How many segments does a figure have?
Source: IMO Shortlist 1989, Problem 17, ILL 59
September 18, 2008
combinatoricsgraph theoryExtremal Graph TheoryIMO Shortlist
Problem Statement
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.