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:
“Without being forgiven, released from the consequences of what we have done, our capacity to act would ... be confined to one single deed from which we could never recover; we would remain the victims of its consequences forever, not unlike the sorcerer’s apprentice who lacked the magic formula to break the spell.”
—Hannah Arendt (1906–1975)