A shopkeeper called on Quiz Master Shop Towers asking for our advice. She needs to be able to weigh every weight from one kilogram up to 121 kilograms, but only needs to weigh whole numbers of kilograms - that is, integer values only.
Obviously, she wanted to be able to buy the smallest number of weights in order to achieve this, as these weights are quite expensive.
So, how many weights of what values did we advise that she bought?
Assuming that she could place the weights on both sides of her weighing scales, the weights have to be powers of three - that is, 1, 3, 9, 27 and 81 kilograms.