Similar to 2-dimensional chess board imagine a 3-dimensional chess box-board, rooks can attack in a straight line in the direction of the coordinate axis.

What is the minimum number of rooks which can dominate a 12 x 12 x 12 chessboard?

The domination solution I gave is, of course, not the only solution. Any of the 12 planes can be in any order, along any or all of the height, depth and width dimensions.

Total possible solutions using my method = (12!)^3 = 479001600^3 ~= 1.1 x e^26. Time prohibits me from listing them all. Perhaps Charlie can do it. To save space, I suggest not listing reflections or rotations.

*Edited on ***November 10, 2018, 11:18 am**