CHAPTER I. 

 ARITHMETICAL RECREATIONS. 



I commence by describing some arithmetical recreations. 

 The interest excited by statements of the relations between 

 numbers of certain forms has been often remarked, and the 

 majority of works on mathematical recreations include several 

 such problems, which, though obvious to any one acquainted 

 with the elements of algebra, have to many who are ignorant 

 of that subject the same kind of charm that mathematicians 

 find in the more recondite propositions of higher arithmetic. 

 I devote the bulk of this chapter to these elementary 

 problems. 



Before entering on the subject, I may add that a large 

 proportion of the elementary questions mentioned here are 

 taken from one of two sources. The first of these is the classical 

 Problemes plaisans et Electables, by Claude Gaspar Bachet, 

 sieur de Meziriac, of which the first edition was published in 

 1612 and the second in 1624: it is to the edition of 1624 that 

 the references hereafter given apply. Several of Bachet's 

 problems are taken from the writings of Alcuin, Pacioli di 

 Burgo, Tartaglia, and Cardan, and possibly some of them are 

 of oriental origin, but I have made no attempt to add such 

 references. The other source to which I alluded above is 

 Ozanam's Rdcreations mathematiques et physiques. The greater 

 portion of the original edition, published in two volumes at 

 Paris in 1694, was a compilation from the works of Bachet, 

 Mydorge, and Leurechon : this part is excellent, but the same 

 cannot be said of the additions due to Ozanam. In the 

 Biographie Universelle allusion is made to subsequent editions 



