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Discover Ludwig"the solutions" is correct and usable in written English.
You can use it to refer to answers or ideas that one has found in order to solve a problem. For example: "After a long period of research, Johns and his team finally found the solutions to the difficult maths equation."
Dictionary
the solutions
noun
A homogeneous mixture, which may be liquid, gas or solid, formed by dissolving one or more substances.
Exact(60)
What are the solutions?
What about the solutions.
The solutions are not.
We know the solutions.
The solutions have been crude.
A book about the solutions?
Fortunately, the solutions are straightforward.
"And so are the solutions".
The solutions are insoluble.
And the solutions vary.
The solutions were similar.
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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