[extropy-chat] glat test

[Hara Ra]

Well, I don't care to try solving this thing, but had some musings to share:

1.  Solving the general problem of R(x0,y0;x1,y1) might be simpler or same 
difficulty as solving the knights move instance.

2.  Such a solution requires enumerating all of the current carrying paths 
and constraints thereto, looks nasty, like a infinite series of summations 
of infinite series, and how to count these in a 1 for 1 way is tricky.

3.  What is the test actually looking for. If there is a nice closed 
mathematical expression that's one thing, but will "good enough" do? If 
"good enough" does, then it is simple enough, though tedious, to write a 
simulator, say a grid of 100 x 100 resistors and run till it converges. If 
I did that I would email the solution, how I found it and why I did it this 
way.

4.  Of course there's the story about Von Neumann when asked to sum the 
numbers 1 - 1000 and he did't see the obvious pairings of 1,999; 2,998 and 
so on, and when asked how he did the problem he said he just added them all 
up. Wonder if something similar lurks here.

5.  Knights move is a co-ordinate transformation. Think of it as a diagonal 
on a matrix of resistors whose diagonal is the knights move. Probably a 
PITA, just a thought.

 > At 08:22 PM 10/28/2004 -0700, Spike wrote:
> > >
> > >
> > >If you set up a subset of the grid with only 7 resistors
> > >and calculate the hard way, the knight-move nodes Req is 7/5.

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=   Hara Ra (aka Gregory Yob)    =
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