Added a warmup
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Misc/Warm-Ups/wild ttt.tex
Executable file
65
Misc/Warm-Ups/wild ttt.tex
Executable file
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\documentclass[
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solutions,
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hidewarning,
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singlenumbering,
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nopagenumber
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]{../../resources/ormc_handout}
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\usepackage{../../resources/macros}
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% x,y,scale,style
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\def\ttt#1#2#3#4{
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\draw[#4] (#1, #2+#3) -- (#1+#3+#3+#3, #2+#3);
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\draw[#4] (#1, #2+#3+#3) -- (#1+#3+#3+#3, #2+#3+#3);
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\draw[#4] (#1+#3, #2) -- (#1+#3, #2+#3+#3+#3);
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\draw[#4] (#1+#3+#3, #2) -- (#1+#3+#3, #2+#3+#3+#3);
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}
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\title{Warm-Up: Wild Tic-Tac-Toe}
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\subtitle{Prepared by \githref{Mark} on \today.}
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\begin{document}
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\maketitle
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\problem{}
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In wild tic-tac-toe, players may place either an X or O on each move. The player that first completes a
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row of any three symbols wins. Show that the first player always has a winning strategy.
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\vfill
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\begin{center}
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\begin{tikzpicture}[scale=0.60]
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\ttt{0}{0}{2}{line width=0.3mm}
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\ttt{7}{0}{2}{line width=0.3mm}
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\ttt{14}{0}{2}{line width=0.3mm}
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\ttt{0}{7}{2}{line width=0.3mm}
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\ttt{7}{7}{2}{line width=0.3mm}
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\ttt{14}{7}{2}{line width=0.3mm}
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\end{tikzpicture}
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\end{center}
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\vfill
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\problem{}
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Now, say the first player to complete a row loses. Who has a winning strategy now?
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\vfill
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\begin{center}
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\begin{tikzpicture}[scale=0.60]
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\ttt{0}{0}{2}{line width=0.3mm}
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\ttt{7}{0}{2}{line width=0.3mm}
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\ttt{14}{0}{2}{line width=0.3mm}
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\ttt{0}{7}{2}{line width=0.3mm}
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\ttt{7}{7}{2}{line width=0.3mm}
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\ttt{14}{7}{2}{line width=0.3mm}
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\end{tikzpicture}
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\end{center}
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\vfill
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\pagebreak
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\end{document}
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