This is a puzzle that was sent to me by a friend of mine. As a result I put a contract out on his life - for I haven’t been able to regain my piece of mind since. It was published by a dude called Boolos and attributed to another guy called Smullyan. I didn’t come up with this title - hardest logic puzzle ever - it is the title used by Boolos for his paper. He must have been reading digg that day. Anyway it really is hard. Don’t keep reading if you want to keep your sanity intact!

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.

Some clarifications:

* It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).

* What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
* 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.
* Random will answer ‘da’ or ‘ja’ when asked any yes-no question

You want the answer? Too bad! It’s too hard for me. There’s a solution up on Wikipedia. I’ve read it, but still don’t get it. You don’t either? Oh well, welcome to my nightmare!. Anyone who thinks they can explain this simply are welcome to do in the comments

Update

Okay - it’s a bit mean of me not to post a solution. But it takes some work to understand. So what I’ll do is break it up into bits (as does Boolos). The trick is to solve three smaller puzzles first and then put them together to solve the big one. I’ll post the three smaller puzzles first and then for the next few days I’ll post the solutions to those three puzzles. So here they are. (These are considerably easier).

Puzzle 1:

Noting their locations, I place two aces and a jack face down on a table, in a row; you do not see which card is placed where. Your problem is to point to one of the three cards and then ask me a single yes-no question, from the answer to which you can, with certainty, identify one of the three cards as an ace. If you have pointed to one of the aces, I will answer your question truthfully. However, if you have pointed to the jack, I will answer your question yes or no, completely at random.

Puzzle 2:

Suppose that, somehow, you have learned that you are speaking not to Random but to True or False - you don’t know which - and that whichever god you’re talking to has condescended to answer you in English. For some reason, you need to know whether Dushanbe is in Kirghizia or not. What one yes-no question can you ask the god from the answer to which you can determine whether or not Dushanbe is in Kirghizia?

Puzzle 3:

You are now quite definitely talking to True, but he refuses to answer you in English and will only say da or ja. What one yes-no question can you ask True to determine whether or not Dushanbe is in Kirghizia?