Consider a $2n \times 2n$ board. From the $i$th line we remove the central $2(i-1)$ unit squares. What is the maximal number of rectangles $2 \times 1$ and $1 \times 2$ that can be placed on the obtained figure without overlapping or getting outside the board?
Školjka 
board. From the 
th line we remove the central 
unit squares. What is the maximal number of rectangles 
and 
that can be placed on the obtained figure without overlapping or getting outside the board?