# Task 2. (10 points)

Below is a magic square with some numbers missing.

| 20 |  |  |
| :--- | :--- | :--- |
|  | 17 |  |
| 16 |  |  |

Restore the given magic square.

(In a magic square, the sums of the numbers in each row, each column, and on the diagonals are equal).
Solution.

| 20 |  | 2) | 20 |  | $x$ | 3) | 20 | 13 | $x$ | 4) | 20 | 13 | $x$ |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
|  | 17 |  |  | 17 |  |  | $x-3$ | 17 |  |  | $x-3$ | 17 | 19 |
| 16 |  |  | 16 |  |  |  | 16 |  |  |  | 16 | $x+3$ | 14 |

Therefore, $20+17+14=16+17+x \Rightarrow x=18$.

Answer:

| 20 | 13 | 18 |
| :--- | :--- | :--- |
| 15 | 17 | 19 |
| 16 | 21 | 14 |


| Criterion | Evaluation | Points |
| :---: | :---: | :---: |
| Complete solution. | + | 10 |
| Correct answer provided. Not shown that there are no other solutions. |  |  |
| All main logical steps of the solution are provided. Due to a computational error or typo, an incorrect answer is obtained. | $+/ 2$ | 5 |
| The solution does not meet any of the criteria described above. | $-/ 0$ | 0 |
| Maximum score | 10 |  |