Pandiagonal: Franklin Squares

The square of order 8 created by Benjamin Franklin, shows the following properties:

  • All rows and columns sum to 260.
  • Numbers on all left and right half-rows and all upper and lower half-columns sum to 130.
  • Numbers in all bentdiagonals and their parallels sum to 260.
  • The square is compact, which means that all subsquares of size 2x2 sum to 130.

526141320293645
143625146353019
536051221283744
116595443382722
555871023263942
98575641402524
506321518313447
161644948333217

Although the square of Benjamin Franklin ist not magic, but only semimagic, it is possible to create pandiagonal Franklin squares, as the complementary numbers have a fixed structure in all of these 368 640 squares.

Order Method
Most-perfect → Franklin square
Schindel-Rempel-Loly - Nordgren
Morris
Breedijk (Khajuraho Method)
Breedijk (Basic Pattern Method)
Breedijk (Method 3)
Breedijk (Method 4)
8 Breedijk (Method 5)
8 Generalization of different ideas

All algorithms are described in detail in chapter Pandiagonal Magic Squares (german: Pandiagonale magische Quadrate) together with some other PDF documents.

DocumentsDetailed description of algorithms to create magic squares