(related to Problem: The Crowded Chessboard)
Here is the solution. Only $8$ queens or $8$ rooks can be placed on the board without attack, while the greatest number of bishops is $14,$ and of knights $32.$ But as all these knights must be placed on squares of the same color, while the queens occupy four of each color and the bishops $7$ of each color, it follows that only $21$ knights can be placed on the same color in this puzzle. More than $21$ knights can be placed alone on the board if we use both colors, but I have not succeeded in placing more than $21$ on the "crowded chessboard." I believe the above solution contains the maximum number of pieces, but possibly some ingenious reader may succeed in getting in another knight.
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