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.
Equally space 5 planets on an imaginary circle starting at 12 o'clock. Connect them with 5 teleporter pairs forming a 5-pointed star.
Arrange the other 5 planets equally around a larger circle concentric with the first, again starting at 12 o'clock. Connect these 5 planets with teleporter pairs to form a simple pentagon. Now connect each planet in the inner circle with its nearest neighbor in the outer circle.
Briefly: Star in the middle, pentagon surrounding it, connect corresponding vertices.
My solution
