Is it correct to say:
It would be nice to have as general an answer as possible.
I'm not sure... I think I've read similar sentences, if I'm not mistaken.
Any help would be appreciated.
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Yes, that's fine.
as general an answer as possible
means the same thing as
an answer that is as general as possible
In other words, an answer that cannot be any more general. It has already been made general to the extent that is possible.
Grammatically, the adjective phrase as general appears in Predeterminer position, which has that name because it comes before the Determiner an. It licenses the post-head Complement as possible.
This construction is covered in Michael Swan's Practical English Usage (3rd edition) in section 14. For a more technical reference, see The Cambridge Grammar of the English Language, page 435.