On an 8 x 8 chessboard, place three white queens, two white knights, and one white rook so that every cell of the board is under attack by at least one piece not standing on it.
1 Answer
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I used integer linear programming (and, sorry, a computer):
\begin{matrix}&.&.&.&.&.&.&.&.\\&.&.&N&.&N&.&.&.\\&.&.&.&.&.&.&.&.\\&.&.&.&.&.&.&.&.\\&.&Q&.&Q&.&Q&.&.\\&.&.&.&.&.&.&.&.\\&.&.&.&.&.&.&.&R\\&.&.&.&.&.&.&.&.\\\end{matrix}
The solution is unique up to rotation and reflection.