GeekDad Puzzle of the Week: Planetary Paths

Just past UDFj-39546284, one of the most distant galaxies discovered to date by the Hubble telescope, is a small, flat/disc universe with six planets that ring an asteroid field. Over time, robot traders mining this section of space have hewn each of the fifteen direct trading routes from each planet directly to every other through the field, creating a total of thirteen intersections throughout the field.

The law in this part of space is not only strict, but also strictly geared to robot pilots.
* A ship can only travel along a route that is getting it closer to its final destination.
* A ship can only revisit a complete route from one planet to another after exhausting every other possible complete route between those two planets...

Source: http://www.wired.com/geekdad/2012/06/geekdad-puzzle-of-the-week-planetary-paths/

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