Collecting hints to exercises with xsim

Question

I have a few chapters to my book. Inside each chapter there are a few exercises and for each exercise there are solutions and to some of them also a hint.

The last chapter of the book will be a collection of the hints and solutions, collected by chapter.

The command \printhint that is suggested here prints all of the hints again and again.

So I am looking for a command or a way that can print only hints from chapter 1 and only hints from chapter 2 etc.

A MWE:

\documentclass[a4paper,openany]{book}
\usepackage{xsim}

\xsimsetup{
  exercise/within = chapter,
}

% Add hints for the exercises
\DeclareExerciseProperty{hint}
\newcommand\hint[1]{\SetExerciseProperty{hint}{#1}}
\newcommand\printhints{%
  \begin{description}
    \ForEachUsedExerciseByType{%
      \GetExercisePropertyT{hint}
        {\item[Hint to~##3]####1}%
    }%
  \end{description}
}

\begin{document}
\chapter{Algebra}
\begin{exercise}[subtitle={Real numbers}]
Explain why the real numbers form a field.
\end{exercise}
\begin{solution}
Since addition and multiplication are defined and have the usual properties.
\end{solution}

\begin{exercise}
Explain what is a prime number.
\hint{a natural number greater than 1}
\end{exercise}
\begin{solution}
It is not a product of two smaller natural numbers.
\end{solution}

\chapter{Geometry}

\begin{exercise}[subtitle={Pythagoras' theorem}]
  Prove that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
  \hint{Draw the altitude from point C, and call H its intersection with the side AB.}
\end{exercise}
\begin{solution}
  The proof is easy.
\end{solution}

\begin{exercise}[subtitle={Thales's theorem}]
If A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ABC is a right angle.
\end{exercise}
\begin{solution}
Since the sum of the angles in a triangle is equal to $180$\ldots
\end{solution}

\chapter*{Hints and solutions}
\section*{Hints to exercises from chapter 1}
\printhints %All of them are printed <<<
\section*{Solutions to exercises from chapter 1}
\printsolutions[headings=false,chapter=1]

\section*{Hints to exercises from chapter 2}
\printhints %They are all printed again, not good <<<

\section*{Solutions to exercises from chapter 2}
\printsolutions[headings=false,chapter=2]
\end{document}

Answer 1

Note that the ##3 argument is of the form \thechapter.\theexercise, so we can extract the number of the chapter and check if it is equal to the argument of `\printhints.

Edit

It seems that you can get the value of number of the chapter that the exercise been written in with \ExercisePropertyGet, so a simpler solution would be

\documentclass[a4paper,openany]{book}
\usepackage{xsim}

\xsimsetup{
    exercise/within = chapter,
}

% Add hints for the exercises
\DeclareExerciseProperty{hint}
\newcommand\hint[1]{\SetExerciseProperty{hint}{#1}}
\newcommand\printhints[1]{%
    \begin{description}
        \ForEachUsedExerciseByType{%
            \GetExercisePropertyT{hint}
            {%
            \ifnum \ExercisePropertyGet{##1}{##2}{chapter-value}=#1
            \item[Hint to~##3]####1
            \fi
            }%
        }%
    \end{description}
}

\begin{document}
    \chapter{Algebra}
    \begin{exercise}[subtitle={Real numbers}]
        Explain why the real numbers form a field.
    \end{exercise}
    \begin{solution}
        Since addition and multiplication are defined and have the usual properties.
    \end{solution}
    
    \begin{exercise}
        Explain what is a prime number.
        \hint{a natural number greater than 1}
    \end{exercise}
    \begin{solution}
        It is not a product of two smaller natural numbers.
    \end{solution}
    
    \chapter{Geometry}
    
    \begin{exercise}[subtitle={Pythagoras' theorem}]
        Prove that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
        \hint{Draw the altitude from point C, and call H its intersection with the side AB.}
    \end{exercise}
    \begin{solution}
        The proof is easy.
    \end{solution}
    
    \begin{exercise}[subtitle={Thales's theorem}]
        If A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ABC is a right angle.
    \end{exercise}
    \begin{solution}
        Since the sum of the angles in a triangle is equal to $180$\ldots
    \end{solution}
    
    \chapter*{Hints and solutions}
    \section*{Hints to exercises from chapter 1}
    \printhints{1} 
    \section*{Solutions to exercises from chapter 1}
    \printsolutions[headings=false,chapter=1]
    
    \section*{Hints to exercises from chapter 2}
    \printhints{2} 
    
    \section*{Solutions to exercises from chapter 2}
    \printsolutions[headings=false,chapter=2]
\end{document}

With the help of expl3 you can easily generalize \printhints to get a comma separated list of chapter numbers, instead of one number.

