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BISHOPS--UNGUARDED.

(Chessboard Problems)
Place as few bishops as possible on an ordinary chessboard so that every
square of the board shall be either occupied or attacked. It will be
seen that the rook has more scope than the bishop: for wherever you
place the former, it will always attack fourteen other squares; whereas
the latter will attack seven, nine, eleven, or thirteen squares,
according to the position of the diagonal on which it is placed. And it
is well here to state that when we speak of "diagonals" in connection
with the chessboard, we do not limit ourselves to the two long diagonals
from corner to corner, but include all the shorter lines that are
parallel to these. To prevent misunderstanding on future occasions, it
will be well for the reader to note carefully this fact.


Answer:

+...+...+...+...+...+...+...+...+
: ::::: ::::: ::::: :::::
+...+...+...+...+...+...+...+...+
::::: ::::: ::::: ::::: :
+...+...+...+...+...+...+...+...+
: ::::: ::::: ::::: :::::
+...+...+...+...+...+...+...+...+
::B:: B ::B:: B ::B:: B ::B:: B :
+...+...+...+...+...+...+...+...+
: ::::: ::::: ::::: :::::
+...+...+...+...+...+...+...+...+
::::: ::::: ::::: ::::: :
+...+...+...+...+...+...+...+...+
::::: ::::: ::::: ::::: :
+...+...+...+...+...+...+...+...+
: ::::: ::::: ::::: :::::
+...+...+...+...+...+...+...+...+
This cannot be done with fewer bishops than eight, and the simplest
solution is to place the bishops in line along the fourth or fifth row
of the board (see diagram). But it will be noticed that no bishop is
here guarded by another, so we consider that point in the next puzzle.










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