Five pumpkins are weighed two at a time in all ten sets of two. The weights are recorded as 16, 18,19, 20, 21, 22, 23, 24, 26, and 27 pounds. All individual weights are also integers.

How much does each pumpkin weigh?

Dang! I was going to submit a problem like this. Oh, well.

I called the pumpkins A, B, C, D, and E. The smallest pair is A+B. The second smallest pair is A+C. The largest pair is D+E. The second largest pair is C+E. The sum of all ten pairs of weighings is 4*(A+B+C+D+E).

This gives us the following system of equations:

A+B=16

B+C=18

C+E=26

D+E=27

4*(A+B+C+D+E)=216

This is easily solved. A=7, B=9, C=11, D=12, E=15.