It will be seen that only three queens have been removed from their
positions on the edge of the board, and that, as a consequence, eleven
squares (indicated by the black dots) are left unattacked by any queen.
I will hazard the statement that eight queens cannot be placed on the
chessboard so as to leave more than eleven squares unattacked. It is
true that we have no rigid proof of this yet, but I have entirely
convinced myself of the truth of the statement. There are at least five
different ways of arranging the queens so as to leave eleven squares
unattacked.
[Illustration]