In this question, it would be about identifying a pattern. If you start small, you will find this pattern:

When N is a power of 2, the number of the leader that gets selected is 1 and after that it moves in a sequence of odd numbers till the next power hits.

Once you get the sequence, you would be able to solve the question.

We need to find for N = 18.

Nearest power of 2 is 16, for which the number of leader would be 1.

Every subsequent jump of 1 in N will result in a jump of 2 in number of leader.

Jumps in N = 18 - 16 = 2

Jump in number of Leader = 2 x 2 = 4

So, the number of leader who will get selected is 1 + 4 = 5.

After 3 rounds 5 and 13 will remain, beginning with 5, 13 will have to step down.

Thus, 5 will be the leader.