Creating a solution label for an exercise using \declaretheoremstyle

amsthmexercisesthmtoolsxsim

I am writing a book with exercises scattered throughout the text, for which solutions are presented at the end of each chapter.

I want the layout to be as follows:

An exercise environment is introduced inside the text. A solution to this exercise would later appear in the "Solution to exercises" section at the end of the chapter.

In addition, at the end of the exercise environment would be a page reference to the page where its solution is labeled.

A visual example (made artificially) is this:

And the last section of the chapter would be

Is it possible to do that using the amsthm and thmtools packages?

I would assume that the "Solution on page xx" string would be the value of the postfoothook key of the \declaretheoremstyle command of thmtools, but I don't know how to additionally insert a label into that value.

Maybe I am going too far, but I am also open for a way to do that using one of the exercise packages (xsim looks the most promising one). I just haven't stumbled upon this exact layout.

EDIT:

Since the final document is to be typeset in LyX, I think that a better way to achieve my goal is not to work with xsim, since for referencing, LyX works with the basic building stones of LaTeX – label, pageref and their friends.

I think that an appropriate code to be inserted into postfoothook and heading would do the job, but this is where I am asking for help:

The exercises and solutions labels would be in the following format:

ex:ch1:ratio-of-odd-numbers <-> sol:ex:ch1:ratio-of-odd-numbers
ex:ch2:rolling-n-sided-die <-> sol:ex:ch2:rolling-n-sided-die
ex:ch2:the-hotel-problem <-> sol:ex:ch2:the-hotel-problem

What I need is to refer to sol:⟨the exrecise label⟩ inside postfoothook in exercise, and to refer to ⟨the exrecise label⟩ in the heading of solution.

\begin{exercise}\label{ex:ch1:every-prime}
blah blah
\end{exercise}

for which a solution is in the format

\begin{solution}\label{sol:ex:ch1:every-prime}
Solution to blah blah.
\end{solution}

To produce the ref "Solution on page xx" I need to concatenate sol: with ⟨the exrecise label⟩ to produce

\pageref{sol:⟨the exrecise label⟩}

where, in this example, ⟨the exrecise label⟩ is ex:every-prime (to create \pageref{sol:ex:ch1:every-prime}).

To produce the header "Solution to Exercise xx" I need to remove the sol: part from the solution label to produce \ref{⟨the exrecise label⟩}, so in this example it would be, \ref{ex:ch1:every-prime}.

Any help about that?

A MWE:

\documentclass{book}
\usepackage{fontspec,hyperref,amsthm,thmtools}
%%
\declaretheoremstyle[
postfoothook = \rightline{Solution on page \pageref{sol:⟨the exrecise label⟩}
]{exercise}
\declaretheorem[style=exercise]{exercise}

\declaretheoremstyle[
heading = Solution to Exercise \ref{⟨the solution label without "sol:"⟩},
numbered=no,
]{solution}
\declaretheorem[style=solution]{solution}
%%
\begin{document}

\chapter{Prime numbers}
Lorem ipsum
\section{Dolor sit amet}
Consectetur adipiscing elit.

\begin{exercise}[Euclid]{ex:ch1:every-prime}
Prove that for every prime $p$, there is a prime $p^\prime > p$. In particular, the list of primes, $2, 3, 5, 7, \ldots$ , is infinite.
\end{exercise}

\section{Solution to exercises}
\begin{solution}\label{sol:ex:ch1:every-prime}
The proof is straight forward. First note that...
\end{solution}
\end{document}

Edit 2

As a follow up to muzimuzhi Z answer, I would like also to add an "Exercise with no solution" to my book. This environment may be named exercise-nosol and I want it to share the same counter with the exercise environment defined in the accepted answer.

How to do that?

That is, how to define the two environments (exercise with xsim, exercise-nosol with thmtool) so that they share the same counter?

