Source: P. Winkler
In a room stand n armed and angry people. At each chime of a clock, everyone simultaneously spins around and shoots a random other person. The persons shot fall dead and the survivors spin and shoot again at the next chime. Eventually, either everyone is dead or there is a single survivor.
As n grows, what is the limiting probabality that there will be a survivor. :)
Treat at H8 canteen for the person solving it first :)