The Hardest Logic Puzzle Ever

The Hardest Logic Puzzle Ever -- by Raymond Smullyan

I have just received a book on logic puzzles, by Raymond Smullyan. Smullyan would be best described as the craziest and most gifted person in this world. He is a mathematician, a concert pianist, logician, writer, magician, conjurer, raconteur, all packed in one. Here is a masterpiece which I found on the Internet :

In 1992, George Boolos called the following "the hardest logic puzzle ever". I figured that people here would especially like it. It's certainly a Raymond Smullyan inspired puzzle and goes as follows.

"Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which."

Just for the sake of clarity, George Boolos gives the following four clarifications: (1) It could be that one god gets asked more than one question (and thus, some god is not asked any question at all). (2) What the second question is, and to which god it is put, may depend on the answer to the first question (likewise, for the third question). (3) Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely. (4) Random will answer 'da' or 'ja' when asked any yes-no question.

Good luck!

partha

PS: The person who solves the above puzzle will be declared as the "second Smullyan", in this blog. You can email me your ssolutions.

PPS : To know more about Raymond Smullyan, visit ::
http://en.wikipedia.org/wiki/Raymond_Smullyan

PPPS: A solution is here.

PPPPS: This problem is described here