Aladdin’s Conundrum

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The chess historian H. J. R. Murray wrote: ‘A Dresden manuscript of the end of the fourteenth century gives a half-tour without solution and sets as a wager game a tour over a board of 4 by 4 squares’ and: ‘The sixteenth century Persian manuscript on chess in the library of the Royal Asiatic Society makes some remarks on the tour, and promises to give tours on the whole board and on boards of 4 by 8 and 4 by 4 squares, which are lost owing to the fragmentary condition of the manuscript. The author boasts a little, for the tour on the 4 by 4 board is an impossibility.’

In A History of Chess (1913) Murray gives reasons for believing this Persian manuscript may be due to Ala’addin Tabrizi, the leading player at the court of Timur (1336 – 1405). A translation by Duncan Forbes (1860) is subtly different, referring to ‘one quarter of the board’ rather than a 4 by 4 board. The wording is critical, since a closed tour is possible on one particular non-rectangular quarter-board.

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I call this puzzle “Aladdin’s Conundrum”. Whether the author of the manuscript knew of this result we may never know. It makes a good story, appropriate to the name of Aladdin, but there is no firm evidence that this quarter-board tour was known before the Abbé Phillipe Jolivald, alias Paul de Hijo, gave the tour in his 1882 catalogue of all the possible 16-move knight circuits in this form of symmetry. He makes special note of it, though he does not give a diagram.

Partial Tours of the 4×4 Board

There are four half-tours, but no two can be combined to give a full tour since their inner ends are on the 1st or 4th files which have no connecting move. Each is composed of one ‘square’ and one ‘diamond’.

544e7420Four geometrically distinct three-quarter tours are also possible. These part-tours often appear as components in tours of larger boards.

ThreeQuarterTours

3 thoughts on “Aladdin’s Conundrum

  1. I have composed a symmetric Knights tour of 25,600 cells. It is an oblique binary symmetrical tour. I was just wondering if it is the worlds largest symmetrical closed tour. I compose Knights tours as a bit of a hobby. Although all tours are a challenge to complete, I progressed beyond squares and rectangles to composing oblique binary tours of very different shapes that fit together like jig-saw puzzles. To view some examples of my work you can log on to “Mayhematics” the home page of George P. Jelliss….click on Knights tour notes, and then click on “Oblique binary tours”. Mr. Jelliss has inserted 19 examples of my tours. I came across your site simply by interest and chance and just thought that people of likeminded interest may be interested in what I stated. I do not have my own website. Composing Knights tours are just a hobby to me…..they are without doubt nourishment to the neurons of brains of all ages. Kind regards, Michael J. Creighton

    1. The knights tours look great. Very artistic. Maybe you can show them at the next conference. I am sure many people would be interested in viewing the coloured prints.

      1. Hello John,
        I just received your email at 11:10.
        When and where is the next conference? Are these conferences always in the same place? Has anybody ever displayed Knights tours at these conferences before? I would appreciate it if you would let me know.
        Regards.
        Michael Creighton.

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