You have six balls - three red and three black. All the red balls weigh differently, i.e. one of them is heavy, the other medium, and the third light. Each red ball has a black twin of the same weight. A heavy and a light ball put together weigh as much as two medium balls.

What is the least number of weighings required on a balancing scale to determine which is which?

You can sort three balls (say, the red ones) in three weighings, so that would say six weighings is the maximum.

But, you could also consider this problem as equivalent to sorting 6 balls in order. For five potentially all different balls, you need seven weighings and that shows that you need to take into account the fact that you know that there are twin balls, and the relative weights.... more thinking is needed!

*Edited on ***July 7, 2006, 10:22 am**