18. The numbers $2,3,4,5,6,7,8$ are to be placed, one per square, in the diagram shown such that the four numbers in the horizontal row add up to 21 and the four numbers in the vertical column add up to 21 .
Which number should replace $x$ ?
A 2
B 3
C 5
D 7
E 8
Solution: $\mathbf{D}$
If we add all the numbers in the horizontal column and all the numbers in the vertical row, we get a total of $21+21=42$. In doing this sum we add in all the numbers $2,3,4,5,6,7,8$ once except for $x$ which is added in twice. So the total we get is $2+3+4+5+6+7+8+x=35+x$. Since this equals 42, we must have $x=7$.

To complete the solution we should check that with $x=7$, it is possible to place the remaining numbers in the other squares so that the four numbers in the horizontal row add up to 21 , and so also do the four numbers in the vertical column. We ask you to do this in Extension Problem 18.1