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Math Help - Josephus problem with varying k

  1. #1
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    Josephus problem with varying k

    for the condition in Josephus problem - Wikipedia when k is fixed i.e either every 2nd person OR every 3rd person is killed the general recurrence relation is :

    f(n,k)=(f(n-1,k)+k)%n with f(1,k)=1
    Now if there is a situation in which k increases as 1,2,3,.. then how to formulate ? E.g if there are 5 people numbered as 1,2,3,4,5 and k(position of person selected to execute) is 1 for 1st round 2 for second and so on then the position at which survivor should stand is 4
    Thanks.
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  2. #2
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    Re: Josephus problem with varying k

    i tried out a few cases with hand and got the answers for n = 1..12 as 1,2,3,4,4,5,4,7,8,7,11,11 resp ..but i can't see any pattern..
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