Those maddening instructions...

[tangelatm]

Hi there,
I’d like you to help me with the following:
1.As the clues are entirely written in English, and as some of you might ,hopefully, want to work on your own...
Are the second “as” and “hopefully” correctly placed in the sentence?
2.a. There may be some unknown words in the clues as well as in the solutions.(is it ok?)
b. There may be some unknown words in both the clues and the solutions.(is this one ok?)
No grammar explains the use of the definite article in front of two nouns connected by “and” (or at least, I haven’t found any...)
3.a The boys and girls took part in the festivities.
b. The boys and thegirls took part ....
What’s the difference between the two?
Thank you for your time,
Angela

[mykwyner]

Sentence 1 is just fine except for the placement of the comma before hopefully (probably a typo). "...you might, hopefully..."

As for the articles before nouns, if they are distinct from each other you can use two articles.

The bushes and the fences ruin the view.
He got the money and the tickets.

I would not grade these as wrong if the second article were removed.
I would not use the second article with nouns that naturally go together.

The thunder and lightning kept me up.
Check on the hot dogs and hamburgers.
The boys and girls are ready.

[BobK]

I agree about "boys and girls". But, for emphasis, two articles are possible:

[Teachers at front of bus:]
'Right. Have we got everyone?
'All present and correct.'
'What? The boys and the girls?"

b

[weiming]

I agree with BobK:

And so we see the article can be used to emphasise that two things are separate--I fear the storm, the thunder and the lightning.

The boys and girls lumps them together as one group. The boys and the girls marks them as distinct, separate groups.

You also had the repeated preposition.

"There may be clues in the questions and answers."/ "There may be clues in the questions and in the answers (as well)."

The second "in" is slightly redundant, but there's nothing wrong with it grammatically that I can see.