1897-98.] Prof. Tait on Generalization of Josephus' Problem. 165 
On the Generalization of Josephus’ Froblem. By 
Prof. Tait. 
(Read July 18, 1898.) 
In the third Book of The Wars of the Jeios , Chap, VIII. 
§ 7, we are told that Josephus managed to save himself and a 
companion out of a total of 41 men, the majority of whom had 
resolved on self- extermination (to avoid falling into the hands of 
Vespasian) provided their leader died with them. The passage is 
very obscure, and in a sense self-contradictory, hut it obviously 
suggests deliberate fraud of some kind on Josephus’ part. 
“ And now,” said he, “ since it is resolved among you that you 
will die, come on, let us commit our mutual deaths to determina- 
tion by lot. He whom the lot falls to first, let him be killed by 
him that hath the second lot, and thus fortune shall make its 
progress through us all ; nor shall any of us perish by his own 
right hand, for it would be unfair if, when the rest are gone, some- 
body should repent and save himself.” Whiston, Works of Flavius 
Josephus , IV. 39. 
Bachet, in Ho. XXIII. of his Problemes plaisants et deledables , 
makes a definite hypothesis as to the possible nature of the lot 
here spoken of ; so that the problem, as we have it, is really his. 
“ Supposons qu’il ordonna que comptant de 3 en 3 on tuerait 
toujours le troisieme, . . . . il faut que Josephe se mit le trente- 
unieme apres celui par lequel on commenyait a compter, au cas 
qu’il visat a demeurer en vie lui tout seul. Mais s’il voulut sauver 
un de ses compagnons, il le mit en la seizieme place, et s’il en 
voulut sauver encore un autre, il le mit en la trente cinquieme 
place.” 
Thus stated, the problem can be solved in a moment by the 
graphical process of striking out every third, in succession, of a set 
of 41 dots placed round a closed curve. When three only are 
left, they will be found to be the 35th, 16th, and 31st; and, if 
