**Abstracts to the papers that appeared in Journal of Recreational Mathematics 37(4)**

**Mathematics and Geography: The Changing Geographic Midpoint of Baseball’s All-Stars**

Paul M. Sommers

Middlebury College

psommers@middlebury.edu

**Abstract**

The author uses
information on every major leaguer who has ever been selected to baseball’s
All-Star game between 1933 and 2009 to find how the geographic midpoint
of their birthplaces has changed over this 77-year period. Players are divided by league (American and
National) into pitchers and non-pitchers for each of the eight decades. Simple bilinear regression of the latitude
(or longitude of the geographic midpoint) and year shows that the influx of
players from Latin America and more recently Asia has moved the geographic
midpoint for all players from St. Louis, Missouri (in the 1930s) to Pittsboro,
Mississippi (in the 2000s).

**Eat Fresh, Be Happy?**

Daniel A. Crepps, Pathik R. Root, Benjamin K. Wessel,
and Paul M. Sommers

Middlebury College

psommers@middlebury.edu

**Abstract**

The authors
endeavor to explain variation in an index of happiness (based on interviews
conducted by World Values Survey) defined for each of 103 countries in 2008
using contemporaneous data on gross domestic product (GDP) per capita and the
number of SUBWAY® restaurants per 100,000 population. The regression equation using only GDP per
capita indicates that the happiness index reaches a peak at a level comparable
to Norway’s GDP per capita. Adding the
number of SUBWAY® restaurants per 100,000 population to GDP per capita helps
explain 35 percent of the total variation in the happiness index across countries.

**Edge-Matching, Polyominoes and Jigsaw Puzzles – Can They Be Combined?**

Zdravko Zivkovic

**Abstract**

For many years MacMahon’s 24 3-color squares
had inspired generations of puzzle designers, especially those who find the
edge-matching puzzles the most combinatorial and challenging. Many articles are
written on that subject and a lot of books contain at least a paragraph about a
solid color stylish solution that can be achieved with those magic squares. The
first attempt to enhance the original set was a movement of the colors from the
edges to the corners and the result was the corner-colored squares. Instead of
matching color of the adjacent fields on the edges with the new squares, there
was a need to match two colors simultaneously, which was even more challenging.
Unfortunately, that change significantly decreases the number of possible
combinations with the correct solution. The jig-saw puzzles that serious
recreational mathematicians consider childish, because of one ready-made
solution, without any combinatorial possibilities, have one great feature: the
interlocking system that holds all solved pieces together. The purpose of this
paper is to show (1) how the interlocking system can be applied to the
edge-matching puzzles providing full combinatorics of all the pieces and (2) to
show how the MacMahon’s original 24 square set and its variant of corner-colored
square can be replaced with just one 24 3-color hybrid set which can solve each
and any pattern of the ancestors and add the new features non-existent in the
previous sets, thus significantly increasing the total number of correct
combinations.

**Sandwiches**

Dave Miller and Steven Kahan

**Abstract**

For a given
positive integer k, suppose that there are exactly k integers strictly between
x and x*x, where x > 1 is a real number. What can we predict about x in
order for this condition to be satisfied?

**A Few Beautiful Prime Number Sequences**

Henry Ibstedt

**Abstract**

In a recent
study of p ± 2^k where p is a prime number and k is a natural number, I came
across a few interesting sequences.

**Home Prime Reversals**

Jay L. Schiffman

Rowan University

schiffman@rowan.edu

**Abstract**

During a paper
presentation on the Home Prime Conjecture at the Advances in Recreational
Mathematics Contributed Paper Session at MathFest 2011 in Lexington, KY, one of
the editors of

**Journal of Recreational Mathematics**asked if there was any known research on reversing the order of the factors at each steo of the repeated factoring and concatentation process. Since I was unaware of any such research, I undertook a journey through each of the odd composite integers less than one thousand. Utilizing the CAS package of Mathematica 8.0, I generate the results I have secured and facilitate the important infdings via the use of tables.
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