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 pleasure of eloquence is in greatest part owing often to the stimulus of the occasion which produces it,—to the magic of sympathy, which exalts the feeling of each by radiating on him the feeling of all.”
—Ralph Waldo Emerson (1803–1882)