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\pagestyle{fancy}
\lhead{MATH 311--02}
\chead{Problem of the Day\answer{ solution}}
\rhead{}
\lfoot{}
\cfoot{\answer{Page \thepage\ of \pageref{LastPage}}}
\rfoot{due Tuesday, November 25, 2014}

\begin{document}
\question{Let $S=\{1,2,3,\ldots,n\}$; the value of $n$ is
  indeterminate and tyour answers should not depend on a specific
  choice of $n$, although you may find considering specific values
  illuminating. Let $A$ be the set of \emph{unordered pairs} of
  numbers in $S$: for instance, when $n=3$,
  $A=\{(1,1),(1,2),(1,3),(2,2),(2,3),(3,3)\}$, and let $B=\mathcal
  P(S)$.}

\begin{itemize}
\item \question{Explain (you need not prove rigorously) why
    $|A|=\frac{n^2+n}2$.}
  
  \answer{}
  
\item \question{Explicitly describe an injective function
    $f:A\rightarrow B$.}
  
  \answer{}

\item \question{What arithmetic inequality concerning $n$ can you
    derive from the existence of the above injection $f$?}

  \answer{}

\end{itemize}

\end{document}