The Hardest Logic Puzzle Ever

There's a classic logic puzzle in which a person must take a fork in the road, one of which is safe, but the other is a deadly trap. Two men guard the fork, one of which always lies, but the other always tells the truth. The person gets to ask one question in order to determine which path is the safe one.

Mathematician Raymond Smullyan has added another dimension to this puzzle. See if you can figure it out:

There are three guardians, A, B and C. Their names are Knight, Knave and Chaos. Knight always speaks truly, Knave always lies. Chaos tossed a coin this morning to decide whether today he would behave like Knight or like Knave.

Your task is simple: ask three yes-no questions, each of a single guardian, and determine which is Knight, which is Knave, and which is Chaos. There is, alas, a complication: the guardians understand English but will answer in the local language, in which “Da” means yes and “Ja” means no. Or possibly “Ja” means yes and “Da” means no – you cannot remember.

Link via Marginal Revolution | Raymond Smullyan

UPDATE 3/18/10: Here's the solution.

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Very Easy... Ask one of them it does not matter weather he is a knight or a knave. Ask "what will you say if the other guard will point the correct path?" if the guard you asked answered "the left" go to the right.. if he answered "the right" go to left.. simple...
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Ask Guardian A, “If I asked you, “Are you Chaos?” in your current mental state, would you say “ja”?”
If A answers “ja”, he’s Chaos. Then ask Guardian B, “If I asked you, “Are you Knight?”, would you say “ja”?”. The answer is “ja” if B is Knight, and either way the problem is now solved.

If A answers “da”, he’s either Knight or Knave. So ask him instead, “If I asked you, “Are you Knight?”, would you say “ja”?” If the answer is “ja” he’s Knight; otherwise he is Knave.
So, now, ask him “If I asked you, “Is guardian B Chaos”, would you say “ja”?” If he answers “ja”, B is Chaos, and C is the opposite of A. If he answers “da” then C is Chaos and B is the opposite of A.
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