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?)

There are three statements beginning with "All;" B, C, and D.

Statement D says that these statements are either all true or all false. If that is the case, then D is true, hence they all must be true.

However, there is a contradiction in statements B and C, so that cannot be the case; D must be false.

If all three of statements B, C, and D were false, that would make statement D true (we'll assume D is referring to their small group), so one of B or C must be true, and the other false.

If B is true, then there can be only one false statement, since there is only one girl, and all liars are girls.

We already know that D is false, and this assumption would make statement C false as well, so that cannot be the case either.

Therefore, C is true, B is false, and C is the only girl (and the only knight).

Finally, we know that A, a guy, must be lying, and you should take the right fork to get to Truth Town.

Posted by DJ on 2003-09-03 18:01:13