Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag

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.

\includegraphics{A1491_bild.eps}

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)

see also:


  automatically generated: 8/11/2017