27 12 Identical Balls 
27 

12 Identical Balls 
12 Identical Balls
Am I missing something, but isn't the solution much easier? Divide the twelve balls into 2 groups of six and weigh them Discard the lightest set Divide the remaining balls into 2 groups of three and weigh them Discard the lightest set You now have three balls Take two of the three balls and weigh them If they are different weights, you have your answer. If they are the same weight, the ball you did't weigh is the heaviest one context 