Thursday, October 12, 2006

the josephus problem

just watched an episode of the bbc1 roman empire epic dealing with the judean revolt. strangely the romans vespasian and titus were very anglo-saxon and british, whereas the revolting jews - except the finely-boned ed stoppard (son of sir tom) - were rather stubbly (as opposed to the full beards observant jews might have) and a bit swarthy. mr ed was designer-stubbly, which only made him more gorgeous. o, he played josephus. anyway, were not romans italians?

while trying to remind myself whether the original josephus was as self-serving as the bbc use of his writings presented him as being, came across the following from wikipedia. i have omitted the detailed formulae - if you wish to see them, please google.

"The Josephus problem is a theoretic problem occurring in computer science and mathematics. There are n people standing in a circle waiting to be executed. After the first man is executed, k−1 people are skipped and the k-th man is executed. Then again, k−1 people are skipped and the k-th man is executed. The elimination proceeds around the circle (which is becoming smaller and smaller as the executed people are removed), until only the last man remains, who is given freedom.
The task is to choose the place in the initial circle so that you survive (remain the last one), given n and k.

The problem is named after Flavius Josephus, a Jewish historian living in the 1st century. As the legend goes, he and his 40 comrade soldiers were trapped in a cave, surrounded by Romans. They chose suicide over capture and decided that they will form a circle and start killing themselves using a step of three. As Josephus did not want to die, he was able to find the safe place, and stayed alive, later joining the Romans who captured him."

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