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Discover Ludwig"counted by" is a correct and usable phrase in written English
You can use it to indicate that someone or something is calculating or keeping track of a certain number. For example, "The number of participants in the survey was counted by the research assistant."
Exact(59)
Where are ballots counted by hand?
Ballots are then counted by computer.
Where are they counted by machine?
Votes must be counted by people universally perceived as impartial.
The Iraqi dead are counted by the tens of thousands.
These would be recorded and counted by the detectors.
Neither category will be counted by the machine.
Attendance at games could often be counted by hand.
Monopoly money can now be counted by a tablet computer.
Protozoal populations were counted by microscopy.
Necrotic cells were counted by flow cytometry.
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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