IMO 1971 LL SWE41

Consider the set of grid points (m, n) in the plane, m, n inte-

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IMO 1971 LL SWE41

Origin: SWE

Problem

Consider the set of grid points (m, n) in the plane, m, n inte- gers. Let \sigma be a finite subset and define S(\sigma) =  (m,n)\in\sigma (100 −|m| −|n|). Find the maximum of S, taken over the set of all such subsets \sigma.