I defined it using thmtools as follows:

\declaretheoremstyle[
postfoothook = \rightline{(No Solution) $\blacktriangleleft$}
]{exercise-nosol}
\declaretheorem[name=Exercise,numberwithin=chapter,style=exercise]{exercise}

output:

Best Answer

An xsim attempt, based on the "Example 5: Crossreferencing between problems and answers" shown in package manual.

\documentclass{article}
\usepackage{amssymb}
\usepackage{xsim,lipsum,hyperref}
\hypersetup{colorlinks}

\DeclareExerciseHeadingTemplate{custom}
  {\section{\XSIMexpandcode{\XSIMtranslate{default-heading}}}}

\DeclareExerciseEnvironmentTemplate{custom}
  {%
    \IfInsideSolutionTF
      {\label{sol:\ExerciseID}}
      {\label{ex:\ExerciseID}}%
    \paragraph*
      {%
        \XSIMmixedcase{\GetExerciseName}%
        \IfInsideSolutionTF
          {
            to \GetExerciseParameter{exercise-name}%
            ~\GetExerciseProperty{counter}%
            ~(From Page~\pageref{ex:\ExerciseID})
          }
          {%
            ~\GetExerciseProperty{counter}%
            \GetExercisePropertyT{subtitle}{~(\PropertyValue)}
          }%
      }%
  }
  {%
    \IfInsideSolutionF
      {\par\leavevmode\hfill
       Solution on page~\pageref{sol:\ExerciseID}~$\blacktriangleleft$}%
  }
\xsimsetup{
  exercise/template = custom ,
  solution/template = custom ,
  print-solutions/headings-template = custom
}

\begin{document}

\section{Exercises}
\begin{exercise}[subtitle=title]
  \lipsum[1][2]
\end{exercise}
\begin{solution}
  \lipsum[1][2]
\end{solution}

\begin{exercise}[subtitle=second title]
  \lipsum[4]
\end{exercise}
\begin{solution}
  \lipsum[4]
\end{solution}

\clearpage
\printsolutions

\end{document}

Update: Support no-solution exercises

To avoid possible incompatibilities, here is an xsim-only attempt.

A new command \IfSolutionEmptyTF is provided which uses xsim internal \xsim_attribute_get:nn. This might not be the most robust way.

I've tried xsim's \IfExistSolutionTF and it seems to not work as I expected. Also probably due to an xsim issue (see cgnieder/xsim#90), currently you have to provide an empty solution environment for each of no-solution exercises, like

\begin{solution} % no empty lines in env contents
\end{solution}

Full example

\documentclass{article}
\usepackage{amssymb}
\usepackage{xsim,lipsum,hyperref}
\hypersetup{colorlinks}

\ExplSyntaxOn
\cs_generate_variant:Nn \tl_if_empty:nTF {e}

\NewExpandableDocumentCommand{\IfSolutionEmptyTF}{}
  {
    \tl_if_empty:eTF
      {
        \exp_args:Ne \xsim_attribute_get:nn
          {exercise!\ExerciseID} {solution-body}
      }
  }
\ExplSyntaxOff

\DeclareExerciseHeadingTemplate{custom}
  {\section{\XSIMexpandcode{\XSIMtranslate{default-heading}}}}

\DeclareExerciseEnvironmentTemplate{custom-exercise}
  {%
    \label{ex:\ExerciseID}%
    \paragraph*
      {%
        % typset "Exercise <num> (<subtitle>)"
        \XSIMmixedcase{\GetExerciseName}%
        ~\GetExerciseProperty{counter}%
        \GetExercisePropertyT{subtitle}{~(\PropertyValue)}
      }%
  }
  {%
      \par\leavevmode\hfill
      % typeset "Solution on page <page>" or "(No solution)"
      \ifcsname r@sol:\ExerciseID\endcsname
        Solution on page~\pageref{sol:\ExerciseID}%
      \else
        (No Solution)%
      \fi
      ~$\blacktriangleleft$%
  }

