You are given a set of 10 numbers that represent all possible pairwise sums of certain five numbers.

Devise a strategy to find the original five numbers.

Provide a numerical example.

(In reply to

re: Corrected solution (spoiler) by Ady TZIDON)

Well, just to be clear, order the partial sums, with w1 the smallest and w10 the largest.

Let S = their sum divided by 4.

Then

a3 = S - w1 - w10

a5 = w9 - a3

a4 = w10 - a5

a1 = w2 - a3

a2 = w1 - a1

*Edited on ***August 1, 2018, 10:49 am**