Warnsdorff's Rule

Warnsdorff's Rule is a heuristic for finding knight's tours on chessboards. Some research I did in the 1990s at a Research Experience for Undergraduates programme under Paul Cull suggests very strongly that Warnsdorff's rule, with suitable modifications, can give a knight's tour on any square board.

This site is not an introduction to Warnsdorff's Rule (see the Wikipedia article and research paper linked above for this). Instead it provides:

I hope that readers are inspired to learn more about Warnsdorff's Rule, and perhaps to prove that the modified rule will actually produce tours on all square boards (this is known for boards whose size is equivalent to 7 mod 8, thanks to Sam Ganzfried's REU paper on the subject).