Talk:Water, gas, and electricity

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[edit] Three cottage problem solvable ?

I thought there was a solution to this problem if you ran one of the cables/pipes under the middle cottage Wikipedian231 20:56, 20 Mar 2005 (UTC)

I extended the article. Does this answer your question ? MathMartin 17:26, 21 Mar 2005 (UTC)


[edit] Three cottage problem solvable? (Second round)

As the problem is formulated ("Is there a way to do so without any of the lines crossing each other?") the problem should be solvable with the solution "no".

In order to say that the problem has no solution you should formulate the problem as something like "Find a way to do so without any of the lines crossing each other".

I think the best thing is to just say that the answer is no, there is no such way and keep the original problem formulation.

Just my two cents. --130.238.5.7 08:49, 22 April 2006 (UTC)

[edit] Article is misnamed

I am not familiar with the name "three cottage problem", as I've heard it referred to as the "Gas, Water and Electricity problem". My Munkres' topology book uses this name (which is probably where I first saw it). The sole reference for this article uses "3 utilities puzzle" and refers to the "Water, Gas, and Electricity" name and setting to H. E. Dudeney in 1917; its source is apparently Martin Gardner. I also found a 1979 Mathematics Magazine article that explains the long history of the utilities setting[1]. It's apparent to me that this article is misnamed. C S (Talk) 02:57, 21 January 2007 (UTC)

  • I'm fine with moving it. I wrote this article a long time ago, and don't remember exactly why I chose the name. I'm certain I had seen the name somewhere (I wouldn't have just made it up), but this was before it was common to cite sources on Wikipedia, so I didn't cite my source and can't remember what it was now. Some googling indicates that it does seem to be used occasionally (e.g. in some Stanford homework problems, a few Usenet posts from the 1990s, and so on), but you're right, "three utilities problem" and "gas, water, and electricity problem" are far more common. --Delirium 03:28, 21 January 2007 (UTC)
    • We will probably want to keep "three cottage problem" as a redirect. Possibilities for title: three utilities problem, utilities problem; water, gas, and electricity; water, gas, and electicity problem (or various permutations). For the moment, I've created a redirect here for "Water, gas, and electricity", which is tentatively my preferred choice so far. This article caught my attention because I noticed that Impossible Puzzle which I prod'ed is essentially a worse version. Right now I am just replacing the several links to "impossible puzzle" by links to "water, gas, and electricity", since it seems using "three cottage problem" is not a good idea. --C S (Talk) 11:18, 21 January 2007 (UTC)
      • Yeah, "impossible puzzle" is way too vague, since there are plenty of puzzles that are impossible. I also reverted an attempt to merge this article into that one, since this one has by far a longer history, so should be moved to a new title rather than copy/pasted. --Delirium 20:43, 21 January 2007 (UTC)
  • I have a vague recollection that Martin Gardner has dealt with this problem in depth. You might care to look at what name he gave to it. Uncle G 18:09, 22 January 2007 (UTC)

[edit] Solution:

I've worked for a pipeline company before. You HAVE to use common sense in this case.

For one: These are NOT 'dots'. These are houses, actual 'area' in squared feet. And two: NO company in their right mind would provide direct lines of service to houses, they try to avoid that since it costs money. Instead they have one 'main-line' that branches off to houses.

And since the houses/cottages occupy 'area' and are NOT 'non-existant/non-area points', the houses can accept branched pipes.

http://en.wikipedia.org/wiki/Image:3-cottage_solved.JPG —The preceding unsigned comment was added by Mix Bouda-Lycaon (talk • contribs) 10:18, 25 January 2007 (UTC).

lol real life objects is not what this puzzle is about. going through "houses" is illegal, they represent points. plus I don't think your solution would apply to electric circuits. 88.240.13.46 16:12, 31 January 2007 (UTC)
Not 'going through' houses, gas and water lines run in the streets while power-lines tower over houses, all having run-off lines to suplly the house with utilities. Nowhere on here specifies to 'represent points'. I'm talking about the literal problem here, not the metaphor of it. This problem is labeled The 3 Cottages, not The 3 Points. My solution works perfectly. —The preceding unsigned comment was added by Mix Bouda-Lycaon (talk • contribs) 06:39, 6 February 2007 (UTC).
well in real world there is no problem supplying millions of houses with utilities, because we live in a 3 dimensional world. but if there were only 2 dimensions, three of your brain cells would not be able to connect with three other cells, or your digestive system would have to have one only orifice or you would be torn apart. this problem is about constraints in two dimensions imo. regards. 88.241.181.163 12:02, 11 February 2007 (UTC)
The problem is meant to be attempted in two dimensions only. Giving it cottages and utilities just makes it a word problem and easier (and more fun) to visualize. In mathematical terms: "Given two distinct sets of three points in a plane, connect each point to all the points in the other set. As long as they are in the same plane, placement of points is arbitrary, even among sets. Is it possible to do this without having the connecting segments intersect?" That is the real literal question, not the metaphor. Adding the other details just makes it colloquial. The point is, in two dimensions, the solution is impossible, a point clearly made in this page.--WPaulB 14:21, 14 February 2007 (UTC)