The first example of something unusual is this Reversible Magic Square. Its
is 264, but what makes this Magic Square different is that, if you turn it upside down, the
is still 264!
The two photographs to the right are of a solid silver version of this Reversible Magic Square. It was commissioned by Richard Stupple and designed and crafted by Rex Cooper in recognition of my services to the Northamptonshire Magicians' Club.
If each half of each domino is treated as a single digit in its own right, then the "Magic Total" is 13.
The tour is deemed to be "closed" if the knight returns to its starting square, or "open" if it ends up on a different square to the one on which it started.
Although the Knight’s Tour has no apparent link to magic squares, work was started on "magic" Knight’s Tours by Euler in the eighteenth century, and a "semi-magic" square was published by William Beverley, in "The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science", for August 1848.
If each move is numbered, starting at one and ending at 64, then the pattern formed after an "open" tour creates a "semi-magic" square that adds up to a "magic total" of 260:
Note that the two corner diagonals do not add up to 260. It is this fact that prevents it being a full magic square.
Full details may be found in the " Mathematical Magic Show" by Martin Gardner.
Also worth a look is Mario Velucchi's Ultimate Knight's Tour Page Of Links and Dan Thomasson's Knight's Tour pages.
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