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

From: Bruno Marchal <marchal.domain.name.hidden>
Date: Wed, 13 Oct 2004 16:56:51 +0200

At 00:57 13/10/04 -0400, Jesse Mazer wrote:

>Nice work, Eric!

Absolutely. I don't really need to add a thing, although
when I got the time I will compare Eric's solution with Boolos' one
(but I think they are quite the same).
It looks Eric solved what Boolos called "The Hardest Logical Puzzle Ever" ;-)

Bruno

============
>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:
>
>>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":
>
>>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
>

http://iridia.ulb.ac.be/~marchal/
Received on Wed Oct 13 2004 - 10:47:39 PDT

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