Twelve golf balls appear identical, but eleven weigh exactly the same while one ball is either lighter or heavier than the others. Determine the “odd ball” and whether it is lighter or heavier than the others in just three weighings of the balls on a balance scale.

Puzzle problems like this abound and experience has shown that they are quite attractive to students. But this is particularly true in the present case since a solution exists that appears little short of magic. This problem provides excellent motivation for developing reasoning and communication skills. It also provides strong motivation for learning arithmetic in a base other than base 10 and for developing skill at doing mental arithmetic quickly, easily, and accurately.