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\begin{document}
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\centerline{Math 36 --- Weekly Homework}
\centerline{Assigned: 11/5}
\centerline{Due: 11/12}
\begin{questions}
\question
How many different ways can a 3 by 3 grid of nine precincts be divided into three equally sized contiguous districts? Draw each possible map.
\vspace{4 in}
\question
Suppose there is a region with 30 precincts in a 5 by 6 grid, each with 10 individuals. Suppose that in the entire population, there are more supporters of party $A$ than party $B$.
\begin{enumerate}[label = (\alph*)]
\item Is it possible to draw a district plan where $B$ wins every single district? Why or why not?
\vspace{2 in}
\item Suppose there are $m$ individuals are $A$ supporters, and the remaining $300-m$ are $B$ supporters. When there are three evenly sized districts, what is the minimum number of $A$ supporters that need to be packed into the district that $A$ wins for $B$ to win the other two districts.
\vspace{2 in}
\item Now consider this particular population:
\begin{center}
\includegraphics[width = 0.8\textwidth]{figures/WH-Gerry.png}
\end{center}
Each precinct is a square, and the number shows how many $A$ supporters live there.
Draw a district map with three districts so that $B$ wins two seats.
\end{enumerate}
\end{questions}
\end{document}
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