You are walking to a destination, and have to pass through Talking Town. As is common with these problems, you see a fork in the road, and inquire about which way leads to Truth Town. Four people around give you advice, but you don't know their veracity or their gender. You gather from their conversation that all four are either knights or liars, and there is exactly one girl in the group.

A: Take the left fork to get to Truth Town.

B: All liars are girls.

C: All knights are girls.

D: All people who begin their statments with "All" are either all knights or all liars.

Just from these four statements, can you see whether the left or right fork leads to Truth Town? (Also: Which one is the girl?)

The right fork  leads to truth town.

EXPLANATION:

At the outset, the statements made by B and C are self contradictory, so that both of them cannot be the same type and accordingly, precisely  one of B and C is a knight while the other is a liar.  This invalidates D’s statement, implying inter alia that D is a liar. Thus, we have at least two liars.

If B spoke the truth, in accordance with  B’s statement there must be at least two girls. This is a contradiction. Accordingly, B must be a liar so that C is a knight and according to C’s true statement it follows that C is a girl.

Now, if the remaining individual , that is A, were to be a knight,
then it would follow that A is a girl, so that there would have been a total of two girls. This is a contradiction.

Accordingly, A must be a liar and consequently, the right fork in
reality leads to truth town.

Posted by K Sengupta on 2007-07-20 12:38:09