Knight's Tour Magic Square

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In the 18th century, mathematician Leonhard Euler constructed a magic square (actually a semi-magic square) that represented a knight's tour on a chessboard:

 1 48 31 50 33 16 63 18 30 51 46 3 62 19 14 13 47 2 49 32 15 34 17 64 52 29 4 45 20 61 36 13 5 44 25 56 9 40 21 60 28 53 8 41 24 57 12 37 43 6 55 26 39 10 59 22 54 27 42 7 58 23 38 11

Each horizontal and vertical row sums to 260, the magic constant. The top and bottom half of each row and column sum to 130. Most interesting, however, is that, if the magic square were superimposed on a chessboard, a knight in the game of chess could start on the square marked "1," move from there to "2," from there to "3," and land on all 64 boxes in numerical order, a traversal known as a knight's tour.

As mentioned above, this square is only a semi-magic square; the diagonals do not sum to 260. Is there an 8×8 knight's tour magic square where the diagonals do sum to the magic constant? This remained an open question until 2003, when it was discovered that no such tour exists.

You may also be interested in Benjamin Franklin's Magic Square.

Sources used (see bibliography page for titles corresponding to numbers): 45.