You are given a box of nine balls. Eight are of the correct weight but one is too heavy. The only way you can weigh the balls is with a balance; i.e. you can weigh one set of balls against another. What is the minimum number of weighing operations you need to be sure of identifying the faulty ball?
Reveal Solution
You can do it in two weighings. Weigh any three against any other three. If one of these batches is heavier, it contains the heavy ball. If the two batches weigh the same, neither can contain the heavy ball and it is in the three not weighed. In either case we have a set of three balls containing the heavy one. Now weigh any two of these three. If one of these is heavier than the other, we’ve found the heavy ball: if they weigh the same, the heavy ball is the unweighed one. (How many weighings would be needed if we didn’t know whether the faulty ball was heavier or lighter than the others?)
