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.

I began by linking A to 3 others B,C and D.  Then linking each to two others B to E and F, C to G and H, D to I and J.  Then it remained to create the last 6 links between E, F, G, H, I, J.  E to H and J, F to G and I, G to J and H to I

<pre>
      /--------E
     /___F   / |
   B    / |  /   |
  /  /G  |/     |
A-C    X       |
  \  \H  |\     |
   D    \|  \   |
    \----I    \ |
     \______J

 

Posted by Jer on 2005-11-16 12:32:01