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 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.
This is a problem from graph theory. The notation we use is 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.