7*. There is a rectangular plate weighing 10 g. In what ways can it be cut into three parts, each weighing an integer number of grams, so that with their help, using scales, one could determine the weight of any object weighing 1, 2, ..., 10 g?
7. 1 g, 2 g, 7 g or 1 g, 3 g, 6 g. Hint. First consider all cases of determining the mass of an object weighing 9 g. (KvN, 1972, No. 1, p. 74.)