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?

(In reply to Specifically... by Charlie)

Well, down here in my high school, I haven't taken calculus yet, so I wouldn't be able to figure out a specific path. Since this is a puzzle, and it only asks for a safe swim for shore, I'm not going to worry about the events afterwards.

Just thinking about it (no evidence) I'd say that to get to 1/4 out of the lake would take an infinite amount of swimming in circles. The spiral would approach 3/4 as you swim for an infinite amount of time, I think. I say that you only have to get (4-π)/4 out of the lake. Then, you have enough advantage to swim straight to shore. Of course, this only shortens the swim, if we want to try to find that too.

Posted by Tristan on 2003-10-29 19:44:34