...information.

The three wise men puzzle is as follows:

A certain king wishes to test his three wise men. He arranges them in a circle so that they can see and hear each other and tells them that he will put a white or black spot on each of their foreheads but that at least one spot will be white. In fact all three spots are white. He then repeatedly asks them, ``Do you know the color of your spot?'' What do they answer?

The solution is that they answer, ``No,'' the first two times the question is asked and answer ``Yes'' thereafter.

This is a variant form of the puzzle which avoids having wise men reason about how fast their colleagues reason.

Here is the Mr. S and Mr. P puzzle:

Two numbers m and n are chosen such that . Mr. S is told their sum and Mr. P is told their product. The following dialogue ensues:

Mr. P: I don't know the numbers.

Mr. S: I knew you didn't know. I don't know either.

Mr. P: Now I know the numbers.

Mr  S: Now I know them too.

In view of the above dialogue, what are the numbers?

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....''

Halpern and Lakemeyer in [HL95] show that the quantified version of Levesque's logic is incomplete, but this is a different complaint from the one we make here.

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