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a move between two squares is counted as one regardless of the direction. basically, we want to prove that a knight started from any position in a 8*8 chessboard can go to all the possible places in the chessboard. we just want to show that a hamiltonian path exist for such a problem

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    $\begingroup$ Google this, its called the knights tour, it is a well known problem $\endgroup$ – siegehalver Feb 22 at 20:32
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    $\begingroup$ Here is a solution. $\endgroup$ – J.G. Feb 22 at 20:35
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    $\begingroup$ Your title asks about taking every move exactly once. The body of your question asks about a Hamiltonian path - visiting every location exactly once. Those are different. Which question did you intend? $\endgroup$ – jmerry Feb 22 at 20:43

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