Two solutions to one problem

Question

I have defined the solution environment as below:

\newtheorem{solution}{Solution}[subsection]

I have two solutions to problem 1.3.3 as shown in the attached screenshot. However, by using \begin{solution} \end{solution} twice, the second solution would be named as 1.3.4. Is there any way to change the counter so that these two solutions both correspond to the same question? Something like 1.3.3-1 & 1.3.3-2 would be great, but if there's a more elegant way, I'd also love to hear it. Thanks!

Answer 1

I am assuming you are using amsthm to manage your theorems. In that case you can set the parent counter of your solution environment to be the counter of your theorem, like so

\documentclass{article}

\usepackage{amsthm}

\newtheorem{thm}{Theorem}[subsection]
\newtheorem{solution}{Solution}[thm]
% ^^^ Note that as <parent counter> we are using
%     the thm counter 

\begin{document}
  \section{Sec 1}
  \subsection{Subsec 1}
  \begin{thm}
    Test
  \end{thm}
  \begin{solution}
    Sol 1
  \end{solution}
  \begin{solution}
    Sol 2
  \end{solution}

  \section{Sec 2}
  \subsection{Subsec 2}
  \begin{thm}
    Test
  \end{thm}
  \begin{solution}
    Sol 1
  \end{solution}
  \begin{solution}
    Sol 2
  \end{solution}
\end{document}

yielding

Answer 2

The following example should work to number solutions within problems only when there are multiple solutions to the same problem. It basically works by defining a command which stores the number of solutions to a given problem in the .aux file, and by redefining the \thesolution command to display the number of the solution according to the number of solutions to the problem. It's a little complicated, and maybe there's a simpler way to do that, but I couldn't think of any.

Here's the example:

\documentclass{article}
\usepackage{amsmath,amsthm}
\usepackage{etoolbox}
\newtheorem{problem}{Problem}[subsection]
\theoremstyle{remark}
\newtheorem{solution}{Solution}
\newcounter{numsolution}
\numberwithin{numsolution}{problem}

\makeatletter
\AtBeginEnvironment{problem}{%
    \addtocounter{problem}{1}
    \newcounter{solsofprob\the\value{section}.\the\value{subsection}.\the\value{problem}}
    \addtocounter{problem}{-1}
}
\AtBeginEnvironment{solution}{%
    \addtocounter{solsofprob\the\value{section}.\the\value{subsection}.\the\value{problem}}{1}
    \immediate\write\@mainaux{\string\gdef\string\numsolsofprob\romannumeral\the\value{section}@\romannumeral\the\value{subsection}@\romannumeral\the\value{problem}{\the\value{solsofprob\the\value{section}.\the\value{subsection}.\the\value{problem}}}}%
}
\newcommand{\tempnum}{0}
\renewcommand{\thesolution}{%
    \@ifundefined{numsolsofprob\romannumeral\the\value{section}@\romannumeral\the\value{subsection}@\romannumeral\the\value{problem}}%
        {\def\tempnum{0}}%
        {\edef\tempnum{\csname numsolsofprob\romannumeral\the\value{section}@\romannumeral\the\value{subsection}@\romannumeral\the\value{problem}\endcsname}}%
    \ifnum \tempnum > 1
        \stepcounter{numsolution}%
        \arabic{section}.\arabic{subsection}.\arabic{problem}--\arabic{numsolution}%
    \else
        \arabic{section}.\arabic{subsection}.\arabic{problem}%
    \fi%
}
\makeatother

\begin{document}
\section{First section}
\subsection{First subsection}
\begin{problem}
    A problem.
\end{problem}
\begin{solution}
    The solution.
\end{solution}
\begin{problem}
    Another problem. 
\end{problem}
\begin{solution}
    A first solution.
\end{solution}
\begin{solution}
    A second solution.
\end{solution}
\begin{problem}
    Another problem.
\end{problem}
\begin{solution}
    A solution.
\end{solution}
\subsection{Second subsection}
\begin{problem}
    A problem.
\end{problem}
\begin{solution}
    A solution.
\end{solution}
\section{Second section}
\subsection{A subsection}
\begin{problem}
    A problem.
\end{problem}
\begin{solution}
    A solution.
\end{solution}
\begin{solution}
    Another solution.
\end{solution}
\end{document}

The above codes outputs:

I should also mention that, since this solution works by redefining the \thesolution command in a complicated way, it will not be possible to add a label to a solution to reference it later. I will update the code if I think of something to make to labeling work.