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\iffalse{
\newpage

\begin{problem}
In how many ways can I form $n$ cents worth of change using pennies,
nickles, and dimes?

\bparts

\ppart Write a generating function for the number of ways to select a
set of pennies worth $n$ cents.

\solution[\vspace{1in}]{There is exactly 1 way to form $n$ cents with
only pennies: use $n$ of them.  Thus, the generating function is:
%
\[
1 + x + x^2 + x^3 + x^4 + \ldots = \frac{1}{1 - x}
\]
}

\ppart Write a generating function for the number of select a set of
nickles worth $n$ cents.

\solution[\vspace{1in}]{If $n$ is a multiple of 5, then there is
exactly one way to form $n$ cents: use $n / 5$ nickles.  Otherwise,
there is no way to form $n$ cents using nickles alone.  Thus, the
generating function is:
%
\[
1 + x^5 + x^{10} + x^{15} + x^{20} + \ldots = \frac{1}{1 - x^5}
\]

\eparts

\end{problem}
}
