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The phrase "a second difficulty" is correct and usable in written English
It can be used when discussing multiple challenges or obstacles, indicating that there is an additional issue to consider. Example: "After addressing the first issue, we encountered a second difficulty that required immediate attention."
Exact(34)
A second difficulty which may with equal justice be raised is this.
A second difficulty is that prosecutors must convict people under the laws that governed East Germany.
A second difficulty comes from Fredrickson's insistence that racism must involve both difference and power.
A second difficulty is shared by any tradition-bound, authoritarian state facing competition from suppler societies.
There is a second difficulty that must be overcome if video games are to be classified as audiovisual works.
A second difficulty for Hempel's account resulted from his candid admission that he was unable to offer a full analysis of the notion of a scientific law.
Similar(26)
There is also a third difficulty that Hicks didn't address, which is just as serious.
A third difficulty, from the standpoint of regulators and electricity generators, is that profit-driven energy companies are not motivated to build new plants when power prices are low.
A third difficulty arises for the von Neumann model.
A first difficulty lies in the QoS and interference power constraints which may not be met simultaneously.
A first difficulty for some interns is revising their expectations about the kind of work they'll be doing.
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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