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.

52 | 61 | 4 | 13 | 20 | 29 | 36 | 45 |

14 | 3 | 62 | 51 | 46 | 35 | 30 | 19 |

53 | 60 | 5 | 12 | 21 | 28 | 37 | 44 |

11 | 6 | 59 | 54 | 43 | 38 | 27 | 22 |

55 | 58 | 7 | 10 | 23 | 26 | 39 | 42 |

9 | 8 | 57 | 56 | 41 | 40 | 25 | 24 |

50 | 63 | 2 | 15 | 18 | 31 | 34 | 47 |

16 | 1 | 64 | 49 | 48 | 33 | 32 | 17 |

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 | ||

8 | Schindel-Rempel-Loly - Nordgren | |

8 | Breedijk | |

8 | Generalization of different ideas |

All Algorithms are described in detail in chapter *Franklin Squares* together with some other PDF documents.