Etudes sur le probleme de la marche du cavalier au jeu des echecs, et solution du probleme des huit dame

Author: Cretaine, A

Publisher: A Cretaine, Libraire

Location: Paris

Year: 1865



11+42+[19 plates]+[1 blank]+[6 plates (2 folding)] pages with tables and diagrams. Octavo (9" x 5 1/2") bound in wrappers with original spine and covers tipped on. (Bibliotheca Van der Linde-Niemeijeriana: 4085) First edition.

A knight's tour is 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 (so that it could tour the board again immediately, following the same path), the tour is closed, otherwise it is open. The earliest known reference to the knight's tour problem dates back to the 9th century AD. In Rudraṭa's Kavyalankara, a Sanskrit work on Poetics, the pattern of a knight's tour on a half-board has been presented as an elaborate poetic figure ("citra-alaṅkāra") called the "turagapadabandha" or 'arrangement in the steps of a horse.' The same verse in four lines of eight syllables each can be read from left to right or by following the path of the knight on tour. Since the Indic writing systems used for Sanskrit are syllabic, each syllable can be thought of as representing a square on a chess board. One of the first mathematicians to investigate the knight's tour was Leonhard Euler. The first procedure for completing the Knight's Tour was Warnsdorf's rule, first described in 1823 by H. C. von Warnsdorf.

The purpose of the eight queens' problem is to place eight queens of a chess game on an 8 x 8 chess board without the queens being able to threaten each other in accordance with the chess rules (The color of the parts being ignored). Therefore, two queens should never share the same row, column, or diagonal. This problem belongs to the domain of mathematical problems and not to that of the chess composition. For years, many mathematicians , including Gauss, have worked on this problem, which is a particular case of the generalized problem of n- queens, posited in 1850 by Franz Nauck, and which is to place n queens "free" on a chessboard Of n x n cells. In 1874 S. Gunther proposed a method for finding solutions by employing determinants , and JWL Glaisher refined this approach.


Recased with original publisher's wrappers tipped on to new boards, half title loose else a very good copy.