How close can you get to $\pi$ (as close as possible) using these rules?
1) You can only use at most four integers ranging from $1$ to $20$, each only once.
2) You can only use plus, minus, multiply, divide, exponential, and log as binary operators.
3) You can only use integer factorial as a unitary operator.
4) You should work in the real number region.
The best answer that I know currently is $$3 + \frac{16}{5!-7} = \frac{355}{113} = 3.141592920\ldots$$