\documentclass[
	solutions,
	hidewarning,
	singlenumbering,
	nopagenumber
]{../../resources/ormc_handout}
\usepackage{../../resources/macros}

% x,y,scale,style
\def\ttt#1#2#3#4{
	\draw[#4] (#1, #2+#3) -- (#1+#3+#3+#3, #2+#3);
	\draw[#4] (#1, #2+#3+#3) -- (#1+#3+#3+#3, #2+#3+#3);
	\draw[#4] (#1+#3, #2) -- (#1+#3, #2+#3+#3+#3);
	\draw[#4] (#1+#3+#3, #2) -- (#1+#3+#3, #2+#3+#3+#3);
}


\geometry{
	paper      = letterpaper,
	top        = 25mm,
	bottom     = 30mm,
	left       = 20mm,
	right      = 20mm,
	headheight = 75mm,
	footskip   = 15mm
}


% misere ttt

% Numerical Tic Tac Toe is a variation invented by the mathematician Ronald Graham.
% The numbers 1 to 9 are used in this game. The first player plays with the odd numbers,
% the second player plays with the even numbers. All numbers can be used only once.
% The player who puts down 15 points in a line wins (sum of 3 numbers).
% This game can be generalized to a n × n board.


% In Treblecross, both players play with the same symbol.
% The game is played on a 1-by-n board with k equal to 3.
% The player who makes a three in a row of Xs (or black chips) wins the game

\title{Warm-Up: Big-Tac-Toe}
\uptitler{\smallurl{}}
\subtitle{Prepared by Mark on \today.}

\begin{document}

	\maketitle



	We have large tic-tac-toe grid, each cell of which contains another.
	On each turn, one player puts their glyph into a cell of a small grid. When the next player goes,
	they must make their move in the small grid in the same position as the previous player's move.
	\begin{itemize}
		\item The first player to move may pick any small grid to start in.
		\item If a player is directed to a grid that is \textit{full}, that player may go anywhere. \par
		A sub-grid that is \say{won} but not full may still be played in.
	\end{itemize}

	\vspace{2mm}

	The first player to complete a line of three \say{won} subgrids wins the game.

	\vfill\null\hfill
	\begin{minipage}{0.48\textwidth}
		\begin{center}
			\begin{tikzpicture}[scale=0.65]
				\ttt{0}{0}{4}{line width=0.5mm}
				\ttt{0.5}{0.5}{1}{line width=0.25mm}
				\ttt{0.5}{4.5}{1}{line width=0.25mm}
				\ttt{0.5}{8.5}{1}{line width=0.25mm}
				\ttt{4.5}{0.5}{1}{line width=0.25mm}
				\ttt{4.5}{4.5}{1}{line width=0.25mm}
				\ttt{4.5}{8.5}{1}{line width=0.25mm}
				\ttt{8.5}{0.5}{1}{line width=0.25mm}
				\ttt{8.5}{4.5}{1}{line width=0.25mm}
				\ttt{8.5}{8.5}{1}{line width=0.25mm}
			\end{tikzpicture}
		\end{center}
	\end{minipage}
	\hfill
	\begin{minipage}{0.48\textwidth}
		\begin{center}
			\begin{tikzpicture}[scale=0.65]
				\ttt{0}{0}{4}{line width=0.5mm}
				\ttt{0.5}{0.5}{1}{line width=0.25mm}
				\ttt{0.5}{4.5}{1}{line width=0.25mm}
				\ttt{0.5}{8.5}{1}{line width=0.25mm}
				\ttt{4.5}{0.5}{1}{line width=0.25mm}
				\ttt{4.5}{4.5}{1}{line width=0.25mm}
				\ttt{4.5}{8.5}{1}{line width=0.25mm}
				\ttt{8.5}{0.5}{1}{line width=0.25mm}
				\ttt{8.5}{4.5}{1}{line width=0.25mm}
				\ttt{8.5}{8.5}{1}{line width=0.25mm}
			\end{tikzpicture}
		\end{center}
	\end{minipage}
	\hfill\null\vfill

	\problem{}
	Play a few rounds of this game with someone nearby. \par
	Can either player force a win?

