(related to Problem: The Magic Knight's Tour)
Here each successive number (in numerical order) is a knight's move from the preceding number, and as $64$ is a knight's move from $1,$ the tour is "re-entrant." All the columns and rows add up $260.$ Unfortunately, it is not a perfect magic square, because the diagonals are incorrect, one adding up $264$ and the other $256$ — requiring only the transfer of $4$ from one diagonal to the other. I think this is the best result that has ever been obtained (either re-entrant or not), and nobody can yet say whether a perfect solution is possible or impossible.
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