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\textbf{College of the Holy Cross, Fall 2016} \\
\textbf{MONT 106Q -- Mathematical Thinking} \\
\textbf{Midterm Exam, November 4, 2016}
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\leftline{{\bf Your Name:}  $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$ }
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\noindent
{\bf Directions}
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Do all work on the sheets provided (if you use the back of a sheet,
please place a note telling me to look there).  
There is an extra blank sheet of paper at the end that you can 
use either as scratch paper or as extra space for your essay.  You may 
detach that if you like, but please put your name on it and hand it in with your exam
if you do detach it.
The numbers in parentheses next to the questions are there point
values (100 points total).

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\noindent\textbf{Please do not write in the space below}

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\begin{tabular}{|l||r|}
\hline
Problem & Points/Poss \\
\hline\hline
I    & \hfil/ 20\  \hfil \\
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II   & \hfil/ 20\  \hfil \\
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III  & \hfil/ 20\  \hfil \\
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IV   & \hfil/ 40\ \hfil\\
\hline\hline
Total   & \hfil/100\hfil \\
\hline
\end{tabular}
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\noindent
I. 
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A) (10) Express the base 2 number $(1010110)_2$ in base 10.
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\noindent
B) (10) Express the base 10 number $137$ in base 2.
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\noindent 
II.  Compute ``the Egyptian way"
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\noindent
A) (10) $54 \times 763$
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\noindent
B) (10) $1332 \div 12$ (that is, ``calculate with 12 to yield 1332'')
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\noindent
III.  Short answer.  Answer any four of the following.  If you answer
more than four, the best four will be used.
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\begin{enumerate}
\item[A)] (5)  What base 10 number is represented by these Egyptian
hieroglyphs? 
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\item[B)] (5)  What base did the Maya use in their number system?
How would a Maya scribe have represented the number $151$?  
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\item[C)] (5)  What are the principal surviving records of Egyptian mathematics and what are
their approximate dates?
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\item[D)] (5)  What was special about the Egyptian way of 
dealing with fractions? 
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\item[E)] (5)  What was the \emph{meaning} of the numerical information in the
section of the Maya \emph{Dresden Codex} that we studied in Discussion 1?
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\item[F)] (5) The ``months'' in the Maya {\it tzol'kin} calendar are, in order, 
\[\begin{tabular}{|c|l|c|l}
1. & Imix  &   11. & Chuen\\
2. & Ik    &   12. & Eb \\
3. & Akbal &   13. & Ben\\
4. & Kan   &   14. & Ix\\
5. & Chicchan & 15.& Men\\
6. & Cimi  &   16. & Cib\\
7. & Manik &   17. & Caban \\
8. & Lamat &   18. & Etznab \\
9. & Muluc &  19. & Ahab \\
10.& Oc  & 20. & Ahau\\  
\end{tabular}\]
What are the next 3 days after the day 11 Ahab in this system?
\end{enumerate}
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\noindent
IV.  Essay.  (40)  Explain in detail two examples of mathematical problems that 
Christopher Boone discusses in  {\it the curious incident of the dog in the night-time}.  
What do those problems mean for him?  More generally, what is the role of mathematics in 
his life?  Is it fair to say that he relates to the world in mathematical terms?  Why 
or why not?
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$\qquad$
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