Required Mathematical Intelligence

Chapter 3 Weights
When weighing the weight of an object with a balance, weights are always indispensable.Most people can think of setting weights by one gram, two grams, four grams, eight grams..., but this method requires too many weights, and it can be used less in practice.Please re-design a scheme, only four weights can be used to weigh the weight of all integer grams of objects from one to forty grams with a balance.

[Answer: As long as you can imagine that weights can be placed at both ends of the balance, the problem is not difficult.The required weights are: 1, 3, 9, and 27 grams in four specifications.For example: when the weight of 1 gram is added to the object to be weighed and the weight of 9 grams is equal, the weight of the object to be weighed is 8 grams, which is equal to the difference between the two weights.This scheme is feasible in theory, but it is not used in practice because it is cumbersome to apply (requires subtraction). ]
(End of this chapter)