A322150 Number of minimum shadings of an n X n Hitori solution grid as defined in A322125.
1, 4, 6, 74, 6, 900, 3230
Offset: 1
Examples
Case n=3: a(3) = 6: up to rotation and reflection there are 2 solutions: X . . : . X . . X . : . . . . . . : . X . . Case n=5: a(5) = 6: up to rotation and reflection there are 2 solutions: . . X . . : . . . X . . X . X . : X . . . . . . . . . : . . X . . . . . . . : . . . . X . X . X . : . X . . . . For an n X m grid the number of minimum shadings are as follows: ====================================================== n\m| 1 2 3 4 5 6 7 8 9 10 11 12 ---+-------------------------------------------------- 1 | 1 2 1 1 1 1 1 1 1 1 1 1 ... 2 | 2 4 2 12 12 4 48 32 8 160 80 16 ... 3 | 1 2 6 1 13 53 11 100 6 113 2 88 ... 4 | 1 12 1 74 11 44 139 512 1745 5764 19209 96 ... 5 | 1 12 13 11 6 3 2035 ... 6 | 1 4 53 44 3 900 90 ... ... An interesting tight solution set occurs with the 5 X 6 grid. The 3 solutions are: . X . . . : . . X . . : . . . X . . . . . X : . X . X . : X . . . . . . . X . : . . . . . : . X . . . . X . . . : . . . . . : . . . X . X . . . . : . X . X . : . . . . X . . . X . : . . X . . : . X . . .
Crossrefs
Cf. A322125.
Comments