Wednesday, November 29, 2017

logical deduction - The way to Acarien, with Knights and Knaves


Once again, you're on your way to Acarien. You find yourself in a land of Knights and Knaves, who understand your language but don't speak it. You understand nor speak their language, but you do know their words for yes and no, "yok" and "pom". Unfortunately, you don't know which is which. And of course, as always, Knights always tell the truth, while knaves always lie.


You find yourself at a fork in the road, unsure which road to take, when you see someone coming down one of the roads you are considering. You don't know if it's a knight or a knave.


Is there a question you can ask, one single question, answerable with "yok" or "pom", that tells you which way to go?





I do not know if such a question exists, so answers can be either a question that works, or proof that no such question exists.



Answer



Let's test the "If I were to ask you "is left is the correct path?" would you say "yok"?" question.


$$ \begin{array}{ccc|c} \text{opponent} & \text{yok} & \text{Acarien} & \text{answer} \\ \hline \text{knave} & \text{yes} & \text{left} & \text{yok} \\ \text{knight} & \text{yes} & \text{left} & \text{yok} \\ \text{knave} & \text{no} & \text{left} & \text{yok} \\ \text{knight} & \text{no} & \text{left} & \text{yok} \\ \hline \text{knave} & \text{yes} & \text{right} & \text{pom} \\ \text{knight} & \text{yes} & \text{right} & \text{pom} \\ \text{knave} & \text{no} & \text{right} & \text{pom} \\ \text{knight} & \text{no} & \text{right} & \text{pom} \end{array}$$


As shown above I've tried all possible combinations of answerer type, language, and correct path. They all seem to work well.


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