Question 16
An $11 \times 11$ square is partitioned into 121 smaller $1 \times 1$ squares, 4 of which are painted black, the rest being white. We cut a fully white rectangle (possibly a square) out of the big $11 \times 11$ square. What is the maximal area of the rectangle we can obtain regardless of the positions of the black squares? It is allowed to cut the rectangle along the grid lines.