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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). |
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