Eric J. Fimbel - Research results and data sets - home page    back to tower of London

Problem space of the Tower of London

Number of direct paths from a configuration

(the paths do not contain loops)


row = initial configuration; column = distance

grey: identical to lines 11..16 (same physical configurations)

  0 1 2 3 4 5 6 7 8
11 1 2 5 11 21 35 68 126 193
12 1 3 7 13 21 37 73 126 192
13 1 4 8 11 22 44 77 117 187
14 1 3 7 13 23 43 75 120 194
15 1 4 8 13 24 45 74 120 200
16 1 2 5 13 21 34 65 113 180
21 1 2 5 11 21 35 68 126 193
22 1 3 7 13 21 37 73 126 192
23 1 4 8 11 22 44 77 117 187
24 1 3 7 13 23 43 75 120 194
25 1 4 8 13 24 45 74 120 200
26 1 2 5 13 21 34 65 113 180
31 1 2 5 11 21 35 68 126 193
32 1 3 7 13 21 37 73 126 192
33 1 4 8 11 22 44 77 117 187
34 1 3 7 13 23 43 75 120 194
35 1 4 8 13 24 45 74 120 200
36 1 2 5 13 21 34 65 113 180
41 1 2 5 11 21 35 68 126 193
42 1 3 7 13 21 37 73 126 192
43 1 4 8 11 22 44 77 117 187
44 1 3 7 13 23 43 75 120 194
45 1 4 8 13 24 45 74 120 200
46 1 2 5 13 21 34 65 113 180
51 1 2 5 11 21 35 68 126 193
52 1 3 7 13 21 37 73 126 192
53 1 4 8 11 22 44 77 117 187
54 1 3 7 13 23 43 75 120 194
55 1 4 8 13 24 45 74 120 200
56 1 2 5 13 21 34 65 113 180
61 1 2 5 11 21 35 68 126 193
62 1 3 7 13 21 37 73 126 192
63 1 4 8 11 22 44 77 117 187
64 1 3 7 13 23 43 75 120 194
65 1 4 8 13 24 45 74 120 200
66 1 2 5 13 21 34 65 113 180





Copyright: (c) 2009 E.J. Fimbel, S. Lauzon, C. Rainville. This is open-access content distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.