perplexus.info :: General : Connect the planets

Connect the planets (Posted on 2005-11-16)

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.

Submitted by Tristan

Rating: 4.2500 (8 votes)

Solution: (Hide)

My favorite way to draw the diagram is like this:
There is a star, with a larger pentagon around it. Five lines connect each point of the star with the closest corner of the pentagon. The points of the star represent the first five planets, and the corners of the pentagon represent the last five.
In other words, connect planets A, B, C, D, and E in a pentagon. Next, connect planets F, G, H, I, and J in a star (F to H, H to J, etc. ). Then, connect planets A and F, B and G, C and H, D and I, E and J.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: No Subject	Tristan	2005-11-28 11:28:04
No Subject	marc	2005-11-28 09:21:02
My solution	Ken Haley	2005-11-16 23:52:33
A variation on a previously posted solution	Sing4TheDay	2005-11-16 16:25:18
Mt drawing	Jer	2005-11-16 12:32:01
Answer in words (Spoiler)	Vernon Lewis	2005-11-16 10:59:03
Another diagram	fractaloon	2005-11-16 10:29:58
my method	Charlie	2005-11-16 10:21:05
Simpler drawing	Bob Smith	2005-11-16 09:32:57
solution	Bob Smith	2005-11-16 09:10:28

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