Mathematics Problem Of the Week

Spring 2006

POW #4

Stairway to Heaven

Define a stair-diamond as the region obtained from four staircase shapes of the same height by gluing them together along the straight edges. For example, the stair-diamonds of size 1, 2, and 3 are:

A single domino covers 2 adjacent squares (sharing a common side). There are 2 domino tilings of the stair-diamond of size 1:

1. How many tilings are there of the size 2 stair-diamond?

2. How many tilings are there of the size 3 stair-diamond?

3. Can you find a general formula for the number of domino tilings of the stair-diamond of size n?

Due Friday, February 24^th Noon

Solutions should be submitted to Dr. R. Lock's mailbox in the Math office or sent via e-mail to rlock@stlawu.edu.