One ring per person?

Hi. Which is correct? For my questions, let's say we need to say that each person is putting a ring in his or her nose and that's what he noticed. Does the sentence below say that? Also, is it correct to put the phrase "a ring" instead of "the ring" in the sentence below? How about just writing, "He noticed people putting rings on their noses. He thought it was very strange"? I think it is correct, although it leaves possibility that they might have been putting more than one ring in their noses.

He noticed people putting the ring (a ring?) in their nose. He thought it was very strange.

How about this sentence? Does it say one ring per person? Also, like above, I think it is correct to write "Sometimes they put rings in their noses." Thank you in advance for your help.

Sometimes they put the ring (a ring) in their nose.