According to the DR. Math website... It is unsolvable in a 2 dimensional plane.
http://mathforum.org/library/drmath/view/57927.html
Getting All the Utilities to Each House
Date: 17 May 1995 08:43:27 -0400
From: Anonymous
Subject: Puzzle
I've been stumped-here's the problem: Draw 3 one inch squares representing
houses horizontally across the page. Draw three circles, one under each
square. Number your squares and put a G for gas , E for electric, and W for
water in each circle. Your job is to connect each utility to each home
WITHOUT crossing any lines. You may not pass a line through a house or
other utility circle. Leave an inch and a half between each house. Put each
circle an inch below each square.
Mr. Borstein.
Date: 9 Jun 1995 11:05:33 -0400
From: Dr. Ken
Subject: Puzzle
Hello there!
I'm afraid your problem kind of got lost in the shuffle of problems. Also,
I hope I can make you feel a little better about the fact that you couldn't
solve it, because there is no solution possible.
What's neat (and you might want to pass this along as a challenge to your
students) is that while the problem can't be solved in the Euclidean plane,
it CAN be done on the surface of a torus (a doughnut). See if your students
can figure out why.
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Three Houses, Three Utilities
Date: 07/15/99 at 01:43:02 From: Chris Subject: Lines, etc. I know that you have answered this before: the question about the three houses and the three utilities (gas, electricity, water). Well, the guy who gave me this puzzle says there is a way of solving it in 2D, without any tricks. He says that it is simple, once you figure it out. I don't get it. Everywhere, it says that it can only be done using 3 dimensions. Can you solve it using 2 dimensions? How? Thank you very much
Date: 07/15/99 at 12:38:34 From: Doctor Rob Subject: Re: Lines, etc. Thanks for writing to Ask Dr. Math! You can only solve this if you allow one of the utility lines to run through someone else's house, or through one of the other utility companies, which I suppose is possible, but is usually forbidden by the conditions of the puzzle. - Doctor Rob, The Math Forum
http://mathforum.org/dr.math/ Date: 07/15/99 at 12:46:43 From: Doctor Peterson Subject: Re: lines, etc. Hi, Chris. He may not call it a trick, but any solution that's really 2D (that is, done just by drawing non-intersecting curves on a flat sheet of paper) has to twist the rules somehow. He might, for example, draw the houses as rectangles and say that it's legal to open the front and back doors of one house and pass a pipe through. I call that a trick. Another trick is to solve it on the surface of a donut (a torus) and point out that any surface is itself 2-dimensional, even though it exists in a 3-dimensional space. Or you can allow going around to the other side of the paper through a hole, which is essentially the same thing, as this answer points out:
http://mathforum.org/dr.math/problems/tone.7.19.96.html When the problem is stated carefully in mathematical terms (continuous non-intersecting curves from each of three points to each of three other points), there's no solution; but presented in terms of houses and utilities (which are inherently three-dimensional), there are lots of ways to get around it. I'd like to hear what his answer is. - Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
