### Defining macros within 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 replace part of the macro:

      \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.