Question

Difficult Puzzle! 100 people standing in a circle in an order 1 to 100....Which number survives at the last?100 people standing in a circle in an order 1 to 100. No.1 person 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?

Answer 1

73rd person is the one who survives

Answer 2

At the end of the rounds:  those who remain:
1st:           1, 3, 5, 7, 9, 11, 13, 15, 17, .....  91, 93, 95, 97, 99
2nd:          1, 5, 9, 13, 17,, ... , 89, 93, 97
3rd :          1, 9, 17, 25, .... 57, .... 81, 89,  97
4th:            9, 25, 41, 57, 73, 89
5th:            9, 41,  73,
6th:            9, 73
7th:            73