A queen on an English chessboard is able to attack in the same row, column and diagonal. The probability that 2 randomly placed queens on a 8 by 8 chessboard will be able to attack each other can be expressed as ab, where a and b are co-prime integers. What is a+b? Clarification: The 2 queens will not be placed on the same square.
mrcausality2012-09-17T07:39:49Z
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You must mean "a/b", otherwise we aren't talking about probabilities. If we call P(n) the probability on an nxn board, I get the general formula for even n:
This was obtained by decomposing the probability into a sum over conditional probabilities where the 1st queen is placed on the outer edge square (i.e. anywhere on the perimeter), the first inner edge square, and so on.