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#189968 - Tue Aug 12 2003 09:20 PM Water / Gas / Electricity
Astrix Offline
Mainstay

Registered: Wed Jan 05 2000
Posts: 769
Loc: Canada
I am trying to recall a puzzle wherein there would be three separate houses drawn along the top of a page and then the letters "W", "G" and "E" along the bottom of the page, under the houses - i.e. "W" under house #1, "G" under house #2, "E" under house #3. The letters stand for water, gas and electricity.

The challenge was to connect a service line for each utility to each of the houses without crossing over any line (9 lines in total). I can't remember if there was a solution or not to this old puzzle, but it has recently come up in a conversation around here, so now it's bugging me as to what the solution might have been.

I do remember that you can circle around (i.e. draw the line up, over and around the roofs if necessary). They didn't have to be straight-arrow lines leading to the foundations of the houses. The only rule is that you can't cross any lines.

I'm not sure how the answer can be shown in this forum. Maybe it is posted somewhere on the web and a link can be provided, or maybe by scanning a drawing. Any suggestions?

** Even if you don't come up with an answer, can you at least post your efforts so that I have an idea how many people tried and for how long (so that I don't feel too discouraged that I couldn't find the answer either.) Thanks.

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#189969 - Tue Aug 12 2003 09:29 PM Re: Water / Gas / Electricity
gtho4 Offline
Administrator

Registered: Sun Dec 26 1999
Posts: 54492
Loc: Sydney
oz downunder
have a look at the bottom of this page:
http://members.cox.net/mathmistakes/discrete1.htm
is that the one?

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#189970 - Tue Aug 12 2003 11:36 PM Re: Water / Gas / Electricity
Astrix Offline
Mainstay

Registered: Wed Jan 05 2000
Posts: 769
Loc: Canada
gtho4... I love you!
(oops.. hope your wife didn't hear).

Seeing that drawing reminded me that you can solve this puzzle on paper by drawing the last service line by first dog-earring the corner of the top-right of the page and then drawing the last line over the newly exposed verso of the page; thereby not having to cross over a line that is drawn underneath. As per that link's explanation: "The term non-planar simply means it cannot be drawn on a plane (ie. piece of paper) without crossing lines. It does not rule out other surfaces."

Thanks so much.

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#189971 - Wed Aug 13 2003 01:40 AM Re: Water / Gas / Electricity
gtho4 Offline
Administrator

Registered: Sun Dec 26 1999
Posts: 54492
Loc: Sydney
oz downunder
not a problem
ma'am, it was a pleasure

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