Question 53
Let quasi-square be a figure that consists of an $n \times n$-square with one more $1 \times 1$ square attached along one of its sides, so that the unit square shares a side with one of the unit squares of an $n \times n$-square as well as shares a vertex with one of the corner squares of the $n \times n$-square. Thus, the upper two figures on Fig. 3 are quasi-squares, whereas the lower two are not. Determine all possible integer $n \ge 3$ for which a plane can be filled with the identical quasi-squares. Quasi-squares can be rotated and reflected but are not allowed to overlap.
Fig. 3
Fig. 3