Question 1
On a square $2012 \times 2012$ checkerboard, L-triominoes like those shown below are placed without overlapping (each L-triomino covers exactly $3$ squares of the board). Determine how many L-triominoes can be placed as a maximum on the board if for any two rows and any two columns, at least one of the four intersection unit squares is not covered by an L-triomino.
