Content of \setbox does not respect pagebreaks

Question

The following MWE demonstrates that the list of answers accumulated into a box does not respect page breaks when printed (code adapted from Multiple Choice Answer Key in exam package at the end of document:

\documentclass[answers]{exam}
\usepackage{pgffor}

\newbox\allanswers
\setbox\allanswers=\vbox{}

\newenvironment{answer}
{%
    \global\setbox\allanswers=\vbox\bgroup %
    \unvbox\allanswers%
    \thequestion. \thechoice\\
}%
{%
    \egroup%
}

\newcommand{\CC}{\CorrectChoice \leavevmode\begin{answer}\end{answer}}
\newcommand{\showallanswers}{%
    \ifprintanswers \centering Here are the answers: \par \usebox\allanswers \fi}


\begin{document}
    \begin{questions}
        \foreach \i in {1,...,50}{
        \question[5] Important Question 1
        \begin{choices}
            \CC 100
        \end{choices}
    }
    \end{questions}

    \newpage
    \showallanswers
\end{document}

How can I format the content of the box so that it stays into the document margins (ideally it should be printed in a multicol environment, but I can't seem to do it)?

Answer 1

A box cannot be split across pages, it is an indivisible unit.

However, you can “unbox” it:

\newcommand{\showallanswers}{%
  \ifprintanswers
    {\centering Here are the answers: \par}
    \unvbox\allanswers
  \fi
}

This will append the vertical list of the vbox to the current vertical list. Note that no interline glue is added at either end of an “unvboxed box”, so spacing could need some adjustment.

I would use a different method, though.

\documentclass[answers]{exam}
\usepackage{environ,pgffor}

\newtoks\allanswers

\NewEnviron{answer}
{%
 \edef\temp{%
   \the\allanswers % the previous ones
   \thequestion. \thechoice
   \noexpand\par % maybe \par has been redefined
   \unexpanded\expandafter{\BODY}%
 }
 \global\allanswers=\expandafter{\temp}
}

\newcommand{\CC}{\CorrectChoice \leavevmode\begin{answer}\end{answer}}
\newcommand{\showallanswers}{%
    \ifprintanswers {\centering Here are the answers: \par} \the\allanswers \fi}


\begin{document}
    \begin{questions}
        \foreach \i in {1,...,50}{
        \question[5] Important Question 1
        \begin{choices}
            \CC 100
        \end{choices}
    }
    \end{questions}

    \newpage
    \showallanswers
\end{document}

This avoids typesetting the answers in advance, so you can better use multicols at the time of printing the answers.