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) WaterRetention

Harry White has done similar investigations on our set of bimagic 8x8-squares. See: MultiMagic (External Link)

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