7. Evita wants to write the numbers 1 to 8 in the boxes of the grid shown, so that the sums of the numbers in the boxes in each row are equal and the sums of the numbers in the boxes in each column are equal. She has already written numbers 3,4 and 8 , as shown. What number should she write in the shaded box?

A 1
B 2
C 5
D 6
E 7
Solution
$\mathbf{E}$

Let the unknown numbers in the boxes be $p, q, r, s$ and $t$, as shown. The sum of the numbers 1 to 8 is 36 and hence the sum of the numbers in each row is $36 \div 2=18$ and the sum of the numbers in each column is $36 \div 4=9$. Therefore $p=9-3=6, r=9-8=1$ and hence $s=18-6-4-1=7$. Therefore Evita should write the number 7 in the shaded box.