Suppose you have N numbers, A1 .. An, you calculate all sums of 2, e.g A1 + A2, A1 + A3 etc., and name them S12, S13 etc., so you end up with n * (n - 1) / 2
sums,
My question is, given all these sub sums, how can I recover those N numbers,
If I have only 3 numbers, that's easy,
A1 = (S12 + S13 + S23) / 2 - S23 A3 = (S12 + S13 + S23) / 2 - S12 A2 = (S12 + S13 + S23) / 2 - S13
But when it comes more than 3 numbers, is there a more general formula that would work ? It looks like solving some complexed equation with linear algebra, but I'm not sure