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?)

Take the right fork to get to Truth Town, and C is the girl.

First, D cannot be a Knight. If he were, then C wouuld be a Knight, and B,C, and D would all be girls, which we know is false.

Therefore either B or C is a Knight (since D is a liar, his statement is false and so B and C cannot both be liars).

If B were a Knight, then D must be girl. Since there is only one girl, it is not B (since D is), and hence C is a liar (and therefore a girl). Too many girls, so B is a liar.

Therefore C is a Knight. Hence C is a girl. Furthermore, since there is only 1 girl there is only one Knight, so A is a liar.

Thus the right fork goes to Truth Town, which is presumably inhabited by Knights. And all Knights are girls, so I see why you might find it an interesting place to visit....

Posted by Brian Wainscott on 2003-09-03 17:30:19