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The phrase "ability to solve all" is correct and usable in written English.
It can be used when discussing someone's or something's capability to address every problem or challenge without exception.
Example: "The new software boasts an impressive ability to solve all technical issues that users may encounter."
Alternatives: "capacity to address everything" or "capability to resolve all".
Exact(3)
While most Americans maintain a little healthy skepticism about government's ability to solve all our problems, that skepticism began to escalate during the presidency of George W. Bush.
A Valleywag advice column titled "Dear Miss Disruption" boasts the ability to solve all your problems with three simple words: learn to code.
According to Jess' prediction, will we see one app or one interface with the ability to solve all your basic human problems?
Similar(57)
It demolished the notion of an objective reality with all that it implied: the unity of nature, both human and physical, the universality of natural laws, the determination of physical processes, and the ability of science to solve all problems of the natural world.
To solve all voice recognition problems key-pad response ability could be added to the system for times when the voice recognition fails.
Try to solve all questions.
Minio hopes to solve all of these.
Is it going to solve all of the problems?
Moreover, to implement the algorithm, all that is required is the ability to solve univariate equations with monotonicity and to execute simple algebraic steps.
It is too early to know, though, if all the enthusiasm will improve government's ability to solve urban problems.
Regardless though, people are unique among all the animal kingdom in their ability to solve problems.
More suggestions(1)
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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