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Knight's Tour
This challenge takes place on a chessboard, using only a knight.
The knight is only allowed to move in the same way it does in
chess - either two squares horizontally and one vertically, or
two squares vertically and one horizontally, resulting in an
L-shaped move, The X's in the diagram below denote all the current
squares to which the knight can travel from the current position.
Note that the knight can move over already occupied squares,
and that each time the knight moves, it will land on the opposite
color square of the one it previously occupied.
The challenge itself is to move the knight, starting at any given square, about the board so that it visits each square only once, and visits EVERY square on the board. To get an idea of just how challenging this is, try it here (use level 1). Magicians have done it by memorizing whole lists of 64 steps around the board (a good mental feat in and of itself!). Mathematicians have done it by breaking the board down into series of matrix math equations. Computer programmers have found that an efficient way to solve it is to allow the knight to backtrack when he gets trapped. Is it then possible to solve this puzzle with no backtracking from any square by only relying on your mind? Not only is it possible, but it's surprisingly simple. Magicians are looking for the quickest path to the flashiest show. Mathematicians and computer programmers are trying to break it down into numbers. The method I'll teach requires you understand a few simple patterns that will greatly simplify the problem. First, I'll teach you a system for solving the puzzle starting from any square on the board. Next, if you desire to continue, I'll show you how to modify this system to allow you to solve this puzzle when someone else chooses both the starting AND ending squares! By the way, you won't often see magicians, mathematicians or computer programmers tackle this latter version of the challenge, as this added restriction makes it much too difficult by their methods. You'll be able to handle it without worry, though. If you're ready to begin, click here: Learn the knight's tour |










