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two-neighbour set with lattice point

Source: Nordic Mathematical Contest 1994 #2

October 4, 2017
lattice pointscombinatorics

Problem Statement

We call a finite plane set SS consisting of points with integer coefficients a two-neighbour set, if for each point (p,q)(p, q) of SS exactly two of the points (p+1,q),(p,q+1),(p−1,q),(p,q−1)(p +1, q), (p, q +1), (p-1, q), (p, q-1) belong to SS. For which integers nn there exists a two-neighbour set which contains exactly nn points?
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