Is this sentence correct? - "Every one of them could not solve it."

Thank you for checking out my question. Even though I asked a similar question earlier, another confounding issue showed up here.

Is this sentence grammatically correct or, at least, acceptable?

Every one of them could not solve it.

I know that it should rather be written like;

None of them could solve it.

However, I failed to clearly point out what is wrong with this sentence. I would be delighted so much if you kindly give advice to me.

Thank you so much for your time!

Let's take a closer look at your sentence:

• "Every one of them" does not sound so incorrect but it is definitely less correct compared to "All of them" (no emphasis), "Every single one of them" (emphasizing all individuals) or "Each and every one of them" (emphasizing individuals even more). Yours is somewhere in between. You could go for one of these in a sentence without a negation in it. Which brings me to the next part of your phrase.
• 'Selecting construction' + negation (= "Every one of them" + "not"). It is common in the English language to include the negation in the construction at the beginning of the phrase, following your meaning of the phrase this would boil down to "None of them". However, "Not every one of them" means something else, an ambiguation that should be avoided. This is the reason that the construct at the beginning of your phrase draws the negation to it, to result in one meaning and one meaning only. It is up to the writer of the sentence to put the negation in the right place among the selecting construction.