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?
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.
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.
50 survivors.
100 people standing in a circle but not make a circle (as not clear in the q.).
Clear Explanation
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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