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Math Help - A puzzle

  1. #1
    Amy
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    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.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Amy View Post
    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
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  3. #3
    Amy
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    Quote Originally Posted by Jhevon View Post
    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.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Amy View Post
    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
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  5. #5
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    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.
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  6. #6
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    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.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    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
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  8. #8
    Grand Panjandrum
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    Quote Originally Posted by Jhevon View Post
    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
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