A miller sells flour and uses a conventional beam weigher. In the two scales bowls are weights and flour. The miller wants to accelerate the weighing and therefore only use as few weights as possible. He goes to the blacksmith and gives the following order:
"I would like to be able to weigh any integer mass between 1 and 13 kilograms with as few weights as possible, always with only one weighing." Can you make such weights for me? "
The blacksmith is happy about every job and immediately agrees. But then he comes pondering. How should he fulfill the order of the miller? After all, he has an idea - and the weights are ready the next morning.
How many are and how heavy are they?
