Latest L&T Aptitude Question SOLUTION: there is 6561 no. of balls in a bag. out of which one is heavy ball. In how many minimum no. of weighing you can find the heavy ball?

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there is 6561 no. of balls in a bag. out of which one is heavy ball. In how many minimum no. of weighing you can find the heavy ball?

Asked In L&T apeksha (8 years ago)

Solved sonal Read Solution (5)

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Ahamad Husain  (7 years ago)

Ans: 8

1: Distribute all the balls into 3 group. Each group having 2187 balls.From these three group we can find one group which has heavy ball in one weighing.

2:Now distribute 2187 balls into three group.Each having 729 balls.And do the same, find one group which has heavy ball in one weighing.

Repeat this process .......And last we will have 3 balls,and we can find heavy ball in these three in one weighing.

6561-> 2178 , 2187 , 2187 one way
2187-> 729 , 729 , 729 one way
729 -> 243 , 243 , 243 one way
243 -> 81 , 81 , 81 one way
81 -> 37 , 27 , 27 one way
27 -> 9 , 9 , 9 one way
9 -> 3 , 3 , 3 one way
3 -> 1 , 1 , 1 one way
-----------------
8 ways

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Navnit Dhyani  (8 years ago)

NOT MY SOLUTION I HAVE GOOGLED AND FOUND THIS ONE GRT EXPLANATION !!!

Take two balls randomly. If you are lucky, they will weigh different. The ball with the larger weight is the one you are looking for. The minimum number of times you need, is 1.

If you are looking for a sureshot method, divide the number of balls by the smallest prime divisor possible, here 3. For 6561 balls, you need to divide into groups of 3, then identify the heaviest group, and then further that heaviest group you will continue dividing until you come to 3 balls, then finally in 2 steps you will get the required ball. This means you need

3 ^ x = 6561 , where x will be your answer. Here 8.

However, as this is a sureshot method, this will be the largest number of weighings you'll need to do: the smallest number of weighing being 1. ( For the lucky ones :p )

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Puja Rani  (8 years ago)

6561=6560+1, now 6560 balls can be divided into 8 groups i.e. 820 balls each .when all group of ball will be weighed gives same weight except the one group of balls which will be having the heavy ball.
so minimum 8 weighs has to be done.

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sonal  (8 years ago) Best Solution

answer is 8 heavy ball

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yogi  (6 years ago)

Divide 6561 in 3 parts..2187 of each
Keep 2 of parts in weight machine...Take the heavy part n again divide in 3 parts
If they are eual then take the 3rd part..

2187>729>243>81>27>9>3>1

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