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.
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’.