Magic tricks info

In a Pandiagonal magic cube, all 3m planar arrays must be pandiagonal magic squares. The 6 oblique squares are always magic. Several of them MAY be pandiagonal magic.

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 pandiagonal magic squares and 6 simple magic squares (one or two of these MAY be pandiagonal). A Perfect magic cube has 9m pandiagonal magic squares.

A proper pandiagonal magic cube has exactly 9m² lines plus the 4 main traigonals suming correctly. (NO broken triagonals sum correct.)

Order 7 is the smallest possible pandiagonal magic cube.

See also

• Magic cube classes

References

• J.R.Hendricks, Magic Squares to Tesseracts by Computer, Self-published 1999. ISBN 0-9684700-0-9
• J.R.Hendricks, Perfect n-Dimensional Magic Hypercubes of Order 2n, Self-published 1999. ISBN 0-9684700-4-1
• Harvey Heinz: All about magic cubes