Abstracts to the papers that appeared in Journal of Recreational
Mathematics 36(2)
The Fourteen biLLies, A New Polynomial Puzzle Family
Paulus Gerdes, Maputo, Mozambique
paulus.gerdes@gmail.com
Charles Ashbacher
Abstract
The
fourteen biLLies are formed by putting two L-trominoes together. They provide a
new avenue for exploration and creation of shapes made by putting the biLLies
together. This paper introduces this set of polyominoes.
Sudoku Puzzles as Erasure Correcting Codes
Linzy Phillips
Stephanie Perkins
Paul Roach
Derek Smith
Derek Smith
University of South Wales
Abstract
In
2007, Soedarmadji and McEliece introduced a new class of erasure-correcting
codes based on Latin squares and Sudoku grids. This paper investigates the
merit of this proposal, and suggests an evaluation of other puzzles for the
same purposes.
Methods
for encoding and decoding for the Sudoku grid and for the smaller 6 x 6 Rodoku
grid are presented. Performance as erasure correcting codes is analyzed and
shown for this structure to be disappointing.
Analysis suggests that other puzzle based structures may perform better.
The Factorial Power
N. E. Myridis
Aristotle University of Thessaloniki,
Greece
Abstract
In this short paper a collection of
different forms of factorial functions are defined and the notational
representations are given.
A Group Theoretic Solution to the Alien Tiles Puzzle
Glenn C. Rhoads
Rutgers University
Abstract
Alien Tiles is an online puzzle game invented
by Dr. Cliff Pickover and can be found at http://www.alientiles.com/.
You are given a square board of tiles, each of which can be one of four colors
that are ordered in the cycle Red -> Green -> Purple -> Red. Clicking
on a tile rotates the color of every tile in that row and column to the next in
the sequence. The puzzle is to find a sequence of clicks that will convert the
board from the initial configuration to a desired one. This is a problem that
can be solved using the principle of group theory and that is what is done in
this paper.
Are First-Round NFL Draft
Picks Better Than Second-Round Picks?
Jeffrey S. Everson and Paul M. Sommers
Middlebury College
psommers@middlebury.edu
Abstract
National
Football League (NFL) fans believe that first-round draft picks are more
valuable than second-round picks and higher first-round picks are more valuable
than lower first-round picks. The
authors compare average “Approximate Value”
(a metric used to assess player worth at any position in any year) of
all first- and second-round draft picks between 2005 and 2008 in each of their
first two seasons in the NFL. The results
show that Round 1 picks outperform Round 2 picks in their rookie year as well
as in their second year as a pro. Yet,
there is no evidence that first-round
picks develop any faster into better players than second-round picks.
Remaining Integers
Joseph L. Yucas
Southern Illinois University
joeyucas@yahoo.com
joeyucas@yahoo.com
Abstract
A
self-working card trick leads to a recurrence. We investigate a general version
of this recurrence.
An Interview With Dr. Matrix and Richard Stein
Owen O’Shea
Ireland
owenoshea4@eircom.net
owenoshea4@eircom.net
Abstract
Dr. Irving Joshua Matrix was a literary character created by Martin Gardner
to serve as the proponent of pseudoscience and dubious mathematics and inject
an element of humor. This paper is a tribute by the author to Martin Gardner
shortly after his passing and contains a set of references to some of the
numeric curiosities regarding the dates of the birth and death of Gardner. As
the title suggests, the author uses Dr. Matrix to present these facts to the
world.
A Catalan Identity With an
Interesting Byproduct
Thomas Koshy
Angelo
DiDomenico
Framington State
University
Abstract
The well-known Catalan numbers C(n) are given
by C(n) = [1 / (n + 1)] * C(2n,n), where n ≥ 0 and C(2n,n) is the binomial
coefficient. We develop a Catalan identity and then extract an interesting
byproduct from it.
Alphametric Problems in Social
Psychology Research
Kevin Mullaney
United States
Naval Academy
Harold R. Carey
COLSA
International
Patrick R.
Laughlin
University of
Illinois at Urbana- Champaign
Abstract
While readers of “Journal of Recreational
Mathematics” know that alphametric problems are addictive and keep the mind
sharp, they may not be aware that alphametric problems have a distinguished
history in Social Psychology research. The paper opens with a few brief
historical references where alphametrics were used and then there is a summary
of recent work at the University of Illinois where alphametrics were used to
investigate the performance of small groups compared to that of individuals
working separately.
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