Solution #92: A Weighty Problem I
If the weights can be placed in either of the scale pans,
then you can solve the problem with weights of 1, 3, 9, and 27 pounds only.
With that combination any weight from 1 to 40 pounds can be measured.
If the weights can be placed in one scale pan only, then you need the weights
1, 2, 4, 8, 16, and 32 pounds, which enables you to measure any weight up to 63
pounds. This latter solution is really an example of counting with a binary
number system where any number can be expressed as the sum of 2 raised to
various powers. For example, 63 expressed in binary form is 111111.
Source: Sloane, Paul
Categories: Reasoning, Number sense, Bases