Rectangle is partitioned into finitely many small rectangles
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October 31, 2010
geometryrectanglecombinatorics unsolvedcombinatorics
Problem Statement
A rectangle is partitioned into finitely many small rectangles. We call a point a cross point if it belongs to four different small rectangles. We call a segment on the obtained diagram maximal if there is no other segment containing it. Show that the number of maximal segments plus the number of cross points is more than the number of small rectangles.