Here is a problem that has never yet been solved, nor has its
impossibility been demonstrated. Play the knight once to every square of
the chessboard in a complete tour, numbering the squares in the order
visited, so that when completed the square shall be "magic," adding up
to 260 in every column, every row, and each of the two long diagonals. I
shall give the best answer that I have been able to obtain, in which
there is a slight error in the diagonals alone. Can a perfect solution
be found? I am convinced that it cannot, but it is only a "pious
opinion."