(2) Chess: What is the proof for Warnsdorff's rule of the Knight's tour? - Quora

(2) Chess: What is the proof for Warnsdorff's rule of the Knight's tour? - Quora

The heuristic is to visit a square which has less number of non-visited neighbors. This is quite intuitive because if we have to visit all the squares in a tour, we better visit those squares which are remote  and are difficult to be reached.
As with any heuristic, there is no mathematical proof for Warnsdoff's rule that it will always produce a valid tour.

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