Articles

How many Knight's Tours are there?

17 Sept 2026

The question has four different correct answers, and most quoted figures do not say which one they are answering. We counted the 5x5 exactly and watched the problem explode.

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A 5x5 chessboard with one complete Knight's Tour drawn as a connected path through all twenty-five squares, the starting square marked in green.

The best square to start a Knight's Tour on each board size

27 Aug 2026

Knowing a tour exists from a square does not mean it is easy to find. We measured every legal opening on all six boards, and the gap between the best and the worst is wider than it looks.

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A 5x5 chessboard with the four corners and the centre square ticked, marking the five openings from which Warnsdorff's rule always completes a tour.

Why some squares can never start a Knight's Tour

15 Aug 2026

On the 5x5 board twelve of the twenty-five squares cannot begin a tour at all. The reason is a counting argument about square colour, and it says exactly which squares are safe.

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A 5x5 chessboard with the twelve squares that cannot begin a Knight's Tour crossed out, leaving the thirteen that can.

What the Knight's Tour teaches you about real chess

11 Aug 2026

The Knight's Tour trains the one piece most beginners misjudge. What it teaches, what it does not, and where to practise the rest.

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A knight on the centre square of a 5x5 board, with the eight squares it can reach marked and each L-shaped path drawn.