JF Ptak Science Books Post 2243

The idea behind this extraordinary image below is the construction of an 8x8 magic square capable of describing BOTH the Knight's tour (" a sequence of moves of a knight on a chessboard such that the knight visits every square only once...if the knight ends on a square that is one knight's move from the beginning square) WITH the resulting moves forming a series of magic squares. It is the product of a Kiwi engineer named Sturmer, and appeared in the *Scientific American Supplement* for 1888.

Eric Weinstein says in his article "There Are No Magic Knight's Tours on the Chessboard" on Wolfram's Mathworld site says, well, such a thing is not possible. "After 61.40 days of computation, a 150-year-old unsolved problem has finally been answered. The problem in question concerns the existence of a path that could be traversed by a knight on an empty numbered 8 x 8 chessboard."

Weinstein is concise: "Not surprisingly, a knight's tour is called a magic tour if the resulting arrangement of numbers forms a magic square, and a semimagic tour if the resulting arrangement of numbers is a semimagic square. It has long been known that magic knight's tours are not possible on *n* x *n* boards for* n* odd. It was also known that such tours are possible for all boards of size 4*k* x 4*k* for *k* > 2. However, while a number of semimagic knight's tours were known on the usual 8 x 8 chessboard, including those illustrated above, it was *not* known if any fully magic tours existed on the 8 x 8 board."

Source: http://mathworld.wolfram.com/news/2003-08-06/magictours/

And this, from the *British Chess Maagzine,* 1888, page 278:

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