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

[Jesse Mazer]

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