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.

Looking at Charlie's solution now, I see that we handled the first eight the same way, but Charlie derived DJHFI then CBG, while I did the reverse.  We handled KLE identically, and finished with A by default.

For those pondering the distances graph, I used the following for the rows/columns (symmetrical) -- one initial counting error held me back awhile:

A .  9  12  10  13  5 8 7 8 10 11 14

B .. 11 9 12 6 7 9 7 11 10 13

C ...6 5 9 4 9 6 14 7 13

D ....7 7 2 10 4 12 5 6

E ..... 10 5 13 7 15 8 11

F ......5 5 5 7 8 11

G....... 8 2 10 3 6

H ........ 8 6 11 14

I ........ 9 5 8

J .......... 13 16

K ............ 9

L across same as L down.

This is rather unreadable, but could be rewritten into a 12x12 table, where row 1 = col 1 etc to complete the grid.

Not a bad problem, though the drudgery of building the table took longer than the inferences. Perhaps someone will offer a more elegant method of solution.

Posted by ed bottemiller on 2008-07-25 19:09:12