"A/an" or "any"

Are the following sentences grammatically correct:

Do you know a woman who can solve this problem?

Do you know any woman who can solve this problem?

Dear members, I am not a native speaker. I doubt if my second sentence is also grammatically correct because I think "any" is used with plural countable nouns. So the correct sentence might be

Do you know any women who can solve this problem?

I see many people use "any" followed by singular nouns with this kind of sentence structure. can someone tell me what the rule of using "any" is? And does the first sentence mean the same as the second?

Any suggestions would be helpful.

Solution 1:

"Any" is usually used with plural or noncount nouns. So, what you may be seeing as a singular noun may actually be a noncount noun. For example, "Do you have any cake left?" is perfectly fine, because in this case, "cake" is a noncount noun.

However, "any" is also used with singular count nouns to

• emphasise the idea of free choice

For example,

Ask any doctor - they'll all tell you that alcohol is a poison.

• express doubt

Thus, it is perfectly fine to use "any woman" in that question if you intend to express doubt — you want to emphasise that you doubt that there is a woman out there that can solve that problem. The "free choice" meaning is not really applicable here.

However, if you want the meaning of the question to be the same as the first sentence ("a woman"), then it should be "any women", like you said.