Closed Bimagic Queen's Tours on an 8x8 Board |
A closed bimagic* queen's tour which is pandiagonally magic.
Introduction |
More details can be found in our Paper on Bimagic Queen's Tours | (PDF) |
Classification of the 44 closed bimagic queen's tours |
These tours are different representatives of only 4 classes of semi-bimagic squares. Attention, none of the normalized representatives shown below is a magic tour. |
semi-bimagic class a 01 08 27 30 42 47 52 53 16 09 22 19 39 34 61 60 20 21 10 15 59 62 33 40 29 28 07 02 54 51 48 41 38 35 64 57 13 12 23 18 43 46 49 56 04 05 26 31 55 50 45 44 32 25 06 03 58 63 36 37 17 24 11 14 |
semi-bimagic class b 01 08 27 30 44 45 50 55 16 09 22 19 37 36 63 58 20 21 10 15 57 64 35 38 29 28 07 02 56 49 46 43 39 34 61 60 14 11 24 17 42 47 52 53 03 06 25 32 54 51 48 41 31 26 05 04 59 62 33 40 18 23 12 13 |
semi-bimagic class c 01 08 27 30 42 47 52 53 16 09 58 63 20 21 38 35 23 18 33 40 11 14 61 60 26 31 04 05 49 56 43 46 36 37 22 19 64 57 10 15 45 44 55 50 06 03 32 25 54 51 48 41 29 28 07 02 59 62 13 12 39 34 17 24 |
semi-bimagic class d 01 08 28 29 43 46 50 55 16 09 34 39 61 60 19 22 23 18 57 64 38 35 12 13 26 31 03 06 52 53 41 48 36 37 14 11 17 24 63 58 45 44 56 49 07 02 30 27 54 51 47 42 32 25 05 04 59 62 21 20 10 15 40 33 |
The complementary pairs (two entries with sum 65) have three different structures. |
Structure X semi-pandiagonal complementary entries have the distance dx=1, dy=1. |
Structure Y pandiagonal complementary entries have the distance dx=4, dy=4. (To avoid chaos only 6 pairs are shown.) |
Structure Z complementary entries have different distances. |
Structure X Class a |
Structure X Class b |
Structure Y Class a |
Structure Y Class b |
Structure Z Class c and d |
The 62 open bimagic queen's tours as semi-bimagic squares
The 44 closed bimagic queen's tours as semi-bimagic squares
All 62·8 = 496 open tour matrices
All 44·8 = 352 closed tour matrices
The 62 open bimagic queen's tours in chess notation
The 44 closed bimagic queen's tours in chess notation
Back to Bimagic Squares | Walter Trump, Nürnberg, Germany, (c) 2020-08-24, last update 2020-09-05 |