Monday, 25 April 2011
Magic Rook Tours
The image shows three diagonally magic rook tours that I constructed on 20-21 May 1986 but then seem to have forgotten about. (It was a busy year for me!) The tours have biaxial symmetry and each quarter tour is a bisatin (i.e. uses two cells in each rank and file). If the numbering is shifted by one quarter, so 17 becomes 1, 18 becomes 2 and so on, the rank and file magic property is automatically retained. However for the diagonals to remain magic there must be two numbers less than or equal to 16 in each (i.e. the bisatin has to be diagonal as well). The work was inspired by a less structured diagonally magic rook tour by J. Brugge that appeared in the German chess problem magazine Die Schwalbe in August 1985. Anyone care to enumerate all the diagonal bisatins that could be used?