Well written! Would you mind sharing how you came up with the "middle out" numbering system? I can never seem to come up with something this inspired when I'm doing math problems by myself.
There's an apocryphal story about Richard Feynman about how he used to keep a dozen or so random problems in the back of his mind and made a little bit of progress on them every time he saw a connection, until finally he'd solve one and everyone would think he magically figured it out instantly. This was a bit similar except I'm not nearly at that level and I've only been able to do that for one problem instead of a dozen.