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?
(In reply to
so then... by Steven Lord)
You are correct about A's and B's types. However, you are wrong about the reasoning for A's second statement. A does not know that he is insane. A believes that A and B are both sane, and as a knight, says that they are both sane.
Here is the correct version of the table.
A B B B B
----------------------------------
SK SK,2 SL,1 IK,3 IL,1
SL SK,1 SL,3 IK,1 IL,2
IK SK SL,1 IK,2 IL,1
IL SK,1 SL,2 IK,1 IL,3
A's first statement implies that A and B are of the same type, so put a 1 in the cases where they are different types. B's statement implies that if they are both knights, then they are of different sanities, and if they are both liars, then they are of the same sanity. Put a 2 in the cases where they are both knights of the same sanity or both liars of different sanities. A's second statement eliminates the cases (SK, IK), (SL, SL), and (IL, IL). Put a 3 in these cases. Then, the solution is (IK, SK).
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Posted by Math Man
on 2023-11-17 13:21:37 |
re: so then...
