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Two squares of an 8 by 8 chessboard are chosen at random.  What is the probability that they are adjacent (vertically or horizontally, but not diagonally)?

 Dec 2, 2019
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I split the board up into zones.

Zone 1 is the 4 corner squares.  Each of those has 2 adjacent squares

Zone 2 are all the other edge squares. Each of those has 3 adjacent squares

Zone 3 is all the squares in the middle. Each of those has 4 adjacent squares.

 

I am going to work those out seperately but I will have counted every pair of squares twcie so I have to halve  my answer.

 

So i get

 

((36/64)*(4/63)+(24/64)*(3/63)+(4/64)*(2/63))/2 = 0.0277777777777778

 

This is my best guess.  If you think it is incorrect than please state why you think so.

 Dec 2, 2019

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