41 men in a circle, kill every third, which two spots survive?
According to a mathematical retelling of Flavius Josephus's own account, he and 40 fellow soldiers, trapped in a cave by Roman troops in 67 AD, drew lots to kill each other rather than surrender. Mathematicians later modelled the story as a circle of 41 people where every third remaining person is eliminated. If you had to guess in advance, which two positions would be the last ones left?
Reveal the answer
Positions 16 and 31 survive when 41 people are arranged in a circle and every third person is eliminated, solved by French mathematician Claude-Gaspard Bachet de Meziriac in the 17th century. Josephus himself wrote that he and one other man were the last two left, and both surrendered to the Romans rather than die. From Flavius Josephus's 'The Jewish War' (c. 75-79 AD); the general elimination puzzle is now known as the Josephus problem in mathematics and computer science.
— Flavius Josephus, The Jewish War — Book III, on the siege of Yodfat, c. 75-79 AD