1. ## A puzzle

A figure of 3 houses is attached. We should give water, gas and power connection to each houses directly.
But there is one condition. No two connections should cross. it is only a two dimensional puzzle.
Can you help me to solve this ? Please show me the answer.

2. Originally Posted by Amy
A figure of 3 houses is attached. We should give water, gas and power connection to each houses directly.
But there is one condition. No two connections should cross. it is only a two dimensional puzzle.
Can you help me to solve this ? Please show me the answer.
i suppose we are to draw lines from the houses to the water, gas, and power supply...

...are we allowed to use curved lines? i don't think it can be done with straight lines only

3. Originally Posted by Jhevon
i suppose we are to draw lines from the houses to the water, gas, and power supply...

...are we allowed to use curved lines? i don't think it can be done with straight lines only
No. we are not allowed to use curved lines. That is why it is difficult.

4. Originally Posted by Amy
A figure of 3 houses is attached. We should give water, gas and power connection to each houses directly.
But there is one condition. No two connections should cross. it is only a two dimensional puzzle.
Can you help me to solve this ? Please show me the answer.
This is a well known puzzle and has no solution in the plane (or on a surface of genus 0). See here for a discussion.

RonL

5. I don't know how to draw here, so I will just describe the connections.

The power goes to the rigth, turns vertically up at some distance to the right of house #3, stop at spome distance higher than the houses, then drops connections downwards to each of the 3 houses as it travels horizontally to the left up to above the house #1.

The water goes vertically up at some distance below the house #1, shoots from there a connection under house #1, then turns to the right and shoots connections upwards to the bottoms of houses *2 and #3 asit tavels horizontally up to below house #3.

Finally, the gas goes vertically up also but below the waterline, turns rightward, turns upward before hitting the powerline, turn to the rightside of house #3, continues leftwards through house #3 till it connects to house #2, goes through house #2 till it connects to house #1.

6. This is a problem from graph theory. The notation we use is $\mathcal{K}_{3,3}$ where this means one side has three vertices (here houses) and the other side has 3 vertices (here utilities). The question asks whether or not this graph is 'planar'*. The answer it no, it is a well-known fact.

*)Planar means it can be fully connected by non-intersecting lines.

7. Originally Posted by ThePerfectHacker
This is a problem from graph theory. The notation we use is $\mathcal{K}_{3,3}$ where this means one side has three vertices (here houses) and the other side has 3 vertices (here utilities). The question asks whether or not this graph is 'planar'*. The answer it no, it is a well-known fact.

*)Planar means it can be fully connected by non-intersecting lines.
i figured, but i know nothing about graph theory and i could tell it can't be done.

i don't like puzzles that have no solution

8. Originally Posted by Jhevon
i figured, but i know nothing about graph theory and i could tell it can't be done.

i don't like puzzles that have no solution
Then try it on a torus.

RonL