Prove that for every positive integer we can find a finite set of points in the plane, such that given any point of , there are exactly points in at unit distance from .
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Prove that for every positive integer $m$ we can find a finite set $S$ of points in the plane, such that given any point $A$ of $S$, there are exactly $m$ points in $S$ at unit distance from $A$.
Izvor: Međunarodna matematička olimpijada, shortlist 1971
Školjka 
we can find a finite set 
of points in the plane, such that given any point 
of