Ancient Judea, 67 CE. The town of Yodfat is seized by Roman forces. A group of 41 Jews, led by Josephus, is trapped in a cave. The Romans will not let them out. What are Jews to do?

Well, commit mass suicide, of course! And not just your standard mass suicide. They decide to stand in a circle and count off by threes. Whoever is the lucky number, gets to fall on his sword. Literally. And this keeps going and going until there is no one left. Rather elaborate for its purposes. We wonder who came up with such a brilliant plan.

So, basically, Jews start killing themselves, and, as we can imagine, the smell is getting atrocious, when lo and behold, there are only two people left. Josephus and some other guy. We'll call him Jerry. They look at each other and decide... hey, maybe this mass suicide is not all it's cracked up to be. So they walk out of the cave and get captured by Romans. Note: they are NOT killed.

Josephus' ordeal gave rise to the eponymous theoretical problem: given n people whether each kth is eliminated... you know, we're not gonna bore you with the details. For n = 41 and k = 3, the last two safe spots are 16 and 31.

We're not sure what happened to Jerry, but Josephus became a famed historian. He lived for 30 more years, while 39 of his comrades were rotting in a cave. For them, being captured by Romans might not have been such a bad alternative...