Anyone/ Any one

[Noego]

Hello!

Could anyone provide a clear explanation as to the difference between anyone and any one?

I've read that any one is usually (always) followed by a prepositional phrase starting with of.

Anyone could do this.
Any one of them could do this.

Am I right?

There was a question in the exam that I'm correcting and it went something like this:

The investigation was so vague that ________ of us could have.... (can't remember the rest).

I would say that any one is definitely the right answer there, but the book says otherwise.

What do you think?

[Buddhaheart]

I believe it’s correct to say that any one is usually (NOT always) followed by a prepositional phrase starting with of.

Anyone is a pronoun that takes the meaning of anybody or any person; any person at all.

Any one means any single person or thing; any single member of a group of persons or things; whatever one (person or thing) of a group.

Anyone could do this. = Anybody or any person could do this.
Any one of them could do this. = any single one of them could do this.

As to your final question, give us more background before we could definitively say yes or no. I probably agree with your take of it.

[Casiopea]

Additionally,

anyone or any one. The one-word form anyone means “any person.” The two-word form any one means “whatever one (person or thing) of a group.” Thus, Anyone may join means that admission is open to everybody. Any one may join means that admission is open to one person only. When followed by of, only any one can be used: Any one (not anyone) of the boys could carry it by himself.

Source § 11. anyone. 1. Grammar. The American Heritage Book of English Usage. 1996