Term has re-started so it is time to restart the Sunday puzzle thread! (Not sure whether to hyphenate re-start or not – any views? Ed)
I think this one, from the puzzles-for-dinner thread on math overflow, is rather fun. I look forward to hearing your solutions:
There is a plane with 100 seats and we have 100 passengers entering the plane one after the other. The first one cannot find his ticket, so chooses a random (uniformly) seat. All the other passengers do the following when entering the plane (they have their tickets). If the seat written on the ticket is free, one sits on this seat, if not he chooses a other (free) seat at random (uniformly). What is the probability the last passenger entering the plane gets the correct seat?
