A knight remembers a banquet that he had:

"Oh, that was a really nice banquet; all the liars and the knights of the kingdom were there, even the village fool. We all ate and drank and at the end of it the king asked each one of us to make a statement about someone else, I mean, to say if he is a liar or a knight. finaly, one statement was said about each one of us, and every one made the same statement except for the village fool who made a different statement. By the way, can you tell me how many people were in the banquet?"

"No", you say, "but I can tell you something else about the NUMBER of people that were in the banquet."

What can you tell? What statement did each one of the participants make?

(In reply to A single possibliity (solution) by Gamer)

I think your solution might be too restrictive.  Are you assuming the the Fool says the "opposite" of all the others?  The problem only says that the Fool says something "different".  I assume that to be anything, except a repeat of the statement made by all others.

Hence you could have N+1 Liars, N Knights, start with a Liar and alternate.  The last Liar would then call the Fool a Liar, which he is not, and the Fool could say anything he wanted about the Liar at the head of the line, and the conditions are met. Or, you could have N Knights & N Liars, as in my original post.

Edited on February 10, 2007, 7:21 pm

Posted by Kenny M on 2007-02-10 19:20:34