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.
For example, there are exactly five (5) different paths from any planet to one of the planets immediately adjacent to it. (Go ahead and check, I’ll wait.) The set of robot pilots that fly between those two planets only visit each complete route every five trips. In this part of space, each complete path takes the same amount of time to traverse – one Earth day. It happens that these “adjacent planet” pilots complete an integer number of sets of trips in their Local year — that is, the Local year is a multiple of five earth days.
If all sets of robot pilots in this part of space complete integer numbers of sets of trips during their Local year, how long is their Local year in Earth days? Send your solution to GeekDad Puzzle Central for your chance at this week’s $50 ThinkGeek gift certificate.