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?
New answer: A is an Insane Knight and B is a Sane Knight:
A: First A incorrectly appraises B as a Liar,
then lies about his belief, calling B Knight.
B: Next B correctly appraises A as Insane and
correctly reports this.
A: Finally A, obliged to make a false statement
and knowing that he himself is insane, says
that they are both Sane, a guaranteed falsehood.
Here is the revised table. The numbers
indicate which line of dialog disqualified
that choice. (IK, SK) remain valid. I have
also distinguished the need to simply utter
falsehoods (perhaps unknowingly)
with an 'F', as opposed to lying
(telling other than what you believe to be true.)
A B B B B
----------------------------------
SK SK,2 SL,1 IK,2 IL,1
SL SK,1 SL,2 IK,1 IL,2F
IK SK SL,1 IK,2F IL,1
IL SK,3F SL,1 IK,1 IL,3F
Edited on November 13, 2023, 12:20 pm
so then...
