The rock will suffice in as few as four pieces(!) That's right- only four. The trick in solving the puzzle is realizing that rock framents can be placed on either plate, coupled with what you're trying to weigh. If you have, say, a one pound chunk and a three pound chunk, you can weigh a two pound item. Simply weigh the item AND the one pound rock against the three pounder. If they balance, it's two pounds. Having established this, the next problem is deciding on the rock sizes which allow all integer combinations.