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Mathematics-Online problems:

Interactive Problem 23: Rooks on a Chessboard

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
On a chessboard $ w$ white and $ b$ black rooks are to be placed in such a way that rooks of different color cannot capture each other.

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How many different possibilities exist for the cases with 1 or 2 rooks of each color as they may occur in a game?


Answer:

$ (w,b) = (1,1)$: possibilities
$ (w,b) = (2,1)$: possibilities
$ (w,b) = (2,2)$: possibilities

Hint : A rook can move only in straight line. This means that on each vertical and horizontal line only rooks of the same color may be placed.


   

(From: Day of Mathematics 1998)
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  automatically generated: 8/11/2017