Question 48
We call a finite plane set $S$ consisting of points with integer coefficients a two-neighbour set, if for each point $(p, q)$ of $S$ exactly two of the points $(p+1, q)$, $(p, q+1)$, $(p-1, q)$, $(p, q-1)$ belong to $S$. For which integers $n$ does there exist a two-neighbour set which contains exactly $n$ points?