On a hot summer day, tired by long discussions, three wise sages were slumbering inthe shade of a tree. A prankster was walking by, and couldn't pass up such an opportunity. He took a piece of charcoal, and put a black spot in the middle of each sage's forhead, careful not to wake them.
When the men did wake, they looked at each other, saw the black marks and began laughing. Each one thought that his two friends had the mark, while his own forhead was clean.
Suddenly, one of them stopped laughing, having realized that his forhead must be dirty as well. How did he arrive at this conclusion?
Let us denote the sages as A, B and C and in particular, let us assume without loss of generality that the Sage A stopped laughing.
His reasoning is as follows:
If Sage A's forehead is clean then Sage B must be laughing at Sage C whose forehead is dirty. In which case, Sage C would notice that Sage B is laughing and if Sage A's forehead was clean, then Sage B would immediately conclude that his (Sage B's) forehead was dirty, and would stop laughing.
Since, Sage B did not stop laughing, it follows that he must be laughing at Sage A, whose forehead was dirty.
Consequently, Sage A concluded that his forehead was dirty, and stopped laughing.