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

 Messages: [ Previous | Next ]
 William Elliot Posts: 2,637 Registered: 1/8/12
X/O Grid
Posted: Dec 19, 2012 1:32 AM

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?

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