	\vfill

	\problem{}
	Modify the rules of this game to disallow play in won subgrids. \par
	How does your strategy change?

	\vfill
	\pagebreak


	\null\vfill\null\hfill
	\begin{minipage}{0.48\textwidth}
		\begin{center}
			\begin{tikzpicture}[scale=0.65]
				\ttt{0}{0}{4}{line width=0.5mm}
				\ttt{0.5}{0.5}{1}{line width=0.25mm}
				\ttt{0.5}{4.5}{1}{line width=0.25mm}
				\ttt{0.5}{8.5}{1}{line width=0.25mm}
				\ttt{4.5}{0.5}{1}{line width=0.25mm}
				\ttt{4.5}{4.5}{1}{line width=0.25mm}
				\ttt{4.5}{8.5}{1}{line width=0.25mm}
				\ttt{8.5}{0.5}{1}{line width=0.25mm}
				\ttt{8.5}{4.5}{1}{line width=0.25mm}
				\ttt{8.5}{8.5}{1}{line width=0.25mm}
			\end{tikzpicture}
		\end{center}
	\end{minipage}
	\hfill
	\begin{minipage}{0.48\textwidth}
		\begin{center}
			\begin{tikzpicture}[scale=0.65]
				\ttt{0}{0}{4}{line width=0.5mm}
				\ttt{0.5}{0.5}{1}{line width=0.25mm}
				\ttt{0.5}{4.5}{1}{line width=0.25mm}
				\ttt{0.5}{8.5}{1}{line width=0.25mm}
				\ttt{4.5}{0.5}{1}{line width=0.25mm}
				\ttt{4.5}{4.5}{1}{line width=0.25mm}
				\ttt{4.5}{8.5}{1}{line width=0.25mm}
				\ttt{8.5}{0.5}{1}{line width=0.25mm}
				\ttt{8.5}{4.5}{1}{line width=0.25mm}
				\ttt{8.5}{8.5}{1}{line width=0.25mm}
			\end{tikzpicture}
		\end{center}
	\end{minipage}
	\hfill\null\vfill

	\vfill\null\hfill
	\begin{minipage}{0.48\textwidth}
		\begin{center}
			\begin{tikzpicture}[scale=0.65]
				\ttt{0}{0}{4}{line width=0.5mm}
				\ttt{0.5}{0.5}{1}{line width=0.25mm}
				\ttt{0.5}{4.5}{1}{line width=0.25mm}
				\ttt{0.5}{8.5}{1}{line width=0.25mm}
				\ttt{4.5}{0.5}{1}{line width=0.25mm}
				\ttt{4.5}{4.5}{1}{line width=0.25mm}
				\ttt{4.5}{8.5}{1}{line width=0.25mm}
				\ttt{8.5}{0.5}{1}{line width=0.25mm}
				\ttt{8.5}{4.5}{1}{line width=0.25mm}
				\ttt{8.5}{8.5}{1}{line width=0.25mm}
			\end{tikzpicture}
		\end{center}
	\end{minipage}
	\hfill
	\begin{minipage}{0.48\textwidth}
		\begin{center}
			\begin{tikzpicture}[scale=0.65]
				\ttt{0}{0}{4}{line width=0.5mm}
				\ttt{0.5}{0.5}{1}{line width=0.25mm}
				\ttt{0.5}{4.5}{1}{line width=0.25mm}
				\ttt{0.5}{8.5}{1}{line width=0.25mm}
				\ttt{4.5}{0.5}{1}{line width=0.25mm}
				\ttt{4.5}{4.5}{1}{line width=0.25mm}
				\ttt{4.5}{8.5}{1}{line width=0.25mm}
				\ttt{8.5}{0.5}{1}{line width=0.25mm}
				\ttt{8.5}{4.5}{1}{line width=0.25mm}
				\ttt{8.5}{8.5}{1}{line width=0.25mm}
			\end{tikzpicture}
		\end{center}
	\end{minipage}
	\hfill\null\vfill

\end{document}