\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}