04/14/11          MATHEMATICS DEPARTMENT, FERRIS STATE UNIVERSITY

MATH COLLOQUIUM, THURSDAY, APRIL 14, 11:00 AM, STARR 138

SPEAKER:    James Howard, Associate Professor,

Department of Mathematics, Ferris State University

# TITLE: Covering Rectangular Regions with Brick Pavers

When constructing a rectangular brick patio, walkway or driveway, it is desirable that there be no straight line that separates the rectangular region without cutting through at least one brick.  This presentation will discuss what rectangular regions can and cannot be covered in such a desirable way using only whole bricks.  I will also present a way to expand any such rectangular region.   By a “covering” we mean that the entire region is covered except for the cracks between bricks which are often filled with sand.  The problem can be stated as follows:

Suppose we have an mxn rectangular region completely covered by 1x2 brick pavers.  Let a proper covering be one in which every straight line through the interior of the rectangle cuts through at least one brick.  What rectangular regions can and cannot be properly covered?  If we have exactly one 1x1 brick paver, what additional rectangular regions can be properly covered?

Those who are interested might want to look at the 6x6 case before attending the talk, but it’s certainly not necessary.  The 6x6 case was one of Mike Dekker’s problems of the week.

REFRESHMENTS:  11:00 AM,  STARR 138