Gabriel draws squares divided into nine cells and writes the natural numbers from 1 to 9, one in each cell. He then calculates the sum of the numbers in each row and each column. The figure shows one of Gabriel's squares; note that the sum of the numbers in the third row is \(5+8+2=15\) and the sum of the numbers in the second column is \(9+7+8=24\). In this example, the six sums are 6, 12, 15, 15, 18, and 24.

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

a) Gabriel filled in a square and made only five sums: 9, 13, 14, 17, and 18. What is the missing sum?

b) Explain why it is not possible for all the sums in one of Gabriel's squares to be even numbers.

c) Fill in the square so that the sums are 7, 13, 14, 16, 18, and 22.

![](https://cdn.mathpix.com/cropped/2024_05_01_1c2853cb1112cfb2ee2dg-05.jpg?height=240&width=248&top_left_y=228&top_left_x=1007)