An old Sam Lloyd classic that has to be dusted off every now and again. It's deceptively simple, and more fun to solve than to Google.
A square phalanx of soldiers, 100 feet on a side, marches forward at a constant speed. The company mascot, a small terrier, trots along with them, starting at the center of the rear rank. Since he moves more quickly than the soldiers, he is able to trot at constant speed around the outside of the square, keeping as close as possible to the soldiers at all times. When he returns to his starting position at the rear of the formation, the soldiers have moved forward a distance of 50 feet. How long is the dog's path?