Boobs. And bacon strips.
Also, that the problem with infinite dwarfs gotta be a strange joke from mathematician (which sounds somewhat like magician). Since the dwarfs can talk a lot and fast in a very short time, it suggests that they go through a bunch of functions which returns the colour of the hats. But as there are infinite dwarfs and the outcome of the function should only consist of a limited ammount of mistakes, the dwarfs would have to go through an infinite ammount of functions. No matter how you turn it, the gap between infinite and finite stays. The oh-so-great hint that one can choose an axiom of choice is more like saying: do whatever you want, just make it sound somewhat logic and add the word 'function'. So I'll just put up the axiom: There exists a limited ammount of functions which can represent an infinite ammount of returnvalues with only a finite range of mistakes. Yay, problem solved, even though that doesn't make any sense at all. Reminds me of trollphysics. Yay, for trollmathematics! This thing is bugging me now too long, I think I'll just surrender to the dwarfs, give each one a cookie and stay the rest of eternity in hell, distributing cookies to dwarfs.
But mostly boobs and baconstrips.