I came up with the first sentence to Chapter 19 12 minutes ago. I've been so productive that I am now up to six sentences. I may have to lie down soon.
The great thing to me is that this first paragraph is a clue to the reader about the solution, but is not overt in any way, shape, or form. It also links it to the end of the previous chapter and is just overall a pretty keen piece of work. I'll probably end up deleting it at some point.
Such is the life of a writer.