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        riddles >> medium >> Neighbors 
        
(Message started by: codpro880 on Feb 26th, 2009, 11:47am)
Title: Neighbors
Post by codpro880 on Feb 26th, 2009, 11:47am
If three squares are chosen randomly from an 8x8 chessboard, what is the probability that no pair of squares share an edge?

*Note* I don't have the answer
Title: Re: Neighbors
Post by rmsgrey on Mar 2nd, 2009, 1:45pm
There's an easy answer for a 64 square torus - 59/64*54/64 (if you can choose the same square more than once) or 59/63*55/62 (if you have to choose different ones)

The edges are going to make it trickier to calculate for an actual chessboard...
Title: Re: Neighbors
Post by Eigenray on Mar 2nd, 2009, 9:41pm
For a 2n x 2n board, there are
2 [ 2*(2(m-2)+1) + 4(n-1)*(3(m-3)+3) + 2(n-1)2*(4(m-4)+6) ]
ways that don't work, where m = 2n2.  Hint: [hide]Pick a black square first, then two white ones[/hide].

The formula for an arbitrary rectangle is left to the reader.


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