Timothy goes to the island of knights and liars searching for gold. On the way,he meets a native.

What one question could Timothy ask the native to find out if there is gold on the island?

(In reply to re: A Different Solution by Charlie)

The point of these problems is how many times you negate the original question (if the person is a liar). In this case, the original question would be, "Is there gold on this island?" If you ask that question to a liar, he will answer oppositely, and a knight will answer truthfully, leaving you with no conclusion.
If you ask, as I first posed, "Would you say that there is gold on this island?" the person's answer to the first question (implicitly, "Is there gold on this island?") will be negated if the person is a liar, and then negated again ("Would you say.."), so that a liar is forced to give a truthful answer. A knight, of course, will give you the correct answer regardless. So, there needs to be an even number of questions implicitly asked.

In Lewis's solution, suppose, as you did, the person is a liar and there is gold on the island. Then, if asked, the person would say that there was no gold. If a knight were asked about this, he would say the same, that the person would say there is no gold. But if you ask the liar about the knight's response, he will lie about that and answer yes (..a knight would say that I would say that there is gold on this island). Again, for a knight, the answers to each intermediate question will be the same. This case poses four questions, and makes for a quadruple negative in the case of the liar. I think, Charlie, that you missed "would a knight say that you would say...," thus making the solution messy, but valid.

In the version you suggested, "Would the opposite kind of person say that there's gold on the island?" is pretty much equivalent to "Would you say that there's gold on the island?" In the latter case, you might as well as "Would the same kind of person say that there's gold on the island?" in which any person of the same type, not necessarily the one you are talking to, would give the same answer. When you look at it that way, it's easy to see that the version you suggested is merely the opposite of the other, and that is why it yields the opposite answer. In either case, there are still only two questions being asked; in Lewis's solution, there are four.

Posted by DJ on 2003-05-29 17:59:05