Talkin Sport

You are given 5 bags. There are 10 beads in each of the bags. In four of the bags, the beads each weigh 10 kilograms. In the remaining bag, each bead weighs only 9 kilograms. All the bags and beads look identical. You must find out which bag has the lighter beads. The problem is that all the bags look identical and all the beads look identical. You can use a scale, but it has to be a single-tray scale, not a two-tray balance scale. Also, you may use the scale only once. How can you find out which bag has the lighter beads?
Solution
If all 15 weighed 10 kilograms, the scale would register 150 kilograms. But since one or more of the beads weighs only 9 kilograms, the scale will register less than 150. Subtract the number on the scale from 150. Your answer will tell you the number of the bag with the lighter beads. (If the scale registers 148, it’s bag #2. If the scale registers 145, it’s bag #5.)
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