There are 6561 balls. One of the balls is heavier than the others. You are provided with a two pan balance scale. Find the minimum number of weighings needed to identify the heavier ball correctly.
8 weighings are required to find out the heavy ball.
Divide the balls into 3 groups of 2187 balls each. Put 2 groups on the scale and determine which group is heavier. If both groups are equal in weight, the heavier ball is in the 3rd group.
Repeat the process by breaking the group with the heavier ball into 3 smaller groups of balls again. For the 2nd round, each group will have 729 (2187 / 3 ) balls each. This process has to be repeated 8 times.
1st weighing – 6561 balls are divided into 3 groups of 2187 balls each.
2nd weighing – 2187 balls are divided into 3 groups of 729 balls each.
3rd weighing – 729 balls are divided into 3 groups of 243 balls each.
4th weighing – 243 balls are divided into 3 groups of 81 balls each.
5th weighing – 81 balls are divided into 3 groups of 27 balls each.
6th weighing – 29 balls are divided into 3 groups of 9 balls each.
7th weighing – 9 balls are divided into 3 groups of 3 balls each.
8th weighing – 3 balls are divided into 3 groups of 1 ball each.