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?

If A and C are knights, then B is a liar. D would not say that C is a knight and is therefore a liar. So C would not say that A is a knight, but C is a knight, therefore A and C are not both knights.

If A is a knight and C is a liar, B is a knight. D would say that C is a knight and is therefore a liar. C would say that A is a knight, which cannot be the case since C is a liar. This combination is impossible.

If A is a liar and C is a knight, B is also a knight. D would say that C is a knight, and so D is a knight.  But C would not say that A is a knight, so this combination is also impossible.

Therefore A and C are both liars, and B is also a liar. D would not say that C is a knight and is therefore a knight. C would say that A is a knight, which is true. E would say that F is a knight. E cannot be a knight, since E and F make contradictory statements, therfore E and F are both liars and the right fork should be taken.  

Posted by Iain on 2004-05-14 15:44:25