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The Knight's Tour

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Of the many tricks and patterns one can find on a chessboard, perhaps none are more famous than the knight’s tour. Performing a knight’s tour may look difficult at first glance – and your friends won’t be able to do it if they aren’t familiar with how the pattern works – but it’s actually a very learnable exercise that’s also a useful way to help your chess vision.

What is a Knight’s Tour?

A knight’s tour is any sequence of moves in which a knight visits every single square on the board once, without landing on any square twice. A knight’s tour can start on any square; the only restriction is that all knight moves are legal, and that no square is visited more than once.

This makes the knight’s tour a very mathematical problem, as it is just as much about pattern recognition as having any particular chess skill. This has made the knight’s tour a popular problem in computer science classes, as computers (properly programmed) can quickly find many of the more than 26 trillion possible solutions.

Of course, the knight’s tour is perfectly within human understanding as well. The knight’s tour was known to shatranj players as early as the 9th century AD, and has been of interest to mathematicians since at least the early 1800s.

Solving the Knight’s Tour

With a nearly limitless number of ways to solve the knight’s tour, it may seem like almost any sequence of moves would work. However, it turns out that the task is somewhat more difficult than the numbers make it sound, as knights can easily get trapped in positions where no unused squares are remaining late in the exercise.

There are many patterns one can use to solve the knight’s tour, including simply memorizing one of the many patterns found online (this is especially useful if you can memorize a closed pattern, in which the path is a circular closed loop, and can thus begin from any point on the board). However, a simple method that will usually steer you on the right path is Warnsdorff’s rule.

Warnsdorff’s rule says that when attempting a knight’s tour, we should always move the knight to the square with the fewest possible moves remaining. While this seems counterintuitive, it allows us to immediately use squares that may become difficult to get to (or from) later in the tour. Simply keep this up throughout the entire tour; towards the end, a clear pattern should emerge for the last few squares in order for you to complete the tour!

Benefits of the Knight’s Tour

The knight’s tour is mainly done for fun, and using the techniques above, you can solve it without any chess knowledge whatsoever (as long as you know how the knight moves). But beginners can also use the knight’s tour to help them visualize how knights move around the board. The knight is often a tricky and dangerous piece for beginners to deal with, as its unusual jumping pattern makes it more difficult to anticipate where it may attack two or three moves down the line. By playing around with knight visualization exercises like the knight’s tour, new players will find they’re more confident in playing with (and against) knights.

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