Exam Class: Making an empty Box but with dotted lines inside

Question

I need to print a box very similar to that created by the \makeemptybox{\stretch{1}} command in exam.cls except that I would like to add dotted lines inside the box. Specifically, I would like to add 12 dotted lines first and then fill the rest of the box with empty space (see image below).

Here is what I have so far:

\documentclass[10pt,a4paper,addpoints]{exam}

\begin{document}
\begin{questions}
\question[5] In a class of 30 students, 18 have a dog, 20 have a cat and 3 have neither. A student is selected at random. What is the probability that this student has both a cat and a dog? 
\makeemptybox{\stretch{1}}
\newpage

\question[6] A pencil case contains 5 faulty and 7 working pens. A boy and then a girl each need to take a pen. 
    \begin{parts}
    \part Determine the probability that two faulty pens are chosen. 
    \part Determine the probability that at least one faulty pen is chosen. 
    \part Given that exactly one faulty pen is chosen, what is the probability that the girl chose it? 
    \end{parts}
\makeemptybox{\stretch{1}}
\newpage
\end{questions}
\end{document}

Any ideas? I am new to LaTeX so any advice would be helpful! Thank you in advance.

Answer 1

Using mdframed package and with 2 counter, following solution can be used in exam package.

\documentclass[answers]{exam}

\makeatletter
\newcount\my@repeat@count
\newcommand{\myrepeat}[2]{%
  \begingroup
  \my@repeat@count=\z@
  \@whilenum\my@repeat@count<#1\do{#2\advance\my@repeat@count\@ne}%
  \endgroup
}
\makeatother

\newcount\myloopcounter

\newcommand{\repeatit}[2][10]{%
  \myloopcounter0% initialize the loop counter
  \loop\ifnum\myloopcounter < #1 % Test if the loop counter is < #1
  #2%
  \advance\myloopcounter by 1 % 
  \repeat % start again
}

\usepackage{mdframed}
\newenvironment{mymdf}
  {\mdfsetup{
    innertopmargin=15pt   
    }
  \begin{mdframed}%
  }  
  {\end{mdframed}}



\begin{document}

\begin{questions}

\question Approximate $\displaystyle \int_0^1 \sin x^2 \, dx$ within $.001$ of
its true value.
\begin{mymdf}
\repeatit[3]{\myrepeat{150}{.}\\} %3 row, 150 dot per row.
\end{mymdf}

\question A question with a long solution.
\begin{mymdf}
\repeatit[10]{\myrepeat{150}{.}\\} %10 row, 150 dot per row.
\end{mymdf}

\end{questions}
\end{document}

Answer 2

Here is a solution that redefines the macro \do@fillwithdottedlines. The macro now prints a bounding box around the dotted lines. Parts are reused from the \do@emptyboxmacro. The solution box first prints vertical white space, then prints dotted lines and then prints vertical white space again. The vertical white spacing is hard coded because \do@fillwithdottedlines takes only one argument (the vertical spacing with dotted lines). For some reason, unclear to me, the vertical white spacing must be a multiple of \dottedlinefillheight otherwise the vertical rules will show gaps. There is also a small negative vskip to get unbroken vertical lines (why is also unclear to me). I didn't test it with other solution boxes.

\documentclass[a4paper,addpoints]{exam}
% Use next line to show the solutions
%\documentclass[a4paper,addpoints,answers]{exam}

\makeatletter

\setlength\dottedlinefillheight{.25in}

\newlength{\mylength}
\setlength{\mylength}{\textwidth}

\def\do@fillwithdottedlines#1{%
  \hbox to \hsize{\hskip\@totalleftmargin \leaders\hrule\hfill}%
  \begingroup
  \advance \mylength by -\@totalleftmargin
  \advance \mylength by -4em
  \ifhmode
    \par
  \fi
  \hrule height \z@
  \nobreak
  \setbox0=\hbox to \hsize{\hskip \@totalleftmargin \vrule \hskip 2em
          \vrule height \dottedlinefillheight depth \z@ width \z@
          \leavevmode\hbox to \mylength {\dotfill\hfil} \vrule}%
  \setbox1=\hbox to \hsize{\hskip\@totalleftmargin
          \vrule height\dottedlinefillheight \hfill \vrule}%
  % We use \cleaders (rather than \leaders) so that a given
  % vertical space will always produce the same number of lines
  % no matter where on the page it happens to start:
  \cleaders \copy1 \vskip 1\dottedlinefillheight%
  \vskip -\minboxheight%
  \vskip -1.5pt % Dirty hack
  \cleaders \copy0 \vskip #1%
  \vskip -\minboxheight%
  \vskip -1.5pt % Dirty hack
  \cleaders \copy1 \vskip 4\dottedlinefillheight%
  \hbox to \hsize{\hskip\@totalleftmargin \leaders\hrule\hfill}%
  \endgroup
}% \do@fillwithdottedlines

\qformat{\textbf{Question \thequestion{}} (\totalpoints \@pointname) \hfill}

\makeatother

\begin{document}

\begin{questions}
\question[10]

Calculate $1+1$.

\begin{solutionordottedlines}[2in]
2
\end{solutionordottedlines}

\question[10] Please give the answer to the ultimate question of life, the universe, and everything. 
\begin{solutionordottedlines}[1.4in]
42
\end{solutionordottedlines}

\end{questions}

\end{document}