There were not many tape recorders around in the 1st century AD. Comparative linguists can make all sorts of speculations based on rhymes, scansion and relations to other languages, but at the end of the day whether, for instance, Caesar actually said “veni”, “weni” or even “feni” or “beni” is conjectural.
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The real trick is just to sit to the right of the commander who came up with the scheme.
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I got a little lost after the power of 2 thing, but I think I got most of it.
Let me attempt to explain just that part…
If you stop killing people after you’ve gone around the circle, you’ve killed half the people (rounded down).
So after 1 pass in a 12 person ring, you’re left with a circle that’s the same as a 6 person ring. (Then a 3 person ring).
With an odd numbered group, you’re off by one, so you have to rotate by 1 and continue, but you’re still removing half rounded down (dividing by 2).
So in binary, if you multiply by 2, you can just add zeros to the right every time you multiply by 2.
- 101 (5) >> 1010 (10) >> 10100 (20) >> 101000 (40)
Conversely, when you divide by 2, you just chop off the rightmost digit.
- 11011 (27) >> 1101 (13) >> 110 (6) >> 11 (3)
Because of this, we can get into all sorts of “fancy” tricks when dealing with things that can be expressed relating to the powers of 2.
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I think I missed a lot with the assumption I wasn’t good at maths.
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You’re totally right. My mistake.
Simplified: You have a 1/3 chance of winning on the second round because there is always going to be one person in front of you, and you always have a 1/3 chance of hitting.
And then on subsequent rounds, your chances of living and winning are better if your opponent is worse.
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The best place to sit in a “suicide circle” if you really don’t want to die is OUTSIDE.
I’m frankly baffled it took so long in the discussion to reach the true answer.
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He is using an odd pronunciation of the name. The norm for classical historians is Joe-see-fuss with the accent on the second syllable.
Worse, according to Josephus the way each decided who to kill was by drawing lots. He didn’t go into a lot of detail, but somehow in the end there were two survivors - Josephus, and an unnamed guy.
Still, as @jerwin notes, focus on the math. The faux-historical trappings are just there to teach you about an algorithm and algorithmic thinking.
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Oh, definitely. The math is the most important part and the most interesting. Just was… bothered.
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