diff --git a/Misc/Warm-Ups/wild ttt.tex b/Misc/Warm-Ups/wild ttt.tex new file mode 100755 index 0000000..e6d6662 --- /dev/null +++ b/Misc/Warm-Ups/wild ttt.tex @@ -0,0 +1,65 @@ +\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} +\subtitle{Prepared by \githref{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} \ No newline at end of file