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 can not 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 shore?
If the man were to swim directly to a point diametrically opposite the tiger's initial position, he travels distance, 1 unit. The tiger must travel all the way around the lake, distance PI units. This is less than 4 times the man's distance, and therefore, the tiger would beat him there.
However, if the man swims in a spiral... he could keep the tiger running around the lake, chasing a 'moving closest point'. So, I think a 'loose' enough spiral path would be a solution to this, and the man could get to shore a bit ahead of the tiger.
Now... a remaining question is... once to shore, can the man RUN at least as fast as the tiger...?
first thought
