I'm not sure why folks think they need to hold all this in their head. For me, at least, the "think about the problem stage" involves a lot of:

* Scribbling out some basic design notes. * Figuring out the bits I'm not completely sure about * Maybe coding up some 'prototype' code to prove out the bits I'm less sure about * Repeat until I think I know what I'm doing/validated my assumptions * Put together a 'more formal' design to share with the team. Sometimes my coworkers think of things that I hadn't, so it's not quite a formality. :) * Code the thing up.

By the time I get to the "code it up" stage, I've probably put in most of the work. I've written things down as design, but nothing hyperdetailed. Just what I need to remind myself (and my team) of the decisions I've made, what the approach is, the rejected ideas, and what needs doing. Some projects need a fair bit on paper, some don't.