Magic and Semi-Magic Order 16 Closed Knight's Tours
Here are some Magic and Semi-Magic Closed Knight's Tours that I designed based on H. J. R. Murray's "Extended Quarte's Method." For the Magic Squares, all rows, columns, and main diagonals add up to 2056. By simply reversing the counting order, (i.e., 256 = 1 and 1 = 256), all rows and columns add up to 2056 for the Semi-Magic Square, while the main diagonals add up to 2048 and 2064.
The Closed Semi-Magic Knight's Tour-1 comes from Section 1 of 17 - 180° Rotation-Symmetric Tours. I used the same Modular Knight's Tour-2 from Four Basic 16-Move Closed Mini Knight's Tours that Helga Em. de Vasa used nearly 60 years ago. By rotating or flipping the modular Knight's Tours, many new tours can be constructed.
The Closed Semi-Magic Knight's Tour-1 comes from Section 1 of 17 - 180° Rotation-Symmetric Tours. I used the same Modular Knight's Tour-2 from Four Basic 16-Move Closed Mini Knight's Tours that Helga Em. de Vasa used nearly 60 years ago. By rotating or flipping the modular Knight's Tours, many new tours can be constructed.
Knight's Tour-1
Knight's Tour-2
Knight's Tour Red Lines-1
Knight's Tour Red Lines-2
Remove all the red lines in the blue and green Knight's Tour images above.
Put the blue Knight's Tour in the center and connect the green Knight's Tour to all four corners of the blue Knight's Tour to make an Order 16 Knight's Tour.
Put the blue Knight's Tour in the center and connect the green Knight's Tour to all four corners of the blue Knight's Tour to make an Order 16 Knight's Tour.
- Connect the Knight's Tour Red Lines-2 to the top right side of the blue Knight's Tour Red Lines-1.
- Flip the green Knight's Tour vertically and connect it to the bottom right corner of the blue Knight's Tour.
- Flip the green Knight's Tour at the bottom right horizontally and connect it to the bottom left corner of the blue Knight's Tour.
- Flip the green Knight's Tour at the bottom left vertically and connect it to the top left side of the blue Knight's Tour.
Order 16 Semi-Magic Square
and 180° Rotation-Symmetric Closed Knight's Tour I
and 180° Rotation-Symmetric Closed Knight's Tour I
Order 16 Semi-Magic Square by Dan Thomasson, 12-04-2005
Order 16 Magic Square
and 180° Rotation-Symmetric Closed Knight's Tour II
Select image for tour sequence. Dan Thomasson, 12-04-2005
Order 16 Magic Square
and 180° Rotation-Symmetric Closed Knight's Tour III
Select image for tour sequence. Dan Thomasson, 12-07-2005
Select the links below to see a few more examples of Order 16 Magic or Semi-Magic Knight's Tours along with how they were constructed.