100 people with sword puzzle
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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?
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.
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