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Random Chess Pieces Poser (Posted on 2016-08-29) Difficulty: 3 of 5
A queen, a rook and a bishop are randomly placed on distinct squares of an ordinary chessboard. Find the probability that:.
(i) The queen is under attack from either the bishop or the rook.
(ii) The bishop is neither under attack from the queen, nor under attack from the rook.

No Solution Yet Submitted by K Sengupta    
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Solution re(3): computer aided solution (corrected answer) Comment 6 of 6 |
(In reply to re(2): computer aided solution by Steve Herman)

On the other had (re by previous post), I did have a bug in my program. I had


If br <> qr Or bc <> bc Then

in order to avoid placing the bishop and queen on the same square. The "bc <> bc " should of course be "bc<>qc" (bishop's column not equal queen's column.

I looked for the bug when the probability of the queen and the rook being on the same row or column was not 14/63.

Now it comes out correctly. Out of all 249984 cases the following are the counts of rook on same row or column, bishop on same diagonal, both those coinciding, and the resulting sum and difference:

55552 34720 7840   82432

The final answer comes out to 23/72 for part i

and

1 - 47/93 = 46/93 for part ii

  Posted by Charlie on 2016-08-30 21:30:02
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