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

(via Chess.com)

(via Chess.com)

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Paul Huxleysays:It can be done loads of ways and many of them are pretty.

hobosays:I know, such a cool design.

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

Davesays:????? 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.

Armensays: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.

Roysays:Understanding is more important – period! But memorization of some key positions and concepts is necessary for practical play.

By the way, the knights tour is not really a chess problem – it’s a mathematical problem. It’s actually easier than it looks. The key is to keep to the edges where possible – that’s it!

http://www.ultimatechesscourse.com

http://www.ultimatechesscourse.com/blog

Biffingtonsays: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.

That guysays:It does say *exactly* once….

hugh janussays: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.

AnotherLaurasays:Maybe so, but that’d be a helluva game.

Eric Bourgaultsays:The knight doesn’t start on that square!

pusnasays:So true! I was thinking the same thing. :(

crojonsays:it does if a pawn promotes to it :P

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

Beet Saladsays:Nerd alert!!

Waltsays:Am I missing something? In the example above, the knight is visiting multiple squares more than once.

Kevin Ruizsays:Umm… nooo…. it does not visit any square more than once

Kirisays: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!

Jamessays: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.

slygensays:This is possible; it’s called a closed tour.

This here is an open tour because the knight isn’t threatening the initial square. I agree with you– a closed tour is much more elegant.

http://en.wikipedia.org/wiki/Knight%27s_tour

ricosays:63 movea 64 squares…nice

nstonesays: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.

Imransays:Go to the end of this article:http://en.wikipedia.org/wiki/George_Koltanowski

Andrewsays: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

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

Danielsays: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.

slayerwulfesays: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.

Richard Headsays:When the animation was in sync with my music, i nerdgasmed.

Erol Sandoversays: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.

Ssays:IF you guys are impressed by this let me show you my gif of the queen visiting all of the squares once.

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

Jarodsays:Did anyone else notice the starting position is wrong

Billsays: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