MathDB

An L-shaped region is formed by attaching two

2

5

rectangles to adjacent sides of a

2

2

square as shown below. [asy] size(6cm); draw((0,0)--(7,0)--(7,2)--(2,2)--(2,7)--(0,7)--cycle); real eps = 0.45; draw(box( (0,0), (eps,eps) )); draw(box( (7,0), (7-eps,eps) )); draw(box( (7,2), (7-eps,2-eps) )); draw(box( (0,7), (eps,7-eps) )); draw(box( (2,7), (2-eps,7-eps) )); label("

7

", (0,3.5), dir(180)); label("

7

", (3.5,0), dir(270)); label("

2

", (7,1), dir(0)); label("

5

", (4.5,2), dir(90)); label("

5

", (2,4.5), dir(0)); label("

2

", (1,7), dir(90)); [/asy] The resulting shape has an area of

24

square units. How many ways are there to tile this shape with

2

1

dominos (each of which may be placed horizontally or vertically)?

Problem Statement