Subsets of bimagic 8x8-squares |

Sets with essentially different bimagic squares of order 8

Each ess. diff. SQ can be transformed into 192 unique SQ (including the SQ itself) by magic transformations.

Each SQ is written in standard position for ess. diff. magic 8x8-squares.

Amount | Discription of the squares | Download | Sample |

841 | Centrally symmetric | Data (TXT) | |

0 | Axially symmetric | Proof (PDF) | |

0 | Compact | Proof (PDF) | |

472 | Made of two diagonal Latin squares | Data (TXT) | Sample |

448 |
Non-symmetric but with symmetric main diagonals | Data (TXT) | |

3567 |
Complementary invariant - non-symmetric main diagonals which consist of 4 complementary pairs of numbers | Data (TXT) | |

2424 |
Complementary invariant - one main diagonal is the complement of the other | Data (TXT) | |

There are no further complementary invariant SQ.
Total amount: 841 + 3567 + 2424 = 6832 |

Sets with unique bimagic squares of order 8

Each SQ is written in standard position for unique magic 8x8-squares.

Certain magic properties of special magic squares are not invariant with respect to magic transformations.

For example magic diagonals that are not main diagonals. Therefore sets with unique SQ are necessary.

Amount | Discription of the squares | Download | Sample |

29376 | Complete | Data (ZIP) | |

7288 | Pandiagonal but not complete | Data (ZIP) | |

10496 |
Complete with bimagic semi-diagonals (can be transformed in centrally symmetric squares) | Data (ZIP) | |

640 |
Complete with bimagic semi-diagonals made of two Latin squares with Latin main diagonals | Data (TXT) | Sample |

256 | Pandiagonal with 8 bimagic diagonals | Data (TXT) | Sample |

96 | Symmetric with 4 semi-magic 4x4-squares | Data (TXT) | Sample |

448 | Central magic 4x4-square | Data (TXT) | Sample |

715 |
Water retention at least 500 units Maximum water retention: 620 | Data (TXT) |
Water Retention |

Back to Bimagic 8x8-Squares | Walter Trump, Nürnberg, Germany, (c) 2014-06-12, last update: 2014-06-19 |