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% \usepackage[nott]{kpfonts}
% \usepackage{fourier}
\usepackage{lmodern}


% Delete any of the following that are not needed
\usepackage{lettrine} % Drop caps
\usepackage{wrapfig} % Let's wrap some images
\usepackage{enumitem} % Control spacing in lists
\usepackage{setspace} % Better control over line-spacing
\usepackage{nicefrac} % Use nice fractions
\usepackage[bottom]{footmisc} % Keep the footnotes at the bottom of the page
\usepackage{microtype} % Make things neater. 
\usepackage{tabularray} % Easy tables
\usepackage[]{footmisc}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{ninecolors}
\usepackage{lipsum}

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%% Commands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\graphicspath{{images/}} % Where are our images?
\usepackage{multicol} % Include two- or three-column sections
\counterwithout{footnote}{chapter} % Stop resetting the footnote count after each chapter
%\NumTabs{18} % Define 18 tab stops (at 1/4" intervals) [tabto package]
\raggedbottom  % Don't force text to fill page
\setlength{\belowcaptionskip}{4pt} % Adjust space between caption and figure
%\renewcommand*\contentsname{In This Issue…} % Change the name of the TOC

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%% Document Setup%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{geometry}
\geometry{
	paperheight=8.5in, 
	paperwidth=5.5in, 
	margin=15mm,
%	a5paper % Comment out for half-letter paper
}
\addtolength{\topmargin}{10mm} % Adjust and bottom margin
\addtolength{\textheight}{-15mm} % Adjust the bottom margin


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\usepackage{fancyhdr}
\pagestyle{fancy}
 \fancyhf{}
 \fancyhead[LE,RO]{\textit{Sudoku}}
 \fancyhead[RE,LO]{Issue \#006}
 \cfoot{Page \thepage}
\renewcommand{\footrulewidth}{0.5pt}


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\usepackage{titlesec}
\titleformat{\chapter}[display]
    {\normalfont\huge\bfseries}
    {\chaptertitlename\ \thechapter}
    {20pt}
    {\Huge}
\titlespacing*{\chapter}{0pt}{0pt}{40pt}


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% Make a nice border and box for the tops of our examples
\newcommand\klab[3]{\vspace{#1}\noindent{}\hrulefill\fbox{\texttt{~#2~}}\hrulefill\vspace{#3}}

% Add an \hrule with space above and below
\newcommand\krule[2]{\vspace{#1}\hrule\vspace{#2}}

% Make hrefs easier (must load package hyperref}
\newcommand\kref[2]{\href{#1}{{\texttt{#2}}}}


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% Draw a sudoku grid with labels
\newcommand{\kgridl}{
% Thick horizontal lines
	\draw [ultra thick](0,0)--(9,0);
	\draw [ultra thick](0,3)--(9,3);
	\draw [ultra thick](0,6)--(9,6);
	\draw [ultra thick](0,9)--(9,9);
% Thick vertical lines
	\draw [ultra thick](0,0)--(0,9);
	\draw [ultra thick](3,0)--(3,9);
	\draw [ultra thick](6,0)--(6,9);
	\draw [ultra thick](9,0)--(9,9);
% Thin horizontal lines
	\draw (0,1)--(9,1);
	\draw (0,2)--(9,2);
	\draw (0,4)--(9,4);
	\draw (0,5)--(9,5);
	\draw (0,7)--(9,7);
	\draw (0,8)--(9,8);
% Thin vertical lines
	\draw (1,0)--(1,9);
	\draw (2,0)--(2,9);
	\draw (4,0)--(4,9);
	\draw (5,0)--(5,9);
	\draw (7,0)--(7,9);
	\draw (8,0)--(8,9);
% Labels
	\begin{footnotesize}
	\node at (-0.5,0.5) {R1};
	\node at (-0.5,1.5) {R2};
	\node at (-0.5,2.5) {R3};
	\node at (-0.5,3.5) {R4};
	\node at (-0.5,4.5) {R5};
	\node at (-0.5,5.5) {R6};
	\node at (-0.5,6.5) {R7};
	\node at (-0.5,7.5) {R8};
	\node at (-0.5,8.5) {R9};
	\node at (0.5,-0.5) {C1};
	\node at (1.5,-0.5) {C2};
	\node at (2.5,-0.5) {C3};
	\node at (3.5,-0.5) {C4};
	\node at (4.5,-0.5) {C5};
	\node at (5.5,-0.5) {C6};
	\node at (6.5,-0.5) {C7};
	\node at (7.5,-0.5) {C8};
	\node at (8.5,-0.5) {C9};
	\end{footnotesize}
}

