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If I understand it correctly, a "vexed question" is bothering, annoying, and frustrating us; not being bothered, annoyed, and frustrated by us. As such, I'd expect the active (present, -ing) participle, not the passive (past, -ed).

Yet, Google N-Gram shows that the term "vexed question" is about 3 times as prevalent as the "vexing question", and decades ago it was 10 or 20 times as widespread.

I remain vexed by this vexing issue.

Fab
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    Appears to be mostly a Britishism. Here in the US I'm only familiar with "vexing question". – Hot Licks Dec 27 '20 at 23:25
  • Interesting! Indeed, the counter-intuitive imbalance is much stronger in BrE than AmE, although the "vexed question" is still ahead in the Google American English corpus. – Fab Dec 27 '20 at 23:34
  • Understand that Google Books "American English" is biased by British English, either by books by British authors, or by American authors that adopt a British style. – Hot Licks Dec 28 '20 at 00:15

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If you search vexed question in the available dictionaries, you will find that it is a British idiomatic expression which, according to Collins, means

an issue that is much debated and discussed

If you look up vexing question, however, it is interesting that Google still gives entries for vexed questions, and only one or two instances of vexing treated on its own. For example, MWebster defines it as

causing or likely to cause vexation : VEXATIOUS. Ex: a vexing problem

Therefore, I believe that a vexing question is simply a question that vexes or annoys, whereas a vexed question is rather a complicated problem that has caused a lot of discussion and argument and is difficult to solve.

fev
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