sum of digit

[kinu]

Let \(S = \left\{20,21,22,23,.....210\right\}\).Consider all positive differences of elements of \(S\).

If \(M\) is the Sum of all these differences,find the Sum of the digits of \(M\)

[Sobolev]

The difference between elements of S can be any number between 1 and 189. Computing explicitly their sum, M, and addind up the digits of M, we get 27.