题目描述

Merchants measured many commodities using weights and a two-pan balance. If you are using a limited set of weights, however, you can only measure certain quantities accurately. For example, suppose that you have only two weights: a $1$-ounce weight and a $3$-ounce weight. With these you can easily measure out $4$ ounces, as shown in Figure 1.

It is somewhat more interesting to discover that you can also measure out $2$ ounces by shifting the $1$-ounce weight to the other side, as shown in Figure 2.