A traveler passing through the land of liars and knights stops in at a pub, where he meets a group of six friendly locals. Their stories all are funny, but he doesn't know which ones to believe, so he asks them (tactfully) who the liars and knights are in the group. They make one statement each:

Amery: Cuthbert and Fredo are both liars.
Brant: Everard and Fredo are both knights.
Cuthbert: Brant is a liar and Everard is a knight.
Derek: Amery and Brant are both liars.
Everard: Cuthbert and Derek are both knights.
Fredo: Derek is a liar and Amery is a knight.

Which of the men are liars, and which are knights?
Remember: only part of a logical AND statement needs to be false for the entire statement to be false.

Suppose A is a knight.

Then, C and F are both liars, and at least one of the statements made by each must be false.

F said that A is a knight, which we have alerady assumed to be true, so the other part of his statement must be false, and Derek is a knight.

However, Derek says that A is a liar, so we have a contradiction, and our original assumption must be false.

Therefore, A is a liar, and at least one of his statements must be false (either C or F is a knight).

F cannot be a knight, since he says A (a liar) is a knight.

C must be a knight.

C says that B is a liar and E is a knight, which must both be true.

Finally, E (a knight) says that C and D are knights, and we now know what each person is:

A - liar


B - liar


C - knight


D - knight


E - knight


F - liar

Going through the remaining statements shows no contradictions.

Posted by DJ on 2003-09-05 15:28:15