The Distribution of the Knight

Dr Colin Rose
 

Solutions:   3 × m

For any given starting point, how many solutions exist to the Knight's Tour problem?
This page displays the answer for all (3 × m) chess boards, for m ≤ 12.

3 × 3
0 0 0
0 0 0
0 0 0

Solutions: 0


3 × 4
2 0 0 2
4 0 0 4
2 0 0 2

Solutions: 16


3 × 5
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0

Solutions: 0


3 × 6
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0

Solutions: 0


3 × 7
8 0 4 0 4 0 8
0 28 0 0 0 28 0
8 0 4 0 4 0 8

Solutions: 104


3 × 8
82 20 4 24 24 4 20 82
68 48 0 20 20 0 48 68
82 20 4 24 24 4 20 82

Solutions: 792


3 × 9
172 0 8 0 64 0 8 0 172
0 96 0 40 0 40 0 96 0
172 0 8 0 64 0 8 0 172

Solutions: 1120


3 × 10
448 156 48 64 160 160 64 48 156 448
512 416 32 80 256 256 80 32 416 512
448 156 48 64 160 160 64 48 156 448

Solutions: 6096


3 × 11
2604 0 292 0 900 0 900 0 292 0 2604
0 2000 0 520 0 1120 0 520 0 2000 0
2604 0 292 0 900 0 900 0 292 0 2604

Solutions: 21344


3 × 12
9658 1880 952 1444 3156 1888 1888 3156 1444 952 1880 9658
6344 5616 352 2092 2712 2176 2176 2712 2092 352 5616 6344
9658 1880 952 1444 3156 1888 1888 3156 1444 952 1880 9658

Solutions: 114496