Find the survivor


100 people standing in a circle in an order 1 to 100. No.1 has a sword. He kills next person (i.e. no. 2) and gives sword to next to next (i.e no.3). All person does the same until only 1 survives. Which number survives at the last?

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  • 6 Answer(s)

    Consider the case when there are 2^n numbers in the circle. Each time the number reduces by half and the number 1 remains till the end.

    In the given question, 1 kills 2, 3 kills 4 and so on till 71 kills 72. 36 people have been killed till now. 64 people remain in the circle. 64 is a power of 2. So the first guy after 72 will be the new number 1 in a circle of 2^6. So 73 will survive.

    paki312 Starter Answered on 7th September 2015.
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    This is the famous Josephus Problem. The solution requires getting the nearest smaller number that is the power of 2,in this case 64 and subtract it with the given number.100-64=36.Now we apply the formula 2n+1. 2*36+1=72+1=73.

    John123 Expert Answered on 20th July 2015.

    You should  check before using a formula …. the formula ou are using is when 1 person is being skipped.

    on 5th September 2015.

    Yes, and that is exactly the problem… one person is skipped.

    on 25th March 2016.
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    50 survivors.
    100 people standing in a circle but not make a circle (as not clear in the q.).

    Sanjaybansor Starter Answered on 3rd June 2016.
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    Clear Explanation

    Siva Bharath Starter Answered on 1st July 2016.

    but the question mentions that the person with the sword kills the next .
    since they are standing in a circle, by the end of the first round 99 has the sword so he should be killing 1 and the series continues . Am i missing some part of the question which makes me think in this way?

    on 10th September 2016.

    99 kills 100 – hands sword to 1

    on 18th November 2016.
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    The answer should be 89.

    Rajeshkumar Default Answered on 1st April 2016.

    Probably 69

    on 25th May 2016.
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    alokbhatia17051955 Default Answered on 31st May 2016.
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