josephus_problem

Let's say we label each person starting with index 0, for N persons, we have
0, 1, 2, 3, ...., N-1. 

Fn(N, K) return the index of the last person, with starting position at 0

Given N persons, after removing the Kth person, then the next starting position will be K%N

Fn(N-1, K) return the position of the survivor with starting position at 0 then for starting position of K%N

(Fn(N-1, K) + K)%N will return the position of the survivor.  

so Fn(N, K) = (Fn(N-1, K) + K)%N