I'd like to note (and confirm) the following (inconsistency):
Equations (3) and (4) are complex.
The 3rd and 4th equation are complex.
The full version of the sentences:
Equation (3) and equation (4) are complex.
The 3rd equation and 4th equation are complex.
I was told the reason that it was singular in the second sentence was due to the intention of the full version in fourth sentence. Same logic, though, doesn't apply to the first sentence.
I changed the sentences from 'fine' to 'complex' not to confuse when someone says that the sentence is fine. I'm also adding more details since there might be a disagreement in the comments about the second sentence--that is should be equations and not equation.
It all started here:
The surfers example isn't good since beginner isn't an adjective, but you get the idea.
Back then, I asked Neil about it and he said:
It should be singular in the case when you use the definite article in front of the adjectives.
"He fed a small and a big dog."
There is an elision of a word in that sentence [* elision doesn't seem to refer to this; maybe whiz deletion?], which is fine in English. It is shorthand for "He fed a small dog and a big dog." You can omit the first instance of the noun and still be OK but you do not pluralize the remaining instance.
But the indefinite [* I think he meant definite] article or no articles require a plural:
He fed small and big dogs.
He fed the small and big dogs.
He fed the small and the big dogs.
He fed a small and a big dog.
So, in the case in the forum, it should be: We are a beginner and an advanced surfer.
The definite article is what forces the singular noun.
I asked him about two links:
and he added:
There is an overlapping case where either the plural or the singular works, as noted in the first of your examples.
He fed the small and the big dogs -> implies that there is at least one of each
He fed the small and the big dog -> implies there is exactly one of each
He fed a small and a big dog -> implies that there is exactly one of each
He fed a small and a big dogs -> is wrong
I'm still not clear if
He fed the small and big dog.
is okay (implying one of each), and if not why.
Similarly, I'm not sure if I can say:
It involves a technological and theoretical challenge,
where I mean that it involves a technological challenge and a theoretical challenge. It might be confused with involving a single technological, theoretical challenge.
I tweaked a bit the above edits.
I think that even if technically I can use a single in/definite article with a singular noun (describing two objects), due to the risk of confusion (that I made a mistake and used 'and' between two adjectives preceding a noun), I should avoid it.
This puts some doubt on the correctness of the 2nd sentence even though it should be clear that I'm referring to two equations (it's an elision of the 4th sentence) and not a single equation that is both the 3rd and 4th.
Seeking more confirmation since it became convoluted