Who will survive the Killings! Logical Puzzle!

 

100 people standing in a circle in an order 1 to 100.
No. 1 has a sword. He kills the next person (i.e. No. 2) and gives the sword to the next (i.e. No. 3).

All people do the same until only 1 survives.

Which number survives at the last?

For Answer

73 is the answer!

How?

When 2 person are there, No 1 will survive –> One will kill the 2.
when 4 person are there even then 1 will survive –> 1 will kill2, 3 will kill 4 and 1 will kill 3.
Similairy for 8, 16, 32, 64, No 1 will survive. ( powers of 2 )

so its a case when there 2^numbers in circle. Each time the number reduces by half and finally at the last number 1 will remain.

So our aim here should be to reach to a figure when 2^n number will come and person who will be holding the sword at that moment will survive.

when there are 100 people – closet 2^number will be 64.
so here our target it to find the person who is holding the sword when 64 people are remaining.

64 people remaining means 36 people killed.
As every alternate person is being killed so double of 36 i.e 72. So 72 person was killed at that moment and the sword was passed to 73 from 71 after killing 72.

so the moment when 64 people were remaining, 73 was holding the sword, 
so 73 will survive the killings!!!