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.

Skip the chart of all possible distances, and instead look at the required ones--specifically that two pairs of cities are both 4km apart. Looking at the graph, there are only two pairs of letters that are 4km apart, CG and DI, and so these must be Fugund, Rigel, Atlas, and Kuma in some order.

One of these four (Fugund) must also be 12km from a letter (Cona), and of CGDI only DJ and CA have this property so Cona must be either J or A. Cona is 6km from Poris, though, and A isn't 6km from anything while J is (H), so:

D = Fugund
I = Rigel
J = Cona
H = Poris

CG = (Kuma, Atlas)

Next note that Vega is 5km from Poris (H) and so

F = Vega

Vega is also 5km from Mares so

A = Mares

One of CG is 11 km from something (Supra). C is 11km from B and G is 11km from nothing unassigned so

C = Atlas
G = Kuma
B = Supra

that leaves only Direb, Bodov, and Tolima which must be E, K, and L in some order. Bodov must be 8km from one and 9km from the other. EL = 11km, so neither is Bodov. KE = 8km and KL = 9km so

K = Bodov
E = Tolima
L = Direb

Posted by Paul on 2008-07-25 23:06:51