# signs doubled in macros?
The way to think of this is that ## gets replaced by # in just the
same way that #1 gets replaced by `whatever is the first argument'.
So if you define a macro and use it as:
\def\a#1{...#1...#1...#1...} \a{b}
the macro expansion produces `...b...b...b...', which people find normal. However, if we now fill in the `...':
\def\a#1{---#1---\def\x #1{xxx#1}}
\a{b} will expand to `---b---\def\x b{xxxb}'. This
defines \x to be a macro delimited by b, and taking no
arguments, which people may find strange, even though it is just a
specialisation of the example above. If you want \a to
define \x to be a macro with one argument, you need to write:
\def\a#1{---#1---\def\x ##1{xxx##1}}
and \a{b} will expand to
`---b---\def\x #1{xxx#1}', because #1 gets replaced by `b'
and ## gets replaced by #.
To nest a definition inside a definition inside a definition then
you need ####1, as at each stage ## is replaced by
#. At the next level you need 8 #s each time, and so on.