Answer: b.

Explanation:
Everyone is singular — it means “every person.” We would say “on every person’s mind,” so we should also say “on everyone’s mind.”

Bonnie Trenga explains further for Grammar Girl:

“Although I’ll focus on the words everyone and everybody, the same rules apply to the words no one, nobody, anyone, anybody, someone, and somebody. Earlier I stated that grammarians don’t agree on the issue of indefinite pronouns. There are actually two issues concerning this topic: Are the words everyone and everybody singular or plural? And can I use a plural pronoun (such as their) to refer to these words? Grammarians actually agree that the words everyone and everybody are singular. Grammar Girl (that is I!) herself explains the answer in her upcoming book. She says, everyone sounds like a lot of people, but in grammar land, everyone is a singular noun and takes a singular verb. For example:

* Everyone loves Squiggly. (This is right because everyone is singular and paired with a singular verb, loves.)
* Everyone are happy. (This is wrong because it’s pairing the singular noun everyone with a plural verb, are.)
* Everyone hates subject-verb agreement. (This is right because everyone and hates are both singular.)

It’s OK to hate subject-verb agreement, but sometimes you just have to do things you don’t want to do. I promise to pick weeds if you promise to make sure your subjects agree with your verbs.”

Thanks to@biggreenpen for the idea for this question!

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Answer: a.

Explanation:
Although Word finds it hard to accept, there are constructions where doubled words are appropriate and this is one. Word will just have to get over it.

For Grammar Girl, Bonnie Trenga explains the use of doubled words in English writing:

“Another double you might encounter is “had had,” and Frank from New York would like to know if it’s a correct phrase. It is correct, though it too might seem a bit awkward. To understand “had had,” we need to take a look at the present perfect and past perfect tenses. Take this sentence: “I have had too many chocolates today.” That sentence is in the present perfect tense. You use that tense when you’re talking about a past action that is continuing into the present. This sentence means that I started eating chocolates in the past but the chocolate eating is continuing up to the present. Present perfect tense uses “has” and “have” plus the past participle, as in “have had” and “has gone.”

Now let’s put the chocolate sentence in the past tense. To do so, we’ll use past perfect tense, which uses “had” plus the past participle, as in “had had” and “had gone.” So in the sentence “I had had too many chocolates, so I was too full to eat dinner yesterday,” two things happened in the past. First was eating chocolates; second was trying to eat dinner.

When you have two past-tense occurrences, you use past perfect to express the action that came first. If you are using the verb to have in past perfect, you need to use two hads.”

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