When you are trying to get to Truth Town, you get to No Knaves Town, a city comprised of only Liars and Knights. Each of the three forks leading away from the town (not including the one you came from) leads to a different city.

There are 6 people around. Wanting to know who is what so you can ask them which fork to take, you ask them who is a liar and who is a knight.

A: C would say that B is a liar
B: D would say that C is a knight
C: E would say that F is a liar
D: C would say that A is a knight

Tired of these responses, you ask what fork leads to Truth Town.

E: The left fork leads to Truth Town
F: The middle fork leads to Truth Town

Which fork should you take to get to Truth Town?

First of all, according to what E and F said, they can't both be knights. Either one is a liar and the other is a knight, or they are both liars (in which case the fork on the right would be the correct fork).

Let's start with assuming that D is a liar. D says that C would say that A is a knight. If C is a knight then A would be a liar. If C is a liar then A is a knight. A says that C would say that B is a liar. If A is a liar and C is a knight then B would be a knight. But if A is a knight and C is a liar then B is still a knight. Now B says that D would say that C is a knight. Since we are starting with the assumption that D is a liar and we've figured that B has to be a knight, then that means C really is a liar. C says that E would say that F is a liar. C is a liar so E would really say that F is a knight. So they are either both knights or both liars. By what they said, they are both liars, and so the answer would be the fork on the right.

Now, to be complete we also have to see what happens when we start with the assumption that D is a knight. He says that C would say that A is a knight. If C is a knight then so is A. If C is a liar then A is a liar too. A says C would say that B is a liar. If A and C are both knights then B would be a liar. If A and C are both liars then B would still be a liar. Now B says that D would say that C is a knight. Since we are starting with the assumption that D is a knight and we've figured that B has to be a liar, then that means that C must really be a liar. So no matter how you look at it, C must be a liar and therefore E and F must also be liars.

So the answer must be you take the fork on the right.

Edited on May 14, 2004, 5:16 pm

Posted by Danny on 2004-05-14 14:53:55