<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">%\iffalse meta-comment
%Copyright (c) 2022 Peter Rowlett
%
%Permission is hereby granted, free of charge, to any person obtaining a copy
%of this software and associated documentation files (the "Software"), to deal
%in the Software without restriction, including without limitation the rights
%to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
%copies of the Software, and to permit persons to whom the Software is
%furnished to do so, subject to the following conditions:
%
%The above copyright notice and this permission notice shall be included in all
%copies or substantial portions of the Software.
%
%THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
%IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
%FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
%AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
%LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
%OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
%SOFTWARE.
%\fi
%\section{Background}
%
%\lstinline|nimsticks| is a package for \LaTeX{} that draws sticks for representating games of multi-pile Nim. 
%
%Nim objects could be anything, of course, but conventionally sticks or stones are used. There are various types of dot in LaTeX that might look like stones, but somehow a line of dots didn't seem satisfactory. There are various ways to draw a line (e.g. just typing IIIII), including some tally markers (e.g. in hhcount). My problem with these (call me picky) is that they are all identical lines, and a `heap' of them just looks very organised. Really, I want a set of lines that looks like someone just threw them into heaps (though probably without crossings for the avoidance of ambiguity).
%
%The way this works is it draws a thick vertical line in TikZ with a little wobble added so each one doesn't look extremely well-lined-up with its neighbour, achieved by adding or subtracting a small random number to the top and bottom coordinate. There are various built-in options to customise the size and colour of the sticks, and flexibility to draw heaps of different objects.
%
%N.B. The precise look of example output in this document is affected by random wobble in the sticks.
%
%\section{Basic usage}
%
%\subsection{Draw a game of multi-pile Nim}
%
%For example, the input \lstinline!\nimgame{5,3,4}! will produce output like this: \nimgame{5,3,4}
%
%This is designed to look like a 3-pile Nim game with 5 sticks in the first pile (or heap), 3 in the second and 4 in the third.
%
%\lstinline|\nimgame| will happily work with one heap, so for example the input \lstinline!\nimgame{7}! will produce output like this: \nimgame{7}
%
%The command \lstinline|\nimgame| presents the Nim game as its own paragraph with \lstinline!\centering!. An optional flag \lstinline|inline| can be used to produce the Nim game inline without the \lstinline|\centering|. For example, the command \lstinline!\nimgame[inline]{5,3,4}! will produce outline like this: \nimgame[inline]{5,3,4}
%
%\subsection{Draw a single Nim stick}
%
%It is likely the user will want to use \lstinline|\nimgame| and not \lstinline|\drawnimstick| directly, but the input \lstinline|\drawnimstick| will produce output like this: \reinitrand[first=-100,last=100,seed=256]\drawnimstick 
%
%\section{Customisation}
%
%\subsection{Colour}
%
%A command \lstinline|\setnimstickcolour{colour}| is used to set the colour of the sticks, by default black. The input \lstinline|colour| can be any named colour defined in the document.
%
%\begin{verbatim}\nimgame{3,4,5}
%
%\setnimstickcolour{blue}\nimgame{3,4,5}
%
%\setnimstickcolour{magenta}\nimgame{3,4,5}
%
%\definecolor{lightcornflowerblue}{rgb}{0.6, 0.81, 0.93} % from https://latexcolor.com/
%\setnimstickcolour{lightcornflowerblue}\nimgame{3,4,5}\end{verbatim}
%
%\nimgame{3,4,5}
%
%\setnimstickcolour{blue}\nimgame{3,4,5}
%
%\setnimstickcolour{magenta}\nimgame{3,4,5}
%
%\definecolor{lightcornflowerblue}{rgb}{0.6, 0.81, 0.93}
%\setnimstickcolour{lightcornflowerblue}\nimgame{3,4,5}
%
%\setnimstickcolour{black}
%
%\section{Size}
%
%\subsection{Basic size configuration}
%
%\lstinline|\nimgame| and \lstinline|\drawnimstick| respond to the current text size, as demonstrated below. This is because their size is defined in ex, with the default height of a stick 3.3ex (roughly twice the size of a capital letter in the current font). 
