Find the box of defective balls

♠ Posted by GeekyFry in , at 9:48 AM

You have 10 boxes of golf balls (each ball weighing exactly 10 gm) with one box with defective balls (each one of the defective balls weigh 9 gm). You are given an electronic weighing machine.  How will find out which box has the defective balls? How many chances will you take to weigh?



Possible Solution:

If you are thinking along the lines of weighing one ball from each box in whichever fashion, believe me you are thinking in wrong direction. The answer is one. Yes ! Read on to find out how…
The trick here is to take different balls from different boxes. First you need to number each of the boxes from 1 to 10. Now take out 1 ball from box #1, 2 from box #2… 10 from box #10
Now we have total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
So total weight now should be 55 * 10 = 550 gms.
Now suppose box #7 had defective balls. So when you weigh the 55 balls together, the weight would be 7 * 1 = 7 gms less. i.e. 543 gm.
This way you can find out the right box with defective balls.
So if the weight is (550 – x) gms, x is the defective box #.

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