The discussion on Hermione in the short stories thread reminded me of a certain idea.

Time Paradox

(Hermione Granger)

There was a story somewhere on gurochan where Hermione wonders why it is prohibited to meet yourself in the past, so to find it out she does exactly that. The result is that the past Hermione feels uncontrollable urge to eat the future Hermione, and so she does.
When I have read it, a though occured to me, what if... Hermione instead wondered what would happen if one goes to the past and kills their past self? What will happen to the world, what trick will it play? She considers trying it, and as soon as she thinks about it, another Hermione from future appears. The past Hermione lets the future Hermione kill her with no objections as this is the point of the experiment (maybe have some sex first cause why not, if it's with herself, it's not different from masturbation). Then, as the past Hermione is dying, she realises, whatever happens to the world, she has no way of knowing it, as she will be dead. So that must be the trick! If something is unverifyable, it is not scientific, but verifying that something is unveryfiable (which is what Hermione did) is scientific, so in the end she considers the experiment a success before finally dying.
So, what happens to the world though?
Okay, in case it wasn't obvious: we never know and that's the trick: to know you have to die, but if you die you can't know.
And the past Hermione died satisfied because she understood this trick.

There is another variant of this story though:
After hermione reveals her time turner, or after they use it all as in the book, but before Hermione gives it back, Harry and/or Ron wonders what would happen if one goes to the past and kills their own past self. Hermione shrugs it off with "it's prohibited to even meet with your past self", but it actually makes her think of it a lot in the next days, but it's not like she can just try and do it? Or is it? The future Hermione appears and the past Hermione understands that it means she decided (will decide) to do it after all, and lets the future Hermione kill her (maybe have some sex first cause why not, if it's with herself, it's not different from masturbation). Then after the past Hermione dies, Ron comes in and says to the "future Hermione": "wow, that was hell of a show, totally worth all of the effort to make the Polyjuice Potion, Harry", and "future Hermione" revealed to be Harry asnwers: "yeah, I know we have purpousely put this idea in her head, but it was still surprising how easily she let me do it" or soemthing along the lines.
Harry and Ron's roles can be reversed, whichever option you consider would fit better.