Research Papers Published since 1989 (with one exception)

These papers are all in pdf format. You must have Adobe Acrobat Reader to access these files.

A Magic Pentagram, Mathematics Teacher, 75 (March 1983), 174-177.

A Complete Solution to the Magic Hexagram Problem, with David Ritchie, The College Mathematics Journal, 20 (1989), 307-316. The website Magic 9x5 Hexagons  has a great summary of the paper. 

Trends in Calculator Use in Mathematics Competitions, with Betty Reiter, Mathematics and Computer Education, 25 (Spring 1991), 174-178.

Graceful Graphs and Sparsely Marked Rulers, with L. R. King, The College Mathematics Journal, 22 (1991), 232-234.

An Excursion in Discrete Mathematics, Mathematics and Computer Education, 26 (Spring 1992), 35-39.

Measuring Difficulty and Diagnositicity in a Weighted Multiple Choice Exam, with Nancy Schoeps, Terry Hartman, and Betty Reiter, Mathematics Competitions, 6 (Fall 1993), 64-85.

The Fifth International Olympiad in Informatics: The Argentine Diary, with Donald Piele, Mathematics Competitions, 7 (Fall 1994), 80-96.

The ``Join the Club'' Interpretation of Some Graph Algorithms, with Isaac Sonin, The College Math Journal, 27 (1996), 54-58.

The Space of Closed Subsets of a Convergent Sequence, with Ashley Reiter, Mathematics Magazine, 69 (June, 1996), 217-221.

The Chinese Restaurant Approach to Integer Representation Problems, Mathematics and Informatics, 7 (1997), 20-26.

American Mathematics Competitions Report of the Task Force, Mathematics Competitions, 10 (Fall, 1997), 32-43.

Counting Snakes, Differentiating the Tangent Function, and Investigating the Bernoulli-Euler Triangle, Mathematical Mayhem, (Spring, 1999), 39-46.

The ``Join the Club'' Interpretation of Some Graph Algorithms, in Russian, with Isaac Sonin, Mathematical Education, 3 (1999), 208-212.

Games and Representations, unpublished.

A Nimlike Game on the Integers, with Arthur Holshouser, Mathematics and Informatics Quarterly 4/2001, vol.11, pp. 174-5.

The American High School Mathematics Examination: A 50 Year Retrospective, Mathematics Competitions, with Stephen B. Maurer and Leo J. Schneider, vol.14, Number 2, 2001, pp. 45-66.

Dynamic One-Pile Nim, with Arthur Holshouser and James Rudzinski, The Fibonacci Quarterly, vol 41.3, June-July, 2003, pp 253-262.

Pilesize Dynamic One-Pile Nim and Beatty's Theorem,  with Arthur Holshouser and James Rudzinski, or click here Integers, Electronic Journal of Combinatorial Number Theory, vol 4(2004).

A Generalization of Beatty's Theorem,  with Arthur Holshouser,   Southwest Journal of Pure and Applied Mathematics, Issue 2, December, 2001 pp.24-29. A complete pdf version is available here.

Dynamic One-Pile Blocking Nim (local version) and Dynamic One-Pile Blocking Nim (as it appeared in EJC) with Arthur Holshouser and Achim Flammenkamp,  Electronic Journal of Combinatorics, Volume 10(1), 2003. Specifically, click here.

Blocking Combinatorial Games,  with Arthur Holshouser, submitted to the Integers. 

Three Pile Nim with Move Blocking,   with Arthur Holshouser, Mathematical Mayhem October, 2003; pp. 362-365. Also see Three-Pile Nim with Blocking.

One Pile Nim with Arbitrary Move Function (local version) and   One-Pile Nim with Arbitrary Move Function (as it appeared in EJC) with Arthur Holshouser, Electronic Journal of Combinatorics, Volume 10(1), 2003.

Just The Factors, Ma’am, first appeared in Mu Alpha Theta Mathematical Log, Summer, 2002.

Single Pile (Move Size) Dynamic Blocking Nim with Arthur Holshouser.

Nimlike Games with Generalized Bases with Arthur Holshouser, Rocky Mountain Journal of Mathematics, Vol 35, pp 539-546, Number 2, 2005.

You can access my problems published in the Sunday (London) Times Problems

Nim with Twists with Arthur Holshouser, unpublished.

Dynamic Single-Pile Nim Using Multiple Bases, with Arthur Holshouser, Electronic Journal of Combinatorics, Dynamic Single-Pile Nim Using Multiple Bases, Volume 13(1), 2006.

Quarto without the Twist, with Arthur Holshouser, Mathematics and Informatics Quarterly 2/2005, vol.16, pp. 50-55.

Eight Versions of n-Pile Nim, with Arthur Holshouser, Mathematics and Informatics Quarterly 3/2005, vol.15, pp 108-111

Abstract Combinatorial Games, with Arthur Holshouser, unpublished.

Closed Form, Recursion, and Mindreading; Defining Sequences by Various Means, to appear in the Mathematics and Informatics Quarterly.

Games and Number Representations, presented at the International Congress in Math Education, Copenhagen, Denmark, July, 2004.

Two Pile Move-Size Dynamic Nim, and Discrete Mathematics and Theoretical Computer Science, 2005, vol 7, pp 1-10.

Is this Modified Nim Game a Game of Chance? with Arthur Holshouser, unpublished.

Misere Games, with Arthur Holshouser, Mathematical Mayhem, May 2005, pp 211-214.

Abstract Composite Games with Moves in All Components Compulsory, Part I, with Arthur Holshouser, submitted.

Dynamic One and Two Pile Nim Games Using Generalized Bases, with Arthur Holshouser, submitted.

