Sane knights believe true statements and say true statements. Sane liars believe true statements, but say false statements. Insane knights believe false statements and say false statements. Insane liars believe false statements, but say true statements. You meet two people, A and B. Each is either a sane knight, a sane liar, an insane knight, or an insane liar.

A:I believe that B is a knight.
B:A is insane.
A:We are both sane.

What are A and B?

You are all correct about A being an insane knight, but wrong about B's type. They cannot both be insane knights because B's statement would be true that A is insane, and insane knights cannot make true statements. If A is an insane knight and B is an insane liar, then A would believe that B is a knight. However, A would not believe that A believes that B is a knight, so A would not say, "I believe that B is a knight."

Posted by Math Man on 2023-11-12 12:49:52