
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 singletray scale, not a twotray
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.)



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.)

