My friend told me this complex story. Everyone in it is either a knight, knave, or liar (more than one person can have the same status). Knights always tell truths, liars always lie, and knaves always alternate every statement.

Everyone knew the status of everyone else except for my friend (he knew nothing at first). If anyone lied about what someone said, they didn’t lie about who, when, or whether they said it; they only lied about what the person said. The story goes as follows.

Aaron and Bill were talking to me.
Aaron told me what he was.
At this point, I could tell what Aaron was.
Bill told me one thing that he wasn’t.
Aaron told me that Cassie was a knight.
I then could figure out what Cassie was.
Bill told me that Cassie was a knave.
I thought about this for a minute.
I soon found that the previous thing Bill said allowed me to know for sure what the last of the three people were.

What type is everyone? The puzzle is solvable.

(In reply to Pointing out... by Tristan)

(stopped reading comments at the post to which this replies.)

Well, based on your statements in the puzzle, it doesn't make sense for you to be either a liar or a knave, so if you must be one of the three (which I doubt), then you must be a knight.<o:p></o:p>

Your friend certainly could be a knight, since it was assumed he was telling the truth to arrive at the previous given solutions, and that led to no unresovable contradictions.  From what he said, the statements can't all be lies, so he can't be a liar.
Could he be a knave?  Let's assume so and see what happens.

If his first statement were false, then his second would have to be also, so his first statement must be true.
2 is false, so A must have said what he wasn't.
3 is true so he knows what A is, therefore A's answer must have been "I'm not a knight".  So A is a knave telling truth.
4 is false so B says he's either knave or knight or a liar.
5 is true so A is lying and C is either knave or liar.
6 is false so friend doesn't yet know what C is.
7 is true so B says C is knave.
8 is false -irrelevant
9 is true.  Since we don't yet know what C is, the only way this is possible is if we already know what B is, which means B's statement about himself was that he is a liar, which we know is false, so he is a knave and his next statement (about C) is true so C is a knave.

So everyone being a knave gives us another possible solution.
But which solution is correct?  Either there is no way to tell, in which case the riddle is unsolvable or else the clue lies in the title and the last statment contradicting each other, giving us the hint that everyone is in fact a knave.

(now on to the remaining comments)

Posted by Galendir on 2004-03-21 08:26:02