The Knight Tour is a pattern of moves by a Knight
on any grid. He visits every square once and once only and completes the journey in the same number of moves as there are squares on the board.
We will deal with the 8x8 grid as that is the regulation chessboard, this tour to be completed in 64 moves. A closed tour is when the final position is a Knight's move away from the first position. All other tours are known as open tours.
There are an infinite number of solutions but they are difficult to find as you will see. There are also magic tours and semi-magic tours. These get their name through the patterns they take.
Knight Tour: Closed
The earliest references are from the 9th century AD. The pattern of a Knight's path on a half-board was created by Indian poet Rudrata.
Not surprisingly, it was originally difficult to work out correct patterns for the tour simply by trial and error. There are literally billions of possible paths the Knight could take across the board so mathematicians were needed to make the breakthrough.
Leonhard Euler (1707-1783) devised a method for plotting a path in 1759. Others like Warnsdorff also contributed significant work on the Knight's Tour riddle.
Knight Tour Solution
Having heard a little bit about this you may feel it's time to give it a try. There are a number of good places on the web to do so. Might I suggest for instance The Knight's Tour
to get you started.
These links will open in a new tab. The diagram shows one of virtually countless solutions. This is something that has sparked a wide interest and there is plenty of related material out there.
I would like to point you to the definitive directory on the Knight's Tour
The Knight's Tour is an intriguing subject with extensive work invested over the centuries. It is essentially a mathematical problem that takes some solving without the aid of sophisticated algorithms and plenty of time.
You may find it easier to study the solutions and let others worry about the complicated calculations. Let's face it, trying to work it out on the board is more fun than struggling with the calculator. That is at least until you start pulling your hair out.
Eventually you may feel that you can do with a break from the Knight and certainly the move should be burned into your mind by now. For a change of scenery you can now turn to the Bishop