Question 38
A $2n \times 2n$ square is covered, without going outside the square, without gaps or overlaps, with $1 \times 2$ rectangles and pieces like those in the figure (each covering exactly 4 squares $1 \times 1$). The pieces may be rotated or turned over. Prove that the covering contains at least $n + 1$ rectangles $1 \times 2$.