Let's walk along the 1048 2KT paths from start 11 (D2)

These Tours have several properties :

     1) Idem Moves : move between 32 and 33 is the same as move between 1 and 64

     2) Auto shift32 : shift 32 on every indexes provides an identical chessboard

     3) Close Tour : knight move between index 1 and index 64

     4) Auto Dual : direct and reverse path are identical

     5) Full Magic : tour is magic in the diagonal as well

     6) 1/4 Magic : each quarter of chessboard is magic (sum of 130)

The number of solutions on each of these properties are outlined in the table below. Furthermore, solutions were grouped according to their specific move 32-33. First and Last column state both indexes (min and max) of the set of the solutions.

 

Id Card 11

The slider below presents by default all the tours from 1 to 1048 (start is D2). it's possible to configure the slider in order to display only a type of tour among the 6 options. The focus of these tours can also be expanded with a specific 32-33 move using the second radio box.

 

2KT image
2KT image
   A1-H8 Diagonal :  -     -
   H1-A8 Diagonal :  -
   1/4 Magic :  -
   Full Magic :  -
   Close tour :  -
   Move 1-64 :  -
   Move 32-33 :  -
   Idem Moves :  -
   "Auto Shift 32" :  -
   shift 32 square :  -
   shift32 rank :  1
   "Auto-Dual" :
   Dual square :  -
   Dual rank :  -

Type of tours depends on selection. For this choice, the displayed tour is 

1

 / 

1048

Select type of Tours for the slider with the choices below

 

A page with all 2KT chessboards from D2

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Author :  Yann DENEF  mailto:ydenef@orange.fr