In the given $5 \times 5$ grid, many squares can be formed using the grid lines. How many of these squares contain the shaded $1 \times 1$ square?
(A) 15
(B) 16
(C) 11
(D) 12
(E) 14

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-033.jpg?height=282&width=285&top_left_y=1060&top_left_x=1343)
There is 1 square that is $1 \times 1$ that contains the shaded square (namely, the square itself). There are 4 squares of each of the sizes $2 \times 2,3 \times 3$ and $4 \times 4$ that contain the shaded square.
![](https://cdn.mathpix.com/cropped/2024_04_20_33a8a6559d675f59baa2g-065.jpg?height=292&width=1196&top_left_y=1378&top_left_x=518)

Finally, there is 1 square that is $5 \times 5$ that contains the shaded square (namely, the $5 \times 5$ grid itself).

In total, there are thus $1+4+4+4+1=14$ squares that contain the shaded $1 \times 1$ square.

ANSWER: (E)