The maximum number of rectangular islands

Attila Máder, Géza Makay

In this paper we consider the combinatorial problem of rectangular islands by elementary means. The topic of islands and the methods for its investigation is suitable also for high school students, although some of the corresponding results are quite new. The arising questions need no advanced mathematical knowledge. Because most of the problems are of finitary type, experimental mathematics with computer support proves to be useful for the formulation of general conjectures related to the bounds of the number of islands in particular configurations.