4.1. In an $11 \times 11$ square, the central cell is painted black. Maxim found a rectangular grid of the largest area that is entirely within the square and does not contain the black cell. How many cells does it have?
Answer: 55

Solution. If both sides of the rectangle are not less than 6, then it must contain the central cell, since the distance from the painted cell to the sides is 5 cells. If one of its sides is not more than 5, then the other is definitely not more than 11, and therefore its area is not more than 55.