THE EIGHT STARS.
(
Chessboard Problems)
[Illustration:
+---+---+---+---+---+---+---+---+
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+---+---+---+---+---+---+---+---+
| |///| | | | |///| |
+---+---+---+---+---+---+---+---+
| | |///| | |///| | |
+---+---+---+---+---+---+---+---+
| | | |///|///| | | |
+---+---+---+---+---+---+---+---+
| | | |///|///| | | |
+---+---+---+---+---+---+---+---+
| | |///| | |///| | |
+---+---+---+---+---+---+---+---+
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+---+---+---+---+---+---+---+---+
|///| | | | | | |///|
+---+---+---+---+---+---+---+---+
]
The puzzle in this case is to place eight stars in the diagram so that
no star shall be in line with another star horizontally, vertically, or
diagonally. One star is already placed, and that must not be moved, so
there are only seven for the reader now to place. But you must not place
a star on any one of the shaded squares. There is only one way of
solving this little puzzle.
Answer:
The solution of this puzzle is shown in the first diagram. It is the
only possible solution within the conditions stated. But if one of the
eight stars had not already been placed as shown, there would then have
been eight ways of arranging the stars according to this scheme, if we
count reversals and reflections as different. If you turn this page
round so that each side is in turn at the bottom, you will get the four
reversals; and if you reflect each of these in a mirror, you will get
the four reflections. These are, therefore, merely eight aspects of one
"fundamental solution." But without that first star being so placed,
there is another fundamental solution, as shown in the second diagram.
But this arrangement being in a way symmetrical, only produces four
different aspects by reversal and reflection.
