How to get sum of pages under a certain pagenumber style

Question

I construct an article with three kinds of pagenumber style.

- fist part: \pagenumbering{Roman}

- Sencond part: \pagenumbering{arabic}

- third part: \pagenumbering{Alpha}

Q1:

How can I get the sum of pages of each part? For example, there are 3 pages in the first part with pagenumber style Roman, and 5 pages in the second part with pagenumber style arabic. The answer to this question will be used in the Q2.

Q2:

In the foot of every page in each part, I'd like typeset the page number like this: Page\ \thepage\ of\ \totalpages{Roman}(or arabic, Alpha for related part). I know @abspage@last, but it just give a total page number of an whole article. So is it possible to make a macro like \totalpages{Roman/arabic/Alpha...} to achieve this? No other packages preferred.

Example:

\documentclass{article}
\usepackage{geometry,fancyhdr}
\pagestyle{fancy}\fancyhf{}

\newcommand\totalpages[1]{...}

\begin{document}
part 1:
\pagenumbering{Roman}
\cfoot{Page\ \thepage\ of\ \totalpages{Roman}}
...
part 2:
\pagenumbering{arabic}
\cfoot{Page\ \thepage\ of\ \totalpages{arabic}}
...
part 3: \pagenumbering{Alpha}
\cfoot{Page\ \thepage\ of\ \totalpages{Alpha}}
...
\end{document}

Answer 1

EDIT: I have added an alternative solution (currently commented out) that gives Page A of 4 instead of Page A of D. It needs some hackery, using LaTeX internals, however.

Here is a solution with an extra macro \changepagenumbering. This remembers the last page number of the previous chunk and puts it in a label. It also does a\newpage, because changing page numbers mid-page doesn't make sense. Maybe it also works without this \newpage. I then use \pageref to pick up this number in \totalpages. You will need at least one extra LaTeX run to get the numbers correct.

\documentclass{article}
\usepackage{geometry,fancyhdr}
\pagestyle{fancy}\fancyhf{}
\usepackage{lipsum}

% Start a new page numbering scheme. Remember the number of pages of the
% previous scheme and start a new page (changing page numbering mid-page
% doesn't make sense)
%
\newcommand\previousnumbering{}
\newcommand\changepagenumbering[1]{%
  \label{last-pagenumber-of-\previousnumbering}%
  \newpage
  \renewcommand\previousnumbering{#1}%
  \pagenumbering{#1}%
}
\newcommand\totalpages[1]{\pageref{last-pagenumber-of-#1}}

% If you want the number of pages in decimal use this instead of the above:

% \newcommand\mypagecount{\arabic{page}}
% \makeatletter
% \newcommand\mylabel[1]{\@bsphack
%   \protected@write\@auxout{\let\mypagecount\relax}%
%          {\string\newlabel{#1}{{\@currentlabel}{\mypagecount}}}%
%   \@esphack}
% \makeatother
% \newcommand\previousnumbering{}
% \newcommand\changepagenumbering[1]{%
%   \mylabel{last-pagenumber-of-\previousnumbering}%
%   \newpage
%   \renewcommand\previousnumbering{#1}%
%   \pagenumbering{#1}%
% }
% \newcommand\totalpages[1]{\pageref{last-pagenumber-of-#1}}

\begin{document}
\changepagenumbering{Roman}
\cfoot{Page\ \thepage\ of\ \totalpages{Roman}}
\section{part 1}

\lipsum

\changepagenumbering{arabic}
\cfoot{Page\ \thepage\ of\ \totalpages{arabic}}
\section{part 2}

\lipsum[1-40]

\changepagenumbering{Alph}
\cfoot{Page\ \thepage\ of\ \totalpages{Alph}}
\section{part 3}

\lipsum[10-30]

% end with a dummy one
\changepagenumbering{arabic}
\end{document}