22. In each of the cells, a number is to be written so that the sum of the 4 numbers in each row and in each column are the same.
What number must be written in the shaded cell?
A 5
B 6
C 7
D 8
E 9
Solution
C

Let $x$ be the number in the bottom right cell. Then the column total is $x+15$. Since each row and column has the same total, we can now find the other missing values. The third column requires $x$ in its missing cell to make the total up to $x+15$. The top row requires $x+5$. The second column requires 1. The bottom row is now missing 7 , hence this goes in the shaded square. [The other cells in the left column are $x+3$ and 4.]