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The phrase "a number of difficult cases" is correct and usable in written English.
It can be used when referring to multiple challenging situations or examples that require attention or resolution.
Example: "The committee has been reviewing a number of difficult cases that have arisen in the past year."
Alternatives: "several challenging situations" or "multiple tough cases".
Exact(1)
My attitude brings me a number of difficult cases.
Similar(59)
Use of a kingdom-specific HMM library therefore effectively reduces the "twilight" zone and finds a significant number of difficult cases that might otherwise be missed.
The book takes on a number of difficult technical challenges.
Quantum gravity raises a number of difficult philosophical questions.
However, a number of cases are difficult to categorise and remain indeterminate on ultrasound.
Applying accounting rules can be difficult, and in a number of other cases the staff disagreed with the way the auditing firms had applied the rules and companies ended up restating their financial statements.
In borderline situations the matter is difficult to resolve, a number of intermediate cases being known, and there has been much controversy as to the validity of the distinction between the bimolecular and the unimolecular mechanisms.
There were a number of cases, where it was difficult or even impossible to decide from the picture itself, whether it is situated inside or outside a built-up area.
Having said that, when you mix religions, you are likely to come across contradictory advice in quite a number of cases, and it can be difficult to believe in two different views of life at the same time.
However, in a number of cases, such as clinical tissues, the relevant cell type may be difficult to purify or in low abundance.
The case of the businessman, Liu Yaping, is among a number of increasingly difficult legal disputes that have received prominent attention from United States officials, politicians and human rights groups.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com