Josephus problem – Sword Killing and Survival Puzzle

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100 people are standing in a circle in an order of 1 to 100.

No.1 has a sword he kills the 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 no. survives?

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  • 1 Answer(s)

    The 73rd person will survives.

    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.

    vishal Scholar Answered on 29th July 2015.
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