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The phrase "at three different" is correct and usable in written English.
It can be used when referring to three distinct items, locations, or instances in a context where differentiation is necessary.
Example: "The conference will be held at three different venues across the city."
Alternatives: "in three separate" or "at three distinct".
Exact(59)
Annealing was performed at three different temperatures.
"It was severed at three different places in the knee...
PREDIMED looked at three different groups of women.
He was a millionaire at three different times.
Experiments were conducted at three different isothermal temperatures.
That needs to take place at three different levels.
Recoveries at three different concentrations ranged from 75.50 to 96.48%.
Dust classification at three different solid rates is simulated.
The results show simultaneous mode-locking at three different wavelengths.
These components are applied at three different levels.
IPM practices in tomatoes were demonstrated at three different farms this year.
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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