\DeclareExerciseEnvironmentTemplate{custom-solution}
  {%
    \IfSolutionEmptyTF{}
    {
      \label{sol:\ExerciseID}
      \paragraph*
        {%
          \XSIMmixedcase{\GetExerciseName}
          to \GetExerciseParameter{exercise-name}%
          ~\GetExerciseProperty{counter}%
          ~(From Page~\pageref{ex:\ExerciseID})
        }%
    }
  }{%
    \par
  }
\xsimsetup{
  exercise/template = custom-exercise ,
  solution/template = custom-solution ,
  print-solutions/headings-template = custom
}

\begin{document}

\section{Exercises}
\begin{exercise}[subtitle=title]
  \lipsum[1][2]
\end{exercise}
\begin{solution}
  \lipsum[1][2]
\end{solution}

\begin{exercise}[subtitle=no solution]
  \lipsum[3][1] aaa
\end{exercise}
% You still need to provide an empty solution environment.
\begin{solution}
\end{solution}

\begin{exercise}[subtitle=third title]
  \lipsum[4][1-3]
\end{exercise}
\begin{solution}
  \lipsum[4][4-6]
\end{solution}

\begin{exercise}[subtitle=fourth title]
  \lipsum[4][1-3]
\end{exercise}
\begin{solution}
  \lipsum[4][4-6]
\end{solution}

\clearpage
\printsolutions

\end{document}

Related Solutions

[Tex/LaTex] Solutions of exercises produced with tcolorbox

It is possible to prepend the \chapter command to write some information about the chapter into the record file. This will fail for the first chapter since the recording has not started then.

It will also fail if the chapter number is reset.

Since the prepending occurs before the chapter number is increased, I've decided to trick \c@chapter using a number increased by one within a TeX group, so the counter value is not really changed but \thechapter will use the tricked value for while and apply the correct format as defined for \thechapter. This is better than using something like \arabic{chapter} etc, in my point of view.

Change the \solutionchapterformat macro at will to produce any nice/fancy heading of the solution-chapter-group (but leave the \bgroup... \egroup)

\documentclass{book}

\usepackage[most]{tcolorbox}

\usepackage{xpatch}

% Formatting command as a 'headline' of the solutions of chapter X
\NewDocumentCommand{\solutionchapterformat}{m}{%
  \noindent \bgroup\bfseries Solutions of the exercises of the chapter #1\egroup%
}
\makeatletter


\xpretocmd{\chapter}{%
  \begingroup
  \ifnum\value{chapter}>0\relax
  \tcbrecord{\string\clearpage}% Write a clearpage after the first chapter for each new chapter
  \fi
  \c@chapter \numexpr\c@chapter+1% Increase the count register `\@chapter` by one to trick `\thechapter` using the 'correct' chapter number
  \tcbrecord{%
    \solutionchapterformat{\thechapter}}%
  \endgroup
}{}{}

\NewDocumentCommand{\extrasolutioncontent}{+m}{%
  \tcbrecord{Extra solution stuff\par}% Remove this later on!
  \tcbrecord{\detokenize{#1}}%
}

\newcommand{\fetchsolutions}{%
%For the first chapter
\begingroup
\c@chapter1%
\solutionchapterformat{\thechapter}%
\endgroup% Now get the rest of the stuff
\tcbinputrecords
}
\makeatother

%\tcbuselibrary{skins,breakable}

%\usepackage{polyglossia}
%\setmainlanguage{english}
%\usepackage{fontspec}
%\setmainfont{Times New Roman}
%\setsansfont{Arial}
%\setmonofont{Courier New}


