Imagine a game like this, N man lined in circle, and numbered from 1 to N. Starting from the man with number one, he shout "in", the next one (man number two) shout "out", the next one (man number 3) shout "in", the next number 4 shout "out"..., and so on... The man shout "out" will get out of the circle immediately. The game runs till one member remained in circle. The question is which position (number) of the last one remained in circle.
if N = 2, the last one is 1
N = 3, the last one is 3
N = 6, the last one is 5
N = 20, the last one is 9