CH. I] ARITHMETICAL RECREATIONS 3 



issued in 1720, 1735, 1741, 1778, and 1790; doubtless these 

 references are correct, but the following editions, all of which 

 I have seen, are the only ones of which I have any knowledge. 

 In 1696 an edition was issued at Amsterdam. In 1723 — six 

 years after the death of Ozanam — one was issued in three 

 volumes, with a supplementary fourth volume, containing, 

 among other things, an appendix on puzzles. Fresh editions 

 were issued in 1741, 1750 (the second volume of which bears 

 the date 1749), 1770, and 1790. The edition of 1750 is said to 

 have been corrected by Montucla on condition that his name 

 should not be associated with it ; but the edition of 1790 is 

 the earliest one in which reference is made to these corrections, 

 though the editor is referred to only as Monsieur M***. 

 Montucla expunged most of what was actually incorrect in the 

 older editions, and added several historical notes, but un- 

 fortunately his scruples prevented him from striking out the 

 accounts of numerous trivial experiments and truisms which 

 overload the work. An English translation of the original 

 edition appeared in 1708, and I believe ran through four 

 editions, the last of them being published in Dublin in 1790. 

 Montucla's revision of 1790 was translated by C. Hutton, and 

 editions of this were issued in 1803, in 1814, and (in one 

 volume) in 1840 : my references are to the editions of 1803 

 and 1840. 



I proceed to enumerate some of the typical elementary 

 questions connected with numbers which for nearly three 

 centuries have formed a large part of most compilations of 

 mathematical amusements. They are given here largely for 

 their historical — not for their arithmetical — interest ; and per- 

 haps a mathematician may well omit this chapter. 



Many of these questions are of the nature of tricks or puzzles, 

 and I follow the usual course and present them in that form. 

 I may note however that most of them are not worth proposing, 

 even as tricks, unless either the method employed is disguised 

 or the result arrived at is different from that expected ; but, as 

 I am not writing on conjuring, I refrain from alluding to the 



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