Integre Technical Publishing Co., Inc. Mathematics Magazine 77:1 October 17, 2003 1:14 p.m. notes.tex page 46 Tiling Deficient Rectangles with Trominoes Summary: Integre Technical Publishing Co., Inc. Mathematics Magazine 77:1 October 17, 2003 1:14 p.m. notes.tex page 46 N O T E S Tiling Deficient Rectangles with Trominoes J. MARSHALL ASH DePaul University Chicago, IL 60614 mash@math.depaul.edu SOLOMON W. GOLOMB Communication Sciences Institute University of Southern California Los Angeles, CA 90089-2565 A tromino (rhymes with domino) is a shape made up of three 1 × 1 squares assembled as shown. Figure 1 A tromino We will classify a variety of nearly rectangular shapes into those that can be tiled by trominoes and those that cannot. From now on we will simply say tiled to mean tiled by trominoes. We will consider shapes that are integer-dimensioned rectangles with each dimension at least 2, and with one or two 1 × 1 squares removed. If one square is removed, call the resultant shape a deficient rectangle. If the removed square was a corner square, call the resulting deficient rectangle a dog-eared rectangle. The Collections: Mathematics