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I think much in much more complex problems is grammatically correct because it modifies more complex though it convey a different meaning from many more complex problems. Do you think my assumption to be right?

(A)They are capable of solving many more complex problems compared to other birds, such as chickens.

(B)They are capable of solving much more complex problems compared to other birds, such as chickens.

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    In B, much isn't an adverb or quantifier which are the usual usage. See much. And how does much modify "problems", as you say? "Much (complex) problems" makes no sense. – user3169 Jan 26 at 3:07
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Here are two possible interpretations that indicate what the sentences could be taken to mean.

(A) They are capable of solving many more complex problems compared to other birds, such as chickens.

This means that they are capable of solving many more problems that are complex.

It's referring to quantity, not quality:

(A) They can solve more problems of a complex nature than other birds.


Note that it could also be referring to a combination of quantity and quality:

Then can solve a lot of problems of a more complex nature compared to other birds (who can only solve a few).

This is similar to the following interpretation, but subtly different.


(B) They are capable of solving much more complex problems compared to other birds, such as chickens.

This means that they are capable of solving problems that are much more complex.

It's referring to quality, not quantity:

(B) They can solve problems of a more complex nature than other birds.

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    @Araucaria Noted. I had wanted to provide a simple comparison. However, I've updated my answer to include this other sense. – Jason Bassford Jan 31 at 13:48

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