Three gods puzzle (aka “The Hardest Logic Puzzle Ever”, I didn’t make that name up!) for reference. Try to solve the puzzle first, I’ve appended the text. The referenced link contains the solution.
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.
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.
The first time I read that I thought “what difference there is between speaking truly in a language where da means yes and ja means no, and speaking falsely in a language where ja means yes and da means no?” and assumed that the solution was that there’s no solution. (I was wrong.)
Differences: The Three Princess riddle only allows for one binary question, however, the princess (same setup of of True, False, Random) answer in plain English. You win if you (edit:) choose a princess who is not random. 1, 2, 3.
Actually, you win if you are able to choose a princess other than Random—you do not need to know which of the two remaining ones is Random. Otherwise, this would clearly be impossible since the answer provides only one bit and there are three possibilities. (And that’s not even considering that under sensible interpretations of the rules, you don’t get any information if you happen to ask Random—i.e., you’re not allowed to ask e.g., “Is it true that (you are False) OR (you are Random and you’ve decided to answer truthfully this time)”, which, if allowed, would be answered in the affirmative iff the one you asked is Random.)
Yes, True and False have to be omniscient to be able to answer consistently correctly or incorrectly, for any arbitrary binary question. There’s a version of the answer which (spoiler) relies on asking unanswerable questions, which only Random would answer. There’s also solution that doesn’t rely on such gimmicks, however.
There are questions for which you don’t know the answerability, so either the rules must be that questions asked are provably answerable, or else you are allowed to glean information from whether the god answers it or not.
Assuming that True and False do not know the future results of questions to Random, an example is a question to A (True) of “Would B say 1 + 1 = 2?” If B is False, it is answerable (with a ‘no’). If B is Random, it is unanswerable.
Three gods puzzle (aka “The Hardest Logic Puzzle Ever”, I didn’t make that name up!) for reference. Try to solve the puzzle first, I’ve appended the text. The referenced link contains the solution.
Here’s my solution. Not 100% sure it works.
rot13
The first time I read that I thought “what difference there is between speaking truly in a language where da means yes and ja means no, and speaking falsely in a language where ja means yes and da means no?” and assumed that the solution was that there’s no solution. (I was wrong.)
This looks superficially similar to the Three Princesses.
Differences: The Three Princess riddle only allows for one binary question, however, the princess (same setup of of True, False, Random) answer in plain English. You win if you (edit:) choose a princess who is not random. 1, 2, 3.
Actually, you win if you are able to choose a princess other than Random—you do not need to know which of the two remaining ones is Random. Otherwise, this would clearly be impossible since the answer provides only one bit and there are three possibilities. (And that’s not even considering that under sensible interpretations of the rules, you don’t get any information if you happen to ask Random—i.e., you’re not allowed to ask e.g., “Is it true that (you are False) OR (you are Random and you’ve decided to answer truthfully this time)”, which, if allowed, would be answered in the affirmative iff the one you asked is Random.)
They all speak the same language?
Yes.
Does each god know which god is which? And can I ask the same question twice to the same god?
Yes, True and False have to be omniscient to be able to answer consistently correctly or incorrectly, for any arbitrary binary question. There’s a version of the answer which (spoiler) relies on asking unanswerable questions, which only Random would answer. There’s also solution that doesn’t rely on such gimmicks, however.
Do True and False know what answer Random would give, or are they required to say “I don’t know?”
I interpreted it to mean that the question must be answerable with yes or no.
There are questions for which you don’t know the answerability, so either the rules must be that questions asked are provably answerable, or else you are allowed to glean information from whether the god answers it or not.
Assuming that True and False do not know the future results of questions to Random, an example is a question to A (True) of “Would B say 1 + 1 = 2?” If B is False, it is answerable (with a ‘no’). If B is Random, it is unanswerable.
Provably answerable from your own knowledge.
There’s nothing in your wording that suggests random is not able to refuse an unanswerable question as one of it’s potential random responses.
A fair coin can’t refuse to answer.