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LI. Description of a Method of moving the Knight over every 
square of the Chess-hoard.^ without going twice over any one 
commencing at any given square, and eliding at any other 
given square of a different colour. By P. M. Roget, M.Z)., 
^Sec. R.S. 
[Illustrated by Plate T.] 
To the Editors of the Philosophical Magazine and Journal, 
Gentlemen, 
problem of carrying the knight, in a course of his 
^ own moves, over every square of the chess-board, with- 
out going twice over any square, has engaged the attention 
and exercised the ingenuity of mathematicians during the 
last hundred years''^'. Even the great Euler condescended to 
put forth a portion of his giant strength in grappling with 
the difficulties it presents, and bringing it within the grasp 
of his powerful analysis f. Vandermonde attempted to con- 
struct a general algebraic formula for its solution J. Others, 
confining their efforts to the attainment of mere practical 
results, have contented themselves with the search of parti- 
cular methods of resolving the problem in limited cases, and 
under the simplest conditions only ; such as that of being 
obliged to commence the journey of the knight from a given 
square ; one of the corner squares having usually been se- 
lected for that purpose§. The next step was the contrivance 
of methods fulfilling a further condition, namely, that the 
square at which the tour of the knight terminates shall be 
so situated as to be one move from the square from which it 
was begun. It is evident that whenever this has been ac- 
complished, we have obtained a recurring or circular course, 
which the knight might again traverse by continuous moves : 
so that such a course gives us the power of commencing with 
any given square whatsoever, and of traversing through the 
whole series of 64? squares, until the entire circuit is com- 
pleted. 
Various circuits of this kind have been devised, and de- 
scribed in different memoirs, which have, from time to time, 
been published |1 ; and the problem, under this form, has been 
* See Ozanam, Recrmtions MatMmatiques et Physiques^ nouvelle^editiony 
Paris, 1750 , tom. i. p. 260, where De Montmort, De Moivre, and De Mairan, 
are quoted as having treated this subject. 
t Memoires deV Ac adimie de Berlin for 1759, p. 310. 
+ In a paper entitled “ Remarques sur les Problemes de Situation^ in the 
Mhioires de V Acadmiie Royale des Sciences^ 1771, p. 566. 
§ This is the point at which the problem is left by Ozanam. 
11 See Journal of Science and the Arts, iii. 72. March, 1817 ; and also 
Edin. Phil. Journal, iv. 397, ix. 236. 
PhiL Mag, S. 3, Vol. 16. No. 103. Jpril 184fO. X 
