Order 16 Magic and Semi-Magic Square
Closed Knight Tours

Here are some Magic and Semi-Magic Closed Knight Tours that I designed based on H. J. R. Murray's "Extended Quartes 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 shown below on the left comes from Section 1 of 17 - 180° Rotation-Symmetric tours. I used the same modular Knight Tours from Four Basic 16-move Closed Mini-Tours shown below on the right that Helga Em. de Vasa used over 40 years ago. By rotating or flipping the modular Knight Tours, many new tours can be constructed.

    

Remove all the red lines

    

Combined Tours for Semi-Magic Knight's Tour

Order 16 Magic Square
and 180° Rotation-Symmetric Closed Knight's Tour
by Dan Thomasson, 12-04-2005

Click on tour above to see number sequence.
For plain-text, select 16x16MSKT-80.txt

Order 16 Magic Square
and 180° Rotation-Symmetric Closed Knight's Tour
by Dan Thomasson, 12-07-2005

Click on tour above to see number sequence.
For plain-text, select 16x16MSKT-80b.txt

   

www.BordersChess.org/16x16SMKT-80.htm   modified 2005.12.12