Rebuild this concept from first principles

Something you use by rote and want to be able to derive rather than memorise.

Derive the thing below from the ground up, so I could reconstruct it without memorising it.

1. State the problem being solved, before any solution exists.
2. State the constraints: what any solution must satisfy.
3. Try the obvious naive approach first, and show precisely where it fails.
4. Introduce each element of the real solution as the fix to a specific failure. I should never see a component appear without knowing what would break without it.
5. At the end, list every design decision and the alternative that was rejected, with the reason.
6. Tell me which parts are forced by the constraints and which are conventions that could have gone another way.

Subject:

Explaining a concept. Getting an idea across at the depth you need, with analogies, origins and first principles.