You have 12 billiard balls.
You have 12 billiard balls. To the naked eye, they all look identical, and in your hand, they all feel identical. One of the balls, however, is slightly heavier or slightly lighter than the others, but you don’t know which ball or whether it is heavier or lighter.
You do, however, have a balance scale. You can place any equal number of balls on each side of the scale, and the scale will tilt if one side differs in weight. (Note: There is no use in weighing different numbers of balls against each other — the weight difference is so slight that if the scale has more balls on one side, that side will always be heavier.) However, you can only use the scale three times.
How can you determine which ball is different, and whether it is heavier or lighter?