Problem

Source: VIII International Festival of Young Mathematicians Sozopol 2017, Theme for 10-12 grade

Tags: combinatorics, dominoes, Tiling



We say that a polygon is rectangular when all of its angles are $90^\circ$ or $270^\circ$. Is it true that each rectangular polygon, which sides are with length equal to odd numbers only, can't be covered with 2x1 domino tiles?