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

From: Eric Cavalcanti <eric.domain.name.hidden>
Date: Mon, 11 Oct 2004 17:42:16 +1000

> 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.)

Bruno,

That is a nice one. It seems on a first thought that
whatever question I decide to ask, if I point on the jack the
answer will be random, so that I can't gain perfect information.

I came up with a way out, but by making an assumption that
is not explicit in your statement - that I can make a question
which does not have an answer.

I could ask you: "Is the answer to this question no?"

In case I point to an ace, you cannot answer it. In case I point
to a jack, you answer randomly.

One other solution would be if I could ask a question about
other cards. I could then point to the first one and ask:
is any of the first two a jack? If you answer 'no' I know that
card 2 is an ace. If you answer yes I know that card 3 is an
ace.

Is any of these the book's solution?

Eric.
Received on Mon Oct 11 2004 - 03:43:03 PDT