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How many Knight moves is it possible to execute on an empty chess board before the Knight lands on a square it has already landed on in its previous moves? The most I've ever been able to land on was 54 squares, usually 50-52.

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Meta discussion migrated here: meta.boardgames.stackexchange.com/questions/492/… –  tttppp Jun 20 '11 at 13:02
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up vote 9 down vote accepted

There is a famous puzzle called the Knight's Tour in which the aim is to visit every square exactly once. Since this has several solutions, the answer to your question is that it can visit all 64 squares.

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Questions are expected to relate to board games. (This one barely is.) They shouldn't be "too local," but chess is a global game. They are expected to have a reasonably objective answer acceptable to most people, which I believe this one does.If you want to know whether this, or any other question is on/off topic, the place to ask is on meta. –  Tom Au Jun 20 '11 at 13:53
    
Ok, thanks; I wasn't sure who to ask. Sorry for the newbie-ness! –  Daniel δ Jun 20 '11 at 14:19
    
Thanks for the link! The animated wikipedia solution is not intuitively obvious. –  Daniel δ Jun 20 '11 at 14:25
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