04/14/11 MATHEMATICS
DEPARTMENT, FERRIS STATE UNIVERSITY

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

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**SPEAKER: **James Howard,** **Associate Professor,

Department of Mathematics, Ferris State University** **

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# TITLE:
Covering
Rectangular Regions with Brick Pavers

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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

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### Please visit Math Colloquium website at

http://www.ferris.edu/htmls/colleges/artsands/Math/MATH_COLLOQUIUM/ColloquiumWeb/index.html

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