\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);
}


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

\begin{document}

	\maketitle


	\problem{}
	In wild tic-tac-toe, players may place either an X or O on each move. The player that first completes a
	row of any three symbols wins. Show that the first player always has a winning strategy.

	\vfill
	\begin{center}
		\begin{tikzpicture}[scale=0.60]
			\ttt{0}{0}{2}{line width=0.3mm}
			\ttt{7}{0}{2}{line width=0.3mm}
			\ttt{14}{0}{2}{line width=0.3mm}

			\ttt{0}{7}{2}{line width=0.3mm}
			\ttt{7}{7}{2}{line width=0.3mm}
			\ttt{14}{7}{2}{line width=0.3mm}
		\end{tikzpicture}
	\end{center}

	\vfill

	\problem{}
	Now, say the first player to complete a row loses. Who has a winning strategy now?

	\vfill
	\begin{center}
		\begin{tikzpicture}[scale=0.60]
			\ttt{0}{0}{2}{line width=0.3mm}
			\ttt{7}{0}{2}{line width=0.3mm}
			\ttt{14}{0}{2}{line width=0.3mm}

			\ttt{0}{7}{2}{line width=0.3mm}
			\ttt{7}{7}{2}{line width=0.3mm}
			\ttt{14}{7}{2}{line width=0.3mm}
		\end{tikzpicture}
	\end{center}


	\vfill
	\pagebreak

\end{document}