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.

A must have said "I'm a Liar", which only allows for his being a Knave; no other could say so.

Bill must have said "I'm not a Liar" or "I'm not a Knave", since I couldn't tell what he was right then. In the first case he could be a knight or a knave, and in the second case, he could be anything.

A said C was a knight; since A is a knave, and he had already lied, then C *is* a knight.

B said C was a knave; this is false, so we know B (at least sometimes) lies.

If B had said "I'm not a liar", he could be either a knave or a liar, so as I could tell what he was, he must have said "I'm not a knave", and he actually *was* one.

Posted by e.g. on 2004-02-02 08:36:56