Re: Helix, Ring, and Bracelet

On Feb 7, 6:13 pm, Bill Taylor <w.tay...@[EMAIL PROTECTED]
> wrote:
>
> Here is a "proof".
> ____________________
> |            :              :           |
> |.....       :               \..........|    Dotty has a N-S loop,
> |     \......: ...                      |    and also a NW-SE loop.
> |            :    \........             |
> |            :             \            |     Blanky can have the
> whole rest
> |______:_______:______|    of the board, and not any loop!
>
> Now, look at this path.  From the central intersection,
> go up the vertical line, up it from the bottom, turn right
> down the diagonal line, and go right around to come in
> from the left again, back to the intersection.
>

"go right around"  ??  The only way to go encircle the board from E to
W is to follow the entire helix.

> This path has done a complete west-to-east
> cir***navigation, and (a careful tracking will show!)
> no N-S cir***navigation at all.
>

That's totally absurd.  The only way to encircle the board from E to W
is to follow the entire length of the helix.  By doing that you also
encircle the board from N to W.

In spite of the confusing instructions, I think I finally understand
your game.  You're saying that Z can win by forming a non-helical E-W
loop or either type of helix, and that N can win by forming a non-
helical N-S loop or either type of helix.  In the case that two
helices are formed, one black and one white, the slope determines the
winner.  Am I right?

>
> And you might also try to be less touchy, egotistical, and
> dismissive of others.
>

Of course I'm touchy.  I announce my game and you come on and shout
"Hey, that's my game!  Except I explained it more clearly and drew
pictures!"  What an ass!  Your rule set is totally different from
mine.  You are also not the first to announce a toroidal game here.
You're the third!

> >*And* my game has the property that a filled board
> > produces exactly one winner.
>
> Of course we all do.  Try not to be so childishly egocentric.
>

I'm not being egocentric.  I'm responding to your charge that a
similar, hexagonally tessellated game can't have the property that a
filled board has exactly one winner.  My game *is* played on a
hexagonally tessellated board and *does* have that property, proving
your assumption wrong.