You have 5 bags of beans – they are very large, the kind the settlers took with them on their journey across the overland trail!!

For some reason instead of being weighed individually, they were weighed in all possible combinations of two: bags 1 and 2, bags 1 and 3, bags 1 and 4, bags 1 and 5, bags 2 and 3, bags 2 and 4, and so on.

The weights of each of the these combinations were written down and arranged in numerical order, without keeping track of which weight matched which pair of bags!! The weights in kilograms were 80,82,83,84,85,86,87,88,90, and 91.

Your Task

Your initial task is to find out how much each bag weighs. In particular, you should determine if there is more than one possible set of weights, and explain how you know. Once you are done looking for solutions, look back over the problem to see if you can find some easier or more efficient way to find the weights.