Cleanup

Misc/Proof Techniques/parts/2 induction.tex

@@ -189,11 +189,8 @@ For example, see the proof of the statement in \ref{binomsum} on the next page.
 
 \pagebreak
 
-\makeatletter
-\@makeORMCbox{tmpbox}{Alternative Proof}{ogrape!10!white}{ogrape}
-\makeatother
 
-\begin{tmpbox}
+\begin{ORMCbox}{Alternative Proof}{ogrape!10!white}{ogrape}
 	Consider the following problem: \par
 	How many ways are there to write a number $x$ as an ordered sum of positive integers? \par
 	\note{
@@ -237,7 +234,7 @@ For example, see the proof of the statement in \ref{binomsum} on the next page.
 	We've found that the number of ways to split $x$ can be written as either
 	$\sum_{n = 1}^{x-1} \binom{x-1}{n}$ or $2^{x-1}$,
 	and therefore $\sum_{n = 1}^{x-1} \binom{x-1}{n} = 2^{x-1}$.
-\end{tmpbox}
+\end{ORMCbox}
 
 
 \pagebreak

Misc/Warm-Ups/rootbound.tex

@@ -0,0 +1,117 @@
+\documentclass[
+	solutions,
+	hidewarning,
+	singlenumbering,
+	nopagenumber
+]{../../resources/ormc_handout}
+\usepackage{../../resources/macros}
+
+\def\utri#1#2{
+	\draw (#1,#2) -- ++(60:1) -- ++(-60:1) -- cycle;
+}
+\def\dtri#1#2{
+	\draw (#1,#2) -- (#1+1, #2) -- ++(-120:1) -- cycle;
+}
+
+\def\board#1{
+	\begin{center}
+		\begin{tikzpicture}[scale=#1]
+			\draw (0,0) -- (6, 0);
+			\foreach \y in {0,...,5} {
+			\foreach[expand list] \x in {-6,-5,...,\y} {
+					\utri{\x + 6 - 0.5 - \y * 0.5}{\y * -0.86603 - 0.86603}
+				}
+			}
+			\foreach \y in {5,...,0} {
+				\foreach[expand list] \x in {-5,-4,...,\y} {
+					\utri{\x + 5 - \y * 0.5}{\y * 0.86603 - 12 * 0.86603}
+				}
+			}
+			\draw (-3, -6 * 0.86603) -- (0, -12 * 0.86603);
+			\draw (9, -6 * 0.86603) -- (6, -12 * 0.86603);
+		\end{tikzpicture}
+	\end{center}
+}
+
+\title{Rootbound}
+\uptitler{\smallurl{}}
+\uptitlel{Warm-ups}
+\subtitle{
+	Prepared by Mark on \today. \par
+	Based on \url{https://cjffield.com/rules/rootbound.pdf}
+}
+
+\begin{document}
+
+	\maketitle
+
+	\generic{Playing the game:}
+	% Official size is 7 spaces per side, but variations work.
+	You will need a pencil, an eraser, and a printed hexagonal board. \par
+	Draw your pieces lightly---you may need to erase them. \par
+	Turns alternate. Each player draws distinct pieces (for example, circles and squares).
+
+	\vspace{2mm}
+
+	An example board is drawn below. \say{Spaces} are the corners of the triangular cells, \textit{not} the cells themselves.
+	Points on the edge of the board are also spaces.
+
+	\board{0.3}
+
+	During the first turn of the game, the first player must place one piece onto any empty space.
+	From then on, each player may place either one or two pieces onto empty spaces, respecting the restrictions below.
+	Players may not skip their turn unless they have no legal move.
+
+
+	\generic{Claimed regions:}
+	A \textit{claimed region} is an area of empty spaces that is only adjacent to pieces of a single color. \par
+	No regions are considered \say{claimed} until both players have had a turn.
+
+
+	\generic{Dead groups:}
+	A group of pieces is considered \textit{dead} if it is cut off from all other same-colored groups and is not
+	adjacent to a claimed region. At the end of each turn (except each player's first), erase all
+	dead pieces that belong to the inactive player.
+
+	\generic{Restrictions:}
+	\begin{itemize}[itemsep=1mm]
+		\item A piece may not be placed inside a claimed region.
+		\item A piece may not be placed adjacent to two (or more) same-colored pieces if those pieces are also
+		neighbors of each other. In other words, you may not form small triangles of one color.
+
+		\item When placing two pieces adjacent to each other in a tun, they may not form a
+		straight line with a third pre-existing piece of their color.
+	\end{itemize}
+
+
+	\generic{Ending the game:}
+	The game ends when both players run out of legal moves.
+	Each player's score is calculated by counting the number of empty spaces in regions they have claimed. \par
+	The player with the highest score wins.
+
+	\vfill
+
+	\begin{ORMCbox}{Notes}{ogrape!10!white}{ogrape}
+		\begin{itemize}
+			\item
+			Each player needs to make multiple groups before the first player's second turn. \par
+			Otherwise, all their pieces will be removed from the game, resulting in an early loss. \par
+			Do not make your first placements next to each other!
+
+			\item
+			Live groups are easiest to secure near the corners or along the edges. Play there first. \par
+		\end{itemize}
+	\end{ORMCbox}
+
+
+
+
+	\pagebreak
+
+	\null\vfill
+	\board{1.4}
+	\vfill\null
+
+	\pagebreak
+
+\end{document}

