A man is standing on a rock in the middle of a circular lake of radius 1. There is a tiger on the shore of the lake that can run four times as fast you can swim; however, the tiger cannot swim. The tiger is hungry and always attempts to keep the distance between the two of you at a minimum. How can you safely swim to the shore?
Assume that as long as you can get to the shore before the tiger gets to you (even if it is only a split-second before), you will be safe.
Answer
Until you are more than 1/4 of the radius away from the rock, you can swim fast enough so that you may keep the tiger the furthest distance possible from you. Regardless of which direction the tiger moves around the circle, you swim the other way, always keeping the rock between you and the tiger. While you are doing this, you will be able to move outward since you will have some energy to spare.
Before long you will be 1/4 of the radius away from the centre and the tiger will be 180 degrees away. At this point swim straight to the point on the shore furthest from the tiger. You will be able to get there in 3/4 units of time, while it will take the tiger pi/4 = 0.7854 units of time.
