2000 Gauss 8 Problem 22

The homes of Fred (F), Sandy (S), Robert (R), and Guy (G) are marked on the rectangular grid with straight lines joining them. Fred is considering four routes to visit each of his friends:

(i) F \to R \to S \to G

(ii) F \to S \to G \to R

(iii) F \to R \to G \to S

(iv) F \to S \to R \to G

If FS = 5 km, SG = 9 km and SR = 12 km, the difference between the longest and the shortest trip (in km) is

\textbf{(A)}\ 8\quad \textbf{(B)}\ 13\quad \textbf{(C)}\ 15\quad \textbf{(D)}\ 2\quad \textbf{(E)}\ 0

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.