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%----------Title-------------
\title{Groupwork: Homework X}
\author{Leonard Euler, \textbf{Carl Gauss}, \textit{Isaac Newton}, Bernhard Riemann} % READ: The scribe is to be bolded, chief italicized
\date{\today}

\begin{document}

\pagestyle{plain}

\maketitle


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%\setcounter{section}{1}   

\section{Meet-First}

The game Meet-First is played by two players A and B, who take turns to move towards another on a narrow bridge. Initially, the two players are at opposite ends of the bridge, at a distance of $n$ feet from each other (here, $n$ is an arbitrary positive integer). When it is their turn, they are allowed to jump 1, 2, or 3 feet toward each other. A player must move forward on their turn.

The game begins with A making the first move, and then B and A alternate turns. The game ends when one player is able to meet (i.e. jump on top of) the other player. The player who is able to jump on top of the other player first is declared the winner.

\begin{enumerate}
  \item{Does either player have a strategy to guarantee a win if $n = 4$?}
  \begin{proof}[Solution]
  	
  \end{proof}

  \item{What about when $n = 8$?}
  \begin{proof}[Solution]
  	
  \end{proof}

  
  \item{What about when $n = 21$?}
  \begin{proof}[Solution]
  	
  \end{proof}

  
  \item{What if $n$ is an arbitrary positive integer? (Hint: How does the answer for $n$ relate to the answer for $m$, where $m$ is an integer such that $m < n$?)}
  \begin{proof}[Solution]
  	
  \end{proof}

\end{enumerate}


\end{document}