Semi-Magic Square Knight Tours

(31 Geometrically Distinct Closed Tours)

Here is the breakdown of the number of geometrically distinct closed tours, or "geometry classes" as coined by George P. Jelliss.

    Section 1 = 16 Geometry Classes

Though there are 17 tours in this section, two of the tours (smkt40 & smkt121) have the same geometric pattern, or geometry class. Therefore, there are only 16 geometrically distinct tours in this section.

    Section 2 = 1 Geometry Class

    Section 3 = 7 Geometry Classes

    Section 4 = 6 Geometry Classes

    Section 5 = 1 Geometry Class

Therefore, the following tours represent all 31 separate geometry classes out of the 63 closed tours.


Section 1 = 16 Geometry Classes

              

              

              

              


Section 2 = 1 Geometry Class




Section 3 = 7 Geometry Classes

              

         


Section 4 = 6 Geometry Classes

              

    


Section 5 = 1 Geometry Class

www.BordersChess.org/GeometryClasses.htm   modified 2006.12.14