using only your present knowledge

This strikes me as an un-lifelike assumption. If I had to explain things in this way, I would expect to encounter some things that I don't explicitly know (and other that I knew and have forgotten), and to have to (re)derive them. But I expect that I would be able to rederive almost all of them.

Refining my own understanding is a natural part of building a complex explanation-story to tell to others, and will happen unless I've already built this precise story before and remember it.