66 lines
1.4 KiB
TeX
Executable File
66 lines
1.4 KiB
TeX
Executable File
\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} |