Heavy ball

Puzzle Level :- Moderate

PUZZLE

       There are 8 identical looking metal balls. One of them is heavier than the other 7 balls.
You have simple mechanical balance to weigh balls.

What is the minimum number of times we have to use balance to find heavy ball

ANSWER

    2

SOLUTION

        Generally we think that, by keeping four balls in each side we can eliminate 4 balls 

and then two balls on each side and then one ball on each side to find heavy ball.

but here 3 iterations is needed to find heavier ball.

     We can improve this and find heavier ball in 2 iterations.

I am assigning numbers to each ball for easy explanation 

Total balls {1,2,3,4,5,6,7,8}

First take 3 , 3 balls in each side of balance and keep 2 balls aside

{1,2,3}(left side) -- {4,5,6}(right side)       {7,8}(kept aside)

CASE-1 

        If balance is equal on both sides  then either of {7,8} is heavy then in next iteration we can weigh and find which is heavier by keeping these balls on each side of balance.

CASE-2 

       if balance is heavier on left side{1,2,3} then one of these balls {1,2,3} is heavier

Then in next iteration take one one ball on both sides of balance and  keep one aside

{1}(left side) --{2}(right side)     {3}(kept aside)

if balance is equal then 3 is heavier 

if balance is lean left then 1 is heavier otherwise 2 is heavier

CASE-3 

       if balance is heavier on right side{4,5,6} then one of these balls {4,5,6} is heavier

Then in next iteration take one one ball on both sides of balance and  keep one aside

{4}(left side) --{5}(right side)     {6}(kept aside)

if balance is equal then 6 is heavier 

if balance is lean left then 4 is heavier otherwise 5 is heavier

So in two iterations we can find the heavier ball.

Same logic can be applied even for 9 balls OR  one ball is lighter instead of heavier.

We can follow similar logic for this kind of simple balance problems

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