The diagram below shows cities A, B, C, ..., K, and L.
+A ++ ++++
     
++ + B C + D E
   
F++++G++
   
H + ++ I + ++
     
+++ J K+ +L
Knowing that each line segment measures 1 km and the distances (along the lines) between two cities, are:
Bodov  Direb: 9 km
Vega  Mares: 5 Km
Fugud  Rigel: 4 km
Tolima  Bodov: 8 km
Atlas  Supra: 11 km
Cona  Poris: 6 km
Kuma  Atlas: 4 km
Fugud  Cona: 12 km
Poris  Vega: 5 km
Identify the cities.
After making a table of all the distances involved between the lettered points:
D  I = 4 and C  G = 4 while Fug  Rig = 4 and Kum  Atl = 4.
Fug  Con = 12 and Con  Por = 6, while Por  Veg = 5
D and C each have a 12 (while I and G don't), so could be Fug.
C's 12 is with H which has a 6 with J, but J has no 5 to serve for Veg.
D's 12 is with J which has a 6 with H, which has a 5 with F.
So D=Fug, J=Con, H=Por, F=Veg, I = Rig
leaving C and G as Kum and Atl, not necessarily respectively.
Atl  Sup = 11
G has no 11, but C  B = 11 so
C=Atl, B=Sup, G=Kum
Now, Bod  Dir = 9 and Bod  Tol = 8
K  L = 9, but L's 8 is Rig, not Tol; K's 8 with an unassigned letter is with E.
so
K=Bod, L=Dir, E=Tol
leaving
A=Mar, which checks out.
Edited on July 25, 2008, 12:00 pm

Posted by Charlie
on 20080725 11:51:00 