Agatha Christie didn’t decide who did it until most of the story was already written.

I always assumed she just knew who did it, in the same way that, well, a murderer knows exactly who they want to kill. Certainly, at the end of her books, she always made you feel that the story couldn’t have happened any other way. It had only ever seemed otherwise because you couldn’t see it. But it turns out that for many of her books, Christie often ran through multiple scenarios for the victim, the method of death, and the identity of the murderer. Curran finds that even the denouement of Endless Night, in which you innocently follow the narrator until you find in the last few pages that he is the murderer, was one of the later parts of the plot to be sorted out.

Isn’t that the easiest way to do it?  Just like multiplying numbers is easier than factoring, it would be simpler to take some facts as given and thread a murder plot through them than to start with the plot and think up facts that fit.  After all it is supposed to be a surprise in the end.  Writing the facts before you know the mystery ensures you don’t give away the surprise.  via kottke.