27 Aug '06 00:26

If a rook and a bishop are placed on two randomly chosen squares of the board, what is the probability that either one of them will attack the other?

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27 Aug '06 18:212 edits

Isn't it the probability that two queens attack each other? That can't be too hard to figure out...*Originally posted by ThudanBlunder***If a rook and a bishop are placed on two randomly chosen squares of the board, what is the probability that either one of them will attack the other?**

...Edit: if you count placing them on the same square as "attacking each other" then it's

(64 + 64*14 + B)/(64*64)

where the B is the total number of squares a bishop can attack by placing it on all 64 squares of the chessboard. Starting from the middle four squares in the centre, and working outwards in concentric squares, we see

B = 4*13 + 12*11 + 20*9 +28*7 = 560

so the probability is 95/256. If you're not counting them being on the same square then take off the first 64 above to yield 91/256.- Joined
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