Knights and Knaves

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.