Knight's Tour

Published on Sunday, January 19, 2014 in , , , , , ,

Mbdortmund's chess knight photoI love it when two old friends visit and get along!

Numberphile recently took a look at one of my favorite challenges: The Knight's Tour! This is a chess-based puzzle that challenged some of the greatest minds in mathematics.

In a rare video appearance, Brady himself describes some of the fascinating aspects of the Knight's Tour in the following video:

If you'd like to try the Knight's Tour out for yourself online for free, I've created 2 versions you can play. This version is in the Mental Gym (select level 1 for the classic challenge), and here's a more modern version hosted on Dropbox (select “New Game” > “All 64 Squares” for the classic challenge).

When it's a new challenge, it can seem quite difficult. Often, you get past about 50 squares, and then start having difficulty. If you want to be able to tackle this challenge, I have provided a complete Knight's Tour tutorial over in the Mental Gym. If you can understand and remember a few simple patterns, you can not only solve the Knight's Tour starting from anywhere, you can even have someone select a starting AND ending position, and still be able to solve it!

My dropbox version of the Knight's Tour offers various settings, including the ability to show a numbered path, as in the video. This version also auto-detects whether the numbered path is a semi-magic square, as discussed in the video, starting at about the 2:23 mark.

If you can learn to solve it, as in the Mental Gym tutorial, is it possible to learn to start anywhere and create a semi-magic knight's tour square? The answer is almost. Magician Harold Cataquet has done some incredible work on working out just how to do this, and it's written up in the ebook Mind Blasters, by Peter Duffie. If you're really interested in being able to the Knight's Tour AND finishing with a semi-magic square, the article is worth the price of this one book alone.

As Brady mentions in the video, there's an amazing amount of mathematical research done on the Knight's Tour. You can see many of the directions in which this challenge was taken over at Knight's Tour Notes, for a start.

Play around and enjoy the Knight's Tour. If you have any interesting discoveries you'd like to share, I'd love to hear about them in the comments!

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