> 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.
