Minimum Number of Weights

A wholesale merchant came to me with this problem.
Every day in his business he has to weigh amounts from 1 pound to 121 pounds, to the nearest pound.


To do this, what is the minimum number of weights he needs and how heavy should each weight be?

Solution:

Hopefully, 5 weights will be needed which are 1, 3, 9, 27, and 81 pounds.

Let’s see the solution :

1 = +1
2 = +3–1
3 = +3
4 = +3+1
5 = +9–3–1
6 = +9–3

41 = +81–27–9–3–1

121 = +81+27+9+3+1