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## Question

there are 3 houses next to each other... all 3 houses need a connection to the gas company water company and electric companies. How can these be done with no lines crossing

H1 H2 H3

G W E

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there are 3 houses next to each other... all 3 houses need a connection to the gas company water company and electric companies. How can these be done with no lines crossing

H1 H2 H3

G W E

It can't be done, it's impossible with no lines crossing.

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Use three dimensions to connect the houses to the companies.

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One of the lines is routed underneath - or through - a neighbor's house.

No lines cross; third dimension not used.

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That article forbids going under or through a neighbor's house or a utility.

Those are the two solutions.

If you forbid all solutions, everything is impossible.

Their article is written from a graph theoretical perspective.

In graphs, you can't go out of the plane, and you can't go through nodes.

In the OP, where you are forbidden only to cross any lines, you can do both..

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That article forbids going under or through a neighbor's house or a utility.

Those are the two solutions.

If you forbid all solutions, everything is impossible.

Their article is written from a graph theoretical perspective.

In graphs, you can't go out of the plane, and you can't go through nodes.

In the OP, where you are forbidden only to cross any lines, you can do both..

Ohhh ... I thought it is a plane. Thanx Bonanva for the correction.

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You can keep things in a plane [so to speak] by running the last connection through one of the houses to the last house.

It's kind of like cheating, except the OP does not forbid doing it.

That approach keeps lines from crossing each other, which technically would mean one is above and the other is below - going into the 3rd dimension.

"outside the box" in this puzzle translates to "inside the house"

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I tried this with pencil & paper when I was young (before computers )... it can't be done.

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wouldnt this work?

view from top down

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wouldnt this work?

view from top down

I guess if the homeowner in the middle house doesn't have a problem with it, it would work.

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H1 H2 H3

G E W

in that order...

H1

[

G-E-W

H2

[

G-E-W

H3

]

G-E-W

The spacing might not work out right, but H1 is above G, and connects to G, then E, then W.

H2 is above E, and connects directly to E, with E branching to the left to G, and the right to W.

H3 is above W, and connects directly to W, which connects to E, which connects to G

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