Start by putting nine marbles on each side of the scales. If they balance, the heavier marble is one of the nine that have stayed off the balance. Otherwise, it’s obviously on the side that tips down. Discard the 18 marbles that you now know all weigh the same, and then repeat the process with the remaining nine, putting three marbles on each side. After a third and final weighing with one marble on each side, the heavier marble is identified.