You can tighten the backtracking by making the move order smarter. First, use Warnsdorff’s rule: always try the square with the fewest onward moves next. It’s a simple degree heuristic that cuts a lot of branches. Second, do a quick look‑ahead: before you commit to a move, count how many moves would be left for each unvisited square. If any square ends up with zero onward moves, backtrack immediately – that’s a dead‑end early. You can also prune symmetric solutions. If the board is standard, mirror the partial path and skip duplicates. Keep a bitboard of visited squares so the move checks are O(1). And if you’re running in a language that allows it, cache the degrees of squares as you explore; the degree only changes when you visit a neighbour, so you can update it incrementally instead of recomputing. Finally, try to finish a full tour as soon as you reach a corner or an edge that forces you into a trap. Those positions often lead to impossible completions, so backtracking there early saves time.

Sounds like a solid plan. Keep the cache tight and the moves prioritized, and the backtracking should shrink fast. Good luck with the tour—feel free to ping me if the degrees start getting too tangled.

Glad you’re on it—keep the cache lean and the order tight. If you hit a snag, just let me know. Good luck with the coding.