IMO Shortlist 1969 problem 11


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2. travnja 2012.
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(BUL 5) Let Z be a set of points in the plane. Suppose that there exists a pair of points that cannot be joined by a polygonal line not passing through any point of Z. Let us call such a pair of points unjoinable. Prove that for each real r > 0 there exists an unjoinable pair of points separated by distance r.
Izvor: Međunarodna matematička olimpijada, shortlist 1969