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.
Link five planets as Group 1- AC AD BD BE CE
Link other 5 planets as Group 2 - FG GH HI IJ JF
Link each planet in group 1 to a corresponding planet in Group 2 - AF BG CH DI EJ
If you arrange planets in a circle and name consecutively Group 1 forms a five pointed star and Group 2 a pentagon (or a circle if you use curved lines.)
Simplest geometric diagram I can think of is placing the star inside the pentagon.
Thanks Tristan - first puzzle I have solved before reading any hints - and now I can draw 5 pointed stars without getting lost.
Edited on November 16, 2005, 11:02 am
Answer in words (Spoiler)
