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\usepackage{chessboard}

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\def\myurl{http://www.math.toronto.edu/~drorbn/}

\def\bbC{{\mathbb C}}
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\begin{document}

Name (Last, First): $\underline{\hspace{3in}}$ \hfill Student ID: $\underline{\hspace{2in}}$

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{\small
  \href{\myurl}{Dror Bar-Natan}:
  \href{\myurl/classes/}{Classes}:
  \href{\myurl/classes/\#1415}{2014-15}:
  \href{\myurl/classes/15-475-ProblemSolving}{MAT 475 Problem Solving Seminar}:
  \hfill\url{http://drorbn.net/15-475}
}

\vskip 3mm

{\large\bf Quiz 9} on March 17, 2015: ``Pursue Parity''. You have 25 minutes to solve two of the three problems below. Please write on both sides of the page. \hfill {\bf Good Luck!}

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\noindent{\bf Marking Comment.} My decision remains to simplify the management of this course and mark the quizzes myself, though at a delay of one week, in a symbolic acknowledgement of the ongoing TA strike.

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\parpic(0pt,0pt)(0mm,42mm)[r]{\setchessboard{smallboard, showmover=false, setpieces=rg4}\chessboard}
\noindent{\bf Problem 1.} Can you cover an $8\times 8$ chessboard with $21$
rectangles of size $3\times 1$ and a single extra $1\times 1$ square? If you can, what chessboard positions might the $1\times 1$ square occupy? (You need to justify your assertions, of course). For reference, in the chessboard on the right, the rook is at position \verb$g4$.

\vskip 2mm\noindent{\bf Problem 2} (Larson's 1.10.1, reworded). Given $9$ distinct points in $\bbZ^3$, show that there is some point in $\bbZ^3$ which is exactly half way between two of these $9$ points.

\vskip 2mm\noindent{\bf Problem 3} (Larson's 1.10.10, reworded). Show that for every positive integer $a$, the equation $x^2-y^2=a^3$ has solutions with $x,y\in\bbZ$.

\end{document}