\NewTColorBox[auto counter,number within=chapter]{exercise}{m+O{}}{%
    enhanced,
    colframe=green!20!black,
    colback=yellow!10!white,
    coltitle=green!40!black,
    fonttitle=\bfseries,
    underlay={\begin{tcbclipinterior}
        \shade[inner color=green!80!yellow,outer color=yellow!10!white]
            (interior.north west) circle (2cm);
        \draw[help lines,step=5mm,yellow!80!black,shift={(interior.north west)}]
            (interior.south west) grid (interior.north east);
        \end{tcbclipinterior}},
    title={Exercise~ \thetcbcounter:},
    label={exercise:#1},
    attach title to upper=\quad,
    after upper={\par\hfill\textcolor{green!40!black}%
        {\itshape Solution on page~\pageref{solution:#1}}},
    lowerbox=ignored,
    savelowerto=solutions/exercise-\thetcbcounter.tex,
    record={\string\solution{#1}{solutions/exercise-\thetcbcounter.tex}},
    #2
}

\NewTotalTColorBox{\solution}{mm}{%
    enhanced,
    colframe=red!20!black,
    colback=yellow!10!white,
    coltitle=red!40!black,
    fonttitle=\bfseries,
    underlay={\begin{tcbclipinterior}
        \shade[inner color=red!50!yellow,outer color=yellow!10!white]
            (interior.north west) circle (2cm);
        \draw[help lines,step=5mm,yellow!80!black,shift={(interior.north west)}]
            (interior.south west) grid (interior.north east);
        \end{tcbclipinterior}},
    title={Solution of Exercise~\ref{exercise:#1} on page~\pageref{exercise:#1}:},
    phantomlabel={solution:#1},
    attach title to upper=\par,
}{\input{#2}}

\tcbset{no solution/.style={no recording,after upper=}}

\begin{document}
\chapter{The first chapter}

\tcbstartrecording
\begin{exercise}{Ex1}[coltitle=cyan!80!black]
Compute the derivative of the following function:
\begin{equation*}
f(x)=\sin((\sin x)^2)
\end{equation*}
\tcblower
The derivative is:
\begin{align*}
f’(x) &= \left( \sin((\sin x)^2) \right)’
=\cos((\sin x)^2) 2\sin x \cos x.
\end{align*}
\end{exercise}
\vspace*{1cm}
The solution of the exercise \ref{exercise:Ex1} is in the page \pageref{solution:Ex1}
\vspace*{1cm}
%\tcbstoprecording
%\tcbinputrecords
\chapter{The second chapter}

%\tcbstartrecording
\begin{exercise}{Ex2}[coltitle=cyan!80!black]
Compute the derivative of the following function:
\begin{equation*}
f(x)=(x^2+1) \sqrt{x^4+1}
\end{equation*}
\tcblower
The derivative is:
\begin{align*}
f’(x) &= \left( (x^2+1) \sqrt{x^4+1} \right)’
= 2x\sqrt{x^4+1} + \frac{2x^3(x^2+1)}{\sqrt{x^4+1}}.
\end{align*}
\end{exercise}
\vspace*{1cm}
The solution of the exercise \ref{exercise:Ex2} is in the page \pageref{solution:Ex2}
\vspace*{1cm}

\chapter{The third chapter}

\begin{exercise}{Ex3}[coltitle=cyan!80!black]
Compute the derivative of the following function:
\begin{equation*}
f(x)=(x^2+1) \sqrt{x^4+1}
\end{equation*}
\tcblower
The derivative is:
\begin{align*}
f’(x) &= \left( (x^2+1) \sqrt{x^4+1} \right)’
= 2x\sqrt{x^4+1} + \frac{2x^3(x^2+1)}{\sqrt{x^4+1}}.
\end{align*}
\end{exercise}
\vspace*{1cm}
The solution of the exercise \ref{exercise:Ex3} is in the page \pageref{solution:Ex3}
\vspace*{1cm}


