There are 6561 balls out of them 1 is heavy. Find the minimum number of times the balls have to be weighed for finding out the heavy ball.Correct answer is '8'. Can you explain this answer?

Question

Answer

Divide the balls into 3 groups - each of size 6561/3 = 2187.

Comparing weight of two groups. Now take the heaviest - and sub-divide into 3 more groups 2187/3 = 729

Take the heaviest - divide into 3 - 729/3 = 243.

Similarly continue weighing the group of balls.

Take the heaviest - divide into 3 - 243/3 = 81.

Take the heaviest - divide into 3 - 81/3 = 27.

Take the heaviest - divide into 3 - 27/3 = 9

Take the heaviest - divide into 3 - 9/3 = 3.

Take the heaviest - divide into 3 - 3/3 = 1.

So, minimum number of weights = 8

Answer

Problem: There are 6561 balls out of them 1 is heavy. Find the minimum number of times the balls have to be weighed for finding out the heavy ball.

Solution:
To find the heavy ball, we can use the concept of binary search. We can divide the balls into 3 groups and weigh two of them. Based on the result, we can determine which group has the heavy ball. We can repeat this process until we find the heavy ball.

Step 1: Divide the balls into 3 groups of equal size - 2187 each.

Step 2: Weigh any two of the groups against each other. There are three possible outcomes:
- If the weight is equal, then the heavy ball is in the remaining group of 2187 balls.
- If the weight is not equal, then the heavy ball is in the group that weighs more.

Step 3: Repeat step 1 and step 2 with the group that contains the heavy ball until we find the heavy ball.

Number of weighings: We need to repeat step 1 and step 2 a total of 8 times to find the heavy ball. This is because 3^8 = 6561, which is the total number of balls. Therefore, the minimum number of times the balls have to be weighed to find the heavy ball is 8.

Conclusion: The heavy ball can be found by dividing the balls into 3 groups and weighing two of them. We need to repeat this process a total of 8 times to find the heavy ball.

Answer

Divide the balls into 3 groups - each of size 6561/3 = 2187.

Comparing weight of two groups. Now take the heaviest - and sub-divide into 3 more groups 2187/3 = 729

Take the heaviest - divide into 3 - 729/3 = 243.

Similarly continue weighing the group of balls.

Take the heaviest - divide into 3 - 243/3 = 81.

Take the heaviest - divide into 3 - 81/3 = 27.

Take the heaviest - divide into 3 - 27/3 = 9

Take the heaviest - divide into 3 - 9/3 = 3.

Take the heaviest - divide into 3 - 3/3 = 1.

So, minimum number of weights = 8

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