Source
r/puzzles•
RT17

A question about 'the world's hardest logic puzzle ever'.

This is the puzzle I am referring to:

Three gods A, B, and C are called, in no particular 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.

I'm looking to clarify something but I don't want to accidentally stumble upon the solution.

I was hoping someone who knows the puzzle could help.

My question is this: if I were to ask True a question about how Random would respond to a question (e.g. "Would B say 'yes' if I asked him 'does 1+1=2?'"), does the True god answer randomly to reflect the that Random would answer randomly? Or can True 'see the future' and his answer reflect what Random will if/when I ask him that question?

Or is that kind of question just not valid?

Posted Apr 17, 2015, 3:24 AM UTC

09
brendantheraven•

Good question. I thought I knew the puzzle, but I've never thought about the question you pose. Since I already know one solution, I read up on your question for you, and can give you an answer without giving you the answer. Basically, George Boolos' original presentation of the puzzle did not address the question you pose. So the question is either not valid in his conception of the puzzle or just doesn't move you toward the answer the way he envisioned it. Later, another author presented a version of the puzzle in which, when faced with the situation you describe, True would be unable to answer and would therefore remain silent. This author said that with this condition the puzzle could be solved in two questions instead of three.

4
edderiofer•

The simplest way to determine (in three questions, not two) who's who in the latter case is to ask "What would Random reply if asked this question" to each one in turn. The first person to reply is Random, the person who agrees with Random is True, and the person who disagrees with Random is False.

1
palparepa•

There is another version in which a god would smite you if it can't answer.

1
RT17OP•

Thanks for the answer, it's very helpful.

0
palparepa•

Also, how frequently does Random "switch"? Can it switch while pondering a response?

For example, given the question: "what would you say if I asked you if 1+1=2?" True would say "True", False would say "True", but maybe Random would answer with "False", if he decides to say the truth, but the simulation of itself, decides to go with falsehood.

1
brendantheraven•

That's another important question brought up by later authors, who decided that in order for the problem to be as difficult as Boolos intended, Random's behavior should be thought of as if a coin flips in his head, and if it comes up heads, he answers ja, and if it comes up tails, he answers da.

This addresses two weaknesses in the original formulation: the switching possibility you mention, and the fact that Boolos originally described Random's behavior as if a coin flips in his head and this determines whether he answers as a truth-teller or a liar. In both cases, you could come up with a question that would force Random to tell the truth, making the problem solvable in fewer than three questions.

1
mrfooacct•

It doesn't seem solvable as written: Random could imitate the answer of any god, and therefore be indistinguishable from that god if you got unlucky with his random answers.

1
now_look_here•

But you don't know the identities so how would you know whom you are asking?

1
RT17OP•

The goal is to figure that out. Understanding how particular god would answer a particular question is rather crucial to figuring that out.

1