MathDB

Define a size-

n

tromino to be the shape you get when you remove one quadrant from a

2n \times 2n

square. In the figure below, a size-

1

tromino is on the left and a size-

2

tromino is on the right. http://i.imgur.com/2065v7Y.png We say that a shape can be tiled with size-

1

trominos if we can cover the entire area of the shape—and no excess area—with non-overlapping size-

1

trominos. For example, a

23

rectangle can be tiled with size-

1

trominos as shown below, but a

33

square cannot be tiled with size-

1

trominos. http://i.imgur.com/UBPeeRw.png
a) Can a size-

5

tromino be tiled by size-

1

trominos?
b) Can a size-

2013

tromino be tiled by size-

1

trominos? Justify your answers.

Problem Statement