1 I MONTMORT. 



190. These numerical results were accepted by the disjDutants. 

 We may sum them up thus. The question is whether Paul should 

 retain a certain card, and whether Peter should retain a certain 

 card. If Paul knows his adversary's rule, he should adopt the con- 

 trary, namely retaining when his adversary changes, and changing 

 when his adversary retains. If Peter knows his adversary's rule he 

 should adopt the same, namely, retaining when his adversary re- 

 tains and changing when his adversary changes. 



Now Nicolas Bernoulli asserted that Paul should change, and 

 therefore of course that Peter should. The objection to this is 

 briefly put thus by Montmort, page 405, 



En un mot, Monsieur, si je SQai que vous etes le conseil de Pierre, 

 il est evident que je dois moi Paul me tenir au sept ; et de meme 

 si je suis Pierre, et qui je SQache que vous etes le conseil de Paul, 

 je dois changer au liuit, auquel cas vous aures donne un mauvais con- 

 seil a Paul. 



The reader will be reminded of the old puzzle respecting the 

 veracity of the Cretans, since Epimenides the Cretan said they 

 were liars. 



The opponents of Nicolas Bernoulli at first contended that it 

 was indifferent for Paul to retain a seven or to change it, and also 

 for Peter to retain an eight or to change it ; and in this Montmort 

 considered they were wrong. But in conversation they explained 

 themselves to assert that no absolute rule could be laid down for 

 the players, and in this Montmort considered that they were right ; 

 see his page 403. 



The problem is considered by Trembley in the Memoires de 

 V Acad.... Berlin, for 1802. 



191. The fourth problem which Montmort proposed for solu^ 

 tion is sur le Jen des Tas. The game is thus described, page 281, 



Pour comprendre de quoi il s'agit, il faut s9avoir qu'apres les reprises 

 d'hombre un des Joueurs s'amuse sou vent a partager le jeu en dix tas 

 composes chacun de quatre cartes couvertes, et qu'ensuite retournant la 

 premiere de chaque tas, il ote et met a part deux ^ deux toutes celles 

 qui se trouvent semblables, par exemple, deux Pois, deux valets, deux 

 six, &c. alors il retourne les cartes qui suivent immediatement celles 

 qui viennent de lui donner des doublets, et il continue d'oter et de 

 mettre a part celles qui viennent par doublet jusqu'a ce qu'il en soit 



