Convert "Big-Tac-Toe" to typst
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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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]{../../../lib/tex/ormc_handout}
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\usepackage{../../../lib/tex/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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% misere ttt
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% Numerical Tic Tac Toe is a variation invented by the mathematician Ronald Graham.
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% The numbers 1 to 9 are used in this game. The first player plays with the odd numbers,
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% the second player plays with the even numbers. All numbers can be used only once.
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% The player who puts down 15 points in a line wins (sum of 3 numbers).
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% This game can be generalized to a n × n board.
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% In Treblecross, both players play with the same symbol.
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% The game is played on a 1-by-n board with k equal to 3.
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% The player who makes a three in a row of Xs (or black chips) wins the game
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\title{Warm-Up: Big-Tac-Toe}
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\uptitler{\smallurl{}}
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\subtitle{Prepared by 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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90
src/Warm-Ups/Big-Tac-Toe/main.typ
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90
src/Warm-Ups/Big-Tac-Toe/main.typ
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#import "@local/handout:0.1.0": *
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#import "@preview/cetz:0.3.1"
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#show: handout.with(
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title: [Warm-Up: Big-Tac-Toe],
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by: "Mark",
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)
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#let extra_boards = false;
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#let ttt(s, p) = {
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// s: scale,
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// p: position
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let x = p.at(0) * s
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let y = p.at(1) * s
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cetz.draw.line((-1 * s + x, 3 * s + y), (-1 * s + x, -3 * s + y))
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cetz.draw.line((1 * s + x, 3 * s + y), (1 * s + x, -3 * s + y))
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cetz.draw.line((3 * s + x, -1 * s + y), (-3 * s + x, -1 * s + y))
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cetz.draw.line((3 * s + x, 1 * s + y), (-3 * s + x, 1 * s + y))
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}
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#let btt(s) = cetz.canvas({
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import cetz.draw: *
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set-style(stroke: (thickness: 0.5mm * s))
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ttt(s, (-7, -7))
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ttt(s, (-7, 0))
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ttt(s, (-7, 7))
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ttt(s, (0, -7))
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ttt(s, (0, 0))
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ttt(s, (0, 7))
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ttt(s, (7, -7))
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ttt(s, (7, 0))
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ttt(s, (7, 7))
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set-style(stroke: (thickness: 2mm * s))
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ttt(s * 3.5, (0, 0))
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})
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#problem()
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Consider a 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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- The first player to move may pick any small grid to start in.
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- If a player is directed to a grid that is _full_, that player may go anywhere. \
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A sub-grid that is "won" but not full may still be played in.
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#v(2mm)
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The first player to complete a line of three "won" subgrids wins the game.
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#v(2mm)
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#problem()
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Play a few rounds of this game with someone nearby. \
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Can either player force a win?
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#table(
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stroke: none,
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align: center,
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columns: (1fr, 1fr),
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btt(0.35), btt(0.35),
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);
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#problem()
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Modify the rules of this game to disallow play in won subgrids. \
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How does your strategy change? \
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#if extra_boards { note([Additional boards are available on the next page.]) }
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#v(1fr)
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#if extra_boards {
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pagebreak()
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align(
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center,
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grid(
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stroke: none,
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align: center,
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columns: (1fr, 1fr),
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rows: (1fr, 1fr, 1fr),
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btt(0.35), btt(0.35),
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btt(0.35), btt(0.35),
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btt(0.35), btt(0.35),
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),
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)
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}
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