Michael Daniels

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Learn the Knight's Tour (Advanced)


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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.

Opposite ShapeSame Shape, Opposite Orientation
Opposite Shapes Same Shape, Opposite Orientation
Same Shape and Orientation (Same System)Same System and Same Quadrant
Same SystemSame System and Quadrant

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. 




  

Try your skill at the Advanced Knight's Tour Challenge.

Video Tutorial.for Advanced Knight's Tour

Learn how to solve the Basic Knight's Tour Challenge




 










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