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)?

Guest Dec 2, 2019

#1**+1 **

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.

Melody Dec 2, 2019