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

From: Hal Finney <hal.domain.name.hidden>
Date: Mon, 11 Oct 2004 09:01:28 -0700 (PDT)

> And here is another puzzle, which is not entirely
> unrelated with both the KK puzzles and the current probability
> discussion: I put three cards, two aces and a jack, on their
> face in a row. By using only one yes-no question and pointing
> one of the card, you must with certainty find one of the aces.
> I know where the cards are, and if you point on a ace, I will
> answer truthfully (like a knight), but if you point on the jack, I
> will answer completely randomly!
> How will you proceed? (The puzzle is one invented by Boolos,
> as a subpuzzle of a harder one by Smullyan & McCarthy.
> Cf Boolos' book "Logic, logic, and logic". According to
> Boolos, it illustrates something nice about the practical
> importance of the excluded middle principle. And this is
> a hint, perhaps.)

Although it is true that if you point at a Jack the answer doesn't give
you any information, you don't really need much info in that case as
you know that the other two cards are Aces. As long as you are going to
finally choose a card different than the one you point at, any mistaken
info you get from the Jack won't hurt you. You need to come up with
a question which will work when you are pointing at an Ace, and which
will lead to you choosing another card.

For example, point at the card at one end and ask "Is the card on the
other end an Ace?" If he says yes, choose that card on the other end,
and if he says no, choose the middle card. This of course works if you
are pointing at an Ace because he will tell the truth, and if you are
pointing at a Jack it will work because both other cards are Aces.

Hal Finney
Received on Mon Oct 11 2004 - 12:45:25 PDT