%
%\begin{tabular}{cc}
%    \tiny tiny: &amp; \tiny\nimgame{3,4,5}\\
%    \scriptsize scriptsize: &amp; \scriptsize\nimgame{3,4,5}\\
%    \footnotesize footnotesize: &amp; \footnotesize\nimgame{3,4,5}\\
%    \small small: &amp; \small\nimgame{3,4,5}\\
%    \normalsize normalsize: &amp; \normalsize\nimgame{3,4,5}\\
%    \large large: &amp; \large\nimgame{3,4,5}\\
%    \Large Large: &amp; \Large\nimgame{3,4,5}\\
%    \LARGE LARGE: &amp; \LARGE\nimgame{3,4,5}\\
%    \huge huge: &amp; \huge\nimgame{3,4,5}\\
%    \Huge Huge: &amp; \Huge\nimgame{3,4,5}\\
%\end{tabular}
%
%\subsection{Advanced size configuration}
%
%The size can be further customised by a command \lstinline|\setnimscale{num}|. This controls the height of the sticks, their thickness, the gaps between sticks, the gaps between heaps and the size of the wobble. 
%
%Usage is like \lstinline|\setnimscale{2}\nimgame{3,4,5}|
%
%For example:
%
%\begin{tabular}{cc}
%    \textbf{Nim scale} &amp; \lstinline|\normalsize| \textbf{game}\\
%    0.5: &amp; \setnimscale{0.5}\nimgame{3,4,5}\\
%    0.675: &amp; \setnimscale{0.675}\nimgame{3,4,5}\\
%    1: &amp; \setnimscale{1}\nimgame{3,4,5}\\
%    1.5: &amp; \setnimscale{1.5}\nimgame{3,4,5}\\
%    2: &amp; \setnimscale{2}\nimgame{3,4,5}\\
%    4: &amp; \setnimscale{4}\nimgame{3,4,5}\\
%\end{tabular}
%\setnimscale{1}
%
%
%\section{Advanced use}
%
%\subsection{Changing the look of the Nim sticks/stones/etc.}
%
%There is a command \lstinline|\onenimstick| that includes only the TikZ code for drawing a single Nim stick. This can be redefined to draw different objects as Nim sticks using in principle arbitrary TikZ code. 
%
%\lstinline|\onenimstick| is called from within a \lstinline|tikzpicture| environment. 
%
%You have three randomisation parameters available to you: \begin{itemize}
%    \item \lstinline|\topx| and \lstinline|\botx|: small random numbers which are in the range \(-0.1\) to \(0.1\) (for default scale \lstinline|\normalsize| heaps).
%    \item \lstinline|\lift|: small random number which is in the range \(0\) to \(0.2\) (for default scale \lstinline|\normalsize| heaps).
%\end{itemize}
%
%\subsubsection{Examples}
%
%\begin{enumerate}
%    \item Here we draw each stick as a little circle (to look like stones), with a little vertical \lstinline|\lift| to make them sit irregularly. 
%
%    \begin{verbatim}\renewcommand{\onenimstick}{%
%    \node[draw,black,fill=gray,circle] at (0,\lift) {};
%}
%\nimgame{3,4,5}
%
%\nimgame{5,4,2,3}\end{verbatim}
%
%    \renewcommand{\onenimstick}{%
%        \node[draw,black,fill=gray,circle] at (0,\lift) {};
%    }
%    
%    \nimgame{3,4,5}
%    
%    \nimgame{5,4,2,3}
%    
%    \item Here we draw each stick as a little matchstick, with a little vertical \lstinline|\lift| to make them sit irregularly. 
%    
%    \begin{verbatim}% Colours from https://latexcolor.com/
%\definecolor{goldenrod}{rgb}{0.85, 0.65, 0.13}
%\definecolor{indianred}{rgb}{0.8, 0.36, 0.36}
%\renewcommand{\onenimstick}{%
%    \draw[goldenrod,fill=goldenrod,rotate=\topx*40] (0,\lift) rectangle (0.14,1+\lift);
%    \draw[indianred,fill=indianred,rotate=\topx*40] (0.07,1+\lift) ellipse (0.1 and 0.2);
%}
%\nimgame{3,4,5}
%
%\nimgame{5,4,2,3}\end{verbatim}
%    
%    \definecolor{goldenrod}{rgb}{0.85, 0.65, 0.13}
%    \definecolor{indianred}{rgb}{0.8, 0.36, 0.36}
%    \renewcommand{\onenimstick}{%
%        \draw[goldenrod,fill=goldenrod,rotate=\topx*40] (0,\lift) rectangle (0.14,1+\lift);
%        \draw[indianred,fill=indianred,rotate=\topx*40] (0.07,1+\lift) ellipse (0.1 and 0.2);
%    }
%    
%    \nimgame{3,4,5}
%    
%    \nimgame{5,4,2,3}
%    
%    \item To demonstrate arbitrary drawing, here each item in the Nim heap is a little green rectangle, with size randomised using \lstinline|\topx| and  \lstinline|\botx|, with a little vertical \lstinline|\lift| to make them sit irregularly. 