The Secret of Nim, with Arthur Holshouser, Drew Boyuka, and John Mahoney, unpublished.

Coffee and Mathematics, Once Again, December 2005, Focus, MAA Newsletter.

Marilyn’s Ten-digit Number Problem, with Arthur Holshouser, Mathematics and Informatics Quarterly 1/2 2006, vol.16, pp. 7-8.

The Commutative Equihoop and the Card Game SET, with Arthur Holshouser and Ben Klein, The Pi Mu Epsilon Journal, Fall 2015, Vol. 14, Number 3, 175-190.

Michigan Autumn Take Home Challenge, Mathematics Competitions, with  Arthur Holshouser, vol.19, Number 2, 2006, pp. 42-60.

Dynamic n-Pile Nim with Various Endings, with Arthur Holshouser, unpublished.

Groups that Distribute over Mathematical Structures, with Arthur Holshouser,  International
Journal of Algebra, Vol. 3, 2009, no. 1-4, 157-171.

Groups that Distribute over n-Stars, with Arthur Holshouser,  International
Journal of Algebra, Vol. 3, 2009, no. 1-4, 173-179.

Win Sequences for Round-robin Tournaments , with Arthur Holshouser, The Pi Mu Epsilon Journal, Fall 2009, Vol. 13, Number 1,  37-44.

Win-loss Sequences for Multiple Round Tournaments , with Arthur Holshouser and John W. Moon, November, 2011 in Missouri Journal of Mathematical Sciences.

Groups that Distribute over Stars, with Arthur Holshouser, unpublished. 

Generalized Groups that Distribute over Stars, with Arthur Holshouser, Fall 2012  in Missouri Journal of Mathematical Sciences, volume 24, number 2, pp 124 155.

Linearly Similar Polynomials, with Arthur Holshouser, submitted.

The Theory of Linear Fractional Transformations of Rational Quadratics, with Arthur Holshouser, submitted.

 On a problem of Arthur Engel, Mathematics Competitions, with  Arthur Holshouser, vol.22, Number 1, 2009, pp. 38-59.

Don’t Fence Me In! Counting and Geometrical Thinking with the Lattice Octagon, Mathematics Teacher, to appear in March 2012, with Arthur Holshouser and Patrick Vennebush.

Invariant Relations for the Derivatives of Two Arbitrary Polynomials, with Arthur Holshouser, Fall, 2012 in Missouri Journal of Mathematical Sciences., Volume 24, number 2, pp. 195-201.

A Theory of Linear Fractional Transformations of Rational Functions, with Arthur Holshouser, unpublished.

Mathematics Teachers Circle around Problem Solving, with Anthony Fernandes and Jacob Koehler, Mathematics Teacher, September, 2010, pp 109-115.

The Cubic Function is an Adding Machine, with Arthur Holshouser and Chuck Diminnie,  Pi Mu Epsilon Journal, Volume 13, Number 10, Spring 2014, pp. 619-625.

Using Complex Weighted Centroids to Create Homothetic Polygons, with Arthur Holshouser, Forum Geometricorum, Volume 12 (2012) 247–254.  Also, see http://forumgeom.fau.edu/FG2012volume12/FG201224.pdf.

The Five Stages of Place Value , with Roger Howe, http://www.teachersofindia.org/en/article/five-stages-place-value
Teachers of India, September, 2012.

Using KenKen to Build Reasoning Skills, with John Thornton and Patrick Vennebush, Mathematics Teacher, March 2013.  This is a prelimiary version. Substantial changes were requested by the reviewers.

Magic Hexagon Puzzles, with Arthur Holshouser, submitted.

Applications of the Cevian Group in a Triangle, with Arthur Holshouser, submitted.

Classifying Similar Triangles Inscribed in a Given Triangle, with Arthur Holshouser, submitted.

Creating Semi-Magic, Magic, and Extra Magic n x n Squares when n is Odd, with Arthur Holshouser, submitted.

28,800 Extremely Magic 5 x 5 Squares, with  Arthur Holshouser,  Mathematics Competitions,  vol.27, Number 2, 2014, pp. 50-66.

Invariant Relations for the Derivatives of Polynomials, with  Arthur Holshouser,  to appear.

Apollonius Problems, with Arthur Holshouser and Stas Molchanov,  Pi Mu Epsilon Journal, Volume 14, Number 4, Spring 2016, pp. 261-267.

Applying Poncelet's Theorem, with Arthur Holshouser and Stas Molchanov, Forum Geometricorum, Volume 16 (2016) 141-149.  Also, see http://forumgeom.fau.edu/FG2016volume16/FG201619index.html.

A Special Case of Poncelet'sProblem, with Arthur Holshouser and Stas Molchanov,  Forum Geometricorum, Volume 16 (2016) 151-170.  Also, see http://forumgeom.fau.edu/FG2016volume16/FG201620index.html
A Fraction Problem, with Arthur Holshouser, to appear in Mathematics Competitions, summer 2017.

Monotonic Arrangements of Undirected Graphs, with Ben Klein and Arthur Holshouser, unpublished.

Generating Stern--Brocot Type Rational Numbers with Mediants, with Arthur Holshouser, Missouri Journal of Mathematical Sciences, vol 30. pp 93-104.

The GCD of m Linear Forms in n Variables, with Ben Klein and Arthur Holshouser, submitted.

Using Linear Companion Recursions to Solve Recursive Equations, with Arthur Holshouser, submitted.

Distributive Lattices Generated from Single Polynomials on Generalized Bases, with Arthur Holshouser, to appear, Pi Mu Epsilon Journal, Volume 15, Number 4, Fall 2021, pp. 215-234.