Even harder than The Hardest Logic Puzzle Ever

Tom Ellis at the University of Cambridge has written a good article (find it here) summarizing and extending Boolos' puzzle. There is a nice presentation of how we can screen off the fact that the gods do not speak English and the issue of whether they speak Daisyesjaisno or Jaisyesdaisno and the fact that some of them are liars and the fact that Boolos' random sometimes lies, etc.

The generalization of the puzzle is this: Amongst 2N+1 English speaking gods there are at least N+1 truth tellers, and the others are randomers. In 2N questions determine whether φ is true (where φ is an arbitrary proposition).