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?
Suppose A is an insane liar. Then A believes the false statement that both are sane and as a liar must claim the opposite, so A cannot make the third statement and A is not an insane liar
Suppose A is a sane liar. Then B is not a knight from (1), and since A is not insane, B is a sane liar from (2). But then A can't truthfully claim they're both sane, so A is not a sane liar.
Suppose A is a sane knight. Then B is a knight from (1), but since A is not insane, B is an insane knight from (2). But then A can't falsely claim they're both sane so A is not a sane knight.
By process of elimination, A is an insane knight. A believes B is a knight, so B is a liar, but B truthfully claims A is insane so B is an insane liar
So, they're both insane, and A is a knight and B is a liar.
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Posted by Paul
on 2023-11-11 14:46:45 |
Solution
