16. Given a $7 \times 7$ grid, consider the possible squares (from $1 \times 1$ to $7 \times 7$) formed by the union of one or more cells of the grid. How many of these squares contain the central cell of the grid?
(A) 50
(B) 30
(C) 44
(D) 42
(E) 28

![](https://cdn.mathpix.com/cropped/2024_04_17_e21ecd5de9c42efa6d1eg-2.jpg?height=224&width=224&top_left_y=119&top_left_x=2495)
(16) The correct answer is $(C)$.

The squares that contain the central cell are:

- the single $7 \times 7$ square;
- all 4 $6 \times 6$ squares;
- all 9 $5 \times 5$ squares;
- all 16 $4 \times 4$ squares;
- only the 9 $3 \times 3$ squares that do not touch the outer edge of the grid;
- only the 4 $2 \times 2$ squares that avoid sharing a vertex with the central cell;
- the $1 \times 1$ square consisting of the central cell alone.

In total, there are $1+4+9+16+9+4+1=44$ squares.

Problem proposed by Matteo Rossi.