THE FOUR LIONS.
(
Chessboard Problems)
The puzzle is to find in how many different ways the four lions may be
placed so that there shall never be more than one lion in any row or
column. Mere reversals and reflections will not count as different.
Thus, regarding the example given, if we place the lions in the other
diagonal, it will be considered the same arrangement. For if you hold
the second arrangement in front of a mirror or give it a quarter turn,
you merely get the first arrangement. It is a simple little puzzle, but
requires a certain amount of careful consideration.
[Illustration
+---+---+---+---+
| L | | | |
+---+---+---+---+
| | L | | |
+---+---+---+---+
| | | L | |
+---+---+---+---+
| | | | L |
+---+---+---+---+
]
Answer:
There are only seven different ways under the conditions. They are as
follows: 1 2 3 4, 1 2 4 3, 1 3 2 4, 1 3 4 2, 1 4 3 2, 2 1 4 3, 2 4 1 3.
Taking the last example, this notation means that we place a lion in the
second square of first row, fourth square of second row, first square of
third row, and third square of fourth row. The first example is, of
course, the one we gave when setting the puzzle.
