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Topic: Neighbors (Read 473 times) |
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codpro880
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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
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rmsgrey
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Re: Neighbors
« Reply #1 on: Mar 2nd, 2009, 1:45pm » |
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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...
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Eigenray
wu::riddles Moderator
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Re: Neighbors
« Reply #2 on: Mar 2nd, 2009, 9:41pm » |
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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: Pick a black square first, then two white ones.
The formula for an arbitrary rectangle is left to the reader.
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| « Last Edit: Mar 2nd, 2009, 9:43pm by Eigenray » |
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