An alliance of ten planets has decided to build teleporters so that their economies may mutually benefit from faster travel. The teleporters are huge gateways that come in permanently linked pairs. The idea is that each pair of linked teleporters connects a pair of planets.
In the interest of equality, each planet will build exactly three teleporters. In the interest of efficient travel, the links will be placed such that to reach one planet from another, no more than two teleporters must be used. How will the planets be linked?
Bonus: If you were to draw a diagram of the way the planets are linked, what is the simplest diagram you can think of? Try to find one you can even describe in words alone.
Here's how I would draw the planets:
-Draw the planets in two vertical rows of five.
-Each planet in row A links to the adjacent planet in row B creating rungs in a ladder.
-Each planet in row A connects to the two adjacent planets in the same row with planets at the end connecting.
-Each planet in row B connects to the planets two steps away in the
same row. If a planet is near one of the ends, continue counting
at the opposite end.
Another diagram
