**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Representations, unpublished.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.*