24 AEITHMETICAL RECREATIONS [CH. I 



Hegesippus* says that Josephus saved his life by such 

 a device. According to his account, after the Romans had 

 captured Jotapat, Josephus and forty other Jews took refuge 

 in a cave. Josephus, much to his disgust, found that all 

 except himself and one other man were resolved to kill them- 

 selves, so as not to fall into the hands of their conquerors. 

 Fearing to show his opposition too openly he consented, but 

 declared that the operation must be carried out in an orderly 

 way, and suggested that they should arrange themselves round 

 a circle and that every third person should be killed until but 

 one man was left, who must then commit suicide. It is alleged 

 that he placed himself and the other man in the 31st and 16th 

 place respectively. 



The medieval question was usually presented in the following 

 form. A ship, carrying as passengers 15 Turks and 15 

 Christians, encountered a storm, and, in order to save the ship 

 and crew, one-half of the passengers had to be thrown into the 

 sea. Accordingly the passengers were placed in a circle, and every 

 ninth man, reckoning from a certain point, was cast overboard. 

 It is desired to find an arrangement by which all the Christians 

 should be saved -f\ In this case we must arrange the men thus : 

 GCGGTTTTTGGTGGGTCTTGGTTTGTTGGT, 

 where G stands for a Christian and T for a Turk. The order 

 can be recollected by the positions of the vowels in the follow- 

 ing line : From numbers' aid and art, never will fame depart, 

 where a stands for 1, e for 2, i for 3, o for 4, and u for 5. Hence 

 the order is o Christians, u Turks, &c. 



If every tenth man were cast overboard, a similar mnemonic 

 line is Rex paphi cum gente bona dat signa serena. An oriental 

 setting of this decimation problem runs somewhat as follows. 

 Once upon a time, there lived a rich farmer who had 30 children, 

 15 by his first wife who was dead, and 15 by his second wife. The 

 latter woman was eager that her eldest son should inherit the 

 property. Accordingly one day she said to him, " Dear Husband, 



* De Bella Judaico, bk. m, chaps. 16 — 18. 



t Bachet, problem xxm, p. 174. The same problem had been previously 

 enunciated by Tartaglia. 



