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?
I get they are each Insane Knights (IN)
The table gives the possibilities and the
number gives the statement that
disqualifies the possibility:
A B B B B
-----------------------------------
SN SN,2 SL,1 IN,2 IL,1
SL SN,1 SL,3 IN,1 IL,3
IN SN,3* SL,1 IN IL,3
IL SN,1 SL,2 IN,1 IL,2
* I am not sure about this one.
Maybe A believes something that is not true -
that they are both sane. But he is supposed to
lie, not say that they are both sane.
There is a little ambiguity in the problem,
I think.
You could look at it in two ways:
1) Before it starts, each already believes
what the other is and makes no further
evaluations. (This is what I assumed.) Also,
the phrase "believes false statements" I took
to include "believes false things".
2) Alternatively, one could look at it as they
are reevaluating their opinions of the other
as the statements are made. But I wonder how
they can do that. For example, does "believe
false statements" imply "disbelieve true
statements"?
Using 1) I don't see how A, B could be IN, IL
(Pauls's result). Were this the case, from
the first statement, A would believe B
to a Knight and then call him a liar.
Edited on November 12, 2023, 1:10 am
soln
