**Abstracts to the papers that appeared in Journal of Recreational Mathematics 37(1)**

**Simple – But Little Known – Methods of Generating Pythagorean Triples**

Owen O’Shea

Ireland

owenoshea4@eircom.net

**Abstract**

In this paper,
the special form of Pythagorean triples (a, b and c where a*a + b * b = c*c)
and

the hypotenuse is one greater than the longest leg is examined. A pattern
emerges for the

generating of such triples that involves the use of
triangular numbers.

**abc – Triples and Their Statistical Distribution**

Myriam Le Boulicaut and Bernard Haussy

France

myriam.leboulicaut@reseau.eseo.fr

bernard.haussy@eseo.fr

**Abstract**

This article
describes two new methods for finding abc-triples as well as statistical
considerations on the distribution of the different values of α found by the
algorithms which were programmed. α represents the quality of a triple; the
higher the quality, the better the triple. A beginning search for abc-triples
with low values of α will also be introduced.

**On a Conjecture of Dey and De**

Robert J. MacDawson

Saint Mary’s University

rdawson@stmarys.ca

**Abstract**

In Volume 36 of Journal
of Recreational Mathematics, Dey and De conjecture that any two squares of
primes, each ending (when expressed in decimal notation) in 1, differ by a
multiple of 120; and that any two squares of primes, each ending in 9, differ
by a multiple of 40. In this note, we prove this conjecture, replacing
primality with a weaker condition. A related result for fourth powers is
also given.

**When is the Honeymoon Over for Baseball’s New Stadiums?**

Mark B. Whelan and Paul M. Sommers

Middlebury College

**Abstract**

For the twelve newly-built Major League Baseball
stadiums opened between 2000 and 2009, the authors compare average home
attendance during the last year in the old stadium to the average home
attendance the first, second, and third years in the new stadium. For ten of the teams, the average home
attendance in the opening year was significantly higher than the year
before. Nine of these ten
teams did

*not*enjoy a significantly higher attendance increase in their second year. And in only three of the nine cases was the average attendance higher in the third year than the year before the new stadium opened.**Rezaei Method for Construction of Magic Squares of All Even Orders**

Saeed Rezaei Toroghi

Iran

**Abstract**

An elementary magic square is a square matrix in which
every row, column and diagonal sums to a magic constant and in which the
elements are consecutive integers starting from 1. In order to construct such
squares, different methods have been devised for every type of magic square based
on their number of rows or columns. The problems was that there has not been a
universal algorithm to solve all magic squares with an even number of rows or
columns. Previous methods have provided different methods for magic squares
with a doubly even and singly even number of rows or columns. Here, a universal
algorithm is provided to construct all magic squares with an even number of
rows and columns.

**A Squirtgun Battle**

Stephen Portnoy

University of Illinois at Urbana-Champaign

**Abstract**

In his book, Mathematical Puzzles: a
Connoisseur's Collection, Peter Winkler attributes the following problem to the
Sixth All Soviet Union Mathematics Competition in Voronezh, 1966: `"An odd
number of soldiers are stationed in a field, in such a way that all pairwise
distances are distinct. Each soldier is told to keep an eye on the nearest
other soldier. Prove that at least one soldier is not being
watched." In Allan Gottlieb's ``Puzzle Corner'' (in Technology
Review, 2008), Jerry Grossman changes `"soldiers" to
"children with squirtguns" (again at distinct distances and shooting
at the nearest other child) and adds the problem to show that if n is
even then there are configurations of children where all get wet. In the
course of solving these problems, the following generalization seemed
intriguing and appears to be new: Given n children, what is the greatest
number of children than can remain dry? A special case of the problem is to
consider the two nearest children (A and B) and to ask for the largest number
of other children that can be added so than only A and B get wet. For the
special case, it turns out that a maximum of 7 dry children can be added. It is
not too difficult to use this result to solve the general problem for n
children.

**Amidakuji and Games**

Steven T. Dougherty and Jennifer Franko Vasquez

**Abstract**

We describe two games
based on Japanese ladders. The games are related to finding the minimum
number of a certain type of transpositions to describe a given
permutation. The mathematics of both games is explored.

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