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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.
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