%    
%    \begin{verbatim}\renewcommand{\onenimstick}{%
%    \draw[very thick,draw,fill=green] (0,\lift) rectangle (\topx+0.5,\botx+1+\lift);
%}
%\nimgame{3,4,5}
%
%\nimgame{5,4,2,3}\end{verbatim}
%    
%    \renewcommand{\onenimstick}{%
%        \draw[very thick,draw,fill=green] (0,\lift) rectangle (\topx+0.5,\botx+1+\lift);
%    }
%    
%    \nimgame{3,4,5}
%    
%    \nimgame{5,4,2,3}
%    
%	 \item And, just to get silly:
%
%	 \begin{verbatim}% Colours from https://latexcolor.com/
%\definecolor{coolblack}{rgb}{0.0, 0.18, 0.39}
%\definecolor{arylideyellow}{rgb}{0.91, 0.84, 0.42}
%\renewcommand{\onenimstick}{%
%    \node[draw,coolblack,fill=arylideyellow,rotate=90+\topx*60,anchor=north,rounded
%    corners=0.5ex] at (\topx,\botx) {\(e^{i\pi} + 1 = 0\)};
%}
%\nimgame{3,4,5}\bigskip\end{verbatim}
%
%    \definecolor{coolblack}{rgb}{0.0, 0.18, 0.39}
%    \definecolor{arylideyellow}{rgb}{0.91, 0.84, 0.42}
%	 \renewcommand{\onenimstick}{%
%        \node[draw,coolblack,fill=arylideyellow,rotate=90+\topx*60,anchor=north,rounded corners=0.5ex] at (\topx,\botx) {\(e^{i\pi} + 1 = 0\)};
%    }
%    {\footnotesize \nimgame{3,4,5}
%    
%    \nimgame{5,4,2,3}}
%
%    \renewcommand{\onenimstick}{\draw[very thick,\nimstickcolour] (\topx,0ex) -- (\botx,\nimstickheight ex);}
%\end{enumerate}
%
%\subsection{Creating the same randomisation twice}
%
%The randomisation is done with \lstinline|lcg| and you can set the seed using \lstinline|\reinitrand| from that package. The seed is supposed to be a number from \(1\) to \(2^{31} - 1\), otherwise the package will use a combination of the time, page number and line number to make the seed. So if you reset the randomisation to the same seed before running \lstinline|\drawnimstick| or \lstinline|\nimgame| you'll get the same look to the sticks.
%
%\subsubsection{Examples}
%
%\begin{enumerate}
%    \item Here we generate the same Nim pile twice with exact reproduction of the randomisation. The first pair of Nim games (without \lstinline|\reinitrand|) appear different; the second pair of Nim games appear identical because \lstinline|\reinitrand[first=-100,last=100,seed=1]| is used to reset the randomisation to the same point before each is drawn. Different seeds can be used if there are multiple sets of Nim games that require consistent looks.
%    
%    \begin{verbatim}\nimgame{3,4,5}
%
%\nimgame{3,4,5}
%
%\hrule
%
%\reinitrand[first=-100,last=100,seed=1]
%\nimgame{3,4,5}
%
%\reinitrand[first=-100,last=100,seed=1]
%\nimgame{3,4,5}\end{verbatim}
%
%    \nimgame{3,4,5}
%    
%    \nimgame{3,4,5}
%    
%    \hrule
%
%    \reinitrand[first=-100,last=100,seed=1]
%    \nimgame{3,4,5}
%    
%    \reinitrand[first=-100,last=100,seed=1]
%    \nimgame{3,4,5}
%
%    \item Here we use nimsticks within Beamer with a reveal slide using \lstinline|\only|. On the first slide a Nim game is produced and when the slide is progressed to reveal ``Text'' the Nim sticks all move. On the second slide the Nim sticks do not move when ``Text'' is revealed.
