The N + k Queens Problem Pages
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Amazon Solution Counts


N

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.

N

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.)