Question 41
In each square of the $4 \times 4$ board there must be a natural number from $1$ to $16$ inclusive, without repeating, so that the sum of the four numbers in each of the four rows, the sum of the four numbers in each of the four columns, and the sum of the four numbers in each of the two diagonals are ten consecutive whole numbers, in some order. Nine of the numbers have already been written. Write the seven missing numbers.
| 4 | 5 | 7 | |
|----|----|----|----|
| 6 | | 3 | |
| 11 | 12 | 9 | |
| 10 | | | |
| 4 | 5 | 7 | |
|----|----|----|----|
| 6 | | 3 | |
| 11 | 12 | 9 | |
| 10 | | | |