Abstracts to the papers that appeared in "Journal of Recreational Mathematics 38(1)"

Abstracts to the papers that appeared in Journal of Recreational Mathematics 38(1)

Cereal Killers

Paul M. Sommers

Middlebury College

psommers@middlebury.edu

Abstract

 The author examines the average number of calories, total fat, sodium and sugar content per serving of breakfast cereals across three different companies: Kellogg’s (sample size = 60), Post Foods (44), and General Mills (55).  The results of numerous two-sample t-tests show that not all cereals are created equal.  Post Foods’ breakfast cereals have, on average, more calories and total fat per serving, General Mills’ cereals have more sodium, and Kellogg’s cereals have more sugar than their competitors.

Food for Thought: Average Cost, Marginal Cost, and Pizza

Paul M. Sommers

Middlebury College

psommers@middlebury.edu

Abstract

 Beginning students of economics frequently have difficulty distinguishing the mathematical concept of “average” from “marginal.”  The author uses price information on three different sizes of a plain, cheese pizza ─ small (10” diameter), medium (14”), and large (17”) ─ to calculate for each size the average total cost (ATC) and the marginal cost (MC).  The author shows how the three values for ATC and the two values for MC (that is, the incremental change from “small” to “medium” and then the incremental change from “medium” to “large”) are related to each other as the quantity of pizza (square inches of pizza) increases.   

Fox and the Peacock: A Fable for Super Sunday

Paul M. Sommers

Middlebury College

psommers@middlebury.edu

Abstract

 Nielsen household television ratings for the National Football League’s Super Bowl are examined from 1997 through 2013.  During this period, four different networks have televised this championship game [Fox (6 times), CBS (5), ABC (3) and NBC (3)].  The author uses a multiple regression model to gauge the popularity of each network’s telecast after accounting for differences in the margin of victory and the winning team’s conference affiliation.  The findings suggest that viewers have favored telecasts on NBC and CBS.  

Should the NBA be Done with ‘One and Done’?

Benjamin B. Sweeney, Daniel S. Waldman, Thomas A. Nall, and Paul M. Sommers

Middlebury College

psommers@middlebury.edu

Abstract

 The National Basketball Association’s (NBA’s) “one and done” 2006 rule requires all players to be at least 19 years old and one year out of high school before entering the league’s draft.  The authors compare “player efficiency rating” (PER) of all NBA draft picks between the years 2001 and 2010 who played a minimum of 500 minutes during their rookie NBA season.  These players are then divided into groups that include one-and-dones,  high school graduates (before 2006), players with some college, and college graduates.  The results suggest that the additional playing time in college mandated by the rule does not translate into higher rookie season average PERs.

Product-Sum Differences

Steven Kahan

Abstract

 This paper deals with a generalization of the the question: “Find three positive integers such that their product is equal to their sum.” The generalization is “For k any nonnegative integer, is it always possible to find three integers such that their product exceeds their sum by k?”

 Nonattacking Arrangements of n Queens with Initial Placements

Tricia Muldoon Brown

Armstrong Atlantic State University, Georgia

Abstract

 We give constructions of general solutions to the n queens problem in the case n congruent to zero modulo 6 and in the case n congruent to two modulo 6.

The 6 x n Five Color Lights Out Game

Crista Arangala, Mary MacDonald

Elon University

ccoles@elon.edu

Abstract

 In this article we explore the five color Lights Out, which is a 6 x n rectangular Lights Out game with buttons that can take on five states. Properties of the Chebyshev polynomials related to the games will be explored in determining when a solution exists.