1. In how many ways can two queens, two rooks, one white bishop, one black bishop, and a knight be placed on a standard $8 \times 8$ 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.
2. Can you attack every position on the board with fewer than seven pieces?

Solution

1. Two ways as follow:

Improved chessboard images via this website using Creative Commons.

1. I have an example of 6 queens attacking every position on a chess board (pardon my bad ascii gfx):
: : : : : : Q :
: Q : : : : : :
: : : : : : : :
: : Q : : : : :
: : : : : Q : :
: : : Q : : : :
: : : : : : : :
: : : : Q : : :

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