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Another puzzle

  1. Mar 17, 2005 #1
    Here is another brain Teaser......


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

    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.
     
  2. jcsd
  3. Mar 18, 2005 #2

    Galileo

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    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
     
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