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.

Or should I say the winner is "and." That's the big deal here, the "and." The best way to solve this is to assume someone is a knight and follow the logic. Once you run into a liar, at least one half of the "and" is false, could be both, but that really tells you little.

So the most logical place to start the assumptions turns out to be the answer. E makes a statement that C & D are knights. Assume that to be true and follow the logic through. If it blows up, you know E is a liar, and you can go from there.

If E is telling the truth, then C's statement is true and we learn B is a Liar. If B is a liar and E is a knight, then F is a liar. If F is a liar ... well, here we are stuck because if E is telling the truth, the "D is a liar bit" already makes the statement false so we learn nothing. Dead end, but not contradiction, so go to D is a knight.

D states A & B are liars, which is the complete truth. A says C and F are liars, but C is not, so that one is already a lie -- still ok. C states that A and B are liars, which we've quite established.

Nothing blows up ... E is a knight, so are C and D; the others, A,B,F are liars. You need go through no further iterations.

Posted by Lawrence on 2003-09-05 22:21:39