\begin{center}
\Large{Acknowledgments}
\end{center}

This book owes much to the very interesting books of Christoph
Bandelow \cite{B}, Professor of Mathematics
at the Ruhr-University Bochum in Germany, and David 
Singmaster \cite{Si},
Professor of Mathematics in the Department of
Computing, Information Systems and Mathematics,
South Bank University, London. I thank my fine editor at Johns Hopkins 
University Press, Trevor Lipscombe, for his encouragement and 
for his many excellent suggestions.  
Without them as a source of ideas, this book would not exist. 
This book has benefited greatly from the stimulating discussions, 
encouraging correspondence, and collaborations 
with many people. These people include 
Christoph Bandelow, Dan Hoey,
Ann Luers (now Ann Casey - 
for help with \S\S \ref{sec:Pyraminx}, \ref{sec:2x2},
and parts of chapter \ref{ch:advanced2}),
Michael Dunbar (for help with \S \ref{sec:2x2}),
Mark Longridge, 
Jim McShea (for help with \S \S \ref{sec:15puzzle_mcshea},
\ref{sec:square1}), 
Justin Montague and G. Gomes
(for help with \S \ref{sec:Skewb}, \ref{sec:Skewb2}), Michael Reid, 
%Spencer Robinson (for help with \S \ref{sec:hockeypuck}), 
Andy Southern (for help with \S \ref{sec:rainbow}), Dennis Spellman
(for help with \S \ref{sec:presentation}), Herbert Kociemba
(for \S \ref{sec:kociemba}), several people on the \sage 
development team (detailed below), and many others.


Some of the graphs given below were produced with the 
help of \sage \cite{S}.
Some of the group-theoretical calculations
were determined with the help of GAP \cite{Gap}
or \sage \cite{S}. Some of the biographical 
information included in this book was borrowed from
the award-winning internet site,
the MacTutor History of Mathematics archive
\cite{MT}.

The Rubik's Cube, Pyraminx, Megaminx,
Masterball, Lights Out, and other puzzles
names mentioned frequently are all
trademarked. We shall omit the symbol
(tm) after each occurrence for ease of
reading. I would also like to thank Hasbro Toys 
(who market Lights Out) for the opportunity
to consult for them.

\sage credits: \sage \cite{S} was started in 2005 by William Stein,
who is its lead developer. It is open source, and can be downloaded 
and installed without cost by anyone with a good internet connection. 
The command-line interface used in the examples
in this book uses Ipython \cite{Ip}, started by Fernando Perez. Most people 
actiually prefer the notebook or ``gui'' interface
(I'm in the minority), written primarily by
Tom Boothby and William Stein. This is in the downloadable version
of \sage but is also available online at
\verb+http://www.sagenb.org/+. Most of the commands in this
book can be run online there without having to 
install \sage. 
For all the group theoretic constructions,
\sage uses an interface to GAP \cite{Gap}, a computer
algebra system specializing in group theory which goes back to
the mid 1980's. For the graph theory illustrated in chapter \ref{ch:god},
\sage uses the graph package NetworkX \cite{N}, and some functionality 
written primarily by Emily Kirkman and Robert Miller. 
Bobby Moretti and Robert Miller wrote \sage's Cayley 
graph construction, whereas GAP's GRAPH package
was written by Leonard Soicher \cite{So}. Besides those mentioned above,
\sage code to plot and manipulate the Rubik's cube was
written by Robert Bradshaw, Robert Miller, and myself
(with help from Tom Boothby, who wrote some of the underlying
graphics functions). To keep
expenses down, they are reproduced in greyscale in this book, though 
of course in \sage they are in color.

Much of \sage's development is
funded by National Science Foundation grants 
supporting the number theory research of
William Stein, the lead developer and architect of \sage.
The University of Washington, William Stein's home institution,
has also been a generous supporter. Many thanks to William Stein 
(and the entire \sage development team) for this great 
piece of software. 
 

This version owes much to the careful reading of the following 
people:  Jamie Adams, Lewis Nowitz, David Youd, Roger Johnson, 
Jaap Scherphuis, Michael Hoy, Tom Davis, John Rood, Trevor Irwin, 
Stephen Lepp, Mark Edwards, Carl Patterson, Peter Neumann,
Bill Zeno, Herbert Kociemba, Alastair Farrugia, Matthew Lewis,
Christopher Paul Tuffley, and Robert Bradshaw. I thank them all.

Last, but certainly not least, I thank my wonderful wife 
Elva for more things than I can possibly list here.