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  Number and Math Play

Bags and Beads
Q You are given 5 bags. There are 10 beads in four of the bags. Each bead weighs 10 kilograms. The remaining bag also has 10 beads, but each bead in this bag weighs only 9 kilograms. All the bags and beads look identical.

Your assignment is to find out which bag has the lighter beads. 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? (We're not asking you to find the answer—we don't know that ourselves! But you can devise a strategy.)

A Label the bags from 1 to 5. Take 1 bead out of Bag 1, and label it 1. Take 2 beads out of Bag 2, and label them both with a 2. Take 3 beads out of Bag 3, and label each with a 3. Continue this pattern with Bags 4 and 5. Put these 15 beads on the tray of the scale.

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.)