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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

  

Source: Ash, J. Marshall - Department of Mathematical Sciences, DePaul University

 

Collections: Mathematics