IMO Shortlist 1971 problem 2
Dodao/la:
arhiva2. travnja 2012. Prove that for every positive integer
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
we can find a finite set
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
of points in the plane, such that given any point
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
of
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
, there are exactly
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
points in
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
at unit distance from
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
.
%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 $A$.
Izvor: Međunarodna matematička olimpijada, shortlist 1971