%    
%    \begin{verbatim}\documentclass{beamer}
%\usepackage{nimsticks}
%\begin{document}    
%\begin{frame}
%    \nimgame{2,3,4} \only&lt;2&gt;{Text}
%\end{frame}  
%\begin{frame}
%    \reinitrand[first=-100,last=100,seed=123]\nimgame{2,3,4} \only&lt;2&gt;{Text}
%\end{frame}
%\end{document}\end{verbatim}
%    
%	\item Here two pairs of Nim games are reproduced. Games 1 and 3 are identical using \lstinline|seed=1|, and games 2 and 4 are identical using \lstinline|seed=2|.
%
%    \begin{verbatim}Game 1: \reinitrand[first=-100,last=100,seed=1]\nimgame{5,8,1,4}
%
%Game 2: \reinitrand[first=-100,last=100,seed=2]\nimgame{2,3}
%
%Game 3: \reinitrand[first=-100,last=100,seed=1]\nimgame{5,8,1,4}
%
%Game 4: \reinitrand[first=-100,last=100,seed=2]\nimgame{2,3}\end{verbatim}
%
%	Game 1: \reinitrand[first=-100,last=100,seed=1]\nimgame{5,8,1,4}
%
%	Game 2: \reinitrand[first=-100,last=100,seed=2]\nimgame{2,3}
%
%	Game 3: \reinitrand[first=-100,last=100,seed=1]\nimgame{5,8,1,4}
%
%	Game 4: \reinitrand[first=-100,last=100,seed=2]\nimgame{2,3}
%
%\end{enumerate}
%
%\section{Warnings}
%
%There is no limit in the code to the number of piles or the number in a pile, but this code doesn't do anything to cope when line breaks start happening, and presumably there is a computational limit.
%
%In principle, if you add lots of piles it will just wrap onto multiple lines, though it will start to look less clear. For example, the input\\
%\lstinline!\nimgame{1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1}!\\
%will produce the output:
%\nimgame{1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1}
%Similarly, if you have a lot of sticks in the same heap, it will wrap and look confusing, for example the input \lstinline!\nimgame{128}! will produce the output:
%\nimgame{256}
%
%
%\section{Changes to usage or output}
%
% (for full change log, see GitHub \lstinline|README.md|)
%
% \begin{itemize}
%    \item v2.0.1: documentation tweaks.
%    \item v2.0: rewrite, now based on ex and with options to customise size and colour, though basic usage should remain the same. More detailed documentation. Fixed a bug in v1.2 where a block display \lstinline|\nimgame| didn't start itself in a new paragraph.
%    \item v1.2: \begin{itemize}
%        \item switched \lstinline|\begin{center}| to \lstinline|\centering| (because the former doesn't work in \lstinline|standalone| documents and the latter doesn't add vertical space);
%        \item removed some whitespace that appeared to the right of the last heap.
%    \end{itemize}
%    \item v1.1: added option to make inline Nim game.
%\end{itemize}
%\iffalse
%&lt;*documentation&gt;
\documentclass{article}
\usepackage{nimsticks}
\usepackage{doc}
\usepackage{listings}
\lstset{basicstyle=\ttfamily\footnotesize,commentstyle=\color{white},language=TeX}
\title{nimsticks v2.0.1}
\author{Peter Rowlett}
\begin{document}
\maketitle
    \DocInput{nimsticks.dtx}
\end{document}
%&lt;/documentation&gt;
%\fi

%\iffalse
%&lt;*nimsticks&gt;
\ProvidesPackage{nimsticks}[2022/08/14 nimsticks 2.0.1]
\RequirePackage[first=-100,last=100,seed=0]{lcg}
\RequirePackage{tikz}
\RequirePackage{etoolbox}
\@ifundefined{drawnimstick}{}
    {\PackageWarning{nimsticks}{Command `drawnimstick' already defined}}
\@ifundefined{nimgame}{}
    {\PackageWarning{nimsticks}{Command `nimgame' already defined}}
\@ifundefined{listofgames}{}
    {\PackageWarning{nimsticks}{Command `listofgames' already defined}}
