What is the maximum number of kings that can be placed on an $8 \times 8$ chessboard without any of them attacking each other?

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In a $2 \times 2$ square, no more than one king can be placed. There are 16 non-overlapping $2 \times 2$ squares on a chessboard, so no more than 16 kings can be placed. Indeed, 16 kings can be placed if, for example, they are placed in the top-left corner of each square.

![](https://cdn.mathpix.com/cropped/2024_05_06_b3d98ec29b07c8345931g-17.jpg?height=483&width=552&top_left_y=770&top_left_x=753)

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