Amazon Solution Counts
k=1 |
k=2 |
k=3 |
k=4 |
k=5 |
|
11 or less | 0 | 0 | 0 | 0 | 0 |
12 | 72 | 0 | 0 | 0 | 0 |
13 | 412 | 120 | 0 | 0 | 0 |
14 | 10,320 | 1,664 | 176 | 16 | 0 |
15 | 71,212 | 52,804 | 7,896 | 696 | |
16 | 678,656 | 681,220 | |||
17 | 6,122,160 | ||||
18 |
Table 1. Number of N+k Amazons Problem solutions.
i.e., number of ways to place N+k Amazons (pieces with combined powers of Queen and Knight) and k Pawns on an N x N board so that no Amazons attack each other.
k=1 |
k=2 |
k=3 |
k=4 |
k=5 |
|
11 or less | 0 | 0 | 0 | 0 | 0 |
12 | 9 | 0 | 0 | 0 | 0 |
13 | 53 | 17 | 0 | 0 | 0 |
14 | 1,290 | 209 | 22 | 2 | 0 |
15 | 8,920 | 6,624 | 996 | 89 | |
16 | 84,832 | 85,204 | |||
17 | 765,446 | ||||
18 |
Table 2. Number of fundamental solutions to the N+k Amazons Problem.
A fundamental solution is an equivalence class of solutions, where rotations and reflections of a solution are considered equivalent. (i.e. Two or more solutions that are rotations and/or reflections of each other count as only one fundamental solution.)