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Added TTT warmup

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Mark 2023-10-26 09:02:51 -07:00
parent 9fe9a1aa25
commit a460f4f376
Signed by: Mark
GPG Key ID: AD62BB059C2AAEE4
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Misc/Warm-Ups/ttt.tex Executable file
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\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);
}
\geometry{
paper = letterpaper,
top = 25mm,
bottom = 30mm,
left = 20mm,
right = 20mm,
headheight = 75mm,
footskip = 15mm
}
\title{Warm-Up: Big-Tac-Toe}
\subtitle{Prepared by \githref{Mark} on \today.}
\begin{document}
\maketitle
We have large tic-tac-toe grid, each cell of which contains another.
On each turn, one player puts their glyph into a cell of a small grid. When the next player goes,
they must make their move in the small grid in the same position as the previous player's move.
\begin{itemize}
\item The first player to move may pick any small grid to start in.
\item If a player is directed to a grid that is \textit{full}, that player may go anywhere. \par
A sub-grid that is \say{won} but not full may still be played in.
\end{itemize}
\vspace{2mm}
The first player to complete a line of three \say{won} subgrids wins the game.
\vfill\null\hfill
\begin{minipage}{0.48\textwidth}
\begin{center}
\begin{tikzpicture}[scale=0.65]
\ttt{0}{0}{4}{line width=0.5mm}
\ttt{0.5}{0.5}{1}{line width=0.25mm}
\ttt{0.5}{4.5}{1}{line width=0.25mm}
\ttt{0.5}{8.5}{1}{line width=0.25mm}
\ttt{4.5}{0.5}{1}{line width=0.25mm}
\ttt{4.5}{4.5}{1}{line width=0.25mm}
\ttt{4.5}{8.5}{1}{line width=0.25mm}
\ttt{8.5}{0.5}{1}{line width=0.25mm}
\ttt{8.5}{4.5}{1}{line width=0.25mm}
\ttt{8.5}{8.5}{1}{line width=0.25mm}
\end{tikzpicture}
\end{center}
\end{minipage}
\hfill
\begin{minipage}{0.48\textwidth}
\begin{center}
\begin{tikzpicture}[scale=0.65]
\ttt{0}{0}{4}{line width=0.5mm}
\ttt{0.5}{0.5}{1}{line width=0.25mm}
\ttt{0.5}{4.5}{1}{line width=0.25mm}
\ttt{0.5}{8.5}{1}{line width=0.25mm}
\ttt{4.5}{0.5}{1}{line width=0.25mm}
\ttt{4.5}{4.5}{1}{line width=0.25mm}
\ttt{4.5}{8.5}{1}{line width=0.25mm}
\ttt{8.5}{0.5}{1}{line width=0.25mm}
\ttt{8.5}{4.5}{1}{line width=0.25mm}
\ttt{8.5}{8.5}{1}{line width=0.25mm}
\end{tikzpicture}
\end{center}
\end{minipage}
\hfill\null\vfill
\problem{}
Play a few rounds of this game with someone nearby. \par
Can either player force a win?
\vfill
\problem{}
Modify the rules of this game to disallow play in won subgrids. \par
How does your strategy change?
\vfill
\pagebreak
\null\vfill\null\hfill
\begin{minipage}{0.48\textwidth}
\begin{center}
\begin{tikzpicture}[scale=0.65]
\ttt{0}{0}{4}{line width=0.5mm}
\ttt{0.5}{0.5}{1}{line width=0.25mm}
\ttt{0.5}{4.5}{1}{line width=0.25mm}
\ttt{0.5}{8.5}{1}{line width=0.25mm}
\ttt{4.5}{0.5}{1}{line width=0.25mm}
\ttt{4.5}{4.5}{1}{line width=0.25mm}
\ttt{4.5}{8.5}{1}{line width=0.25mm}
\ttt{8.5}{0.5}{1}{line width=0.25mm}
\ttt{8.5}{4.5}{1}{line width=0.25mm}
\ttt{8.5}{8.5}{1}{line width=0.25mm}
\end{tikzpicture}
\end{center}
\end{minipage}
\hfill
\begin{minipage}{0.48\textwidth}
\begin{center}
\begin{tikzpicture}[scale=0.65]
\ttt{0}{0}{4}{line width=0.5mm}
\ttt{0.5}{0.5}{1}{line width=0.25mm}
\ttt{0.5}{4.5}{1}{line width=0.25mm}
\ttt{0.5}{8.5}{1}{line width=0.25mm}
\ttt{4.5}{0.5}{1}{line width=0.25mm}
\ttt{4.5}{4.5}{1}{line width=0.25mm}
\ttt{4.5}{8.5}{1}{line width=0.25mm}
\ttt{8.5}{0.5}{1}{line width=0.25mm}
\ttt{8.5}{4.5}{1}{line width=0.25mm}
\ttt{8.5}{8.5}{1}{line width=0.25mm}
\end{tikzpicture}
\end{center}
\end{minipage}
\hfill\null\vfill
\vfill\null\hfill
\begin{minipage}{0.48\textwidth}
\begin{center}
\begin{tikzpicture}[scale=0.65]
\ttt{0}{0}{4}{line width=0.5mm}
\ttt{0.5}{0.5}{1}{line width=0.25mm}
\ttt{0.5}{4.5}{1}{line width=0.25mm}
\ttt{0.5}{8.5}{1}{line width=0.25mm}
\ttt{4.5}{0.5}{1}{line width=0.25mm}
\ttt{4.5}{4.5}{1}{line width=0.25mm}
\ttt{4.5}{8.5}{1}{line width=0.25mm}
\ttt{8.5}{0.5}{1}{line width=0.25mm}
\ttt{8.5}{4.5}{1}{line width=0.25mm}
\ttt{8.5}{8.5}{1}{line width=0.25mm}
\end{tikzpicture}
\end{center}
\end{minipage}
\hfill
\begin{minipage}{0.48\textwidth}
\begin{center}
\begin{tikzpicture}[scale=0.65]
\ttt{0}{0}{4}{line width=0.5mm}
\ttt{0.5}{0.5}{1}{line width=0.25mm}
\ttt{0.5}{4.5}{1}{line width=0.25mm}
\ttt{0.5}{8.5}{1}{line width=0.25mm}
\ttt{4.5}{0.5}{1}{line width=0.25mm}
\ttt{4.5}{4.5}{1}{line width=0.25mm}
\ttt{4.5}{8.5}{1}{line width=0.25mm}
\ttt{8.5}{0.5}{1}{line width=0.25mm}
\ttt{8.5}{4.5}{1}{line width=0.25mm}
\ttt{8.5}{8.5}{1}{line width=0.25mm}
\end{tikzpicture}
\end{center}
\end{minipage}
\hfill\null\vfill
\end{document}