[Magictour] nightrider tours

there are graeco-latin nightrider tours on the 8*8 starting
at any square, even if we forbid the long (3,6) moves.

start-square:
number of (1,2)(2,4)(3,6)-tours,
number of (1,2)(2,4)-tours
--------------------------------------
a1:22,10
a2:45,8
a3:36,1
a4:21,3
b2:30,6
b3:27,1
b4:10,3
c3:12,4
c4:16,3
d4:6,2

(symmetric tours are not filtered out)

here is the first:

00 76 52 63 11 47 24 35
53 62 01 77 25 34 10 46
75 40 23 51 07 12 36 64
26 54 70 45 33 61 02 17
41 13 37 22 74 06 65 50
32 27 44 16 60 55 71 03
14 05 66 30 42 73 57 21
67 31 15 04 56 20 43 72

moves:
a8-c7-g5-h3-d1-b2-f4-e6-g7-e8-f6-b4-a2-c1-d3-h5-f1-h2-d4-c6-g8-e7-
a5-b3-d2-b1-a3-e5-f7-h8-g6-c4-b6-a4-e2-g1-c3-d5-h7-f8-h4-d6-c8-a7-
b5-f3-e1-g2-e3-f5-b7-d8-h6-g4-c2-a1-c5-g3-h1-f2-e4-a6-b8-d7

...

 10 solutions starting at 1
nodes : 1 4 26 126 412 840 724 188 912 5850 20326 47720 74192 78766
   45494 8818 22966 99318 238594 399300 438776 361692 164548 36312
 58266 162010 260498 303380 214612 146312 63002 23522 19768 33622
 33904 32778 17242 13498 6678 4552 2098 2290 1794 1674 1192 1150
 860 808 202 172 126 122 124 122 112 110 14 10 10 10 10 10 10 10

total nodes 8(0,0) : 3452589

end-cells for the 10 8(2,4)(1,2) solutions:
0 0 0 0 1 0 0 0
0 0 0 1 0 0 1 0
0 0 0 0 0 0 0 0
0 1 0 0 0 1 0 0
1 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0
0 1 0 0 0 0 2 0
0 0 0 0 0 0 0 0



Guenter



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Received on Thu Dec 04 14:24:18 2001