Question 26
A $27 \times 27$ square board is given. Carla paints some of the cells of the board in blue, so that at least one cell remains unpainted and the following two conditions hold simultaneously:
* In every $2 \times 2$ sub-board, the number of blue cells is even.
* In every $3 \times 3$ sub-board, the number of blue cells is odd.
Determine the maximum number of cells that Carla can paint.
* In every $2 \times 2$ sub-board, the number of blue cells is even.
* In every $3 \times 3$ sub-board, the number of blue cells is odd.
Determine the maximum number of cells that Carla can paint.