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3 Utilities Puzzle

AKG
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Posted 05/11/07 - 11:09 AM: Subject: 3 Utilities Puzzle	#1
Follow the link and play the game, see if you can solve it: http://www.supuzzle.com/ The aim of the game is to connect all 3 houses to the water, electricity and gas suppliers without crossing any lines Is it even possible? If so, print screen and post your solution. If not, prove it. SPOILER 1: It's not possible. Call the houses 1, 2, and 3, and the utilities W, E, and G. If there were a solution, then there would be lines from 1 to W, W to 2, 2 to E, E to 3, 3 to G, and G to 1. These edges would form a simple closed curve, dividing the plane into two connected components, the interior and the exterior. 3 lines are unaccounted for so far, 1E, 2G, and 3W. Each of these lines is either entirely in the interior or entirely in the exterior, otherwise it would at some point cross the boundary between the interior and exterior, thereby crossing one of the lines 1W, W2, 2E, E3, 3G, or G1. If we regard the exterior as a single face (equivalently, regard the problem as taking place on the surface of a sphere, rather than on a plane) then the line 1E will either split the exterior into two faces or split the interior into two. Either way, it will leave us with 3 faces: 1W2E3G, 1W2E, and 1E3G The only one of these faces that has both 2 and G as vertices is the unsplit one, 1W2E3G, so the line 2G must go through this face, splitting it and leaving us with four faces: 1W2G, 2E3G, 1W2E, and 1E3G. None of these faces has both 3 and W as vertices, so there can be no line joining 3 and W, so it really is impossible. SPOILER 2: It is possible. You can probably set it up to get all but one connection. And that single missing connection could be made if you were allowed to go through houses. Well due to something of an "easter egg" you can have lines go through houses. Holding down the left mouse button, draw a line from a utility to near a house. While continuing to hold the left mouse button down, click the right mouse button, then release both buttons. Move the mouse so the arrow/pointer is on the other side of the house, then hold down the left mouse button and continue drawing the line. Edited by AKG on 05/11/07 - 02:05 PM
"The only reason we die... is because we accept it as an inevitability." -- Stewie "To enslave nuance to dogma is folly." -- Lord Hillyer

Atrytone
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Posted 05/13/07 - 11:57 PM:	#2
Thanks for that AKG, I enjoyed it thoroughly.

tridley
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Posted 05/14/07 - 08:29 PM:	#3
I loved it, and couldn't prove it until I rearranged the icons on paper.

Cadrache
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Posted 05/18/07 - 09:29 PM:	#4
mmmm... wasting lots of paper on this one... i'm close I tell ya!!!
"...There was a writer who asked why it was that when we find positive experiences we say that only the physical facts are real, but in negative experiences we believe that reality is subjective. He made an example of those who say that in birth only the pain is real, the joy a subjective point of view, but that in death it is the emotional loss that is the reality." - Tony Ballantyne, Recursion. _____________________________________________ Truth is want. - The internal state of matters. Truth is Need. - The external state of affairs.

eski
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Posted 05/19/07 - 03:16 PM:	#5
yay. I win
gnostiagnostiagnostic- I know that I don't know but I don't know that.

serenityseeker
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Posted 04/08/08 - 07:19 AM: Subject: I joined to post this solution!	#6
My bf asked me this last night, said he's asked around 70 people and no one could figure it out. He bet me $50...needless to say in 20 minutes he now owes me a REALLY nice dinner! You have to solve this problem in 3D - What I did was roll the paper into a cylinder. You can now connect all 3 houses! He said he hadn't heard this solution before, but I checked on some puzzle sites and this solution is posted. Also, his solution is that you can have the lines (pipes)lying on top of each other (so that they are parallel but do not cross) when entering a house...I had also thought about drawing the lines (pipes) through the houses but he had said that wasn't allowed.

SIR2U
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Posted 04/08/08 - 06:33 PM:	#7
I have been trying to solve this and showing it to others for the past fifty years. An old uncle showed it to us he said he got from a friend of his at school. Up to now I have never seen a complete answer with out tricks of some kids. The original rules said that the paper should be flat, not be rolled up or anything. I made a hole in the paper and passed the line to the other side of the paper.
Unknown Alanic wiseman. "Ignorance and bad teeth have at least one thing in common. Keeping your mouth closed makes them both less obvious"

Cadrache
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Posted 04/10/08 - 06:35 PM:	#8
grins I like that answer Sir2u... I haven't quite got the answer yet either. Maybe if I shout something about a fractal algorithmn, i'd be in the good side, and get the answer...
"...There was a writer who asked why it was that when we find positive experiences we say that only the physical facts are real, but in negative experiences we believe that reality is subjective. He made an example of those who say that in birth only the pain is real, the joy a subjective point of view, but that in death it is the emotional loss that is the reality." - Tony Ballantyne, Recursion. _____________________________________________ Truth is want. - The internal state of matters. Truth is Need. - The external state of affairs.

keda
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Posted 04/11/08 - 05:19 AM:	#9
Spoiler: My proof: One resource can only have two connections, as the two houses it connects to each must connect to a resource on each side of the line that consists of the first resource and the two houses it is connected with, thus ancaging the resource, rendering it inaccessible to the third house. Edited by keda on 04/11/08 - 05:25 AM
All about making money Free Europe Now How to fix your country In thought, men distance themselves from nature in order thus imaginatively to present it to themselves--but only in order to determine how it is to be dominated - Adorno and Horkheimer

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