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.

isn't it easier to draw a regular decagon and a line connecting any vertice with the vertice directly opposite it?

Decagon lines:1-2,2-3,3-4,4-5,5-6,6-7,7-8,8-9,9-10,10-1

other lines: 1-5.2-6,3-7,4-8,5-10

Posted by marc on 2005-11-28 09:21:02