THE CROWDED CHESSBOARD.
(
Chessboard Problems)
The puzzle is to rearrange the fifty-one pieces on the chessboard so
that no queen shall attack another queen, no rook attack another rook,
no bishop attack another bishop, and no knight attack another knight. No
notice is to be taken of the intervention of pieces of another type from
that under consideration--that is, two queens will be considered to
attack one another although there may be, say, a rook, a bishop, and a
knight between them. And so with the rooks and bishops. It is not
difficult to dispose of each type of piece separately; the difficulty
comes in when you have to find room for all the arrangements on the
board simultaneously.
Answer:
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.
