3. The seller has a balance scale. Help the seller come up with a set of 4 weights that can be used to weigh any whole number of kilograms from 1 to 12 on these scales. No more than two weights can be used for each weighing; weights can be placed on different pans of the scale.
Solution. For example, the following set of weights will do: 1 kg, 2 kg, 5 kg, and 10 kg. The table in the figure shows how to place the weights on the scales. (It is assumed that the item being weighed is on the left pan.)

Remark. The example provided is not the only one.

| Weight of the item | Left pan | Right pan |
| :---: | :---: | :---: |
| 1 |  | 1 |
| 2 |  | 2 |
| 3 | 1 | $1+2$ |
| 4 |  | 5 |
| 5 |  | 5 |
| 6 | 2 | $5+1$ |
| 7 | 1 | $5+2$ |
| 8 |  | 10 |
| 9 |  | 10 |
| 10 |  | 10 |
| 11 |  | $10+1$ |
| 12 |  | $10+2$ |