Pre-Algebra Word Problem - PLEASE HELP

I have the hardest word problem I have ever come across. It is called The Haybailer Problem here is how it goes....

**The Situation:**

You have five bales of hay.

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

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

**The Task:**

The initial task is to find out how much each bale 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.

Please Help Me!!! :confused: