Consider a \( 12 \times 12 \) board which is to be tiled with \( 1 \times 2 \) dominos. What is the minimum number of (positive) dominos which we have to place, to get an arrangement in which no domino can slip (horizontally or vertically) into another position (still entirely on the board)?
Details and assumptions
The dominos are not allowed to stick out of the board.
The dominos do not slip diagonally. They slide around as a block.
It is obvious that any domino located on the corner will always be able to slip out of the board. The restriction requires the entire domino to still be placed on the board.