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.

First I made a table of the distances between each pair of letters, by inspecting the diagram. Then I looked for forced assignments and/or eliminations until I arrived at the following (in order inferred):

C = Atlas

G=Kuma

B=Supra

D=Fugud

I=Rigel

J=Cona

H=Poris

F=Vega

K=Bodov

L=Direb

E=Tolima

A=Mares

Each time a letter-city pair was established, that reduced the remaining possibilities.  I think the above is the unique solution.

Posted by ed bottemiller on 2008-07-25 18:49:03