The Games and Puzzles Journal, #5+6 - Mayhematics

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.\9 THE GAMES AND PVZZLES JOURNAL
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.s\ Chessboord Mosaics
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$' The numberings from which the mosaics on page 64 were derived are these: A, natural
order; B, diagonal order; C and F, the two magic numberings of the same 'three-leaper
plus knight'tour given in Chessics 26, p119; D, the diagonally magicremperor'(knight plus
wazir) tour given on the same page; E, spiral (or spider?) order.
I 2 4
5 6 1 a
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8 3 Wq
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The numbering that results from rotating the first diagram is (i1 one of its arrangements)
the Durer rnali" square (diagram A')! Ttris was an unexpected discovery. This effect shows
the close relationship of this magic square to the natural order (see for example in Rouse
Ball's Mathematical Recreations, lith edn, p 199, where it is shown that by reversing the
sequen@enaturaloiderproducesamagicsquarethatisapermute
of Durerrs). tne pro6.r, of rotating the mosaic means that where before the rotation it
indicated a move x to y, now it indicates a move 17-y to x'
Rotation of the second diagram gives the numbering B"
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