13. The diagram shows five circles placed at the corners of a pentagon. The numbers $1,2,3,4,5$ are placed in the circles shown, one in each, so that the numbers in adjacent circles always differ by more than 1 . What is the sum of the numbers in the two circles adjacent to the circle which contains the number 5 ?
A 3
B 4
C 5
D 6
E 7
13. $\mathbf{C}$ The position of the 5 is immaterial to the question asked, so let it be placed in the top circle. Now 4 differs by 1 from 5 so neither $a$ nor $d$ equals 4. Therefore either $b=4$ or $c=4$. It doesn't matter which it is, because the answer will be symmetric. So let $b=4$. Since 3 differs by 1 from 4 , neither $a$ nor $c$ can be 3 , so $d=3$. This leaves us with 1 and 2 to place. As 2 cannot be next to $3, c \neq 2$ so $c=1$ and $a=2$. Therefore the sum of the numbers in the two circles adjacent to the circle containing 5 is $3+2=5$.