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
With the Basic Knight's Tour, the starting square is
chosen, but the tour may end on any square. The Advanced Knight's Tour goes one
step further as you are also challenged to end on a specific square!
Sound impossible? Not if you follow the simple rules given here. Learn this
procedure and your friends will be truly astounded at your mental powers!
Try it yourself
Note: You should make sure that you fully understand the principles of the
Basic Knight's Tour, and have practiced the method
until you can complete the tour quickly and easily, before you attempt to learn
the advanced method described here.
Learning the Advanced Knight''s Tour
Start and End Squares
The procedure for completing the Advanced Knight's Tour is similar to the Basic
Tour, but requires some adjustments to the way in which moves are made from one
system to the next.
First, when selecting the start and end squares, you should realize that these
must be opposite colors or else the Knight's Tour is impossible. In other
words, if the start square is white, the end square must be black, and vice
versa.
Once valid start and end squares have been selected, you should note which systems they are in. There are various
possibilities, as shown below (the Knight is on the start square, the target on
the chosen end square).
If you don't understand these systems, they are described in the
Basic Knight's Tour.
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Opposite Shape |
Same Shape, Opposite Orientation |
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Same Shape and Orientation (Same System) |
Same System and Same Quadrant |
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How to Complete the Advanced Knight's Tour
Opposite Shape Systems
For example, the start square is in a square-shaped system and the end square is
in a diamond-shaped system (or vice versa).
This is the easiest of the various problems to solve.
First you should complete the first system as with the Basic Tour, but in the
final quadrant you must select your direction of movement so that you can enter
the opposite-shaped system that is NOT the system occupied by the end square For
example, if the end square is in the left-hand diamond system, you must enter the
right-hand diamond as the second system. Then complete the second and third
systems as normal, making sure that you can enter the final system withour
hitting the end square..
Completing the final system requires you to plan a route through the remaining
squares so that you can finish on the end square. Depending on where you enter
the final system, this may mean that you have to move from one quadrant to
another without having completed all its squares. There are no hard-and-fast
rules for this. You must learn to SEE the route. To do this, you will need to
practice!!!
Same Shape, Opposite Orientation Systems
For example, the start square may be in the left diamond system and the end
square in the right diamond system.
This one is a little trickier, but learning to solve it will teach you an
important principle.
First you should complete the first and second systems as usual, making sure that
you can enter the third system (which contains the target) on a vacant square.
Now you have to move out of the third system and into the next system as
soon as you safely can! Certainly you should move out before you complete the
first quadrant of this system..To ensure that you move out safely, you need to
check that the remaining squares in that quadrant allow you to move both IN
and OUT of the quadrant from adjacent quadrant(s) of the same system when you
return to it later. This
is vital, or else you will get trapped. Depending on the third system, and the
position in which you enteredl its first quadrant, you may be able to leave
three, two or only one of the squares in that quadrant. Practice will teach you
what is needed.
Once you have moved out of the third system, you should complete the new system
in the normal way, making sure that you are able to enter back into the system
containing the end square from your final move
Finally you need to plan your route through the remaining squares so that you
finish on the end square. Again you will need to practice the tours until you
learn to SEE these paths.
Same Shape, Same Orientation (Same System)
For example, both start and end squares are in the right square systems.
Here you must move out of the first system (which contains the target
square) as soon as you safely can! As in the previous case, you should move out
before you complete the first quadrant of this system, checking as you do so that the
remaining squares in that quadrant allow you to move both IN and OUT of the
quadrant from adjacent quadrant(s) of the same system when you return to it
later. If you don't do this,
you will get trapped. Depending on the third system, and the position occupied
by the start square, you may be able to leave three, two or only one of the
squares in the initial quadrant. Practice will teach you what is needed.
Having moved out from the first system, you complete the next three systems as
normal before re-entering the first system.
Finally you again need to plan your route through the remaining squares so that
you finish on the end square.
Same System and Same Quadrant
For example, both start and end squares are in the left diamond system and also
both in the lower right quadrant.
Solving this tour is basically identical to the previous case, except that you
just need to ensure that you can enter the final quadrant (which contains the
end square) and finish on the target.
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