2015/018) 9 balls problem

Of nine similar balls, Eight of them weigh the same. How can you find the ball that is different by using a balance and only three weighing?

Solution

Take 2 sets of 3 balls each. If they are of same weight then the 3^rd set of balls say (1),(2),(3) contain the different ball.  Now weigh (1) and (2). If they are same then 3 is the different ball. If they are different say (1) is heavier then weigh (1) and (3), if they are different the (1) is different ball.  If they are same then (2) is the different ball.

Now say 1^st set is heavier.

We compare the 1^st set and 3^rd set. If 1^st one is heavier then this contains the heavy ball. Compare 2 balls of 1^st set and if they are of same weight then 3^rd ball is different and if not same then heavier ball is different.  If the 2 are same. Then 2^nd set contains the lighter ball. Compare 2 balls of second set and if they are of same weight then 3^rd ball is different and if not same then lighter ball is different