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 wrote:
Insane knights believe that 4 is prime and 2 is not prime and so can only say "4 is prime"
.... maybe not "only"
I agree that if they speak of numbers, it doesn't matter what
they believe - they must tell falsehoods. Since 4 is not prime
they must say 4 is prime.
But, the way the problem is phrased, while they can say the
above, if they speak of beliefs, they can alternatively
say "I believe 4 is not prime" They must say falsehoods,
and this statement is false since it is not what they believe.
The problem is tricky, testing beliefs along with facts.
The only true thing I can say is: I believe I am done with it.
Edited on November 13, 2023, 4:36 pm
two types of falsehoods
