Informational Site NetworkInformational Site Network
Privacy
 
Home Top Rated Puzzles Most Viewed Puzzles All Puzzle Questions Random Puzzle Question Search


CHEQUERED BOARD DIVISIONS.





(Chessboard Problems)
I recently asked myself the question: In how many different ways may a
chessboard be divided into two parts of the same size and shape by cuts
along the lines dividing the squares? The problem soon proved to be both
fascinating and bristling with difficulties. I present it in a
simplified form, taking a board of smaller dimensions.
[Illustration:
+---+------+---+ +---+---+------+ +---+---+------+
| | H | | | | | H | | | | H |
+---+------+---+ +---+---===---+ +---===------+
| | H | | | | H | | | H H H |
+---+------+---+ +---+------+---+ +------------+
| | H | | | | H | | | H H H |
+---+------+---+ +---===---+---+ +------===---+
| | H | | | H | | | | H | | |
+---+------+---+ +------+---+---+ +------+---+---+
+---+---+---+---+---+---+
| | | | | | |
+---+---+---+---+---+---+
| | | | | | |
+---+---+---+---+---+---+
| | | | | | |
+---+---+---+---+---+---+
| | | | | | |
+---+---+---+---+---+---+
| | | | | | |
+---+---+---+---+---+---+
| | | | | | |
+---+---+---+---+---+---+
+---+------+---+ +---+---+------+ +---+---+------+
| | H | | | | | H | | | | H |
+---===---+---+ +---======---+ +---+---===---+
| H | | | | H | | | | | H | |
+---======---+ +---======---+ +---+------+---+
| | | H | | | | H | | | H | |
+---+---===---+ +---======---+ +---===---+---+
| | H | | | H | | | | H | | |
+---+------+---+ +------+---+---+ +------+---+---+
]
It is obvious that a board of four squares can only be so divided in one
way--by a straight cut down the centre--because we shall not count
reversals and reflections as different. In the case of a board of
sixteen squares--four by four--there are just six different ways. I have
given all these in the diagram, and the reader will not find any others.
Now, take the larger board of thirty-six squares, and try to discover in
how many ways it may be cut into two parts of the same size and shape.


Read Answer





Next: LIONS AND CROWNS.




Add to Informational Site Network
Report
Privacy
ADD TO EBOOK




Random Questions

The Village Cricket Match.
Problems Concerning Games.
"strand" Patience.
Problems Concerning Games.
The Knight-guards.
The Guarded Chessboard
The Thirty-three Pearls.
Money Puzzles
New Measuring Puzzle.
Measuring, Weight, and Packing Puzzles.
The Forty-nine Counters.
Chessboard Problems
The Broken Chessboard
MISCELLANEOUS PUZZLES
The Forsaken King.
The Guarded Chessboard
Mrs. Hobson's Hearthrug.
Various Dissection Puzzles
The Puzzle Of The Canon's Yeoman
CANTERBURY PUZZLES
A Family Party.
Money Puzzles
The Motor-garage Puzzle.
Moving Counter Problem
The Sculptor's Problem.
Money Puzzles
A Bank Holiday Puzzle.
Unicursal and Route Problems
The Keg Of Wine.
Measuring, Weight, and Packing Puzzles.