A stupendous puzzle, and I do know the answer. I learn it on an Italian riddle discussion board.

An evil witch kidnaps infinite (countable) dwarves. The witch tells the dwarves that the following day she is going to put all of them going through the identical path and uniformly at random will place on every dwarf’s head a hat that may be both white or black. So that the primary one sees all the opposite dwarves. The second all however the first, and so forth, i.e. every dwarf will then see solely the colour of the dwarves’ hats in entrance of him.

Each dwarf should guess their hat coloration, whoever guesses is free whoever misses dies. The dwarves have one evening to have the ability to focus on a method. The foremost downside is that the dwarves are deaf! So they won’t hear something the opposite dwarves say.
Can you give you a method that may save all however finitely many dwarves?