It has the feel of an ancient problem done right: a merchant, a balance scale, and the need for perfect precision. The beauty here is not in testing combinations one by one, but in discovering the system that makes them all work.
The merchant's weights
Riddle statement
A merchant wants to weigh any whole number of kilograms from 1 to 40 using only four weights.
He has a two-pan balance scale and may place weights on either side of the scale, including on the same side as the object being weighed.
What should the four weights be?