The puzzle is too hard for anybody to slove.
The puzzle is too hard for everybody to slove.
The puzzle is too hard for nobody to slove.
I want to know which of the above three is correct, especially whether the third is informally correct. Thank you.
The third is just wrong - and this isn't the usual double-negative problem; people do indeed say 'There ain't nobody can solve it', informally. But in the case of 'The puzzle is too hard for nobody to solve' the negative that might be doubled ('ain't') is replaced by 'too hard'. So even someone who uses a double negative wouldn't say "...too hard for nobody...".