A set of five numbers are added in all 10 possible pairs like in some of the Pumpkins puzzles.

When sorted the middle six sums are 47, 48, 50, 51, 52, and 54. The two largest sums and two smallest sums are not given, similar to Permuted Sums.

What are the possible sets of the five original numbers?

(In reply to Another possibility by Steve Herman)

In addition to 0.5, couldn't you have pairs of numbers ending with e.g. (0.1,0.9), (0.2,0.8), etc. The 0.5 numbers are special in that they don't have to add in predetermined pairs in order to make the central six integers.  Using a mix of 0.5 numbers and other pairs types makes the possibilities to search much larger, perhaps. 

Posted by Steven Lord on 2020-12-23 09:50:49