A Pre-RMO question! -16

Algebra Level 3

If a>b>c>da>b>c>d are the only elements of a set, and the pairwise sum (taken 22 at a time) of distinct elements of the set in no particular order are 200,185,211,222,x200,185,211,222,x and yy. Find the sum of the digits of the greatest possible value of x+yx+y.

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