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Three Weighings
We have 12 billiard balls (numbered from 1 to 12) and a pair of scales.
One of these balls is heavier than the other balls.
How can we find this ball with a maximum of 3 weighings?
We put 4 balls on each scale.
If both groups of 4 have the same weight, then the heavier ball is one of the 4 balls not on the scales.
If one group of 4 being weighed is heavier, then the heavier ball is in that heavier group.
Now put 2 balls from the heavier group on the scales to determine the heavier group of 2.
Finally put one ball on each scale to find the heaviest ball.