A wholesale merchant came to me one day and posed this problem. Every day in his business he has to weigh amounts from one pound to one hundred and twenty-one pounds, to the nearest pound. To do this, what is the minimum number of weights he needs and how heavy should each weight be?
The minimum number of weights required is five and these should weight 1, 3, 9, 27 and 81 pounds.
The merchant has to use a balance weighing scale to do the job. To weigh 2 pounds, he’ll have to put the 3 pound weight on one pan and 1 pound weight on the other pan. To weigh 5 pounds, he’ll have to put the 9 pound weight on one pan and 1 and 3 pound weights on the other pan.