\extrasolutioncontent{$\textcolor{blue}{E=mc^2}$}

\begin{exercise}{Ex31}[coltitle=cyan!80!black]
Compute the derivative of the following function:
\begin{equation*}
f(x)=(x^2+1) \sqrt{x^4+1}
\end{equation*}
\tcblower
The derivative is:
\begin{align*}
f’(x) &= \left( (x^2+1) \sqrt{x^4+1} \right)’
= 2x\sqrt{x^4+1} + \frac{2x^3(x^2+1)}{\sqrt{x^4+1}}.
\end{align*}
\end{exercise}
\vspace*{1cm}
The solution of the exercise \ref{exercise:Ex31} is in the page \pageref{solution:Ex31}
\vspace*{1cm}


\chapter{The fourth chapter}

\begin{exercise}{Ex4}[coltitle=cyan!80!black]
Compute the derivative of the following function:
\begin{equation*}
f(x)=(x^2+1) \sqrt{x^4+1}
\end{equation*}
\tcblower
The derivative is:
\begin{align*}
f’(x) &= \left( (x^2+1) \sqrt{x^4+1} \right)’
= 2x\sqrt{x^4+1} + \frac{2x^3(x^2+1)}{\sqrt{x^4+1}}.
\end{align*}
\end{exercise}
\vspace*{1cm}
The solution of the exercise \ref{exercise:Ex4} is in the page \pageref{solution:Ex3}
\vspace*{1cm}




\tcbstoprecording
\newpage
\section{Solutions of the exercices}
\fetchsolutions
\end{document}

[Tex/LaTex] Versatile question/answer package

All of the mentioned points should be doable using the xsim package (which is the successor of exsheets). I do not have enough knowledge of other exercise packages to be able to judge if they allow similar things…

Here is a suggestion about how you could use xsim to achieve what you want. Hopefully the code is self-explanatory.

\documentclass{article}
\usepackage{xsim,tcolorbox,needspace}

% declare a boolean property:
\DeclareExerciseProperty*{short}
% declare a tag like property:
\DeclareExerciseTagging{level}

% declare a template which typesets exercises differently according to given
% properties:
\DeclareExerciseEnvironmentTemplate{exercise}
  {%
    \renewcommand*\theenumi{\theexercise.\arabic{enumi}}%
    \par\addvspace{\baselineskip}
    \Needspace*{2\baselineskip}
    \noindent
    \GetExercisePropertyT{level}{\marginpar{\sffamily Level: #1}}%
    \textbf{\XSIMmixedcase{\GetExerciseName}~\GetExerciseProperty{counter}.} %
    \GetExercisePropertyT{subtitle}{\textit{#1}}%
    \IfExerciseBooleanPropertyF{short}{\par\noindent}%
  }
  {}

% declare a tcolorbox template for the solutions:
\DeclareExerciseEnvironmentTemplate{solution}
  {\tcolorbox[colback=yellow,colframe=red]}
  {\endtcolorbox}

% declare a user command for short answers:
\NewDocumentCommand\answer{m}{%
  \IfSolutionPrintT{%
    \UseExerciseTemplate{begin}{solution}%
      #1%
    \UseExerciseTemplate{end}{solution}%
  }{}%
}

% setup exercises and solutions:
\SetExerciseParameters{exercise}{
  exercise-template = exercise ,
  solution-template = solution
}

% remove this option to hide the answers:
% \xsimsetup{solution/print=true}

\usepackage{lipsum}

\begin{document}

\begin{exercise}[level=hard,short]
  Just a short exercise
\end{exercise}
\begin{solution}
  The somewhat longer solution to the short exercise. \lipsum[1]
\end{solution}

\begin{exercise}[subtitle=This one has a title,level=easy]
  Answer the following questions.
  \begin{enumerate}
    \item question \answer{answer}
    \item question \answer{answer}
  \end{enumerate}
\end{exercise}

\begin{exercise}
  A long exercise. \lipsum[4]\answer{The answer}
\end{exercise}

\begin{exercise}[level=medium,short]
  Another short exercise.\answer{The answer}
\end{exercise}

\end{document}

This gives

depending on wether solution/print=true has been set or not.