# davidwhogg/MagicCube

initial structure

 @@ -0,0 +1,13 @@ +.SUFFIXES: .tex .pdf +RM = /bin/rm -fv +PDFLATEX = pdflatex + +all: hogg_cube.pdf + +%.pdf: %.tex + $(PDFLATEX)$* + $(PDFLATEX)$* + $(PDFLATEX)$* + +clean: + $(RM) *.log *.aux *.dvi *.bbl *.blg  @@ -0,0 +1,61 @@ +% Copyright 2012 David W. Hogg (NYU). +% All rights reserved. + +% to-do +% ----- +% - write +% - make figures +% - set algorithm conventions + +\documentclass[12pt,pdftex]{article} + +\newcommand{\by}[1]{{#1}$\times${#1}$\times\${#1}} + +\begin{document} + +\subsection*{The rubik's cube} + +\noindent +\textsl{by David W. Hogg, New York City, 2012 October} +\vspace{1ex} + +\paragraph{\by{2}} + +How do I solve the \by{2}? + +Combinatorics and speed solutions + +Why can't you make a checkerboard on the \by{2}? + +\paragraph{\by{3}} + +How do I solve the \by{3}? + +Pictures and patterns you can make with the \by{3}? + +\paragraph{\by{5} and larger odd cubes} + +How do I solve the \by{5}? + +Choices about edge-first and face-first; trade-offs + +Pictures that you can do with the \by{5} that you can't do with the \by{3} + +How does the \by{5} solution generalize to \by{7} and all higher odd numbers? + +\paragraph{\by{4} and all even cubes} + +How do I solve the \by{4}? + +What happens if you try to do a checkerboard by brute force? + +How do the \by{4} and \by{5} methods generalize to \by{6} and all possible higher cubes? + +\paragraph{playing and insights} + +Alphabet + +How do I solve the \by{4} \emph{within} a larger cube? + + +\end{document}