Can You Prove It? Brain Teaser - 3 Houses & Utilities

[BigStelly]

Here is another brain Teaser...


in 2D not 3D assume crossing lines disrupts the electric field,

3 houses need to be hooked up to electrical, telephone and gas. Is it possible to hook every house up to every building without crossing lines?

I know this is impossible but can anyone prove it, id be interested to see how.

Yeah some teacher once actually told me that same thing a few years ago in high school and i didnt believe them after trying about 500 times to solve the darn thing.

 

[Galileo]

Euler proved a beautiful theorem for polyhedra with the following analogon for graphs (The problem is a graph problem. You have to find a planar graph (i.e. a graph that can be drawn on a flat plane without the lines intersecting).

If you have a planar graph with n>0 vertices, m lines (branches, edges) and r regions (including the outer region), then: n-m+r=2

You can use this to prove the problem has no solution.

I found a site about it:
http://mathforum.org/dr.math/faq/faq.3utilities.html