Reconstruction of de Vasa's
Order 16 Magic Square
Closed Knight's Tour

Ever wondered how Helga Em. de Vasa in 1962 created the following Order 16 Magic Square Closed Knight's Tour based on H. J. R. Murray's "Extended Quartes Method."?

(Click image to see color-coded number sequence)

Helga Em. de Vasa used the closed semi-magic Knight's Tour shown below on the left, as can be seen in Section 2 of Semi-Magic Square Knight Tours. Helga also used modular Knight Tours shown below on the right that can be found in Four Basic 16-move Closed Mini-Tours. Keep in mind that de Vasa created the masterpiece Knight's Tour over 40 years ago, way before I ever created these web pages.

    

Helga used a combination of the four basic 16-move mini-tours, shown below on the right, that made a pattern in the lower left quadrant that was nearly identical to the same pattern of the lower left quadrant in the Closed Semi-Magic Square, shown below on the left. By removing a few lines (shown here in red) from both tours, plus rotating and flipping copies of the combined mini-tour graphic, one larger 16x16 closed tour could be created.

    

Combined Tours

Here are a few of my designs:

Order 16 Magic and Semi-Magic Square Closed Knight Tours

Order 16 Semi-Magic Square Closed Knight's Tour

Additional Order 16 Semi-Magic Square Closed Knight Tours

Mini-Tour Tiling or Superimposing

www.BordersChess.org/Madachy.htm   modified 2005.12.12