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How to connect 3 houses to water, gas, electric cross-free



 
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simple
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Joined: 17 Dec 2005
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PostPosted: Sat Dec 24, 2005 6:01 pm    Post subject: How to connect 3 houses to water, gas, electric cross-free
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ok look


....................(W)....................(G)....................(E)





....................(H)....................(H)....................(H)


Code:
KEY :
W = WATER
G = GAS
E = ELECTRIC
H = HOUSE
.................... = PLEASE IGNORE THESE AND REPLACE THEM WITH BLANK SPACES


Basically you have to connect the W, G, and E up to all three different houses/MAIN LINES without connecting the houses, crossing your lines or touching the lines together......

this has boggled my mind since i was about 8 yrs old and im now nearly 20 lol

if somebody knows the answer please tell me.....................ive been pulling my hai out for 11yrs now

and ive tried every possible way :S:S:S:S

if this isnt a puzzle then i dunno what is !!!!!
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wolfman
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PostPosted: Mon Dec 26, 2005 7:31 am    Post subject:
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whoever gave you this puzzle is a cruel bastard.
It's impossible.
By the way, it's equivalent to finding a planar representation of K(3,3), the complete bipartite graph.
K(3,3) is nonplanar. This problem is impossible.

However, if we are living on a torus (doughnut), I beleive it's possible. Just go around the other way.
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simple
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PostPosted: Thu Dec 29, 2005 1:55 am    Post subject:
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he was a magic teacher called mr. oswald and due to us being a "naughty" class he wouldnt tell us :s

lol

oh well im still gunna be boggled lol Question Exclamation Question Exclamation Question Exclamation Question Exclamation Question Exclamation Question Exclamation Question Exclamation
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wolfman
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PostPosted: Fri Dec 30, 2005 8:30 pm    Post subject:
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Now I don't think it's possible, even on a torus. I think we might need a torus with two holes. ANyway, you didn't really ask me all that.
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database
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PostPosted: Mon Jan 02, 2006 1:52 pm    Post subject:
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Hey brainiacs! THis is simple - I just need to find a way of connecting the third orange line. Aren't you guys supposed to be brilliant at looking at the question to find the answer?

Image
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wolfman
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PostPosted: Mon Jan 02, 2006 7:45 pm    Post subject:
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If it's so simple, finish it up.
You can't. I know for a fact that you can't. I've personally seen it proven that you can't.
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chris
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PostPosted: Sun Jan 22, 2006 10:34 pm    Post subject:
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wolfman wrote:
Open quoteI've personally seen it proven that you can't.Close quote


Maybe you could tell us in a few lines how the proof goes? I mean, not all the details, but maybe what it boils down to. Is it a "characteristic number" of a "cross-free" graph that plays a role? Something like Euler's formula? Just curious.
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wolfman
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PostPosted: Sat Feb 11, 2006 8:51 pm    Post subject:
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it's a little complicated, and I'm a little lazy.
THis should be helpful.
http://www.artofproblemsolving.com/Forum/topic-45997.html
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chris
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PostPosted: Tue Feb 14, 2006 1:08 pm    Post subject:
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There are at least two ways to prove this - and one of them does indeed have to do with teh Euler formula, as I suspected. A good sketch of both proofs is available in Three Houses, Three Utilities.
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four arm
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PostPosted: Tue Mar 06, 2007 3:16 am    Post subject: very simple solution to three houses...
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VERY SIMPLE SOLUTION
NO NEED FOR EQUATIONS OR THREE D MODELS

the problem states that the problem is done on paper. If you fold the paper into a cube shape and draw the houses and utilites seperate on the six sides of the cube, you can easily connect the utilites to the houses without crossing

hope this is useful

Smile
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