Order 16 Closed Semi-Magic Knight's Tour
Here is a Semi-Magic Closed Knight's Tour that I designed based on H. J. R. Murray's "Extended Quartes Method." All rows and columns add up to 2056, while the main diagonals add up to 1944 and 2168.
The Closed Semi-Magic Knight's Tour shown below in Tour-1 comes from Section 1 of 17 - 180° Rotation-Symmetric Tours. I used the same modular Knight Tours from Four Basic 16-Move Closed Mini Knight's Tours shown below in Tour-2 that Helga Em. de Vasa used over 60 years ago. Notice that the 16x16 tour is also 180° Rotation-Symmetric. The two pink lines in the 16x16 tour show where the moves begin or end, running in either direction, to make Semi-Magic Knight Tours.
The Closed Semi-Magic Knight's Tour shown below in Tour-1 comes from Section 1 of 17 - 180° Rotation-Symmetric Tours. I used the same modular Knight Tours from Four Basic 16-Move Closed Mini Knight's Tours shown below in Tour-2 that Helga Em. de Vasa used over 60 years ago. Notice that the 16x16 tour is also 180° Rotation-Symmetric. The two pink lines in the 16x16 tour show where the moves begin or end, running in either direction, to make Semi-Magic Knight Tours.
Closed Semi-Magic Knight's Tour-1
Closed Semi-Magic Knight's Tour-2
Remove all red lines from Tour-A and Tour-B shown below.
Closed Semi-Magic Knight's Tour-A with Red Lines.
Closed Semi-Magic Knight's Tour-B with Red Lines.
Combine Tour-A and Tour-B shown above to make the Order 16 Closed Semi-Magic Knight's Tour
Order 16 Closed Semi-Magic Knight's Tour by Dan Thomasson