Riddle: 40 Pounds in the Balance
You are given a mystery ball and are told that it has a whole-number weight between 1 and 40 lbs (inclusive).
You are then given a balance scale are are allowed to pick four weights, each weighing any whole-number amount. You much 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?
Work your way up. How many weights do you need to measure a mystery ball of between 1 and 5 lbs? How about between 1 and 10 lbs?