olymmath

NMC 1994 Problem 2

    We call a finite plane set SS consisting of points with integer coefficients a twoneighbour 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?

    Dataset text NuminaMath olympiads. Quoted with source.

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