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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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.