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Topic: X/O Grid
Replies: 3   Last Post: Dec 23, 2012 3:07 AM

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 Michael Press Posts: 2,137 Registered: 12/26/06
Re: X/O Grid
Posted: Dec 23, 2012 3:07 AM

In article <Pine.NEB.4.64.1212182213130.17186@panix3.panix.com>,
William Elliot <marsh@panix.com> wrote:

> Consider an n by m grid of x's and o's.
>
> An x-path from the bottom squares of the grid to the top squares of the
> grid considitues a seqence of horizontally or vertically adjacent
> x-squares from some bottom x-square to some top x-square. Similar with
> o-paths.
>
> An exit is a top square that is connected to a bottom square by
> either an x-path or an o-path. For example, in the 8 by 3, x/o grid
>
> x x o o x x o o x
> x o o x o x x x x
> o o x x x o x o x
>
> has two o-exits and three x-exits for a total of five exits.
>
> In an n by m, x/o grid, what is the expected number of exits?

Look up percolation theory.

--
Michael Press

Date Subject Author
12/19/12 William Elliot
12/20/12 Brian Q. Hutchings
12/23/12 Michael Press