The square in Figure I is called special because:

- it is divided into 16 equal squares;
- in each row and in each column, the digits 1, 2, 3, and 4 appear;
- in each of the squares \(A, B, C\), and \(D\) (as in Figure II), the digits 1, 2, 3, and 4 appear.

| 4 | 2 | 1 | 3 |
| :--- | :--- | :--- | :--- |
| 1 | 3 | 2 | 4 |
| 3 | 1 | 4 | 2 |
| 2 | 4 | 3 | 1 |

![](https://cdn.mathpix.com/cropped/2024_05_01_c051a4aaadd76ab6970bg-08.jpg?height=222&width=200&top_left_y=246&top_left_x=1168)

a) Complete the square below so that it becomes special.

![](https://cdn.mathpix.com/cropped/2024_05_01_c051a4aaadd76ab6970bg-08.jpg?height=192&width=203&top_left_y=635&top_left_x=1029)

b) Is it possible to complete the square below to obtain a special square? Why?

![](https://cdn.mathpix.com/cropped/2024_05_01_c051a4aaadd76ab6970bg-08.jpg?height=185&width=206&top_left_y=1001&top_left_x=1028)

c) Show all the ways to complete the square below to obtain a special square.

| 1 | 2 |  |  |
| :--- | :--- | :--- | :--- |
| 3 | 4 |  |  |
|  |  |  |  |
|  |  |  | 1 |

d) How many special squares exist?