A challenge problem for those who enjoy such things: the "bug problem":
You have a square room with walls of length L. In each of the four corners is a small bug. At the sound of a gun, they each start walking at the same rate directly towards the bug on their right. So each bug's first step is towards the corner to their right. But for the second step each bug must adjust its trajectory a bit in order to continue walking directly towards its neighbor because that bug has moved. With each step for each bug to continue to walk directly towards its neighbor causes them all to spiral toward each other. They keep doing this until they all meet at the center or the room. The diagram below I hope makes this clear.
Question: what is the distance each bug travels?