IMO Shortlist 1989 problem 17


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2. travnja 2012.
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Given seven points in the plane, some of them are connected by segments such that:

(i) among any three of the given points, two are connected by a segment;
(ii) the number of segments is minimal.

How many segments does a figure satisfying (i) and (ii) have? Give an example of such a figure.
Izvor: Međunarodna matematička olimpijada, shortlist 1989