+----+----+----+----+----+----+----+----+
| 46 | 55 | 44 | 19 | 58 | 9 | 22 | 7 |
+----+----+----+----+----+----+----+----+
| 43 | 18 | 47 | 56 | 21 | 6 | 59 | 10 |
+----+----+----+----+----+----+----+----+
| 54 | 45 | 20 | 41 | 12 | 57 | 8 | 23 |
+----+----+----+----+----+----+----+----+
| 17 | 42 | 53 | 48 | 5 | 24 | 11 | 60 |
+----+----+----+----+----+----+----+----+
| 52 | 3 | 32 | 13 | 40 | 61 | 34 | 25 |
+----+----+----+----+----+----+----+----+
| 31 | 16 | 49 | 4 | 33 | 28 | 37 | 62 |
+----+----+----+----+----+----+----+----+
| 2 | 51 | 14 | 29 | 64 | 39 | 26 | 35 |
+----+----+----+----+----+----+----+----+
| 15 | 30 | 1 | 50 | 27 | 36 | 63 | 38 |
+----+----+----+----+----+----+----+----+
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.