I went to a crazy party where there were 8 people (whose names are conveniently only one letter long). Each person is either a knight, a knave, or a liar. I didn't know any of them very well, but I didn't want to ask them what they were directly, so I asked each person about two other people. They each gave two statements. Here are their responses:

A: B is a knave. C is a knave.
B: C is a liar. D is a knave.
C: D is a liar. E is a knight.
D: E is a knave. F is a knight.
E: F is a knight. G is a knight.
F: G is a liar. H is a liar.
G: H is a knave. A is a liar.
H: A is a liar. B is a knave.

Whom can I trust?

A: liar
B: knight
C: liar
D: knave
E: knave
F: liar
G: knight
H: knave

H's statements cannot both be true, since that would mean A was a liar, but H's second statement is the same as A's first. If H's statements were both false, then G's statements are both false, making F a knight, E a knave, D a knight, C a liar, B a knave, and A a knave, which contradicts the fact that we previously thought H's second statement (B is a knave) to be false.

So H is a knave, and the only remaining question is whether A is a liar or not. If not, then G is a knave, so F is a liar, E a liar, D a liar, C a knave, B a liar, and A a knave: a contradiction.

So A is a liar, and we have what follows above.

Posted by Avin on 2005-02-14 19:52:42