# How can you tell which of a group of 12 spheres is the lightest or heaviest using three times the balance with two scales?

## Answer

###### Wiki User

###### 03/27/2007

Unfortunately, the question is far too vague to answer. Do we assume that all 12 spheres are unique and have different weights? Are we to determine the lightest of the 12 or the heaviest -- or both? If all 12 spheres are of different weights, it would take numerous comparisons to isolate the lightest or heaviest ball. If, however, there are 11 identical spheres and one bogus sphere, we could then isolate the counterfeit orb in just three comparisons with just one scale! And we could determine whether it's lighter or heavier than the others!!! I have an elaborate proof of the restated problem, but it is rather complex and difficult to follow without a flowchart. I will post the text of the procedure here if anyone expresses an interest.