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\begin{document}

\noindent
{\Large 
Numeration Systems \hfill Name:\underline{\hspace{2.8in}}\\ \\
MA~201}
\vspace{.25in}

\noindent
{\bf WARNING:}  You must {\bf SHOW ALL OF YOUR WORK}.  You will receive 
NO CREDIT if you do not show your work.

\be 
\item  
	\be
	\item Use Egyptian symbols to represent $456,973$.
	\item Use Egyptian symbols to represent $22,145$.
	\item Add $456,973$ and $22,145$ using Egyptian symbols.  Your
	final answer should use the minimum number of symbols possible.
	What exchanges did you make to reduce the number of symbols in your
	answer?  How do these exchanges relate to "carrying" in addition?
	\item Subtract $22,145$ from $456,973$ using Egyptian symbols.
	Your final answer should use the minimum number of symbols
	possible.  What exchanges did you need to make to be able to carry
	out the subtraction algorithm by using take-away?  How do these
	exchanges relate to borrowing in subtraction?
	\ee
\begin{center}
\begin{tabular}{c}
\hline
\hspace{6.5in} \\
\hline
\end{tabular}
\end{center}


\item Jake owns a shipping company.  He has four different box sizes:XL, L,
M, and S.  Today Jake must ship $51,339$ books to Indiana.  Jake wants to
use the minimum number of boxes possible, but he also must be certain that
each box is completely full.  If an XL box holds $7,200$ books, and L box
holds $360$ books, an M box holds $20$ books, and an S box holds $1$ book,
how many boxes of each type must Jake use?
\item Will Jake ever need to use $19$ M boxes for a shipment of books?
Explain briefly.
\item If Jake ships $2$ XL boxes, $6$ L boxes, $18$ M boxes, and $0$ S
boxes to West Virginia, how many books did Jake ship to West Virginia? 


\begin{center}
\begin{tabular}{c}
\hline
\hspace{6.5in} \\
\hline
\end{tabular}
\end{center}

\item Write the Mayan notation for $51,339$. 
\item Do exercise 1(k) on page 152 of your text.
\item How does Mayan notation relate to Jake's shipping problem?

\begin{center}
\begin{tabular}{c}
\hline
\hspace{6.5in} \\
\hline
\end{tabular}
\end{center}

Suppose that you live in Blockville.  The residents of Blockville use
colored blocks for money.  The following table shows how their money system
works.
\begin{center}
\begin{tabular}{|ccccc|}
\hline
Every & $ \displaystyle \left\{
\begin{array}{c}
{\text blue} \\
{\text pink} \\
{\text yellow} \\
{\text brown} \\
{\text orange} \\
{\text green} \\
{\text red} \\ 
\end{array}  
\right\} $
& 
block is worth five &
$ \displaystyle \left\{
\begin{array}{c}
{\text pink} \\
{\text yellow} \\
{\text brown} \\
{\text orange} \\
{\text green} \\
{\text red} \\
{\text white} 
\end{array} 
\right\} $ 
&
blocks. \\
\hline
\end{tabular}
\end{center}
The citizens of Blockville must never carry more blocks than absolutely
necessary.  Answer the following questions based on the above information.
\item One yellow block is equivalent to \spc white blocks.
\item One green block is equivalent to \spc white blocks.
\item Joni has four thousand five hundred fifty-three white blocks.  She
must exchange these blocks so that she has the minimum number of blocks
possible.  In the chart below, record the number of each type of block that 
Joni will have after the exchange.
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline 
blue & pink & yellow & brown & orange & green & red & white \\
\hline
&&&&&&& \\
&&&&&&& \\
&&&&&&& \\
\hline
\end{tabular}
\end{center}
\item Joni has three blue blocks, four yellow blocks, one brown block,
two green blocks, four red blocks, and three white blocks.  All of Joni's 
blocks (taken together) are equivalent to \spc white blocks.
\item Will you ever need to have five orange blocks?  Briefly explain.
\item How is this exercise related to base five notation? 
\ee
\end {document}
