There 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 ?Options2042414878

To find the heavy ball among 6561 balls using a balance scale, we can use a strategy that minimizes the number of weighings. The key is to divide the balls into groups and use the balance scale to eliminate groups of balls that do not contain the heavy ball.

1. Divide the balls into 3 groups: Since we have 6561 balls, we can divide them into 3 groups of 2187 balls each.
2. First weighing: Weigh two of the groups (2187 balls each) against each other.
   • If they balance, the heavy ball is in the third group (2187 balls).
   • If they do not balance, the heavier side contains the heavy ball (2187 balls).
3. Repeat the process: Take the group that contains the heavy ball (2187 balls) and divide it into 3 groups of 729 balls each.
4. Second weighing: Weigh two of the groups (729 balls each) against each other.
   • If they balance, the heavy ball is in the third group (729 balls).
   • If they do not balance, the heavier side contains the heavy ball (729 balls).
5. Continue this process: Each time, divide the group that contains the heavy ball into 3 smaller groups and weigh two of them against each other.

The number of weighings required can be determined by the number of times we can divide 6561 by 3 until we are left with 1 ball.

• 6561 / 3 = 2187 (1st weighing)
• 2187 / 3 = 729 (2nd weighing)
• 729 / 3 = 243 (3rd weighing)
• 243 / 3 = 81 (4th weighing)
• 81 / 3 = 27 (5th weighing)
• 27 / 3 = 9 (6th weighing)
• 9 / 3 = 3 (7th weighing)
• 3 / 3 = 1 (8th weighing)

Therefore, the minimum number of times the balls have to be weighed to find the heavy ball is 8.

So, the correct option is 8.