MONTMORT. 1.33 



Montmort himself had made some progi'ess in the work which 

 he here recommends; see Art. 137. It seems however that his 

 manuscripts were destroyed or totally dispersed ; see Montucla, 



Ilistoire des Mathematiques first edition, preface, page IX. 



229. The next letter is from Nicolas Bernoulli to Montmort ; 

 it occupies pages 401, 402. Nicolas Bernoulli announces that the 

 Ars Conjectandi has just been published, and says, II n'y aura 

 gueres rien de nouveau pour vous. He proposes five problems to 

 Montmort in return for those which Montmort had proposed to 

 him. He says that he had already proposed the first problem in 

 his last letter ; but as the problem does not occur before in the 

 correspondence, a letter must have been suppressed, or a portion 

 of it omitted. 



The third problem is as follows. A and B play with a com- 

 mon die, A deposits a crown, and B begins to play ; if B throws 

 an even number he takes the crown, if he throws an odd number 

 he deposits a crown. Then A throws, and takes a crown if he 

 throws an even number, but does not deposit a crown if he 

 throws an odd number. Then B throws again, and so on. Thus 

 each takes a crown if he throws an even number, but B alone 

 deposits a crown if he throws an odd number. The play is to 

 continue as long as there is any sum deposited. Determine the 

 advantage of A or B. 



The fourth problem is as follows. A promises to give to B 

 a crown if B with a common die throws six at the first throw, 

 two crowns if B throws six at the second throw, three crowns 

 if B throws six at the third throw ; and so on. 



The fifth problem generalises the fourth, A promises to give 

 B crowns in the progression 1, 2, 4, 8, 16, ... or 1, 3, 9, 27, ... or 

 1, 4, 9, 16, 25, ... or 1, 8, 27, 64, ... instead of in the progression 

 1, 2, 3, 4, 5, as in the fourth problem. 



230. The next letter is the last; it is from Montmort to 

 Nicolas Bernoulli, and it occupies pages 403—412. It enters 

 largely on the game of Her, With respect to the five problems 

 proposed to him, Montmort says that he has not tried the first 

 and second, that the foTU'th and fifth present no difticulty, but 

 that the third is much more difficult. He says that it took him 



