Re: S, B, and a puzzle by Boolos, Smullyan, McCarthy

From: Jesse Mazer <lasermazer.domain.name.hidden>
Date: Wed, 13 Oct 2004 00:57:50 -0400

Nice work, Eric! Your solution looks right to me. I now realize my mistake,
I was thinking that if the gods are in a particular order (say, TRF) and Ja
has a particular meaning (say, Ja=yes) and you get a particular series of
answers (say, JJJ) then if you reverse the meaning of Ja and ask the same
questions, that means you'll also get the reverse answers (in this case
DDD). But if the question is of the form "If I asked X, would you say 'Ja'?"
this isn't actually the case. The key seems to be that if you ask a question
of the form "If I asked X, would you say 'Ja'?" then if X is true, both the
knight and the knave will answer "Ja" regardless of whether Ja means "yes"
or "no", and if X is false then both the knight and the knave will answer
"Da" regardless of the meaning of Ja. So with that trick in mind, the
solution to this problem will be exactly like the solution to the problem
where the gods actually say "yes" and "no"...for example, I could take my
previous solution to that problem:

>your first question should be to ask the first God "If I asked you 'is the
>second God the God of Knives', would you say 'yes'?" If the first God
>answers "yes", you know the God of Knives is either the first or the second
>God, so you can ask the third God, "If I asked you 'are you the God of
>Knights', would you say 'yes'?" and after that you can ask the third God
>"If I asked you 'is the first God the God of Knives', would you say 'yes'?"
>and this will be enough to tell you the identity of all three Gods. On the
>other hand, if the answer to your first question was "no", then you know
>the God of Knives is either the first or the third God, so you would ask
>the *second* God the same two subsequent questions as above.

...and simply replace every "yes" with "Ja" and every "no" with "Da":

>your first question should be to ask the first God "If I asked you 'is the
>second God the God of Knives', would you say 'Ja'?" If the first God
>answers "Ja", you know the God of Knives is either the first or the second
>God, so you can ask the third God, "If I asked you 'are you the God of
>Knights', would you say 'Ja'?" and after that you can ask the third God "If
>I asked you 'is the first God the God of Knives', would you say 'Ja'?" and
>this will be enough to tell you the identity of all three Gods. On the
>other hand, if the answer to your first question was "Da", then you know
>the God of Knives is either the first or the third God, so you would ask
>the *second* God the same two subsequent questions as above.

...keeping in mind, again, that if you ask a god "If I asked you X, would
you say 'Ja'?", then if he says "Ja" that means X must be true if the god
was a knight or a knave, and if he says "Da" X must be false if the god was
a knight or a knave.

Jesse
Received on Wed Oct 13 2004 - 01:01:46 PDT