Question: You have 10 boxes of 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 and only one chance at it. How will find out which box has the defective balls?
Answer: Name the boxes from 1 to 10. Pick from balls from each box such that number of balls 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 550 gm.
If box 1 has defective balls, then the total weight should be 1 gm less than expected (only one ball weighing 9 gm). If box 2 has defective balls, then the total weight should be 2 gm less than expected (two balls weighing 9 gm). 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.