Explainers

The Rust-to-WebAssembly backtracker that runs every live demo and checks every number on this wiki. Not a record machine but a reference engine, ported four times and parity-tested byte-for-byte, built so the claims here can be re-run.

The engine behind the 467, the only Eternity II score ever paid, read from Louis Verhaard's own mailing-list posts: forward pruning, comb-search fill orders, depth-gated edge slipping, a Markov-tuned slip schedule. And why his own source-less Win32 binary cannot be built or run on this machine at all.

The research section has two halves: the structural walls that make Eternity II hard, and the algorithms built to climb them. This page is the bridge: each method lined up against the wall it actually attacks, and the score where that wall stopped it.

Edge matching is NP-complete as a family, but that says nothing about one fixed 16×16 board: a single instance is a constant, not a problem. What is true is the family's worst-case hardness and this instance's empirical hardness, and how to write the puzzle for a SAT, exact-cover, or ILP solver with small worked sketches.

Brendan Owen's complex theory estimates how wide the search tree is at every depth, and even how many solutions exist at all. Many in the community consider it the single most important thing to understand about Eternity II.