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\title{Coe College Math Teachers Circle} 
\author{Jon White} 
\date{Today} 


\begin{document}
% October 1 - Initial meeting.
\begin{frame}
\begin{center}
\Huge{Coe College \\ Math Teachers Circle}

\vspace{.25in}

\Large{Meeting 3 \\ 11/11/2023}
\end{center}
\end{frame} 


% intro frame for each week:
\begin{frame} 
\frametitle{Cat and Mouse}
% \small 
\begin{center}
\tikzstyle{mybox} = [draw=black, fill=blue!20, very thick,
    rectangle, rounded corners, inner sep=5pt, inner ysep=10pt]
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\begin{tikzpicture}
\node [mybox] (box){%
	\begin{minipage}{1\textwidth}
    	\begin{center}
	

\noindent Cat and Mouse is a 2-player game. Here's how to play:
\begin{itemize}
\item The cat and the mouse start out in different squares on a $4 \times 4$ grid. The cat starts in the bottom left corner, and the mouse starts in the bottom right corner.
\item The cat and mouse take turns making moves, with the cat going first. On each turn, they can move one square horizontally or vertically, but not diagonally.
\item The cat gets 7 moves to catch the mouse. If the cat catches the mouse by its 7th move, the cat wins. If the cat hasn't caught the mouse by its 7th move, the mouse wins.
\end{itemize}
	\end{center}
	\end{minipage}
};
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\end{center}

\begin{enumerate}
\item Can you beat an expert at this game if you're allowed to choose whether to be the cat or the mouse? 
\item What if the mouse starts in a different square? For which of the possible starting squares for the mouse is it better to be the cat, and for which is it better to be the mouse? 
\item What if the mouse goes first instead of the cat?
\end{enumerate}
% \normalsize
\center{\tiny{Borrowed from https://www.sfmathcircle.org/cat-and-mouse}}
\end{frame} 

\begin{frame}
\frametitle{ChatGPT Factoring}

News story:
https://www.searchenginejournal.com/chatgpt-quality-worsened/492145

\end{frame}

\begin{frame}
\frametitle{Stan Wagon's Problem 1366: Factoring Factorials}
\begin{Large} \begin{center}
Wagon's question is ``Express 30! as a product of triangular numbers?''\\
\vspace{0.1in}
(The triangular numbers are 1, 3, 6, 10, 15,...; $T(n) = \frac{n(n+1)}{2}$.)\\
\vspace{0.2in}
My question: Which factorials can be expressed this way?
\end{center} \end{Large}
\end{frame}

\begin{frame}
\frametitle{Bubbling Cauldrons}
\begin{Large}
You have two cauldrons.  You also have a bunch of numbers, beginning at 1 and counting up, that you want to throw into the cauldrons.  As soon as two numbers within a single cauldron add up to a third number in that same cauldron, \color{red}everything explodes.\color{black}\\
\vspace{.3in}
How many numbers can you fit into the caludrons?

\end{Large}

\vspace{1in}
\center{\tiny{Borrowed from Gord Hamilton's \textit{The Infinite Pickle}}}
\end{frame}

\begin{frame}
\frametitle{Questions for group consideration}
\begin{huge}
\begin{enumerate}
\item Steering Committee?
\item Web Page?
\item Next Session?
\end{enumerate}
\end{huge}
\end{frame}


\begin{frame}
\center{\huge{Thanks for coming!}}
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\end{document}