None of them have any grammar problems
I liked this explanation so much that I will just copy it here.
Source: The Blue Book of Grammar and Punctuation
indicate portions—some, all, none, percent, fraction, part, majority, remainder, and so forth —look at the noun in your of phrase (object of the preposition) to determine whether to use a singular or plural verb. If the object of the preposition is singular, use a singular verb. If the object of the preposition is plural, use a plural verb.
Examples:
None of the pie was eaten.
None of the children were hungry.
In a sentence like “None were missing,” there is an implicit noun that answers the question, “None of what?” That noun is what determines whether none takes a plural or singular verb.
Examples:
None were missing. (None of the cookies were missing.)
None was missing. (None of the pie was missing.)
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