VIEW THE MOBILE VERSION of www.mathpuzzle.ca Informational Site Network Informational
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 Great Dispute Between The Friar And The Sompnour
CANTERBURY PUZZLES
The Game Of Bandy-ball
PUZZLING TIMES AT SOLVAMHALL CASTLE
A Juvenile Puzzle.
Unicursal and Route Problems
The Rook's Journey.
The Guarded Chessboard
The Magic Strips.
Magic Squares Problem.
The Nine Counters.
Money Puzzles
The Barrels Of Honey.
Measuring, Weight, and Packing Puzzles.
The Educated Frogs.
Moving Counter Problem
Mixing The Tea.
Measuring, Weight, and Packing Puzzles.
The Ploughman's Puzzle
CANTERBURY PUZZLES
Lady Isabel's Casket
THE MERRY MONKS OF RIDDLEWELL
A Puzzling Legacy.
Money Puzzles
The Banner Puzzle.
Patchwork Puzzles
Simple Division.
Money Puzzles
The Four Lions.
Chessboard Problems