How many kings can be placed on an $8 \times 8$ chessboard without them putting each other in check?
Answer: 16. Indeed, we divide the chessboard into 16 blocks of $2 \times 2$: there is at most one king per block, so there are at most 16 kings. Conversely, it is sufficient to see that by placing a king in the top left corner of each block, it works.