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Attack Assay (Posted on 2014-05-14) Difficulty: 3 of 5
A rook and a bishop of a standard chess set and having different colors are randomly placed on a standard chessboard.

Determine the probability that one is attacking the other.

No Solution Yet Submitted by K Sengupta    
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Solution queens solution Comment 3 of 3 |
The problem is equivalent to two mutually attacking queens of different color.  So for each space the first queen is on we must find the number of squares it attacks.

A queen on any of the 28 the outer edge spaces (including corners) attacks 7 ranks, 7 files and 7 diagonals for a total of  21.
21*28 = 588
A queen on any of the 20 squares that are one square from the edge can attack an additional 2 diagonals.
23*20 = 460
A queen on any of the 12 squares that are two squares from the edge can attack two more diagonal squares.
25*12 = 300
Finally a queen on one of the 4 central squares can attack two more diagonals squares
27*4 = 108

For a total of 1456 attacking combinations.

There are 63*64=4032 ways of placing two queens of different color.

1456/4032 = 13/36 is the requested probability.

  Posted by Jer on 2014-05-14 13:19:31
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