Upside down, paragraph style footnotes

Question

I am trying to figure out how to typeset solutions to in-text exercises as an upside down, paragraph style footnote, as in the following image:

I can easily typeset the solutions in a rightside up paragraph style footnote using footmisc with the para option. I can also use a \rotatebox to typeset the footnotes upside down and one-per-line (albeit, in the reverse order from what I want). However, I can't figure out how to get paragraph style footnotes in which the entire footnote is rotated.

I'd like to be able to produce something that looks like the above using code such as:

\documentclass[12pt]{article}
\usepackage{graphicx}
\newcommand{\problem}[2]{...}{...}
\begin{document}
\problem{What is 1+1}{two}
\problem{What is 1+2}{three}
\problem{What is 1+3}{four}
\problem{What is 1+4}{five}
\end{document}

Answer 1

NEW VERSION to respond to revised OP requirements. EDITED to use a \protected@edef as part of \problem to facilitate the use of braces \{...\} in the footnotes.

It uses the syntax \problem[]{question}{answer}. At this stage, the user must invoke the footnotes in one of two ways:

1. \showpageanswers following the final \problem on any given page; or

2. provide anything (other than \relax) as an optional argument to the last \problem on any given page.

I tried to automate this on a page-by-page basis, but was unsuccessful.

The problem counter will carry over page to page.

I modified \showpageanswers so than its invocation without any answers to show will be ignored.

To get the footnote to be able to extend past a single line in length (i.e., paragraph style), I put it in a \parbox. I also kerned -18pt before the rotated \parbox, to account for the footnote indent, and added a \strut to end of inverted footnote definition (\revfootnote), for subsequent vertical spacing.

Note however, if multiple answer sets appear on the same page, saving all the answers for one single footnote invocation per page will prevent the "appearance of" misordered footnotes (since turning them upside down changes the sense of first and last).

Here is the MWE

\documentclass[12pt]{article}
\usepackage{graphicx,lipsum}
\usepackage{enumitem}\newsavebox\fnbox
\def\pageanswers{}
\newcounter{problemNo}
\makeatletter
\newcommand\problem[3][\relax]{%
  \stepcounter{problemNo}%
  \par\smallskip%
  \theproblemNo.~~#2?%
  \par\smallskip%
  \protected@edef\pageanswers{\pageanswers$^{\theproblemNo}$#3\ \quad}%
  \ifx\relax#1\else\showpageanswers\fi%
}
\makeatother
\newcommand\showpageanswers{\if\relax\pageanswers\relax\else%
  \revfootnote{\pageanswers}\def\pageanswers{}\fi}
\newcommand\revfootnote[1]{\renewcommand{\thefootnote}{}%
  \footnotetext{\savebox\fnbox{\parbox{%
  \dimexpr\textwidth\relax}{#1\strut}}\kern-18pt%
  \rotatebox{180}{\usebox{\fnbox}}}}
\begin{document}
Solve these problems.
\problem{What is 1+1}{two $\{abc\}$}
\problem{What is 1+2}{three}
\problem{What is 1+3}{four}
\problem{What is 1+4}{five}
\problem{What is 1+5}{six}
\problem{What is 1+6}{seven}
\problem{What is 1+7}{eight}
\problem{What is 1+8}{nine}
\lipsum[1]
\problem{What is 2+1}{three}
\problem{What is 2+2}{four}
\problem{What is 2+3}{five}
\problem[x]{What is 2+4}{six}

\lipsum[2-4]
Solve these problems.
\problem{What is 1+1}{two}
\problem{What is 1+2}{three}
\problem{What is 1+3}{four}
\problem{What is 1+4}{five}
\problem{What is 1+5}{six}
\problem{What is 1+6}{seven}
\problem{What is 1+7}{eight}
\problem[x]{What is 1+8}{nine}
\lipsum[5-8]
\end{document}

Answer 2

The \hfill is of no use here, but a \raggedleft will shift the rotated box to the right margin`

\documentclass[12pt]{article}
\usepackage{graphicx}
\usepackage{enumitem}
\begin{document}
What is
\begin{enumerate}
\item   1+1?
\item   1+2?
\item   1+3?
\item   1+4?
\end{enumerate}
\renewcommand{\thefootnote}{}
\footnotetext{\raggedleft\rotatebox{180}{$^1$ two\qquad $^2$ three\qquad $^3$ four\qquad $^4$ five\hfill}}
\end{document}