\documentclass[a4paper,openany]{book}
\usepackage{xsim}

\xsimsetup{
    exercise/within = chapter,
}

% Add hints for the exercises
\DeclareExerciseProperty{hint}
\newcommand\hint[1]{\SetExerciseProperty{hint}{#1}}

\ExplSyntaxOn

\NewDocumentCommand \printhints { m } {
    \seq_set_split:Nnn \l_a_seq { , } { #1 }
    \begin{description}
        \ForEachUsedExerciseByType{
            \GetExercisePropertyT{hint}
            {
            \seq_set_split:Nnn \l_b_seq { . } { ##3 }
            \seq_get_left:NN \l_b_seq \l_a_tl
            \seq_if_in:NVT \l_a_seq { \l_a_tl }
            {
             \item[Hint to~##3]####1
            }
        }
    }
    \end{description}
}

\ExplSyntaxOff

\begin{document}
    \chapter{Algebra}
    \begin{exercise}[subtitle={Real numbers}]
        Explain why the real numbers form a field.
    \end{exercise}
    \begin{solution}
        Since addition and multiplication are defined and have the usual properties.
    \end{solution}
    
    \begin{exercise}
        Explain what is a prime number.
        \hint{a natural number greater than 1}
    \end{exercise}
    \begin{solution}
        It is not a product of two smaller natural numbers.
    \end{solution}
    
    \chapter{Geometry}
    
    \begin{exercise}[subtitle={Pythagoras' theorem}]
        Prove that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
        \hint{Draw the altitude from point C, and call H its intersection with the side AB.}
    \end{exercise}
    \begin{solution}
        The proof is easy.
    \end{solution}
    
    \begin{exercise}[subtitle={Thales's theorem}]
        If A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ABC is a right angle.
    \end{exercise}
    \begin{solution}
        Since the sum of the angles in a triangle is equal to $180$\ldots
    \end{solution}
    
    \chapter*{Hints and solutions}
    \section*{Hints to exercises from chapter 1}
    \printhints{1} 
    \section*{Solutions to exercises from chapter 1}
    \printsolutions[headings=false,chapter=1]
    
    \section*{Hints to exercises from chapter 2}
    \printhints{2} 
    
    \section*{Solutions to exercises from chapter 2}
    \printsolutions[headings=false,chapter=2]
    
    \section*{Hints to exercises from chapters 1 and 2}
    \printhints{1,2}
\end{document}

Another option is that the nth call of \printhints would print the hints of the nth chapter

\documentclass[a4paper,openany]{book}
\usepackage{xsim}

\xsimsetup{
    exercise/within = chapter,
}

% Add hints for the exercises
\DeclareExerciseProperty{hint}
\newcommand\hint[1]{\SetExerciseProperty{hint}{#1}}
\newcounter{hintchapcount}
\newcommand\printhints{%
    \stepcounter{hintchapcount}
    \begin{description}
        \ForEachUsedExerciseByType{%
            \GetExercisePropertyT{hint}
            {%
                 \ifnum \ExercisePropertyGet{##1}{##2}{chapter-value}=\value{hintchapcount}
                \item[Hint to~##3]####1
                \fi
            }%
        }%
    \end{description}
}

\begin{document}
    \chapter{Algebra}
    \begin{exercise}[subtitle={Real numbers}]
        Explain why the real numbers form a field.
    \end{exercise}
    \begin{solution}
        Since addition and multiplication are defined and have the usual properties.
    \end{solution}
    
    \begin{exercise}
        Explain what is a prime number.
        \hint{a natural number greater than 1}
    \end{exercise}
    \begin{solution}
        It is not a product of two smaller natural numbers.
    \end{solution}
    
    \chapter{Geometry}
    
    \begin{exercise}[subtitle={Pythagoras' theorem}]
        Prove that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
        \hint{Draw the altitude from point C, and call H its intersection with the side AB.}
    \end{exercise}
    \begin{solution}
        The proof is easy.
    \end{solution}
    
    \begin{exercise}[subtitle={Thales's theorem}]
        If A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ABC is a right angle.
    \end{exercise}
    \begin{solution}
        Since the sum of the angles in a triangle is equal to $180$\ldots
    \end{solution}
    
    \chapter*{Hints and solutions}
    \section*{Hints to exercises from chapter 1}
    \printhints 
    \section*{Solutions to exercises from chapter 1}
    \printsolutions[headings=false,chapter=1]
    
    \section*{Hints to exercises from chapter 2}
    \printhints 
    
    \section*{Solutions to exercises from chapter 2}
    \printsolutions[headings=false,chapter=2]
\end{document}