Lets say we have the groups A B and C.We randomly weigh the groups A and B , now let us say they are equal so group C is the one with the different ball. The only thing to do then is to weigh group C with one of the equals.If we get unlucky and group A is heavier than B, we weigh group A and C... It's always 2 weighs that way!!!

A better solution could be to divide the balls into three groups of 4.Then you only need 2 weighs to find out which ball is the different one and whether it is Lighter or Heavier....

That's Right man