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The Josephus Problem asks where to start taking out every kth person in the circle consisted of n people, such that you are the last "survivor".

The following recursive formula is given: $$\begin{align} f(1,k)&=1, \\ f(n,k)&=((f(n-1,k)+k-1) \bmod n )+1. \end{align}$$

But this is not enough explanation, so I don't get where does it come from.

Can anyone help?

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You mean wiki explanation in general case is not enough? –  user742 Nov 30 '12 at 17:43

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