diff --git a/Misc/Warm-Ups/roots.tex b/Misc/Warm-Ups/roots.tex new file mode 100755 index 0000000..fcbe939 --- /dev/null +++ b/Misc/Warm-Ups/roots.tex @@ -0,0 +1,103 @@ +\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} \ No newline at end of file