Question 70
The central area of a town has a form of the $n \times n$ square, which is formed by $1 \times 1$ tiles. To illuminate the area, one-lamp lampposts are used. The lampposts are placed at the corners of some tiles, including the boundary of the area. The lamp on a lamppost illuminates all tiles with a corner at the lamppost position, and only those.
Find the smallest number of the lampposts required to illuminate the whole area, even if one of the lamps should burn out.
Find the smallest number of the lampposts required to illuminate the whole area, even if one of the lamps should burn out.