\documentclass{article}
\pagestyle{empty}
\usepackage{amsmath}
\usepackage[pdftex,colorlinks=true,linkcolor=blue]{hyperref}
\usepackage{graphicx}
\newcommand{\problem}[1]{ \subsection*{#1}}
\newenvironment{solution}
{\subsubsection*{Solution}\small}{}
\newcommand{\problemnote}[1]{     % <-----------------
}
%do not modify header

\begin{document}
\problem{Give problem some name}
\problemnote{Problem XXX from ...(quote source if possible)}
Text of the problem
\begin{description}
\item{(a)}
First question
\item{(b)}
Second Question
\item{(c)}
Third Question
\end{description}
%this is a figure 
\begin{figure}[t]
\includegraphics[angle=0,width=2in]{figurefile}
\caption{Figure showing our system}
\end{figure}

%solution starts here
\begin{solution}
General ideas.
\begin{description}
\item{(a)}
Answer to first question
\item{(b)}
Second quesiton
\item{(c)}
Third question
\end{description}
\end{solution} 
\end{document}