Problem 5 Solution

The key to this problem is that they are wise men. Assume all three know that all three are wise. Also, every man can see the other two but can't see their own forehead. If you still need the solution scroll down.

Each wise man initially assumes that he isn't painted and can plainly see the other two are.

However, if only two were painted it would not take long for either of the painted wise men to realize they were painted. For either of the painted ones would see the other painted one laughing and know he is laughing at them, since the other guy is not painted. In other words if you saw a wise man laughing and the other guy wasn't he painted he must be laughing at you, thus you must be painted.

After a sufficient period of time if nobody stops laughing then it can no longer be assumed that you are not painted, thus you must be painted as well. When you realize this you stop laughing.

Michael Shackleford, A.S.A.