Added TTT warmup
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173
Misc/Warm-Ups/ttt.tex
Executable file
173
Misc/Warm-Ups/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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\geometry{
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paper = letterpaper,
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top = 25mm,
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bottom = 30mm,
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left = 20mm,
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right = 20mm,
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headheight = 75mm,
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footskip = 15mm
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}
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\title{Warm-Up: Big-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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We have large tic-tac-toe grid, each cell of which contains another.
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On each turn, one player puts their glyph into a cell of a small grid. When the next player goes,
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they must make their move in the small grid in the same position as the previous player's move.
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\begin{itemize}
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\item The first player to move may pick any small grid to start in.
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\item If a player is directed to a grid that is \textit{full}, that player may go anywhere. \par
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A sub-grid that is \say{won} but not full may still be played in.
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\end{itemize}
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\vspace{2mm}
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The first player to complete a line of three \say{won} subgrids wins the game.
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\vfill\null\hfill
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\begin{minipage}{0.48\textwidth}
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\begin{center}
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\begin{tikzpicture}[scale=0.65]
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\ttt{0}{0}{4}{line width=0.5mm}
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\ttt{0.5}{0.5}{1}{line width=0.25mm}
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\ttt{0.5}{4.5}{1}{line width=0.25mm}
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\ttt{0.5}{8.5}{1}{line width=0.25mm}
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\ttt{4.5}{0.5}{1}{line width=0.25mm}
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\ttt{4.5}{4.5}{1}{line width=0.25mm}
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\ttt{4.5}{8.5}{1}{line width=0.25mm}
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\ttt{8.5}{0.5}{1}{line width=0.25mm}
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\ttt{8.5}{4.5}{1}{line width=0.25mm}
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\ttt{8.5}{8.5}{1}{line width=0.25mm}
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\end{tikzpicture}
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\end{center}
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\end{minipage}
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\hfill
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\begin{minipage}{0.48\textwidth}
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\begin{center}
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\begin{tikzpicture}[scale=0.65]
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\ttt{0}{0}{4}{line width=0.5mm}
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\ttt{0.5}{0.5}{1}{line width=0.25mm}
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\ttt{0.5}{4.5}{1}{line width=0.25mm}
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\ttt{0.5}{8.5}{1}{line width=0.25mm}
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\ttt{4.5}{0.5}{1}{line width=0.25mm}
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\ttt{4.5}{4.5}{1}{line width=0.25mm}
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\ttt{4.5}{8.5}{1}{line width=0.25mm}
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\ttt{8.5}{0.5}{1}{line width=0.25mm}
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\ttt{8.5}{4.5}{1}{line width=0.25mm}
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\ttt{8.5}{8.5}{1}{line width=0.25mm}
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\end{tikzpicture}
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\end{center}
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\end{minipage}
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\hfill\null\vfill
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\problem{}
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Play a few rounds of this game with someone nearby. \par
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Can either player force a win?
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\vfill
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\problem{}
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Modify the rules of this game to disallow play in won subgrids. \par
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How does your strategy change?
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\vfill
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\pagebreak
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\null\vfill\null\hfill
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\begin{minipage}{0.48\textwidth}
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\begin{center}
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\begin{tikzpicture}[scale=0.65]
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\ttt{0}{0}{4}{line width=0.5mm}
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\ttt{0.5}{0.5}{1}{line width=0.25mm}
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\ttt{0.5}{4.5}{1}{line width=0.25mm}
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\ttt{0.5}{8.5}{1}{line width=0.25mm}
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\ttt{4.5}{0.5}{1}{line width=0.25mm}
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\ttt{4.5}{4.5}{1}{line width=0.25mm}
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\ttt{4.5}{8.5}{1}{line width=0.25mm}
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\ttt{8.5}{0.5}{1}{line width=0.25mm}
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\ttt{8.5}{4.5}{1}{line width=0.25mm}
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\ttt{8.5}{8.5}{1}{line width=0.25mm}
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\end{tikzpicture}
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\end{center}
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\end{minipage}
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\hfill
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\begin{minipage}{0.48\textwidth}
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\begin{center}
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\begin{tikzpicture}[scale=0.65]
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\ttt{0}{0}{4}{line width=0.5mm}
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\ttt{0.5}{0.5}{1}{line width=0.25mm}
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\ttt{0.5}{4.5}{1}{line width=0.25mm}
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\ttt{0.5}{8.5}{1}{line width=0.25mm}
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\ttt{4.5}{0.5}{1}{line width=0.25mm}
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\ttt{4.5}{4.5}{1}{line width=0.25mm}
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\ttt{4.5}{8.5}{1}{line width=0.25mm}
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\ttt{8.5}{0.5}{1}{line width=0.25mm}
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\ttt{8.5}{4.5}{1}{line width=0.25mm}
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\ttt{8.5}{8.5}{1}{line width=0.25mm}
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\end{tikzpicture}
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\end{center}
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\end{minipage}
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\hfill\null\vfill
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\vfill\null\hfill
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\begin{minipage}{0.48\textwidth}
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\begin{center}
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\begin{tikzpicture}[scale=0.65]
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\ttt{0}{0}{4}{line width=0.5mm}
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\ttt{0.5}{0.5}{1}{line width=0.25mm}
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\ttt{0.5}{4.5}{1}{line width=0.25mm}
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\ttt{0.5}{8.5}{1}{line width=0.25mm}
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\ttt{4.5}{0.5}{1}{line width=0.25mm}
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\ttt{4.5}{4.5}{1}{line width=0.25mm}
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\ttt{4.5}{8.5}{1}{line width=0.25mm}
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\ttt{8.5}{0.5}{1}{line width=0.25mm}
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\ttt{8.5}{4.5}{1}{line width=0.25mm}
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\ttt{8.5}{8.5}{1}{line width=0.25mm}
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\end{tikzpicture}
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\end{center}
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\end{minipage}
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\hfill
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\begin{minipage}{0.48\textwidth}
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\begin{center}
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\begin{tikzpicture}[scale=0.65]
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\ttt{0}{0}{4}{line width=0.5mm}
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\ttt{0.5}{0.5}{1}{line width=0.25mm}
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\ttt{0.5}{4.5}{1}{line width=0.25mm}
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\ttt{0.5}{8.5}{1}{line width=0.25mm}
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\ttt{4.5}{0.5}{1}{line width=0.25mm}
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\ttt{4.5}{4.5}{1}{line width=0.25mm}
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\ttt{4.5}{8.5}{1}{line width=0.25mm}
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\ttt{8.5}{0.5}{1}{line width=0.25mm}
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\ttt{8.5}{4.5}{1}{line width=0.25mm}
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\ttt{8.5}{8.5}{1}{line width=0.25mm}
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\end{tikzpicture}
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\end{center}
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\end{minipage}
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\hfill\null\vfill
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\end{document}
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