Re: Tali's Moogies

> I�m quite sure that I could do summing like this:
>
> +----------+----------+----------+----------+
> |          |      ___ |      ___ |      ___ |
> |   . |    |   . |    |   . |   ||   . |___||
> |  / \|    |  / \|    |  / \|    |  / \|    |
> | /___|    | /___|    | /___|    | /___|    |
> | |\ /|    | |\ /|    | |\ /|    | |\ /|    |
> | | X |    | | X |    | | X |    | | X |    |
> | |/_\|    | |/_\|    | |/_\|    | |/_\|    |
> |          |          |          |          |
> +----------+----------+----------+----------+
> | mit�nem  | Wimpel   | oben     |  drauf   |
> +----------+----------+----------+----------+
>
> This means that I had to end the Nikolaushouse at the upper left or right
> corner. Now I tried all possible variations, but cannot do it again. Can
> sumbuddy help?
>
> HJH
> \  \     \ \  \
>  \__\     \ \__\
>   \  \     \ \  \
>    \  \` _ /  \  \

There are two kinds of nodes (places where lines cross, or start or end) -
those with an even number of edges, and those with odd.  If you think about
the odd nodes, you'll notice that you must either start or stop at an odd
node, since you can't "come in and leave" a whole number of times.  If you
could, there would be one edge for every entrance, and one edge for every
leaving, making an even number of edges.  So, since you must either start or
stop at an odd node, you can't have any more than two in a single graph --
one to start at, one to stop at.

Since the Nikolaushaus has its odd nodes at the lower corners (three edges
each: a wall, the floor, and a diagonal), you must start and stop at those.
So you can't start or stop at an upper corner -- and, like Mr. Rossel said,
the picture you have is impossible anyway, since it has more than two odd
nodes.

William J. Keith -- math student, avid reader of a.a-a, first time poster
(well, since one time a *long* time ago)

Sample work: a turtle, swimming, I made for a friend of mine

             ___
          ,+'/.\'+,    ___
        \/\_/\_/\_/\,+' * \
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
       /_/'-------'\_\

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