# Is there a Gas Water Electricity Puzzle Solution?

**URL:** <https://boards.straightdope.com/t/is-there-a-gas-water-electricity-puzzle-solution/234051>\
**Category:** Factual Questions\
**Created:** [March 13, 2004, 6:12am UTC](https://boards.straightdope.com/t/is-there-a-gas-water-electricity-puzzle-solution/234051 "2004-03-13T06:12:54Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![Meeko](https://avatars.discourse-cdn.com/v4/letter/m/e495f1/32.png) [@Meeko](https://boards.straightdope.com/u/Meeko)\
**Post date:** [March 13, 2004, 6:12am UTC](https://boards.straightdope.com/t/is-there-a-gas-water-electricity-puzzle-solution/234051/1 "2004-03-13T06:12:54Z")

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Is there a solution to the Gas Water Electricity Puzzle?

There are Three houses in a line, and a Gas, Water and, Electrcity Plant in a parallel line from the three houses.

```
    -House- -House- -House-

    -Gas- -Water- -Electricity-

```

The Objective is to lay pipes/wires from each plant to each house by drawing a line from a plant to a house, using only straight lines, and not crossing or retracing any already drawn lines. No pipes can be shared… Each house must have its own connection to each of the Gas, Water and Electricity.  
I think the puzzle is pretty common, did I leave any parts out? Are there any variants? Is a solution even possible?

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**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\
**Post date:** [March 13, 2004, 6:16am UTC](https://boards.straightdope.com/t/is-there-a-gas-water-electricity-puzzle-solution/234051/2 "2004-03-13T06:16:20Z")

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It’s impossible to solve in two dimensions, but trivial in three.

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**Author:** ![ianzin](https://avatars.discourse-cdn.com/v4/letter/i/ed655f/32.png) [@ianzin](https://boards.straightdope.com/u/ianzin)\
**Post date:** [March 13, 2004, 6:17am UTC](https://boards.straightdope.com/t/is-there-a-gas-water-electricity-puzzle-solution/234051/3 "2004-03-13T06:17:40Z")

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This is an ancient puzzle and it has been analysed to death. If you hunt around web sites devoted to recreational mathematics you’ll find all the detail you could want (or not).

There’s no ‘normal’ solution - at least one of the lines would have to cross. There are all kinds of slightly weird solutions which count as either cheaty or ingenious depending on your p.o.v. For example, the way the puzzle is usually written out, there’s nothing to stop one of the supply lines going through or under one of the houses, which makes a solution possible. Other people will put the three houses on the surface of a sphere, which I think also makes a solution possible (at least one of the supply lines has to go the ‘long way round the world’). And so on.

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**Author:** ![Trigonal\_Planar](https://avatars.discourse-cdn.com/v4/letter/t/0ea827/32.png) [@Trigonal\_Planar](https://boards.straightdope.com/u/Trigonal_Planar)\
**Post date:** [March 13, 2004, 7:10am UTC](https://boards.straightdope.com/t/is-there-a-gas-water-electricity-puzzle-solution/234051/4 "2004-03-13T07:10:12Z")

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I remember this puzzle from way back in elementary/high school. I just the bent the paper into a cylinder…the teacher didn’t seem to like that answer though! 😛