Knight Tours by Edwin Sturmer - 1888
The following knight tours by Edwin Sturmer C. E. from New Zealand were done around 1888 and 1889.
The above drawing by Mr. Sturmer in 1888 of two knight tour circuits containing 32 moves each became the seed for making 16 variant knight tours by changing various moves in the tour. The tour of tours was found in JF Ptak Science Books Post 2243 and titled: "A Beautiful Idea: the Knight's Magical Magic Square Tour (1888)." The following image is the same tour that I drew using my computer.
The near perfect magic knight's tour shown above by Mr. Sturmer is as close as one can get to designing a magic square with knight moves. The result is semi-magic where all rows and columns total to 260 while the diagonals equal 256 and 264 respectively. No magic knight tours exist for an 8x8 size board. However, there are exactly 140 semi-magic knight tours with an additional 18 tours that are reflections, reversals, or rotations of the original 140 tours that I helped to find in 2003 with a team using many computer processor hours. The above tour can be found at location j-7 on the 140 semi-magic knight tours compilation of tours. Sturmer's tour is oriented 90 degrees left from the image shown in the compilation of tours.
The above semi-magic tour was just one of 16 tours that Sturmer derived from his two-circuit knight's tour of 32 moves.
The above semi-magic tour was just one of 16 tours that Sturmer derived from his two-circuit knight's tour of 32 moves.