An ant stands in the middle of a circle (3 metres in diameter) and walks in a straight line at a random angle from 0 to 360 degrees. Problem is, it can only walk one metre before it needs a break
(Yes, I know. The lengths I'll go to make a 'problem' for the conditions set in the puzzle =P) To make things even more exasperating, the ant has the memory of a fish and forgets what direction it has just walked in. ( [reader] "You're just making this plot up as you go along to fit in with the problem aren't you?" ). Anyway, after the break, it gets all dizzy and thus chooses another random direction from 0 to 360 in an attempt to escape the circle again).
As you can well imagine, it could escape the circle after just 2 walks (just one break needed). Or... it could take 20,000 walks (19,999 breaks needed)!! There might even be the very slim possibility it might take 20,000^20,000 walks. You can probably guess what I'm going to ask.
What is the average amount of walks required for the ant to escape the circle?
http://www.skytopia.com/project/imath/imath.html