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 2008-07-25 11:51:00