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?

this problem is the same as the old 3 prisoners are set up each wearing a hat either white or black picked from a bag of 3 black and 2 white hats.
the first two prisoners can not guess the color of their hats but the third can based on the answers of the firt two. (since neither of the first two sages can tell that they too have a mark they continue to laugh while the third realizes this and knows that only if he too had a mark would the others be laughing. but since this is based on the assumption that the other two would stop if they knew they too were marked all three should stop laughing or the assumption is false or the third sage is wiser than the other two.

Posted by Ariel on 2004-02-28 23:56:12