I'm typing up some assignments with the basic structure
Problem problem number
Solution
and I'm not really satisfied with the LaTeX source I'm making. For example
\section*{Problem 1}
In order to solve $a^2+b^2 = c^2$ ...
This solution is not very good since it doesn't use the automatic counters and though the assignments are short I might have longer ones later and need a table of contents.
Now, problems in my context are logical sections of my documents, and so \section makes sense. Would some type of new command say \problem make more sense?