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Everyone is a knave, including my friend, the narrator.
Assume my friend is a knight. The first statement by Aaron was that he was a liar, because that is the only possibility that lets the narrator know what he is. Therefore, Aaron is a knave who first lies. The next thing Aaron said should be the truth, so Cassie is a knight. The last thing Bill said contradicts this, so Bill lied.
According to statement 4, Bill said one thing he wasn't. If he said he wasn't a knight, the narrator would know him to be a knave, but then Bill's last statement did not help the narrator determine anything he didn't already know (this contradicts the narrator's last statement). It would be impossible for Bill to say he wasn't a knave, because his next statement is a lie. If Bill said he wasn't a liar, the narrator would not be able to figure out Bill's status, again contradicting the narrator's last statement.
Therefore, my friend is not a knight.
My friend's first statement must be true because he cannot have lied that Aaron and Bill were in fact talking to him. So, my friend must be a knave, and only his odd numbered statements are true.
Since statement 2 is false, Aaron did not say what he was; yet statement 3 is true, and the narrator found out what Aaron was anyway. The simplest explanation is that Aaron said that he wasn't a knight rather than what he was. The narrator knew then that Aaron was a knave, and that Aaron's next statement would be a lie. The narrator states truly in statement 5 that Aaron next said Cassie was a knight. Therefore, Cassie cannot be a knight.
Statement 6 is a lie so Bill's first statement can't have revealed what Cassie was. Instead, since statement 9 is still true, Bill had to reveal who Cassie was in his second statement (statement 7), that Cassie was a knave. The only way my friend could have figured anything out from this is if he knew whether Bill was lying or not.
Bill's first statement must have shown to the narrator both what Bill was, and whether he would lie in his next statement; this is the only place from which the narrator could have found this information. Bill couldn't have stated what he wasn't in his first statement, so he must have stated that he was a liar, proving to the narrator that Bill was a knave and that Bill's second statement was true. As stated by his true statement, Cassie is a knave, making all four people knaves.
This problem was named by my friend. |
