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?

All of the solutions given so far have been too limited.  There can be far more knights than liars and vice-versa, when you realize that just because everybody made a statement about everybody else DOESN'T mean that all of their statements go in one circle.
Instead, you can form two circles, one containing all of the knights and one containing all of the liars.  As long as both chains have at least 2 people in them, everyone in each of the chains can say "He's a knight" to the person they're pointing to without creating a contradiction.  You could have 200 knights and 3 liars or vice versa and everyone can still say "He's a knight" about one other person.
I don't know what to do about the "village idiot", because the author needs to make clear what if any rules such an individual must follow.  If none, than he doesn't change the above analysis.  If some, then he does.  See my next post.

Posted by AvalonXQ on 2007-02-11 04:20:27