[Illustration]
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 colour, while the queens occupy four of each colour and the bishops
7 of each colour, it follows that only 21 knights can be placed on the
same colour in this puzzle. More than 21 knights can be placed alone on
the board if we use both colours, 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.