Thursday, April 28, 2016

Abstracts to the papers that appeared in Journal of Recreational Mathematics 36(2)

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
Charles Ashbacher

 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
University of South Wales

 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

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

 Alien Tiles is an online puzzle game invented by Dr. Cliff Pickover and can be found at 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

 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

 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

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

 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

 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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