IMO Shortlist 1971 problem 2
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

.
%V0
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 $A$.
Source: Međunarodna matematička olimpijada, shortlist 1971