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

Slow Cricket.
Problems Concerning Games.
The Dissected Triangle.
Various Dissection Puzzles
Crossing The Moat
THE STRANGE ESCAPE OF THE KING'S JESTER
An Episcopal Visitation.
The Guarded Chessboard
The Honeycomb Puzzle.
Unicursal and Route Problems
A Tennis Tournament.
Combination and Group Problems
Papa's Puzzle.
Patchwork Puzzles
The Parson's Puzzle
CANTERBURY PUZZLES
Making A Flag
MISCELLANEOUS PUZZLES
Mr. Gubbins In A Fog.
Money Puzzles
Plato And The Nines
MISCELLANEOUS PUZZLES
The Bag Of Nuts.
Money Puzzles
The Dovetailed Block.
Unclassified Problems.
The Seven Pigs.
Various Dissection Puzzles
The Dutchmen's Wives.
Money Puzzles