# permutation of “counting out”

Josephus problem*:
circle=1,2,3,4,5,6,7,8,9,10. count=2. (Beginning at 1) The "last man standing" in this case=9.
Order of elimination or permutation (?): 2,4,6,8,10,3,7,1,9

For any size circle and any size count what is the math that produces the order of elimination? e.g. circle=1,2,3,4,5,6,7,8,9. count=10.
Order of elimination (starting at 1): 1,3,6,2,9,5,7,4,8

*(From wikipedia: http://en.wikipedia.org/wiki/Josephus_problem) The Josephus problem is a theoretical problem related to a certain counting-out game. There are people standing in a circle waiting to be executed. The counting out begins at some point in the circle and proceeds around the circle in a fixed direction. In each step, a certain number of people are skipped and the next person is executed. The elimination proceeds around the circle (which is becoming smaller and smaller as the executed people are removed), until only the last person remains, who is given freedom.

(Original post)

(please forgive me if this looks slightly familiar to anyone...)

Hello,

Does anybody know the math for a general case Josephus-like permutation (any size circle, any size count)?

e.g circle=9, count=10.
1,3,6,2,9,5,7,4,8

I only have access to what I can find on the web (Google) and what has previously been suggested doesn't cover this particular aspect (Concrete math; wikipedia....). The nearest I have found is http://mathworld.wolfram.com/JosephusProblem.html
Can anyone help?

TIA, Ian

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Thanks, but no that's not what I mean.. For these inputs e.g circle=9, count=10 this output 1,3,6,2,9,5,7,4,8. Or "dynamically" calculated from each elimination (first calculation produces 1, 2nd 3, 3rd 6,....) – Ian May 19 '12 at 15:24
What do you mean, "does anybody know the math"? Why don't you formulate a precise question, and edit that into your post, and delete the stuff that doesn't actually tell us anything? – Gerry Myerson May 20 '12 at 8:48
I think my question is clear (?) I don't know how to do this and I can't find this question answered anywhere. So, does anybody know? What's wrong with that? Why show your annoyance? Can you answer it? – Ian May 20 '12 at 12:48
Well, Ian, you posted the question 22 hours ago, and no one has had a go at it, and you might want to take that as a sign that I'm not the only person who doesn't think your question is clear. In my experience here, clear questions about elementary topics get answered within minutes of being posted. But, hey, suit yourself. If you're happy with the response you've gotten, don't change a thing. – Gerry Myerson May 20 '12 at 13:07
What is TIA? @Ian – Tomarinator May 20 '12 at 13:45