In Normalville, every inhabitant is either a knight, a liar, or a normal. Knights always tell the truth. Liars always lie. Normals tell the truth and lie completely at random. You are going to Normalville when you see a fork in the road. There are two ways to go. One of them leads to Normalville. You see three inhabitants by the fork, A, B, and C. You know that only one of them is a normal, but you are not sure who it is. In two "yes" or "no" questions, how do you find the way to Normalville? (Each question can only be addressed to one person, but it can be a different person for each question.)

For the second question, we only know that the respondee is a knight or a liar but not which.  Call the routes L and R. I suggest something like:

'If I were to ask you 'Is L the road to Normalville', would you reply 'Yes''? :-
(1) L is the true road: knight would reply 'Y' and so reports 'Y'; liar would reply 'N', but reporting 'N' would be telling the truth, so he must reply, 'Y'.
(2) R is the true road: knight would reply 'N' and so reports 'N'; liar would reply 'Y', but reporting 'Y' would be telling the truth, so he must reply, 'N'.

If the answer is 'Y' then go L, else go R.

Posted by broll on 2012-10-07 06:49:10