For Those of You Who Liked the Airplane Physics Question...

Only one outlet per utility?

 

so let me get this straight:

3 houses, 3 utilities, no intersection of utility lines, utility lines are co-planar

 

sounds like my trailer park.

 

I'll buy the first person that gets it a box of DOUGHNUTS.

 

well that was a waste of 30 mins to find out that whatever i tried someone got shafted on a utility. eh, 2 houses, and one low rent house

 

You haven't answered my question. Only one source per utility? Otherwise each of the houses could have a spearate source across the street. Three nice straight lines for each house.

 

Picture it this way:

Think of the '6' side of a die-> :::

Connect each of the 'dots' in the top row with each of the 'dots' in the bottom row....9 lines that do not intersect.

 

Yup, three for each house, nine total.

 

You drew it?

 

I had my secretary draw ti.
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I guess your secretary thought there are 12 structures. There aren't, there are 6....just like in the six sided die I diagramed. Three houses and one power building, one water building and one gas building - each utility building has three of the same outputs coming from it, each going to its own house. The clues are in this thread. I think the original post was a bit unclear.

 

On a flat plane it is impossible to do this. You could do it on a toroid shape, I think, and I guess that's what you meant by doughnut? But I am guessing, and I don't really think it's a fair question. A toroid would be a three dimensional shape.

Do it on a flat piece of paper. You can't. It can be proven mathematically that you can't, but why bother? It's easier to just try all the permutations. Three houses can be arranged in a line or triangle. Three utilities can be arranged in a line or triangle. Four line and triangle combinations total. Now draw lines with colored pens. Or use colored strings. I couldn't do it. If you can, I would love to see the drawing.

 

The water and the gas are easy. For the electricity, I'm going to put a box to the right of house #3, and run the power lines in conduit under the houses. Now each house has its own service with its own meter for each of the three utilities.
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If you do it on a piece of paper I guess you could cheat:

Punch a hole with you pen nib on the drawing of the water main, then draw on the back of the piece of paper, from that hole, a line to each of the three houses. Once again use your nib to make three more holes in the paper, thus connecting all the houses with all the utilities without ink lines crossing.

I hope this isn’t the answer as it bends the 2D rule, but it is the one that strikes me as the most likely........

 

bends? breaks is more like it.

paper isnt a 2d shape as it has a front AND a back, it must be in a plane to be 2d (a plane is essentially a piece of paper that has no back side (or was it front?) ) technically speaking. on a side note: search "mobius strip", as that is a 2d piece of paper , what can i say im a nerd at heart


this problem is impossible and can be proven using euler path rules (and math) - graph theory - but that was 4 years ago in math for me, so look on the web, there are lots of uber geeks that prove it with really cool pictures

 

The "traditional" answer to this problem is that it can't be solved unless you take advantage of the statement of the problem. I.e., not crossing utility lines is not the same as not crossing houses/utilities. If the house/utility were a point, then the problem is insoluble. But if the house/utility is considered to occupy 2D geometric space, then a "trick" solution is allowed, by using the space the buildings occupy to route a line through in a manner which doesn't "cross" utility lines (see dotted line solution below).
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