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BISHOPS IN CONVOCATION.

(Chessboard Problems)
[Illustration:
+---+---+---+---+---+---+---+---+
| B | B | B | B | B | B | B | B |
+---+---+---+---+---+---+---+---+
| | | | | | | | |
+---+---+---+---+---+---+---+---+
| | | | | | | | |
+---+---+---+---+---+---+---+---+
| | | | | | | | |
+---+---+---+---+---+---+---+---+
| | | | | | | | |
+---+---+---+---+---+---+---+---+
| | | | | | | | |
+---+---+---+---+---+---+---+---+
| | | | | | | | |
+---+---+---+---+---+---+---+---+
| | B | B | B | B | B | B | |
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]
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.


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