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The phrase "a failure of ingenuity" is correct and usable in written English.
It can be used to describe a situation where a lack of creativity or resourcefulness has led to an unsuccessful outcome.
Example: "The project's collapse was ultimately attributed to a failure of ingenuity among the team members."
Alternatives: "a lack of creativity" or "a shortcoming in innovation."
Exact(1)
After all, inability to imagine a proof is commonly due to a failure of ingenuity rather than the non-existence of a proof.
Similar(59)
There has to be a failure of nerve, and above all of ingenuity, at the top.
A failure of democracy.
A failure of coordination?
Is it a failure of leadership?
A Failure of Capitalism: Preface.
There was a failure of oversight.
Identify a failure of condition.
K.K.R.'s pursuit of a public offering has opened a window into a firm struggling with success and failure, ego and greed — and is ultimately a tale of ingenuity and desperation.
So a bit of ingenuity was needed.
"A lot of ingenuity went into this.
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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