Question 67
A $11 \times 11$ grid is to be covered completely without overlapping by some $2 \times 2$ squares and $L$-shapes each composed of three unit cells. Determine the smallest number of $L$-shapes used. (Each shape must cover some grids entirely and cannot be placed outside the $11 \times 11$ grid. The $L$-shapes may be reflected or rotated when placed on the grid.)
