Connecting up boxes mathematically (Puzzle)

Question

How would you connect each black box once to each colored box without any lines overlapping, this is racking my brain so please help.

Note that you can move the boxes where ever you want.

Maybe there's some math trickery involved as I have spent hours trying to crack it but cannot seem to without having no option but to overlap (which I can't) or start again.

I am unsure if this is the correct forum to post in.

Answer 1

You can't do it without trickery. This is known as the three utilities problem and the graph you are trying to draw is $K_{3,3}$ which is known to be non-planar. The types of trickery used are to draw the graph on a torus or to say they are pipelines and one can go over another.

Answer 2

Thanks for the answers.

I have found a solution at least to get my graph completed so far, the example above is just to demonstrate what my problem was.

I decided to create junctions with the lines that all narrow down to just one line I guess it is a mathmatically legal move in the context of what I originally stated because the lines only touch, not cross over so for a real solutuion to a real life problem this works fine.

The solution is this: Please Embed Again