I came across this interesting little math problem by Oliver Roeder that I thought I would pass on. I actually worked it out while I was waiting to board my plane on my return from California yesterday.
There’s an airplane with 100 seats, and there are 100 ticketed passengers each with an assigned seat. They line up to board in some random order. However, the first person to board is the worst person alive, and just sits in a random seat, without even looking at his boarding pass. Each subsequent passenger sits in his or her own assigned seat if it’s empty, but sits in a random open seat if the assigned seat is occupied. What is the probability that you, the hundredth passenger to board, finds your seat unoccupied?
As with all such puzzles, how you arrive at the answer is more interesting than the answer itself.
The above website runs a regular weekly math feature called The Riddler.