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Special partition of a rectangle in smaller rectangles.

Source: ISL 2007, C3 /

March 20, 2008
geometryrectanglecombinatoricsdissectionIMO Shortlist

Problem Statement

A rectangle D D is partitioned in several (≥2 \ge2) rectangles with sides parallel to those of D D. Given that any line parallel to one of the sides of D D, and having common points with the interior of D D, also has common interior points with the interior of at least one rectangle of the partition; prove that there is at least one rectangle of the partition having no common points with D D's boundary.
Author: Kei Irie, Japan
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