9. In order to answer this question it will be helpful to identify the wise men
as A, B and C.  Let's say person A got the right answer.  Here's
what person A did:

Person A saw that B and C both had dots.  A put himself in B's
situation.  Assuming A did not have a dot, then B would see one dot on C
and none on A.  Person B would then think, "if I had no dot, then C would
see no dots and know that C had the only dot, and C would be able to answer
immediately.  However, since C does not answer, I must have a dot."
However, A sees that B doesn't answer, which means A must also have a dot,
so A goes to the king and declares victory.