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The phrase "a maximum number" is correct and can be used in written English.
It is commonly used to refer to the highest or upper limit number in a particular situation. Example: The company has set a maximum number of 50 attendees for the conference due to limited space.
Exact(60)
Wednesday's vote establishes only a maximum number of competitions.
(Turns out Tinder has a maximum number of swipes permitted per day).
"Each ceremony will involve a maximum number of lawyers and political workers across the country".
The result is the display of a maximum number of paintings with a minimum of crowding.
Instead, each factor is assigned a maximum number of potential points, which may vary by model.
Is there a maximum number of med alumni that can attend Sierra Camp weekend?
Is there a maximum number of students admitted from a particular country, region or school?
Can I set a maximum number of open files per process?
But what a real candidate can do is speak the truth about the regime to a maximum number of people".
It also provides the ability to set a maximum number of jobs per schedule and a maximum shift length.
And HE bosses should be in post for a maximum number of years – before returning to academic work.
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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