The rules state the story must be a new one. However if you do a rewrite that is obviously a rewrite then it's okay but you need to do more than just change a few words. Does that help at all? Perhaps the same premise but from a different POV would work.
So basically the way you phrased the question in the second post the answer would be yes. Like say you thought milk would be a great idea for questions but you wrote it and changed your mind. Then you saw this week's topic (current affairs) and your first though was milk! you can still write about milk but instead of posing the question anyone got milk? you could write about how a cow ate purple grass and all of her milk turned purple causing a widespread panic about whether or not one should drink purple milk.
It's the same subject but two very different story and come to think of it I really like the idea of purple milk!