I have 3 houses that need to be connected to 3 utility comp

[MATHGAL]

I have 3 houses that need to be connected to 3 utility companies:

House1 House2 House3

Gas Water Electric

Can 9 lines be drawn to connect each house with each utility without crossing the lines?

 

[Deleted member 4993]

I have 3 houses that need to be connected to 3 utility companies:

House1 House2 House3

Gas Water Electric

Can 9 lines be drawn to connect each house with each utility without crossing the lines?

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

 

[Denis]

Mathgal, do a google search...

 

[qpmathelp]

I have 3 houses that need to be connected to 3 utility companies:

House1 House2 House3

Gas Water Electric

Can 9 lines be drawn to connect each house with each utility without crossing the lines?

impossible since the graph would be the bipartite K3,3 which is non-planar

http://en.wikipedia.org/wiki/Water,_gas ... lectricity

http://rbmix.com/math/graphth/grp.php

 

[Deciheximal]

I had a sixth grade math teacher with a twisted sense of humor. He presented this problem to us and asked us to find the solution. I spent hours drawing lines to try to solve it, came up with tricks like running the lines "under" the houses to try to avoid the lines crossing, even came up with one clever solution by wrapping the edges of the paper together like a globe. He said they were all wrong, but insisted there was a right answer.

This puzzle has no correct solution.

 

[mmm4444bot]

… [my teacher] insisted there was a right answer.

There is a right answer.

-

This puzzle has no correct solution.

That's it.

 

[chivox]

http://mathworld.wolfram.com/UtilityGraph.html

In addition to the links provided earlier, the above link at MathWorld provides an easy-to-follow picture of this graph on a torus. Only one of the lines needs to cross over to the other side, but none of them touch each other. Of course, the question sort of implied all the lines and the points had to be coplanar, but it's still a nice, color-coded diagram.

 

[Deciheximal]

I meant, he insisted that there was a way to solve it.

 

[naus]

I meant, he insisted that there was a way to solve it.

I feel your pain so very much. I'm wondering if we maybe went to the same school... ! One of my teachers did the same exact thing. We had to draw diagrams on posters with markers according to how we thought it could work. I worked and worked on the problem, but I never found a solution. I asked my dad, a scientist, and he laughed and laughed and laughed, then told me there wasn't a way to do it. I left my poster blank, wrote my name on it, and handed it in.

(sorry if I'm off-topic)