http://en.wikipedia.org/wiki/Prisoners_and_hats_puzzle#Countably_Infinite-Hat_Variant http://en.wikipedia.org/wiki/Prisoners_and_hats_puzzle#Count... "In fact,

http://en.wikipedia.org/wiki/Prisoners_and_hats_puzzle#Countably_Infinite-Hat_Variant http://en.wikipedia.org/wiki/Prisoners_and_hats_puzzle#Count... "In fact, even if we allow an uncountable number of different colors for the hats, the axiom of choice provides a solution that guarantees that only finitely many prisoners must die." This is by far the craziest result coming out of AOC.