Semi-Magic Square Knight Tours

Without the aid of a computer, I've easily created many more Knight Tours and even a Semi-Magic Square Knight's Tour where all the rows and columns add up to the same number. In fact, every other vertical pair of numbers adds up to 49 and 81 respectively while the four major quadrants each add up to 520 and the four main sets of 2x2 squares in each quadrant add up to 130. The numbers 49 and 81 are significant since 49 is 7 squared in which 7 represents the shape of the Knight's move. Also, 81 is 9 squared in which 9 represents the first known Magic Square (3x3 square or 9 squares) from about 2200B.C.

With a little bit of research, you will find that others such as William Beverley have created similar Semi-Magic Square Knight Tours. Unlike William Beverley, I've taken an additional step by creating a simple game that will allow anyone to easily make beautiful mathematical Knight's Tour art. Please let me know if you are interested in my other Knight Tours, Knight Tour game, or my basic mathematical findings that provides such easy creation of Knight Tours.

Here are a couple semi-magic Knight Tours that are almost identical. Notice how the first and third columns from the left are interchangeable. I thought I was quite clever coming up with these patterns until I found out that William Beverley designed the first such tour with the same path pattern of the knight around 1847-1848. Check out www.ktn.freeuk.com/1d.htm for more information about Beverley's Knight Tours.

A Medieval Order Magic Knights Tour as an aid to solving ancient mysteries:

As a roving reporter, "Captain Slogg (Mick Martell)," for the British BBC's "Hitch Hikers Guide to the Galaxy," Mick put together the following Semi-Magic Square Knight's Tour information that is based on a closed Knight's Tour originally discovered by "Wenzelides" in 1858, yet rotated and reversed.

Supposing, just supposing that in medieval times, you were running an Ancient and Mystical Order with great treasures to hide. Imagine for a moment you were “The Grand Leader” of some Mystical society with many valuable and dark secrets to protect, then what you needed was a method of encoding your information in such a way that only those schooled in the Societies arts and rituals would be able to access it. What you needed was a secret code.

One method of encrypting your information was called transposition cryptography. In transposition, the message was usually written in rows of letters, arranged in a rectangular block without word divisions. The letters are then transposed in a pre-arranged order, i.e. following the moves in a Knight's Tour, as was used to encrypt the secret message at Rennes-le-Chateau. The message is then either readable as plain text, or is ready for the next stage of deciphering.

A similar example by Dan Thomasson can be found at KnightsTour Cipher.htm.

Magic square?

The true 'Magic square' enthusiasts among you will notice that the two diagonal rows from corner to corner do not add up to 260, proving that this is not a true 'Magic square'. It was proven on August 5, 2003 that no 8x8 Magic Square Knight Tours exist, but there are 140 unique Semi-Magic Square Knight Tours (63 closed and 77 open). See MagicTour.free.fr for more information about the tours.

Check out SMKT.htm for a complete description of all the closed semi-magic square knight tours.

   

www.BordersChess.org/KTmagic.htm   modified 2006.12.14