Select the correct answerThere are 6561 balls are there out of them 1 is heavy. Find the minimum number of times the balls have to be weighted for finding out the heavy ball ?Options2414878204

The answer is 8.

This is a classic problem of dividing and conquering. The strategy is to divide the balls into 3 groups of equal size and then compare the weights of two of these groups.

Here's the step-by-step process:

1. Divide the 6561 balls into 3 groups of 2187 balls each.
2. Weigh two groups. If they balance, the heavy ball is in the third group. If they don't balance, the heavy ball is in the heavier group. This is the first weighing.
3. Now, you have 2187 balls left. Repeat the process: divide them into 3 groups of 729 balls each and weigh two groups. This is the second weighing.
4. Repeat the process with 729 balls, then 243 balls, then 81 balls, then 27 balls, then 9 balls, then 3 balls. These are the third, fourth, fifth, sixth, seventh, and eighth weighings.
5. Finally, you have 3 balls left. Weigh two of them. If they balance, the heavy ball is the third one. If they don't balance, the heavy ball is the heavier one. This is the ninth weighing.

However, the ninth weighing is not necessary if you stop at 3 balls in the eighth step and directly identify the heavier one. So, the minimum number of times the balls have to be weighed to find out the heavy ball is 8.