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The phrase 'solve difficult problems' is correct and usable in written English.
You can use it when referring to a situation in which someone is trying to find a solution to a complex issue. For example: "The software engineers had to solve difficult problems in order to ensure the new system worked properly."
Exact(57)
It's harder to solve difficult problems and after a while harder even to recognise them.
He used geometry-based methods to solve difficult problems in number theory.
Throughout his career, he showed a gift for bringing people together to solve difficult problems and to resolve intractable conflicts.
In thinking about how to solve difficult problems in medicine, it's comforting to remember that progress often comes from mistakes.
These local basins would eventually constitute dynamical memories that solve difficult problems in classifying and recognizing faces.
Technology helps students develop the ability to ask good questions, find and process information, critically and creatively think and solve difficult problems.
"You just have to solve difficult problems 24/7 and spend the rest of your time putting out the resulting fires".
It's being able to deal with, to cope with, to solve difficult problems". Coleman has been nothing if not a difficult -- er, challenging -- problem.
Similar(3)
Because solving difficult problems is the fun part of life.
Curious people are good at solving difficult problems for their employers because they're really solving them for themselves.
Peace and quiet are highly desirable for solving difficult problems at the bridge table, but they are rarely available.
More suggestions(12)
solve challenging problems
solve tough problems
solve complex problems
tackle difficult problems
solving difficult problems
resolve difficult problems
solves difficult problems
tackling difficult problems
address difficult problems
addressing difficult problems
overcome difficult problems
solve difficult issues
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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