The correct choice shall be "No one".
The major problem in this question is "subject". Now, let's exam each of these available choices:
"none" can be used as a pronoun, it can be a subject. However, in this sentence, using "none" is not the best choice (of course, if there is no "No one" available, you can choose it). It is better to write "none of them" to make it clear. From the context of the sentence, you can sense that it is about people. By using "none" in the sentence, it can give a feeling of doubt whether it is about people. Readers might think it is something else when they first read the sentence, because it doesn't specify as "none of what". In a word, using "none" ONLY can NOT give a solid idea what it is. This is why it is NOT the best choice, even though it is grammatically correct.
"Anyone" is also pronoun, but it doesn't fit the context of the sentence. Using it sounds like "asking" a question, not stating a fact.
"No one" is the best choice. Even though "one" can represent things other than people. However, when it is used in a sentence like this, reader can easily determine it is for people. By the way, "no" is an adjective and "one" is a pronoun.
"Not one" cannot be used as a subject. Why? "not" can ONLY be used as an adverb. As you know, adverb can only be use to describe verb, adjective or another adverb. Here, "one" is an adjective, that is why you can use "not" in front of it. Now, you know why "not one" cannot be a subject.
This kind of question is to test your feeling with English, not grammar (although it does use a little). Once you have used English for a while, and get used to it. You can easily pick out the BEST choice. However, if this question can have more than one choice, then "none" is also acceptable choice. Like I said, it is about feeling of English. so it is not easy to explain in word. Hopefully, you can get the idea of my clumsy explanation.
2012-12-03 00:22:44 補充：
都英文，眼花了, I am sorry for my bad!
I use very SIMPLE English, if you can read it calmly, you will understand it.
2012-12-03 00:44:06 補充：
If you still have trouble to understand, please let me know, I might be able to find a person to translate it for you. After all, the important thing is you understand the answer to your question, not how good the answer is.