# 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?**

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.

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

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

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.

50 survivors.

100 people standing in a circle but not make a circle (as not clear in the q.).

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?

99 kills 100 – hands sword to 1

### Your Answer

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