
Seven Bridges of Königsberg - jacquesm
http://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg
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btilly
This reminds me of a fun math problem.

On a piece of paper draw the following shape:

    
    
      -------------
      |     |     |
      |     |     |
      -------------
      |   |   |   |
      |   |   |   |
      -------------
    

We'll count a wall as any straight line segment dividing 2 areas. If you count
them, it has 16 walls. The challenge is to draw a single continuous line on
the plane that passes through each wall once and only once.

Part A: Prove it can't be done.

Part B: Part A notwithstanding, show how to do it. :-)

 _Edit:_ Since I am sure that someone will challenge me on the contradiction,
I put a solution at <http://www.elem.com/~btilly/boxes-solution.txt>.

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bitdiddle
This problem really piqued my interest in graph theory, as well as did my
first homework assignment.

At a certain dance there are two rules that hold:

1\. No boy dances with every girl.

2\. Every girl dances with some boy.

Prove that there are at least two couples that dance, B1-G1 and B2-G2, such
that there is no crossing, neither B1-G2 nor B2-G1

Happy holidays HN!

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rbanffy
"Euler proved that the problem has no solution."

What a defeatist way to see it. Obviously, the solution is to build one more
bridge.

~~~
dlib
A couple of bridges were destroyed during WWII, so right now it can be solved.

~~~
rbanffy
I have to agree that destroying one bridge also makes the problem solvable,
but I was aiming for a more constructive approach.

------
rbanffy
I for one welcome our humorless down-voting obverlords.

