The Knight's Tour 2


after Martin Gardner

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What is the longest possible route without self-crossings for the chess knight to travel on the 6x6 board shown in Figure 1?

To see what the route "without self-crossings" means, let's show any route of the knight by drawing on the board a broken line that will join the centers of the successive cells visited by the knight. The examples of such lines for a single move of the knight are shown in Figure 2.

Now for a 4x4 board such a route without self-crossing may be shown as that in the diagram on the right. This 5-move route is the longest possible for this small board; not unique, though.

There is a 16-move route for a 6x6 board. Try to find it.

After that try to improve this route adding to it one more move. This new 17-move route makes the longest possible tour of the chess knight without self-crossing for a 6x6 board. It's unique, and hard to find. Can you discover it?

To practice you may use the 6x6 board from our special
Print 'n' Play PDF Version and a chess knight (or a simple coin).

Last Updated: October 24, 2006
PDF Version (239 KB)

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