Monday, 13 June 2016

A magic 5 by 7 rectangle tour

This 5 by 7 symmetric magic tour using six move types was composed by me this evening (12 Jun 2016 - our Queen's official 90th birthday) and is the best so far found on this board. The magic constants are 90 and 126 (i.e. 5×18 and 7×18). It uses six different types of move (my previous best was eight). {0,1}{0,2}{1,1}{12}{1,3}{1,4}

This was derived in part from the "arithmic" king tour on this board, but also used the "method of complementary differences" by Charles Planck, as described in Andrews (Magic Squares and Cubes 1917) p.257-262. The example by Planck shown there uses ten move types.