Is "no one of them seems grammatical" ungrammatical? Why?

Question

I wonder if the following sentence will be grammatical in the most bizarre context:

No one of them seems grammatical.

Clearly, there are way better ways to phrase this sentence, either by using the negative determinative "none" or removing the complement "of them" or any other way to get sentences like these:

None of them seems grammatical.
No one seems grammatical.

_{Though it's controversial whether the second sentence really works with accordance to semantic rules.}

My intuition also [rightfully] says there should be a "not" instead of "no" in order to render the sentence grammatical, or at least revise it to a more colloquial state:

Not one of them seems grammatical.

But the question is, is the original sentence undoubtedly an ungrammatical utterance? If so, why should I use "not" instead of "no"? If both sentences are perfectly acceptable, what possible change in meaning does changing "no" to "not" bring on?

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_{See also "Neither", "none", "no one" + [of them] + verb-s — where the highest-voted answer doesn't choose a clear position regarding a similar structure while a deleted (but fairly highly voted) answer claims it's grammatical.}

Answer 1

The phrase no one of them is "grammatical" (taking that to mean that it is both idiomatic and meaningful), but it is not always the same thing as none of them. It is an emphatic form employed to distinguish a proposition concerning a number of entities taken singly from propositions concerning the same entities taken in combination.

Consider the difference between these two propositions concerning three people, Adolphus, Benjamin and Carloman, suspected of murdering Dionysius.

1. None of them killed him. This is taken to assert that all three are innocent of the murder.

2. No one of them killed him. This implies the possibility that two of them—A and B, or A and C, or B and C—or all three, conspired to commit the murder.

So it might be perfectly proper to say of three utterances that "No one of them is grammatical" if you intend to propose that some combination of the utterances is grammatical.