How many solution sets would there be if......?

Question

There are 5 hippos & when weighed in pairs the weights were:
100, 200, 300, 400, 500, 600, 700, 800, 900, 1000lbs

Answer 1

I don't think there are any.

There are five hippos, labeled a, b, c, d, and e, from lightest to heaviest.

The pairs are ab, ac, ad, ae, bc, bd, be, cd, ce, and de. Every hippo got weighed four times.

Adding all the weights together, we get 5500 lbs. If we divide that by 4, we get the total weight of the hippos, 1375 lbs.

The lightest two hippos weight 100 lbs together. The heaviest two weigh 1000 lbs. together. 100 + 1000 = 1100, which means the middle hippo weighs 1375-1100 = 275 lbs.

a + b = 100, so a + c = 200. But c alone = 275.

And we have a contradiction that we can't resolve.