# 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?

ravi Expert Asked on 20th July 2015 in

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.

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.

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.

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.

Rajeshkumar Default Answered on 1st April 2016.

Probably 69

on 25th May 2016.

63

alokbhatia17051955 Default Answered on 31st May 2016.

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