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.

Aaron's first comment gave his identity away. The only way this could happen is if he said the one thing that only a knave could say: "I am a liar."

Aaron's first comment was a lie, therefore his second comment was a truth, therefore Cassie is a knight.

Therefore Bill was lying on his second comment when he said that Casie was a knave, so Bill is either a knave or a liar.

Bill's first comment had to either be "I am not a knight," "I am not a knave" or "I am not a liar"

Neither Bill the truth-telling knave nor Bill the liar would have been able to say "I am not a knave." Similarly, both Bill the knave and Bill the Liar would be able to say "I am not a liar," and the friend would not have worked out the puzzle.
Therefore, Bill must have said "I am not a knight," and was therefore telling the truth, and was therefore a knave.

Aaron: Knave
Bill: Knave
Casie: Knight

Posted by Sam on 2004-02-02 08:25:55