How I know all 298 boards are solvable
The stages are generated, not hand-drawn. So what guarantees an unsolvable board never ships? The solver, and the time I saved search budget and lost two boards because of it.
Writing
Notes on the mathematics of the knight’s tour and on verifying 298 boards.
A 200-year-old rule of thumb is still the best one — Warnsdorff
Among the squares you can reach, step on the one with the fewest onward moves. One line, and most boards fall to it. Why it works, and where it breaks.
Change one rule — closed tours, fixed endings, wrapped boards
Visit every square once. Add a single line to that rule and the puzzle becomes a different puzzle. Three variants, and what went wrong building each.
A 4×4 board has no knight’s tour — a proof
There is no 4×4 stage on this site, and not for lack of trying. Two colorings are enough to prove no tour exists.