Problem of the Week

This problem was suggested by Sudipta Das.  Many thanks!

In how many ways can two queens, two rooks, one white bishop, one black bishop, and a knight be placed on a standard 8 ´ 8 chessboard so that every position on the board is under attack by at least one piece?  (Note: The color of a bishop refers to the color of the square on which it sits, not to the color of the piece.)   Can you attack every position on the board with fewer than seven pieces?

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ã2002 Alberto L. Delgado