Sunday, September 14, 2014

The mystery ball and 40 kilogram in the Balance

 You are given a mystery ball and are told that it has a whole-number weight between 1 and 40 kilogram (inclusive).
 You are then given a balance scale  and you are allowed to pick four weights, each weighing any whole-number amount. You must choose these weights so that no matter what the mystery ball weighs, you will be able to determine its weight using just the balance scale and these four weights.
What weights should you choose?