# Seemingly un-solvable problem (mathish)



## fundash (Nov 7, 2009)

ok, I got this problem for my math class, and I REALLY wonder if it's possible, if so, how?

Here is the problem:

1. There are there houses, and there is water gas, and heat 
http://img145.imageshack.us/i/problem1.png/

2. Water gas, and heat must be hooked to all 3 houses. 
http://img25.imageshack.us/i/problem2k.png/

3. No lines can cross! 
http://img194.imageshack.us/i/problem3c.png/

I'd be amazed if anyone figured this out!


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## 4Chan (Nov 7, 2009)

*Solved. *


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## qqwref (Nov 7, 2009)

This is actually a pretty well-known problem so I think it might be considered cheating if we tell you the real solution.



Spoiler



It's impossible if you aren't allowed to make pipes go through houses or utilities (that is, every house/utility can be treated as a point). The proof is kind of involved and mathematical, and while I could provide a link with a proof I'm not sure if you'd really understand it.


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## Tim Major (Nov 7, 2009)

A common answer to this problem, is drawing one of the pipes so it goes to the edge of the page, flipping over the page and continuing the line to the house, and poking a hole through the paper.


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## shelley (Nov 7, 2009)

The problem is impossible to solve if the three houses and three utilities lie on a plane (lines can't run through houses or utilities). However, it is possible to connect them if they are on the surface of a torus. Try it!


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## qqwref (Nov 7, 2009)

Try thinking with portals.


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## chris410 (Nov 7, 2009)

don't think straight lines only (unless that is a parameter), curve as in the first solution or suggest the 3-D (xyz) approach, two on xy and one under (z) plane.


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## LewisJ (Nov 7, 2009)

In a completely conventional way on a 2D plane with the houses and utilities being simple points and no tricks or anything,


Spoiler



it's impossible like QQ said



But of course,


Spoiler



when you add a bunch of crazy stuff like drawing on the back of the paper or giving size to the houses and utilities and they can be drawn through etc, it is possible


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## Cyrus C. (Nov 7, 2009)

Think 3D.


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## Ranzha (Nov 7, 2009)

qqwref said:


> Try thinking with portals.



+1.


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## Cyrus C. (Nov 7, 2009)

qqwref said:


> Try thinking with portals.



Or you could use petrus.


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## TioMario (Nov 7, 2009)

if you were engineers, you would have been fired.

YOU JUST GOT OWN3D BY TIOMARIO !!!


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## miniGOINGS (Nov 7, 2009)

TioMario said:


> if you were engineers, you would have been fired.
> 
> YOU JUST GOT OWN3D BY TIOMARIO !!!



2 gases are going to the same house.


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## LewisJ (Nov 7, 2009)

TioMario said:


> if you were engineers, you would have been fired.
> 
> YOU JUST GOT OWN3D BY TIOMARIO !!!



Uh, fail. Gas goes to house 3 twice and never gets to house 2.


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## 4Chan (Nov 7, 2009)




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## nitrocan (Nov 7, 2009)

Cubes=Life said:


>



Exactly what I'm thinking...


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## 4Chan (Nov 7, 2009)

@ Nitrocan

Pictures say a thousand words~


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## fundash (Nov 7, 2009)

Cubes=Life said:


> *Solved. *



This seems like a working solution, I'll ask if it voids any rules.


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## LewisJ (Nov 7, 2009)

fundash said:


> Cubes=Life said:
> 
> 
> > *Solved. *
> ...



It voids the rules of:
1. There must be a line FROM each gas/water/electric TO each house, not one line from water to all 3 houses
And
2. Cant put lines through through houses, plus houses are to be treated as points not areas


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## 4Chan (Nov 7, 2009)

So, uh, mister lewisJ?

I don't remember fundash saying those rules. d:
And this is Fudash's challenge.
So for his specific example, it does work.


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## fundash (Nov 7, 2009)

yea, I won't be able to tell anyone if that works until monday...


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## LewisJ (Nov 7, 2009)

The original problem, which I'm sure is what his teacher is going off, specifies that you can't draw through any of the houses (aka they're treated like points on a 2d graph). The problem in its no-tricks form is impossible to solve and I'm sure his teacher knows this.


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## TioMario (Nov 7, 2009)

shhh,the third one goes under the house,don't tell anything...

(i'll just go :fp myself ok?)


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