DE MOIVRE. 139 



Counter out of tlie heap; if 14, ^ shall take out one; and he shall be 

 reputed the winner who shall soonest get 1 2 Counters. 



This is a very simple problem. De Moivre seems quite un- 

 necessarily to have imagined that it could be confounded with that 

 which immediately preceded it ; for at the end of the ninth pro- 

 blem he says, 



Maxime cavendum est ne Prohlemata propter speciem aliquam 

 affinitatis inter se confundantur. Problema sequens videtur affine 

 superiori. 



After enunciating his ninth problem he says, 



Problema istud a superiore in hoc diifert, quod 23 ad pluriraum 

 tesserarum jactibus, ludus necessano finietur ; cum Indus ex lege supe- 

 rioris problematis, posset in aeternum continuari, propter reciproca- 

 tionem lucri et jacturse se invicem perpetuo destruentium. 



247. The eleventh and twelfth problems consist of the second 

 of those proposed for solution by Huygens, taken in two mean- 

 ings ; they form Problems X. and XI. of the Doctrine of Chances. 

 The meanings given by De Moivre to the enunciation coincide 

 with the first and second of the three considered by James Ber- 

 noulli ; see Arts. 35 and 199. 



248. The thirteenth problem is the first of those proposed fur 

 solution by Huygens ; the fourteenth problem is the fourth of the 

 same set : see Art. 35. These problems are very simple and are 

 not repeated in the Doctrine of Chances. In solving the fourth of 

 the set De Moivre took the meaning to be that A is to draw three 

 white balls at least. Montmort had taken the meaning to be that 

 A is to draw exactly three white balls. John Bernoulli in his 

 letter to Montmort took the meaning to be that A is to draw three 

 white balls at least. James Bernoulli had considered both mean- 

 ings. See Art. 199. 



249. The fifteenth problem is that which we have called 

 Waldegrave's problem; see Art. 211. De Moivre here discusses 

 the problem for the case of three players : this discussion is re- 

 peated, and extended to the case of four players, in the Doctrine of 

 Chances, pages 132 — 159. De Moivre was the first in publishing a 

 solution of the problem. 



