We say that the square below is a magic square because the sum of the numbers in each row, each column, and each diagonal is always the same. In the case of the magic square in the figure, this sum is 15.

| 4 | 9 | 2 |
| :--- | :--- | :--- |
| 3 | 5 | 7 |
| 8 | 1 | 6 |

Complete the five missing numbers in the square below so that it becomes a magic square.

| -12 |  | -4 |
| :---: | :---: | :---: |
|  | 0 |  |
| 4 |  |  |
The sum of the numbers in one diagonal is $4+0+(-4)=0$, therefore, the value of the sum of the numbers in each row, each column, and the other diagonal must also be 0. Thus, we immediately obtain the numbers that are missing in the gray cells in the first board, namely 16, 8, and 12, because $(-12)+16+(-4)=0$ in the first row, $(-12)+8+4=0$ in the first column, and $(-12)+0+12=0$ in the diagonal.

| -12 |  | -4 |
| :---: | :---: | :---: |
|  |  |  |
| 4 |  |  |$\rightarrow$| -12 | 16 | -4 |
| :---: | :---: | :---: |
| 8 | 0 |  |
| 4 |  | 12 |$\rightarrow$| -12 | 16 | -4 |
| :---: | :---: | :---: | :---: |
| 8 | 0 | -8 |
| 4 | -16 | 12 |

Now, the number that is missing in the second row of the second board is -8, because $8+0+(-8)=0$. For the third row, we get -16, because $-4+(-16)-12=0$.