JF Ptak Science Books Quick Post
Passing through a later and edited edition of Jacques Ozanam (RECREATIONS MATHEMATIQUES ET PHYSIQUES, Qui Contiennent Plusieurs Problemes d’Arithmetique, de Geometrie, de Musique, d’Oprique, de Gnomonique, de Cosmographie, de Mecanique, de Pyrotechnie, & de Physique. Avec un Traite des Horloges Elementaires. Nouvelle Edition, Revue, Corrigee & Augmentee... and published in Paris in 1749-1750) looking for possible expansions on what he wrote on the Knight's Tour--a chess/math problem where the knight starting at, say, the center position must be moved to touch every square of the board in 64 moves--I found this little diagram showing the spaces to which a knight may not move:
It seemed just a little unusual to me--not being a reader of chess literature--to see what seemed the negative of the knight's movements on a truncated board. But I guess this is what we calculate and just not entirely "see" while playing.
The original problem in the 1672 edition of Ozanam's Recreations looks like this (and titled "faire parcourir au cavalier toutes les cases de l'echiquer"):
in which the knight starts off life at the top right square (h8) and finishes at f3. In the 1803 edition of the work it is pointed out that the knight can be started from any square and moved 64 times to accomplish this same feat.
Here are four further examples of solutions to the knight problem:
And as they say, many more are available.
A more modern version of the solution, this on a 24x24 grid:
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