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The phrase "another order of difficulty" is correct and usable in written English.
It can be used to describe a situation or task that presents a different or greater level of challenge compared to others.
Example: "While solving the initial problem was challenging, the next one presented another order of difficulty that required more advanced skills."
Alternatives: "a different level of difficulty" or "a higher degree of difficulty".
Exact(1)
Doing this while being interrupted by nurses with urgent questions about their patients, referrals from the wards and calls from A&E is another order of difficulty.
Similar(59)
Another method, called bookmark, involves ranking test questions in order of difficulty and having an educator mark the question that could reasonably be expected to divide the proficient students from the non-proficient.
But in the age of bitcoin, that's of a different order of difficulty.
A year's worth of favorite recipes are here, in order of difficulty.
Arranged in ascending order of difficulty, the pieces remain pedagogical favorites.
But Plastiki is of a different order of difficulty and danger from anything he has attempted before.
(The quiz consists of three qualifying questions in increasing order of difficulty, each of which must be correctly answered within 10 seconds).
To that end, in 2015 they asked two hundred people, ranging in age from eighteen to eighty-three, to rank ten magic spells in order of difficulty.
Mikrokosmos An amazing, organic work comprising 153 short pieces for solo piano, arranged in six volumes in ascending order of difficulty.
An automated program grants 10 seconds to answer each of three questions -- in increasing order of difficulty and usually about the correct chronological or geographical order of four events or places.
They are, in rising order of difficulty, coping with a modern economy, accepting the idea of sexual equality, and, hardest of all, learning to absorb the principle of democracy.
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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