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I have a question about possessives.

While "Peter's ball" is easy and clear.

How do I express the notion of "the ball that belongs to agent 2"?

Would it be "agent's 2 ball" or "agent 2's ball" or what else?

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    It's agent 2's ball, same as the King of Spain's daughter (but don't forget the King of Spain's daughter's doll's dress, among other more exotic examples of the Saxon Genitive). Sep 1, 2018 at 17:26

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Your second guess is correct:

Agent 2's ball

The ball is owned by 'agent 2', which is a noun phrase. You should put the apostrophe indicating possession after the complete noun phrase, regardless of whether the noun phrase includes numbers or not.

You can see this form when referring to royalty:

King Henry V's advisors

or to government and military organizations:

Directorate 7's responsibilities

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    When I typed my comment to the question, I took it for granted I'd be closevoting as a dup straight after. But unless my google-fu has deserted me, we've never had this one before. I might have considered voting to migrate to English Language Learners, but I guess your answer sits well enough here. Sep 1, 2018 at 17:34

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