Not one of the boys has cleaned his room.
None of the boys have cleaned their rooms. (follows SANAM)
I see that one of the boys has started his homework.
I see that no one has started his or her homework yet.
One of the boys who were playing in the park has lost his cap.
One of the factors that keep the housing market bubble alive is irrational exuberance.
Detailed explanations are not necessary. I just need confirmation that I am on the right track.