k=1 |
k=2 |
k=3 |
k=4 |
k=5 |
k=6 | k=7 | k=8 | k=9 | k=10 | |
5 or less | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
6 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
7 | 3 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
8 | 16 | 6 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
9 | 52 | 37 | 6 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
10 | 286 | 164 | 66 | 11 | 0 | 0 | 0 | 0 | 0 | 0 |
11 | 1,403 | 1,572 | 751 | 215 | 29 | 1 | 0 | 0 | 0 | 0 |
12 | 8,214 | 13,133 | 9,737 | 3,871 | 879 | 111 | 6 | 0 | 0 | 0 |
13 | 54,756 | 122,279 | 131,672 | 78,560 | 28,268 | 6,066 | 888 | 69 | 2 | 0 |
14 | 389,833 | 1,155,103 | 1,708,295 | 1,443,461 | 759,665 | 263,561 | 62,727 | 10,976 | 1,341 | 133 |
15 | 2,923,757 | 11,347,863 | 22,474,269 | 26,158,142 | 19,373,253 | 9,662,493 | 3,394,860 | 874,338 | 170,117 | 26,426 |
16 | 22,932,960 | 112,182,378 | 289,590,727 | 449,484,829 | ||||||
17 | 184,339,572 | |||||||||
18 |
Table 2. Number of fundamental solutions to the N+k Queens 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.)