Misc/Warm-Ups/roots.tex

@@ -1,103 +0,0 @@
-\documentclass[
-	solutions,
-	hidewarning,
-	singlenumbering,
-	nopagenumber
-]{../../resources/ormc_handout}
-\usepackage{../../resources/macros}
-
-\def\utri#1#2{
-	\draw (#1,#2) -- ++(60:1) -- ++(-60:1) -- cycle;
-}
-\def\dtri#1#2{
-	\draw (#1,#2) -- (#1+1, #2) -- ++(-120:1) -- cycle;
-}
-
-\def\board#1{
-	\begin{center}
-		\begin{tikzpicture}[scale=#1]
-			\draw (0,0) -- (6, 0);
-			\foreach \y in {0,...,5} {
-			\foreach[expand list] \x in {-6,-5,...,\y} {
-					\utri{\x + 6 - 0.5 - \y * 0.5}{\y * -0.86603 - 0.86603}
-				}
-			}
-			\foreach \y in {5,...,0} {
-				\foreach[expand list] \x in {-5,-4,...,\y} {
-					\utri{\x + 5 - \y * 0.5}{\y * 0.86603 - 12 * 0.86603}
-				}
-			}
-			\draw (-3, -6 * 0.86603) -- (0, -12 * 0.86603);
-			\draw (9, -6 * 0.86603) -- (6, -12 * 0.86603);
-		\end{tikzpicture}
-	\end{center}
-}
-
-\title{Rootbound}
-\uptitler{\smallurl{}}
-\uptitlel{Warm-ups}
-\subtitle{Prepared by Mark on \today.}
-
-\begin{document}
-
-	\maketitle
-
-	\generic{Playing the game:}
-	% Official size is 7 spaces per side, but variations work.
-	You will need a pencil, an eraser, and a printed hexagonal board. \par
-	Draw your pieces lightly---you may need to erase them.
-
-
-	Turns alternate.
-	On the first player's first turn, they must place one piece onto any empty space.
-	From then on, players may place either one or two pieces onto empty spaces, respecting the restrictions below.
-	Players may not skip their turn unless they have no legal move.
-
-
-	\generic{Claimed regions:}
-	A \textit{claimed region} is an area of empty spaces that is adjacent to only pieces of a single color. \par
-	No regions are Claimed Regions until both players have had a turn.
-
-
-	\generic{Dead groups:}
-	A group of pieces is considered \textit{dead} if it is cut off from all other same-colored groups and is not
-	adjacent to a claimed region. At the end of each turn (except each player's first), remove all
-	dead pieces that belong to the inactive player.
-
-	\generic{Restrictions:}
-	\begin{itemize}
-		\item A piece may not be placed in a claimed region.
-		\item A piece may not be placed adjacent to two or more same-colored pieces if those pieces are also
-		neighbors of each other (i.e, if they do not form any small triangles of one color).
-
-		\item Additionally, when placing two pieces adjacent to each other in a turn, they may not form a
-		straight line with a third pre-existing piece of their color. Rapid growth cannot go in a straight
-		line.
-	\end{itemize}
-
-
-	\generic{Ending the game:}
-	The game ends when both players run out of legal moves.
-	Each player's score is calculated by counting the number of empty spaces in regions they have claimed.
-	The player with the highest score wins.
-
-%It is important to note that players will need to make multiple groups by the second player’s
-%first turn or the first player’s second. Otherwise, their groups will be considered dead and
-%removed from the game, resulting in an early loss. Do not make your first placements next to
-%each other.
-
-%Live groups are easiest to secure near the corners or along the edges. Play there first. But do
-%not get too greedy by trying to secure too much space. It is very easy for the enemy to invade
-%and ruin your plans.
-
-
-	\vfill
-	\pagebreak
-
-	\null\vfill
-	\board{1.4}
-	\vfill\null
-
-	\pagebreak
-
-\end{document}