Grid environment for exercise solution

Question

Following the example in the tcolorbox manual, p. 148, I produced the following MWE:

\documentclass[11pt]{book}
\usepackage[most]{tcolorbox}
\usepackage{lipsum}
\usepackage[no-math]{fontspec}
% Define box for questions
\newtcbtheorem{exemplo}{\, Exemplo}%
{ % frame stuff
    breakable,
    arc=40mm,
    size=normal,
    enhanced,
    colframe=blue,
    colback=white,colbacklower=white,
    borderline={0pt}{0pt}{blue!10},
    % margens da frame
    top=0.3cm,left=0.2cm,bottom=0.2cm,right=0.2cm,
    lefttitle=0.2cm, toptitle=0.1cm,bottomtitle=0.05cm,
    coltitle=blue,
    fonttitle=\bfseries,
    colbacktitle=blue!10,
}{ex}

\newfontfamily\cooljazz[NFSSFamily=cooljazz,BoldFont={Boogaloo Regular},Scale=0.85,Ligatures=TeX]{cooljazz}
\usepackage[subdued, defaultmathsizes]{mathastext}
\MTfamily{cooljazz}
\Mathastext[cooljazz]
% Environment for solving the questions
\newenvironment{resol}
{   \MTversion{cooljazz}\MTdonotfixfonts
    \setmainfont{cooljazz}[Scale = .8, Extension = .ttf ]
}{\par} 
% define grid backround
\newtcolorbox{notebook}{
    enhanced,
    breakable,
    sharp corners,
    colback=white,
    colframe=white,
    boxrule=0mm,top=0mm,bottom=0mm,left=0mm,right=0mm,
    %left=1.3in,
    underlay={%
    breakable,
        \begin{tcbclipinterior}
            \draw[help lines,step=5mm,blue!25,shift={(interior.north west)}]
            (interior.south west) grid (interior.north east);
    \end{tcbclipinterior}}
}
\begin{document}
    Minimum Working Example
\begin{exemplo}{Exemplo}{}
\lipsum[1-1]
\linebreak
\begin{notebook}

\begin{resol}   
    \lipsum[2-5]
\end{resol} 
\end{notebook}
\end{exemplo}
\end{document} 

The result is:

I can't align the box at the top of the page with the book class. I can with the article class, but, either way the grid box does not break across pages... Also, the last right vertical line of the grid does not show up, neither does the last horizontal bottom line... I wonder if someone has a suggestion on how to solve this....

The problem seems to be that tcolorbox does not allow for a box inside another box to break....

Thanks in advance.

Addition:

I was able to get this effect:

Not perfect, but will do for now. The solution was to add

    \begin{tcbclipinterior}
        \draw[help lines, step=5mm, gray25!20, shift={(interior.north west)}]
        (interior.south west) grid (interior.north east);
    \end{tcbclipinterior}}

to the exemplobox, and then define a blank box for the heading as:

\newtcolorbox{note}{
    enhanced,
    breakable,
    sharp corners,
    colback=white,
    colframe=white,
    boxrule=-2.25mm,top=2mm,bottom=1mm,left=2mm,right=2mm}

It's still not perfect as the top of the grid shows up partially after the box title....

Answer 1

I understant that OP wants a breakable box whith a grid background for the lower part of the box. This can be achieved with an overlay applied only to the lower box. Something like:

\documentclass{article}
\usepackage[most]{tcolorbox}
\usepackage{lipsum}

\newtcolorbox{exemplo}[2][]{%
    enhanced, breakable, segmentation hidden, colback=white,
    colframe=blue,
   overlay={\begin{tcbclipinterior}
        \draw[help lines, step=5mm, blue!50]
        (interior.south west) grid (segmentation.south east);
    \end{tcbclipinterior}},
    title=#2,#1}

\begin{document}

\begin{exemplo}{First}
\lipsum[1]
\tcblower
\lipsum[1-5]
\end{exemplo}

\end{document}

The problem with original codes was the use of two nested boxes. tcolorbox cannot break them. The code in page 148, uses two boxes, one for exercices and one for solutions, but they are not nested, the remain independent.