Note: Shamelessly stolen from Wikipedia.There are countably infinite prisoners in a rather overcrowded prison. Its chimerical warden decides to play an implausible game to determine who should be executed, since trials would be quite time consuming. The prisoners stand on the natural numbers on a number line and face in the positive direction, and the warden places either a hat on each labeled with a randomly chosen natural number, so that each person can only see the numbers on the hats of prisoners in front of him. At a specified time, once the prisoners have seen all the hats in front of them with their infinite eyesight, the prisoners simultaneously guess the number on their hat. No communication is allowed once the prisoners are lined up.
Thankfully, the infinite prisoners are infinitely wise and have infinite time to prepare a strategy in advance to foil the warden's bloodthirsty plot for arbitrary justice. Can the prisoners devise a strategy that will guarantee only finitely many of them are killed?
