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 $A$.