Thursday, March 17, 2016

Abstracts to the papers that appeared in Journal of Recreational Mathematics 37(2)

Abstracts to the papers that appeared in Journal of Recreational Mathematics 37(2)

Is the Gap between ‘Haves’ and ‘Have-Nots’ Really Widening?

Leo R. Moses, Trevor R. Truog, and Paul M. Sommers
Middlebury College

 The disparity between the richest 1% and everyone else has become part of the national discourse.  A common measure of inequality, the Gini coefficient, fails to adequately measure the alleged widening gap between rich and poor.  The authors use two different metrics:  (i) the ratio of the upper income limit of the fourth quintile of all families to the upper income limit of the lowest quintile and (ii) the ratio of the lower income limit of the top 5% of all families to the upper income limit of the lowest quintile. Between 1947 and 2010, the authors show that since the early 1970s both ratios have increased rather dramatically over time.

t-Time on Cruise Ships

Carolyn J. Kooi, Jessica S. Ebersole, and Paul M. Sommers
Middlebury College

 The Vessel Sanitation Program (VSP) at the Centers for Disease Control and Prevention periodically inspects and scores large cruise ships.  The authors compare the scores of all cruise ships belonging to six cruise lines (Carnival, Celebrity, Holland America, Norwegian, Princess, and Royal Caribbean International) between 2007 and 2011.  Apart from the average VSP inspection score, the authors also use the coefficient of variation (a measure of consistency) to compare one cruise line against another.  A series of two-sample t-tests reveals that two cruise lines ─ Norwegian Cruise Lines and Princess  Cruises ─ scored significantly higher than their rivals, although all six cruise lines recorded average scores above 96. 

Marriage Gets An Assist from the NHL

Jaehyuk Lee, Eric M. Wilson, Owen J. Witek, and Paul M. Sommers
Middlebury College

 The authors compare average divorce rates as of 2010 in cities of comparable size (in the continental United States) with and without professional sports teams in baseball (MLB), basketball (NBA), football (NFL), and hockey (NHL). In cities with 200,000 or more inhabitants, average divorce rates are significantly lower in MLB cities.  In U.S. cities with 150,000 or more (or 200,000 or more) inhabitants, average divorce rates are significantly lower in NHL cities.  And, in NHL cities with a population of 200,000 or more, divorce rates are about 10 percent lower than cities that do not have an NHL team.

Consecutive Prime Sums From 2000 to 2099

Steven Kahan
Queens College, CUNY

 In this paper, the likelihood that a randomly selected year from 2000 to 2099 is the sum of consecutive primes as well as the number of ways it can be done is examined. 

Connected Codes
Colin Foster
King Henry VIII School, UK

 This article considers mathematical ways of remembering four-digit security codes, based on special properties possessed by the four-digit numbers. In particular, the author describes four-digit numbers in which the number formed by the first two digits is equal to the product of the last two digits, and determines the cases in which adding 1 to each digit produces another number with the same property.

The License Plate Challenge

Dr. Lidia Gonzalez
York College of the City University of New York

 The most recently issued New York State (NYS) automobile license plates consist of three letters followed by four digits (i. e. ABC1234). I am unaware of any restrictions, so for the purposes of this work, assume that any four digits may appear in a plate and that each digit may be repeated one or more times. The License Plate Challenge is a sort of solitaire that involves using the digits on a plate to construct a valid number sentence. For example, the digits in the plate ABC1234 can be used to create 1 – 2 = 3 – 4. In this article I explore the question of whether, given certain conditions, it is possible to construct such a sentence for all possible plates.

Ranking Sports Teams by Comparing Scores

Gary H. Price


The method of linear least squares matching of model to data is applied
to match predicted scores and those realized in games played between
competing teams in a sports league.  Using this method, parameters
describing the offensive and defensive strengths of each team are
optimized to achieve the best match between predicted and realized
scores.  The teams are then ranked according to the consequent overall
(offensive plus defensive) strength of each team.  Both the analysis
leading to a solution and a computer program for ranking teams based on
this analysis are described in detail.  Some surprising aspects of the
analysis are noted, and team rankings for National Collegiate Athletic
Association (NCAA) Division 1A play during the 2011 season are
calculated to illustrate its use.

Cassini-Like Formulas for the Pell Family Using Cramer’s Rule

Thomas Koshy
Framingham State University

 Using the well-known Cramer’s rule for solving a 2 × 2 linear system, we develop the Cassini-like formulas for Pell and Pell-Lucas numbers, and two additional Pell and Pell-Lucas identities.

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