% Draw a sudoku grid without labels
\newcommand{\kgrid}{
% Thick horizontal lines
	\draw [ultra thick](0,0)--(9,0);
	\draw [ultra thick](0,3)--(9,3);
	\draw [ultra thick](0,6)--(9,6);
	\draw [ultra thick](0,9)--(9,9);
% Thick vertical lines
	\draw [ultra thick](0,0)--(0,9);
	\draw [ultra thick](3,0)--(3,9);
	\draw [ultra thick](6,0)--(6,9);
	\draw [ultra thick](9,0)--(9,9);
% Thin horizontal lines
	\draw (0,1)--(9,1);
	\draw (0,2)--(9,2);
	\draw (0,4)--(9,4);
	\draw (0,5)--(9,5);
	\draw (0,7)--(9,7);
	\draw (0,8)--(9,8);
% Thin vertical lines
	\draw (1,0)--(1,9);
	\draw (2,0)--(2,9);
	\draw (4,0)--(4,9);
	\draw (5,0)--(5,9);
	\draw (7,0)--(7,9);
	\draw (8,0)--(8,9);
}

% Sudoku nodes
\newcommand{\knode}[3]{\node at ($(#1-0.5,#2-0.5)$) {#3};}

% Sudoku fills
\newcommand{\kfill}[3]{\draw [fill=gray#3, line width=0mm] ($(#1-1,#2-1)$) rectangle +(1,1);}

% Sudoku markers
\newcommand{\kfirst}[2]{\fill [red5] ($(#1 - 0.2,#2 - 0.2)$) circle (0.75pt);}
\newcommand{\ksecond}[2]{\fill [red5] ($(#1 - 0.2,#2 - 0.2)$) circle (0.75pt);\fill [red5] ($(#1 - 0.8,#2 - 0.2)$) circle (0.75pt);}
\newcommand{\kguess}[2]{\fill [red5] ($(#1 - 0.8,#2 - 0.8)$) circle (0.75pt);}


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%% Include URLS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Be sure to load this package last
\usepackage[hidelinks]{hyperref} % Inlcude URLs, but load this package last


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Document Information %%%%%%%%%%%%%%%%%%%%%
%% Adjust the TITLE and SUBTITLE as necessary
\author{Kenneth John Odle}
\title{
 {\Huge Sudoku} \\
 \bigskip
 {\footnotesize How to Play \\ How to Win \\
 \bigskip
 Typeset in \LaTeX{} \\
% Issue \#006
 }
}
\date{\begin{small}\the\year\end{small}}


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%% Let's get it started %%%%%%%%%%%%%%%%%%%%%

\begin{document}
\maketitle

\section*{Impressum}
All contents  \copyright{}2025 Kenneth John Odle

FYI, this is made in \LaTeX \,using the report document class. It then gets exported to a letterhalf (5.5 in x 8.5 in) pdf, which then gets made into a booklet using PDF Booklet, which you can find at

\kref{https://pdfbooklet.sourceforge.io/wordpress/}{https://pdfbooklet.sourceforge.io/wordpress/}

If you want to donate financial support for the creation of this zine (and all the hours of research that go into it), you can do so at 

\kref{https://paypal.me/kjodle}{https://paypal.me/kjodle} (Thanks!)


\tableofcontents

\chapter{What Is Sudoku?}

\lettrine[loversize=0.5,nindent=-0.2mm]{S}{udoku} is a number-placement game played on a 9x9 grid for a total of 81 individual cells, with that main grid broken up into 9 subgrids of 9 cells each, as shown in figure \ref{subgrids}. The goal is to enter the numbers 1 through 9 into each cell such that each row, each column, and each subgrid contains each number only once. See figure \ref{fullgrid} for an example with rows and columns labeled.

\begin{wrapfigure}{O}{0.45\textwidth}
\centering
\begin{tikzpicture}[x=5mm,y=5mm]
% Thick horizontal lines
    \draw [ultra thick](0,0)--(9,0);
    \draw [ultra thick](0,3)--(9,3);
    \draw [ultra thick](0,6)--(9,6);
    \draw [ultra thick](0,9)--(9,9);
% Thick vertical lines
    \draw [ultra thick](0,0)--(0,9);
    \draw [ultra thick](3,0)--(3,9);
    \draw [ultra thick](6,0)--(6,9);
    \draw [ultra thick](9,0)--(9,9);
\end{tikzpicture}
\caption[]{A sudoku grid showing only the subgrids.}
\label{subgrids}
\end{wrapfigure}

Sudoku puzzles have anywhere from a few to many of the cells filled in with numbers. Those puzzles with more cells filled in are generally easier to complete than those with only a few cells filled in.

