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.
For purposes of this question, things you can rederive from your present knowledge count as part of your present knowledge.
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