Agnes Scott College

Dame Kathleen Ollerenshaw

On 'most perfect' or 'complete' 8 x 8 pandiagonal magic squares
Proceedings of the Royal Society of London, Series A, Vol. 407 (1986), 259-281


A particular form of pandiagonal magic squares of doubly even order n defined by Emory McClintock in 1896 but not enumerated (except for the well-known 4 x 4 pandiagonal squares), and described by him as "squares of best form" or "most perfect", is discussed. The number of all such squares for n = 8 is found, by use of symmetries and logical argument only, to be 216 x 32 x 5 = 2949120 (that is 213 x 32 x 5 = 368340 essentially different squares). These squares are given in summary form in an appendix.