Problem

Source: 2019 Saudi Arabia JBMO Training Test 7 p2

Tags: Tiling, rectangle, tiles, combinatorics



We call a tiling of an $m\times$ n rectangle with arabos (see figure below) regular if there is no sub-rectangle which is tiled with arabos. Prove that if for some $m$ and $n$ there exists a regular tiling of the $m\times n$ rectangle then there exists a regular tiling also for the $2m \times 2n$ rectangle.