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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.

Source: https://www.amazon.com/dp/048684241X

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    $\begingroup$ Oh wow, you've written a puzzle book! Kudos! $\endgroup$ – hexomino Feb 27 at 16:05
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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.

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