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The maximum of S for the subset σ [ILL 1971]

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January 1, 2011
combinatorics proposedcombinatorics

Problem Statement

Consider the set of grid points (m,n)(m,n) in the plane, m,nm,n integers. Let σ\sigma be a finite subset and define S(σ)=∑(m,n)∈σ(100−∣m∣−∣n∣)S(\sigma)=\sum_{(m,n)\in\sigma}(100-|m|-|n|) Find the maximum of SS, taken over the set of all such subsets σ\sigma.
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