If you have two identical balls , one heavier than the other , you can easily determine which is heavier by putting them on opposite pans of a balance scale . If there are four balls , all the same weight except for one heavier one , you can find the heavier one in two weighings.
Suppose you have nine identical balls, one of which is heavier than the eight others . What is the smallest number of weighings needed for positively identifying the odd ball ?
Two weighings will do the job Divide the nine balls into three sets of triplets. Weigh one triplet against another. If a pan goes down you know the heavy ball is among the three on that pan . Pick any two of these balls and weigh one against other . If one side goes down, you have found the odd ball in two weighings .
Suppose the two triplets balnce on the first weighing . You know then that the heavy ball is in the remaining triplet . As described above , the heavier ball of this triplet is easily identified by weighing any ball of the triplet against any other .