[extropy-chat] glat test
Hara Ra
harara at sbcglobal.net
Fri Oct 29 18:08:37 UTC 2004
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.
==================================
= Hara Ra (aka Gregory Yob) =
= harara at sbcglobal.net =
= Alcor North Cryomanagement =
= Alcor Advisor to Board =
= 831 429 8637 =
==================================
More information about the extropy-chat
mailing list