# Knights and knaves in a foreign language

You die and ascend to heaven, there is a knight (truth-teller), a knave (pure liar) and a joker (random) sitting on a cloud - they all look the same. In order to gain entry you must determine their identities. You have 3 yes/no questions (each directed to only one of them). They will only respond to questions speaking their own heavenly language's words for "yes" and "no" which you do not know - "pluh" and "plit" (unknown which means what).

Are you going to be allowed into heaven?

• A pure liar that made it's way to heaven? Remarkable. Oct 8, 2014 at 13:42
• Indeed. Well let's say is a little device of God's why not Oct 8, 2014 at 13:45
• @Quassnoi The effect of the 2 options is pretty much the same. The answer can neither be depended on to be true or false. You can ask his the same question 2 times and get a different answer, or the same answer (2 nos, 2 yeses, or 1 no 1 yes - there is not way to know) Oct 8, 2014 at 13:58
• @d'alar'cop: "if I asked you if the Pope is Catholic instead of this question, and you answered with same honesty, would you answer pluh?". If the answer is an arbitrarily chosen truth or lie, it is still pluh. If it's random, it can be either. Oct 8, 2014 at 14:15
• What happens when they don't know the answer? Say I happen to ask the Knight about how the Joker will respond. He can't answer truthfully either way. Oct 9, 2014 at 17:00

This is so called The Hardest Logic Puzzle Ever. Wikipedia has a thorough description of it and its solutions, including different versions of formulations of how the joker functions (which was not defined in the OP's question).
I can cite the very basics here:

Formulation:

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.

Solution:

Q1: Ask god B, "If I asked you 'Is A Random?', would you say ja?". If B answers ja, either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is indeed Random. Either way, C is not Random. If B answers da, either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is not Random. Either way, you know the identity of a god who is not Random.
Q2: Go to the god who was identified as not being Random by the previous question (either A or C), and ask him: "If I asked you 'Are you False?', would you say ja?". Since he is not Random, an answer of da indicates that he is True and an answer of ja indicates that he is False.
Q3: Ask the same god the question: "If I asked you 'Is B Random?', would you say ja?". If the answer is ja, B is Random; if the answer is da, the god you have not yet spoken to is Random. The remaining god can be identified by elimination.

• @CaelanO'Toole, what do you mean? " In order to gain entry you must determine their identities" Jun 22, 2016 at 21:03
• Oh, I read that last line as if that was the goal, to figure out which words were yes and no, and then ask. Jun 22, 2016 at 21:16

There are 6 possible outcomes for the assignments of A, B, and C to be T, F, and R. I have a set of 6 questions but will only need 3 questions to solve any case. The rules say that I must ask a yes - no question but it does not say that a god must be able to give a yes - no answer. There are yes - no questions which cannot be answered and the result will be N/A (no answer). Thus, there are 3 possible answers: da, ja, N/A. My strategy is to find R, then find out what da and ja mean, then find T and F. This works for 4 cases, but the last 2 cases required a question that revealed who was T and F without solving for da and ja.

Q1. A, yes or no, will B say C is True? If A says da or ja, then I know that A = R and will ask Q2 and then Q3 to solve the puzzle. Q2. B, yes or no, will C say you are True? B must answer NO, no matter who is T or F, and I will therefore know what da and ja mean. Q3. B, yes or no, will C say he is True? B will answer YES if he is T and will answer NO if he is F. I know what da and ja are, so I can determine who is T and F and I already know A is R so I have solved 2 cases with 3 questions.