The knight can visit each square on a chess board exactly once

August 3, 2011 | By Abraham | 34 comments

(via Chess.com)

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34 Comments

    1. galit says:

      wait a sec after its all done the knight can still move to a previous position so the title is false!

      1. Dave says:

        ????? The knight only goes to each square once. This is called the knight’s tour. I’ve never tried it but I plan to in the near future. I’ll put a coin on each square that the knight goes to so I’ll know where its been. This exercise is good for exercising your memory if you try to memorize the pattern in the animation (which is cool btw). Understanding the pattern of its movement in the animation is also important. Memorization & understanding r 2 of the most important factors in chess.

        1. Armen says:

          In normal chess, do you think memorization is as important as understanding? Because I think memorization should come naturally after understanding… But really, memorization make chess dull and boring, only one sided.

      2. Biffington says:

        The title doesn’t mean only once and no more, like the knight is then incapable of going to a square its already been to. He’s simply saying its possible to make the knight touch every square without having to repeat one.

          1. hugh janus says:

            Exactly once, and not twice.

            To paraphrase the title – It is possible for the knight to visit every square on the board once, and never visit the same square twice.

    1. stefan says:

      it doesnt matter. the point is that it does touch ever square. so it will eventually start on its own beginning square.

  1. Kiri says:

    Some of the designs are lovely, like a Celtic knot.

    Someday they’ll figure out how to put this ‘animation’ on a t-shirt and someone will be RICH!

  2. James says:

    I think it would be prettier if the Knight ended up on a square a Knight’s move away from the beginning square, to make the tour a loop (I’m pretty sure this is possible). Regardless, the animation is pretty cool.

  3. nstone says:

    Makes you wonder what “elegant” means, since every solution uses the same moves, each is equally efficient, and some may have elegance we just don’t see.

  4. Andrew says:

    The only problem with this solution is the starting point. A knight does not start in that square. In order to begin the kinght’s tour on that square, it would have to vist 2 squares twice: G8 and F6

    1. Aabir says:

      It goes to every square … which means you could start on any square … that includes the knight’s starting position ……

      1. Daniel says:

        This is actually not true, because the knight in this example is not a closed loop, i.e. the knight cannot move to his starting position from his ending position. In closed tours, you are correct: the knight can start on any square.

  5. slayerwulfe says:

    Most commentary was patterns and as a beginner I noticed that pattern recognition is more important than the status of individual pieces. The tour may be interesting but it has no practical application in the game. For anyone that explores patterns The circular patterns of a Knight starting on any and all of the sixteen squares of the center define strategy. Try paper boards a compass and a selection of colored pencils. Finish it by extending this pattern to the outer two rows and columns. For a player this is valuable resource material.

  6. Erol Sandover says:

    One might think that since the knight visits every square, any square can be the starting point for the whole tour. But that would only be guaranteed if the ending position for this tour could reach the starting position in one move, which it can’t. The fact that the animation covers all squares in 63 moves does show that the coverage is complete in the minimum number of moves.

  7. Mary says:

    And whoosh! All the chess enthusiasts came out of the woodwork like termites issuing from a rotted plank! More power to ya ;)

  8. Bill says:

    does anyone notice the starting point is not the same as if it were a real chess game. I don’t know if that was its purpose but in a game, you’re wrong

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