adjectives - Many/Much more difficult problems

Pick the correct sentence:

1. There were many more difficult problems than we were thought possible.


2. There were much more difficult problems than we were thought possible.

I think both are correct. The first sentence talks about the amount of problems, many more problems, while the second sentence talks about difficulty, the problems were much more difficult.

Is my reasoning correct? If so, is one of the sentences more correct than the other, e.g. is one of the two more formal than the other?

Answer

Side note: You shouldn't say, "than we were thought possible", just "than we thought possible", or if you prefer "than we were thinking was possible".

But to your question: You are exactly correct. "Many more difficult problems" means that there were a large number of problems. We didn't just have 1 or 2 problems, we had 10 or 20. "Much more difficult problems" means that each problem was more difficult. We might still have had only 2 or 3 problems, but each problem was very difficult.

Neither is better than the other because they mean different things. Use the one that matches the meaning you want to convey.