From a460f4f3769fadd56ed97c2beb4ef2e0ad5a45ce Mon Sep 17 00:00:00 2001 From: Mark Date: Thu, 26 Oct 2023 09:02:51 -0700 Subject: [PATCH] Added TTT warmup --- Misc/Warm-Ups/ttt.tex | 173 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 173 insertions(+) create mode 100755 Misc/Warm-Ups/ttt.tex diff --git a/Misc/Warm-Ups/ttt.tex b/Misc/Warm-Ups/ttt.tex new file mode 100755 index 0000000..84d4033 --- /dev/null +++ b/Misc/Warm-Ups/ttt.tex @@ -0,0 +1,173 @@ +\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} \ No newline at end of file