In a Pandiagonal magic cube, all 3m planar arrays must be panmagic squares. The 6 oblique squares are always magic. Several of them may be panmagic squares.
Gardner called Langman’s pandiagonal magic cube a ‘perfect’ cube, presumably not realizing it was a higher class then Myer’s diagonal magic cube. A diagonal magic cube has 3m plus 6 simple magic squares.
A pandiagonal magic cube has 3m panmagic squares and 6 simple magic squares (one or two of these MAY be pandiagonal). A perfect magic cube has 9m panmagic squares.
A proper pandiagonal magic cube has exactly 9m2 lines plus the 4 main triagonals summing correctly. (NO broken triagonals sum correct.)
Order 7 is the smallest possible pandiagonal magic cube.
Famous quotes containing the word magic:
“The work of adult life is not easy. As in childhood, each step presents not only new tasks of development but requires a letting go of the techniques that worked before. With each passage some magic must be given up, some cherished illusion of safety and comfortably familiar sense of self must be cast off, to allow for the greater expansion of our distinctiveness.”
—Gail Sheehy (20th century)