In general: I explain the outlines of the way it works on this page (http://www.lthr.xyz/programming/13/6/2015/eternity-ii-solver...). This is the technical aspect. But because not everyone likes the technical details, I wrote a parable on this very subject (Theseus, Penepos [a name I created to anthropomorphize P?=NP {PeNePos}], and the Eternal Labyrinth: http://www.lthr.xyz/blog/7/6/2015/theseus-penepos-and-the-et...). This is a core aspect of my project.
You will probably think that I am crazy, but my goal with my program is to simulate, as subtly as possible, the idea that Penepos symbolizes.
But wait, TetraVex puzzles are NP-complete (http://www.sciencedirect.com/science/article/pii/S0020019006...), and my algorithm solves large ones almost as fast it is possible to check them, so maybe Penepos is not just a fantasy... (You may understand with this sentence that I am a strong believer that P = NP).