Writing the code is the hard part mainly inasmuch as it forces you to concretize and clarify previously vague notions. In that sense, it's hard to separate "conceiving the solution" from "writing the code," unless you're perhaps one of those rare geniuses who are simply able to dictate ideas fully formed in their head (I'm thinking of the scene in Amadeus when Salieri examines some clean, uncorrected sheet music and is then shocked to discover that Mozart doesn't make copies and he's holding originals).