Knight’s Tours on the Half Chessboard (1)

FacebooktwitterFacebooktwitterby feather

History

Numerous manuscript copies of collections of chess problems survive that were written before 1500, when the rules of chess changed to replace the short-range fers and alfil of the mediæval game by the long-range queen and bishop of the modern game. Most of these include at least one knight’s tour problem, often on the half chessboard.

The earlier European collections from around 1250 are attributed to a compiler known as ‘Bonus Socius’ meaning Good Companion. One of these manuscripts, written around 1350, and now in a Library in Paris, is unusual in that the scribe of the manuscript is identified. He was Nicolas de Nicolai, a scholar from Picardy who studied and lectured at the Lombard universities in Italy.

As was the custom, he presents a knight’s tour problem in the form of an arrangement of the 32 chessmen in the upper half of a chessboard. The white knight in one corner is to capture the queens, bishops, knights, rooks, pawns and finally the kings. Try to solve this yourself.

HalftourPuzzle

The first half of the tour is determinate, but the sequence of capture of the remaining pawns can be varied, giving six solutions, shown below.

The first of these solutions is the same as that of a similar problem in an earlier Bonus Socius manuscript, written in Anglo-Norman around 1275, which is in the King’s Library of the British Museum, while the last is the knight’s tour given in various later collections whose compiler is known as ‘Civis Bononiae’ which is usually interpreted as Citizen of Bologna.

The Civis Bononiae tour is also in a much later manuscript that is the work of Paulo Guarini di Forli (Paulus Guarinus) who wrote it in 1512. The first printed tour is also the Civis Bononiae example. It occurs in the work: Sensuit Jeux Partis des Eschez printed in Paris around 1530 by Denis Janot. This shows the continuity between these collections.

The six solutions

HalftourSolutions

Leave a Reply

Your email address will not be published. Required fields are marked *