Number puzzles of this type have been around for a long time, with one of the earliest appearing in 1892 in the French newspaper \textit{Le Siècle}, which was a partially completed 9x9 magic square\footnote{A square array of numbers in which the sum of numbers in each row, column, and both diagonals add up to the same number.}

Despite the Japanese name (which translates roughly as ``digit-single'' or ``number-unique''), the modern sudoku puzzle is apparently an American invention, first appearing the May 1979 issue of \textit{Dell Pencil Puzzles \& Word Games} as ``Number Place''. It is apparently the work of a retired architect named Howard Garns, although the evidence is somewhat circumstantial: Garns appeared in the list of contributors in each issue that did contain a ``Number Place'' puzzle, but did not appear in the list of contributors in issues that did \textit{not} contain a ``Number Place'' puzzle.\footnote{See \kref{https://www.mathpuzzle.com/MAA/41-Sudoku Variations/mathgames_09_05_05.html}{https://www.mathpuzzle.com/MAA/41-Sudoku\%20Variations/mathgames\_09\\\_05\_05.html} for more information, which also contains more information on sudoku variations.}

\begin{wrapfigure}{O}{0.5\textwidth}
\centering
\begin{tikzpicture}[x=5mm,y=5mm]
\kgridl
\end{tikzpicture}
\caption[]{A full 9x9 sudoku grid with columns and rows labeled.}
\label{fullgrid}
\end{wrapfigure}

It was later imitated in the 1980's by the Japanese publisher Nikoli who introduced two small improvements: the number of clues was limited to 32, and the clues were distributed in a rotationally symmetric way, meaning that the clues were more evenly distributed across the grid.

In 1997, Wayne Gould, a retired judge from New Zealand who had moved to Hong Kong spotted the puzzles in a Japanese bookshop and then spent the next six years developing a computer program to create sudoku puzzles, and started selling them local newspapers and eventually to the London \textit{Times}. He also publishes them from his own website at \kref{https://sudoku.com/}{https://sudoku.com/}.\footnote{See \kref{https://www.theguardian.com/media/2005/may/15/pressandpublishing.usnews}{https://www.theguardian.com/media/2005/may/15/pressandpublishing.u\\snews} for more information.}

There are 6,670,903,752,021,072,936,960 possible sudoku puzzles possible, but many of them are reflections or rotations of one another. When those are accounted for, there are 5,472,730,538 truly unique sudoku grids, which is a considerably smaller number, but means that you are unlikely to run out of sudoku puzzles to play.\footnote{See \kref{https://web.archive.org/web/20171112153047/http://www.afjarvis.staff.shef.ac.uk/sudoku/}{https://web.archive.org/web/20171112153047/http://www.afjarvis.sta\\ff.shef.ac.uk/sudoku/} for more information on how these numbers were calculated and information on other variants (such as 2x3 and 2x4 grids).}


\chapter{The Rules of Sudoku}

\lettrine[loversize=0.5,nindent=-0.2mm]{T}{he} rules of sudoku are both few and simple:

\begin{enumerate}[noitemsep]
\item Sudoku is played on a 9x9 grid.
\item You can only use the numbers 1 through 9.
\item Each vertical column can only contain the numbers 1 through 9, with no number being used more than once.
\item Each horizontal row can only contain the numbers 1 through 9, with no number being used more than once.
\item Each 3x3 subgrid can only contain the numbers 1 through 9, with no number being used more than once.
\end{enumerate}

Winning is simple: you win when you have filled in the entire 9x9 grid according to the rules above.

\chapter{Strategy}

There are a number of different strategies that you can employ to solve a sudoku puzzle. 

\section{Last Free Cell}

This strategy is based on the rules that each 3x3 subgrid, row, and column, cannot contain duplicate numbers. Thus, if only one cell remains empty, you can use the process of elimination to figure out which one it is.

\begin{wrapfigure}[]{O}{0.5\textwidth}
\vspace{-1\baselineskip}
\centering
\begin{tikzpicture}[x=5mm,y=5mm]
\kfill{9}{9}{9}
\kfill{3}{7}{9}
\kfill{1}{1}{9}
\kgridl
\knode{1}{9}{1}
\knode{2}{9}{2}
\knode{3}{9}{3}
\knode{4}{9}{4}
\knode{5}{9}{5}
\knode{6}{9}{6}
\knode{7}{9}{7}
\knode{8}{9}{8}
\knode{1}{8}{4}
\knode{2}{8}{5}
\knode{3}{8}{6}
\knode{1}{7}{7}
\knode{2}{7}{8}
\knode{1}{6}{2}
\knode{1}{5}{3}
\knode{1}{4}{6}
\knode{1}{3}{5}
\knode{1}{2}{8}
\end{tikzpicture}
\caption[]{The ``Last Free Cell'' strategy.}
\label{lastfreecell}
\vspace{-2\baselineskip}
\end{wrapfigure}

Here we see three variations of this strategy in action, reflecting the three different ways it can be implemented: in a subgrid, in a row, and in a column. See figure \ref{lastfreecell} as a reference.

The Northwest subgrid contains the numbers 1 through 8, with only a blank cell at C3R7. Because we have already used the numbers 1 through 8, the only number that can fit here is 9.

Row 9 already contains the numbers 1 through 8, with only a blank cell at C9R9. Again, this number must be 9.

Column 1 contains the numbers 1, 4, 7, 2, 3, 6, 5,and 8. That leaves only the number 9, so it must be 9 that fits into C1R1.

This is, perhaps, the simplest of strategies, but it easy to overlook once you are solving a difficult puzzle and looking for deeper, more complex strategies. (Ask me how I know!)

\section{Last Remaining Cell}

\section{Last Possible Number}


\end{document}