| | | | | | | | |
+---+---+---+---+---+---+---+---+
| | B | B | B | B | B | B | |
+---+---+---+---+---+---+---+---+

]

The greatest number of bishops that can be placed at the same time on
the chessboard, without any bishop attacking another, is fourteen. I
show, in diagram, the simplest way of doing this. In fact, on a square
chequered board of any number of squares the greatest number of bishops
that can be placed without attack is always two less than twice the
number of squares on the side. It is an interesting puzzle to discover
in just how many different ways the fourteen bishops may be so placed
without mutual attack. I shall give an exceedingly simple rule for
determining the number of ways for a square chequered board of any
number of squares.

300.--THE EIGHT QUEENS.

[Illustration:

+---+---+---+---+---+---+---+---+
| | | | ..Q | | | |
+---+---+---+...+---+---+---+---+
| | ..Q.. | | | | |
+---+...+---+---+---+---+---+---+
| Q.. | | | | | | |
+---+---+---+---+---+---+---+---+
| | | | | | | Q | |
+---+---+---+---+---+---+---+---+
| | Q | | | | | | |
+---+---+---+---+---+---+---+---+
| | | | | | | ..Q |
+---+---+---+---+---+---+...+---+
| | | | | ..Q.. | |
+---+---+---+---+...+---+---+---+
| | | | Q.. | | | |
+---+---+---+---+---+---+---+---+

]

The queen is by far the strongest piece on the chessboard. If you place
her on one of the four squares in the centre of the board, she attacks
no fewer than twenty-seven other squares; and if you try to hide her in
a corner, she still attacks twenty-one squares. Eight queens may be
placed on the board so that no queen attacks another, and it is an old
puzzle (first proposed by Nauck in 1850, and it has quite a little
literature of its own) to discover in just how many different ways this
may be done. I show one way in the diagram, and there are in all twelve
of these fundamentally different ways. These twelve produce ninety-two
ways if we regard reversals and reflections as different. The diagram is
in a way a symmetrical arrangement. If you turn the page upside down, it
will reproduce itself exactly; but if you look at it with one of the
other sides at the bottom, you get another way that is not identical.
Then if you reflect these two w