7.3. Given a rectangular grid of $7 \times 14$ (cells). What is the maximum number of three-cell corners that can be cut out from this rectangle?
Answer: 32 corners. Solution: It is obvious that no more than 32 corners can be cut out, as otherwise, the rectangle must contain no fewer than $33 \cdot 3=99>98$ cells. The image below shows an example of cutting one

![](https://cdn.mathpix.com/cropped/2024_05_06_e36d95600a032a6a37aag-1.jpg?height=363&width=354&top_left_y=975&top_left_x=1525)
7x7 square into 16 corners. The adjacent 7x7 square is cut in the same way.