The Knight's Tour
The Knight's Tour is a famous chess puzzle. The object is to move the Knight
around the board using only valid L-shaped Knight moves, so that each square is
visited exactly once
Solving the puzzle may seem impossible (Try it yourself)
but by following a few simple rules you will soon learn how to complete the tour
speedily and with ease. Your friends will be amazed at your mental powers!
Once you have mastered the basic tour, you can then learn how to solve the
Advanced Challenge in which both starting and end squares are chosen at the
beginning.
Learning the Basic Knight's Tour
Quadrants and Systems
First you have to familiarise yourself with the Four Quadrants of the
chess board, and with the Four Systems of moves.
The Four Quadrants are shown here using different colors for each
quadrant.
|
The Four Quadrants |
 |
The Four Systems are sequences of moves that form a pattern. The moves in
each system can be considered separately from those of the other systems. This
makes completing the Knight's Tour simply a matter of completing the moves in
one system before moving on to the next.
There are two diamond-shaped systems and two
square-shaped systems. The shape is repeated in each quadrant,
collectively forming all the moves for that particular system.
For each shape (diamond or square) there are two orientations, a left-hand
shape and a right-hand shape.
The left-hand diamonds point up to the left, whereas the right-hand diamonds
point up to the right.
The left-hand square has the topmost square on the left side of the quadrant, whereas the right-hand square has the topmost square on
the right side of the quadrant.
The Four Systems are shown in the following illustrations.
|
Left-Hand Diamond System |
Right-Hand Diamond System |
 |
 |
|
|
|
|
Left-Hand Square System |
Right-Hand Square System |
 |
 |
How to Complete the Basic Knight's Tour
Once you understand the quadrants and systems, completing the Knight's Tour is
child's play.
First, you simply note which system the Knight occupies on its opening move. Then
move the Knight around the other three squares of this system within the same
quadrant before moving on to do the same in the next quadrant.
All you have to worry about is that the final move in each quadrant allows you to
move on to the same system in the another quadrant. To do this, you need
to decide whether to move clockwise or anti-clockwise around each quadrant so
that you don't get trapped on your final move. As long as you make sure that
your final move in each quadrant is as near the center of the board as possible,
you will be OK.
When you move into the final quadrant of the system, you must choose your
direction of movement carefully to ensure that the final move in that quadrant
allows you to move on to another system. You then simply repeat this procedure
through the second system, before moving on to the third and finally the fourth
system, until you have fully completed the Knight's Tour!
You should note that the four systems are completed in a particular sequence. A
diamond-shaped system must be followed by one of the square-shaped systems, and
vice versa.
|
