题解决艺术，Art of Problem Solving）维基百科页面https://artofproblemsolving.com/wiki/index.php/AMC_12_Problems_and_Solutions。

本数据集为我们参赛AIMO进步奖赛事时所用的内部验证集。选用2021年之后的试题，旨在规避与MATH训练集产生潜在的数据重叠。

数据集包含以下字段：
- problem：经过修订的试题题干
- answer：适配后的整数答案
- url：对应试题页面的网站链接

## 数据集构建流程

原始AMC12试题均为四选一单项选择题。为契合AIMO进步奖赛事的题型规则，我们将试题题干调整为需输出整数答案的形式，无法完成此类修改的试题已被剔除。

### 原始试题

Flora the frog starts at 0 on the number line and makes a sequence of jumps to the right. In any one jump, independent of previous jumps, Flora leaps a positive integer distance $\frac{1}{2^m}$.
What is the probability that Flora will eventually land at 10?
$\textbf{(A)}~\frac{5}{512}\qquad\textbf{(B)}~\frac{45}{1024}\qquad\textbf{(C)}~\frac{127}{1024}\qquad\textbf{(D)}~\frac{511}{1024}\qquad\textbf{(E)}~\frac{1}{2}$

### 修改后试题

Flora the frog starts at 0 on the number line and makes a sequence of jumps to the right. In any one jump, independent of previous jumps, Flora leaps a positive integer distance $\frac{1}{2^m}$.
What is the probability that Flora will eventually land at 10? Write the answer as a simplified fraction $\frac{m}{n}$, find $m+n$