 
Summary: TILING RECTANGLES, CYLINDERS, AND MOBIUS
STRIPS
PETER G. ANDERSON
Abstract. We present a method for determining the number of ways
various twodimensional grids can be tiled using several small tile reper
toires.
1. Problem Background and Definitions
Figure 1. Tile sets for problems 1, 2, 3, and 4.
How many ways may we tile an m×n rectangular grid (i.e., graph paper)
using a pair of tile shapes from the repertoires show in Figure 1:
(1) Vertical dominoes and squares.
(2) Ltrimonoes and squares.
(3) Large and small squares.
(4) Vertical and horizontal dominoes.
In all cases here, the short dimensions are 1 and the long dimensions are
2. We can modify the problem by identifying the top and bottom edges to
form a cylinder. We can identify the top and bottom edges with orientation
reversal to form a Mobius strip. (Exception: our problem2, Ltrimonoes,
cannot participate in the tilings of nonorientable surfaces.)
2. Our Approach
