Example 7 (2003 University of South Carolina High School Contest Problem) As shown in Figure $14-1, a, b, c, d, e, f, g, h, i$ each represent one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9. By adding 3 numbers in each of the 9 circles, we get 9 sums. If these 9 sums are equal, then the value of $a + d + g$ is $(\quad)$.
A. 15
B. 16
C. 18
D. 19
E. 21
Solution: Choose C. Reason:
Let this common sum be $s$. Adding these 9 sums, we get
$$
9 s=1+2+\cdots+9+2(a+b+\cdots+i)=3 \times 45=9 \times 15 \text {. }
$$

Therefore, $s=15$. The sum of the numbers in the 6 circles is $90=6 s=1+2+4+5+7+8+(a+b+\cdots+i)+a+$ $d+g=27+45+a+d+g=72+a+d+g$.
Thus, $a+d+g=90-72=18$.