\@ifundefined{nimstickcolour}{}
    {\PackageWarning{nimsticks}{Command `nimstickcolour' already defined}}
\@ifundefined{setnimstickcolour}{}
    {\PackageWarning{nimsticks}{Command `setnimstickcolour' already defined}}
\@ifundefined{nimstickheight}{}
    {\PackageWarning{nimsticks}{Command `nimstickheight' already defined}}
\@ifundefined{nimstickthickness}{}
    {\PackageWarning{nimsticks}{Command `nimstickthickness' already defined}}
\@ifundefined{nimstickgap}{}
    {\PackageWarning{nimsticks}{Command `nimstickgap' already defined}}
\@ifundefined{nimheapgap}{}
    {\PackageWarning{nimsticks}{Command `nimheapgap' already defined}}
\@ifundefined{nimheapwobble}{}
    {\PackageWarning{nimsticks}{Command `nimheapwobble' already defined}}
\@ifundefined{nimheaplift}{}
    {\PackageWarning{nimsticks}{Command `nimheaplift' already defined}}
\@ifundefined{nimrandrange}{}
    {\PackageWarning{nimsticks}{Command `nimrandrange' already defined}}
\@ifundefined{setnimscale}{}
    {\PackageWarning{nimsticks}{Command `setnimscale' already defined}}
\@ifundefined{onenimstick}{}
    {\PackageWarning{nimsticks}{Command `onenimstick' already defined}}
\@ifundefined{topx}{}
    {\PackageWarning{nimsticks}{Command `topx' already defined}}
\@ifundefined{botx}{}
    {\PackageWarning{nimsticks}{Command `botx' already defined}}
\@ifundefined{lift}{}
    {\PackageWarning{nimsticks}{Command `lift' already defined}}
\@ifundefined{heap}{}
    {\PackageWarning{nimsticks}{Command `heap' already defined}}
\@ifundefined{heapindex}{}
    {\PackageWarning{nimsticks}{Command `heapindex' already defined}}

% Colour
\newcommand{\nimstickcolour}{black}
\newcommand{\setnimstickcolour}[1]{%
    \renewcommand{\nimstickcolour}{#1}
}

% Size
\newcommand{\nimstickheight}{3.3} % in ex
\newcommand{\nimstickthickness}{0.3} % in ex
\newcommand{\nimstickgap}{0.3} % in ex
\newcommand{\nimheapgap}{5} % in ex
\newcommand{\nimheapwobble}{0.001} % in ex
\newcommand{\nimheaplift}{0.002} % in ex
\newcommand{\nimrandrange}{100}
\newcommand{\setnimscale}[1]{%
    \pgfmathsetmacro{\nimstickheight}{3.3*#1}%
    \pgfmathsetmacro{\nimstickthickness}{0.3*#1}%
    \pgfmathsetmacro{\nimstickgap}{0.3*#1^(0.5)}%
    \pgfmathsetmacro{\nimheapgap}{5*#1^(0.25)}%
    \pgfmathsetmacro{\nimheapwobble}{0.001*#1^(0.25)}%
    \pgfmathsetmacro{\nimheaplift}{0.002*#1}%
    \pgfmathtruncatemacro{\nimrandrange}{100*#1}\reinitrand[first=-\nimrandrange,last=\nimrandrange,seed=0]%
}

% drawing a single Nim stick
\newcommand{\onenimstick}{\draw[line width=\nimstickthickness ex,\nimstickcolour] (\topx,0ex) -- (\botx,\nimstickheight ex);}
\newcommand{\drawnimstick}{%
    \rand\pgfmathsetmacro{\topx}{(\the\value{rand})*\nimheapwobble}%
    \rand\pgfmathsetmacro{\botx}{(\the\value{rand})*\nimheapwobble}%
    \rand\pgfmathsetmacro{\lift}{(\nimrandrange+\the\value{rand})*\nimheaplift}%
    \begin{tikzpicture}
    \node[inner sep=0] at (0,0) {}; % to anchor the diagram so any random movement isn't recentred
    \onenimstick
    \end{tikzpicture}%
}
\newcommand{\nimgame}[2][block]{%
    \ifstrequal{#1}{inline}{}{\par\bgroup\centering}%
    \def\listofgames{#2}%
    \foreach \heap in \listofgames {%
        \foreach \heapindex in {1, ..., \heap} {%
            \drawnimstick\hspace{\nimstickgap ex}%
        }%
        \hspace{\nimheapgap ex}%
    }\hspace{-\nimheapgap ex}%
    \ifstrequal{#1}{inline}{}{\par\egroup}%
}
%&lt;/nimsticks&gt;
%\fi
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