GAUSS8 2000 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:

  1. F \rightarrow R \rightarrow S \rightarrow G
  2. F \rightarrow S \rightarrow G \rightarrow R
  3. F \rightarrow R \rightarrow G \rightarrow S
  4. F \rightarrow S \rightarrow R \rightarrow G

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

Image

Answer Choices
A. 8
B. 13
C. 15
D. 2
E. 0