Locked in a dungeon, you are faced with five doors. One of them leads to freedom. The other four will lead you back to the starting room disoriented and confused, so that you will not remember which of the doors you have already tried and have to start again.
How many attempts do you expect to make on the average (statistically) before making it out?
(In reply to Simpler Solution
by Nick Reed)
Where do you get the N = 1 + 0.8 N equation?