IMO 2007 Shortlist C2

A unit square is dissected into n > 1 rectangles such that their sides are parallel to the sides of the square. Any line...

IMO 2007 Shortlist C2

Category: Combinatorics

Problem

A unit square is dissected into n > 1 rectangles such that their sides are parallel to the sides of the square. Any line, parallel to a side of the square and intersecting its interior, also intersects the interior of some rectangle. Prove that in this dissection, there exists a rectangle having no point on the boundary of the square. (Japan)