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How could you find the box with 9 kgs balls with just 1 weighing?

+1 vote
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There are 10 identical boxes each containing 10 balls. One Of the box has all the balls of 9 kgs while rest of the boxes have balls of 10 kgs. You have an electronic weighing machine. How could you find the box with 9 kgs balls with just 1 weighing?

posted Dec 17, 2014 by Shashi Kant

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1 Answer

+3 votes
 
Best answer

For convenience sake, let’s name the boxes from 1 to 10. In order to solve this problem, you have to leverage the fact that you know exactly what each good ball is supposed to weigh and what each defective ball is supposed to weigh. Many of us instinctively will take one ball out of each box and try to find a way to make it work but the trick to take different number of balls from each box.

The number of balls you pick from each bag is equal to the box number. For example, pick 1 ball from box 1, 2 balls from box 2 and so on. In total you will have 55 balls. If all of the boxes have good balls, then the total weight of these balls would be 550KG.

If box 1 has defective balls, then the total weight should be 1gm less than expected (only one ball weighing 9 kg). If box 2 has defective balls, then the total weight should be 2KG less than expected (two balls weighing 9 kg). So once you weigh the set of chosen balls, find out the difference between the total weight and the expected weight. That number represents the box number which contains the defective balls.

answer Dec 17, 2014 by Cedric Grigory
Nicely explained



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