Knights and Knaves

by filius 4mo10th Jun 20191 comment


In the Knights and Knaves riddle you are facing a fork in the road, with one way leading to freedom and the other to death. There are two persons, a knight and a knave. The former always tells the truth while the latter always lies. You got to ask one yes/no question to find your way into freedom.

One solution is to use truth tables. For example in that the statements of both persons are concatenated together. According to the AND table it does not matter in which order true and false are combinated, the result is false. So if your question goes like »What would the other person say, if I'd ask him if this way leads to freedom?«, you always get a falsified answer and are able to identify the way into freedom.

A general assumption for this riddle is that both persons know the truth about whereto the ways lead. That introduces another approach, in that the knave must diversify between inner and outer opinion. To be able to always lie outwardly, he has to know the truth for himself, so his inner opinion is the truth. To take advantage of that, one could ask »Would you say for yourself, that this path leads to freedom?«. This provokes a contradiction in the knave's answer and can therefore be spotted.

Finally a similiar approach that uses the inner opinion is possible too. If both know of the truth, but are still acting differently, this must be on purpose. So in other words, one wants to harm you and the other not. A simpler question would therefore be »Do you want me to go this way?«. The good guy, you can take at his word, because he has your best interests in mind. The bad guy on the other hand would like to send you to death, but since he's forced to lie, you can take him at his word too.