Image four objects initially situated on the corners of a square whose sides are 100 miles long. Each object chases the object clockwise to him. Each corrects course instantaneously, always heading directly toward his quarry. Each travels at the same speed of 50 miles per hour. Will any object catch is quarry in finite time? If so, how long will it take for one of the objects to catch his quarry? If not, why not? I encountered this problem in a differential equations course and managed to solve it analytically. I later realized that there is an easy intuitive way to obtain the answer.
