correct sentence

yes, isn't it obvious? "every one of them has a black nose"... what else could be the inference?

Thanks, Mame, but a native speaker disagrees with me.

on what conceivable basis? I'm with Mame.

And, um, just asking here, why are their noses black?

There are 20 men and every one of them has a black nose.

Is the sentence correct and makes clear that each of the 20 men has a black nose?

Yes, it's correct. The normal understanding would be as you mentioned but it wouldn't have to be so. It could be,

There are 20 men [pointing] [there] and every one of them [pointing to another place] has a black nose.

The context leads you to the conclusion.

"There are thirty men with a rugby ball" would probably lead you to a different conclusion.

As would "Thirty men with one aim in mind." But maybe I digress.

I agree with Mame and JTT of course.

Thanks, everybody.

I think that native speaker is trying to 'bully' me as I'm not a native speaker. However, he doesn't know that I've friends in this forum who most willingly help me.

Thanks, once again, everybody.

Best wishes