  Raymond Smullyan came up with a puzzle that George Boolos called "The Hardest
Logic Puzzle Ever".[1] The puzzle has truthful, lying, and random gods who
answer yes or no questions with words that we don't know the meaning of. The
challenge is to figure out which type each god is. The puzzle has attracted
some general attention -- for example, one popular presentation of the puzzle
has been viewed 10 million times.[2] Various "top-down" solutions to the puzzle
have been developed.[1,3] Here a systematic bottom-up approach to the puzzle
and its generalization is presented. We prove that an n gods puzzle is solvable
if and only if the random gods are less than the non-random gods, for arbitrary
cardinals. We develop a solution using 4.15 questions to the 5 gods variant
with 2 random and 3 lying gods.
